Independent Metering Electro-Hydraulic Control System 9819963710, 9789819963713

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Ruqi Ding Min Cheng

Independent Metering Electro-Hydraulic Control System

Independent Metering Electro-Hydraulic Control System

Ruqi Ding · Min Cheng

Independent Metering Electro-Hydraulic Control System

Ruqi Ding East China Jiaotong University Nanchang, Jiangxi, China

Min Cheng State Key Laboratory of Mechanical Transmission Chongqing University Chongqing, China

ISBN 978-981-99-6371-3 ISBN 978-981-99-6372-0 (eBook) https://doi.org/10.1007/978-981-99-6372-0 Jointly published with Shanghai Jiao Tong University Press. The print edition is not for sale in China (Mainland). Customers from China (Mainland) please order the print book from: Shanghai Jiao Tong University Press. © Shanghai Jiao Tong University Press 2024 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publishers, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publishers nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore Paper in this product is recyclable.

Foreword

The first author of this book is Prof. Ding Ruqi from East China Jiaotong University, and the second author of this book is Prof. Min Cheng from Chongqing university. They both have been rooted in teaching and researching advanced electro-hydraulic control systems for a long time. Compiling textbooks not only requires the author to have rich scientific research practice but also needs the correct grasp and understanding of the frontier of scientific and technological development in related fields. It can be said that the book is the conclusion of his long-term scientific research work. The subject of this book is the study of advanced technology used in hydraulic systems. The technology in question is termed Independent Metering (IM). Because of its many advantages, Independent Metering Control Valve or System (IMCV or IMCS) has become the research hotspot and is used in a range of very important applications such as construction machinery. The IMCS was proposed in the 1980s by Professor Backe. W of RWTH Aachen University in Germany. In China, Zhejiang University also carried out research on the IMCS for decades, in which Professor Qingfeng Wang and I have cultivated a large number of talents in this field. Each generation follows in the footsteps of their predecessors, and the younger generation gradually takes on the responsibility of society. The new era of the fluid power transmission and control needs more and more youngers like the author of this book. This book is rich in content and rigorous in structure. The publication of this book will further promote in-depth research in the field of the IMCS. This book consists of seven chapters and shows the independent metering electro-hydraulic system involving its flexible hardware layouts, complex software control, representative products, and interesting applications. Starting from the traditional electrohydraulic system, the background and motivation of IMCS are deeply analyzed. In addition, various hardware layouts are summarized involving the utilized hydraulic components and circuits, together with their advantages and disadvantages. Followed by the flexible configuration, a variety of working modes can be realized. Then, multivariable control strategies including three levels: load, valve, and pump, as well as the fault-tolerant control under the fault condition, are demonstrated in detail. Finally,

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Foreword

products of IMCV and their applications in some typical construction machinery are reviewed in the state of the arts. Therefore, this book has great significance and reference value for the application of the IMCS in engineering. Research on the IMCS will learn a lot from this academic monograph. I hope that more and better excellent monographs will be published in the future. This book is interesting and useful to a wide readership in the various fields of fluid power transmission and control.

September 2023

Bing Xu Executive Deputy Director of the State Key Laboratory of Fluid Power and Mechatronic Systems Zhejiang University Hangzhou, China

Preface

Due to several advantages, such as a high power-weight ratio and high load capability, fluid power transmission technology has been used in all types of construction machines, such as excavators, rotary drilling rigs, concrete pump trucks, and other construction machinery. The electro-hydraulic control system is the core driving and controlling device of construction machinery, which directly determines its energy efficiency, control performance, and safety reliability. Traditional electrohydraulic control systems, such as load-sensing systems and positive/negative flow control systems, are most commonly utilized in construction machinery, such that a trade-off between energy efficiency and steering quality can be captured. However, three typical drawbacks are inevitable in traditional systems: low energy efficiency, insufficient compatibility, and poor controllability. Therefore, due to the complexity and inflexibility of conventional mobile hydraulic systems, it is difficult to meet the growing demand, which motivates the development of better components and creative circuits to overcome the three aforementioned weaknesses. By decoupling the inlet and outlet, an Independent Metering Control System (IMCS) improves the freedom of control and provides the possibility for a more intelligent control strategy. At the same time, it can improve energy efficiency while meeting the control requirements. The content of this book is derived from the scientific research practice of the authors. This book’s publication will help readers understand different control theories of electro-hydraulic systems and promote the development of electro-hydraulic control systems. In Chap. 1, the concept and characteristics of an IMCS are introduced in detail. From the aspects of energy efficiency, compatibility, and controllability, the characteristic of an IMCS is presented. In Chap. 2, the valve assembly used in the IMCS and the possible layout of the main and pilot stages are described in detail. In Chap. 3, multiple operating modes are established according to the achievable flow paths by the independent metering control, and the energy-saving functions, including regeneration and recuperation, are realized. In addition, energy-saving characteristics and force-velocity capability are analyzed to design the mode-switching logic, such that the most efficient operating mode without losing controllability for precise motion tracking can be automatically selected. In Chap. 4, the different independent vii

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metering valve control architectures are described. To minimize the strong vibration generated by low damping, a hybrid control method combining dynamic pressurefeedback control with independent metering control is proposed for active damping compensation. In Chap. 5, the pump-valve coordinate control system is established by incorporating the electronically controlled pump (ECP) into the IMCS, and a novel method for three-level multi-mode transfer, considering the cylinder, valve, and pump, is developed. In Chap. 6, both active valve and sensor fault-tolerant control systems parallel to the normal controller are proposed to adapt to valve or sensor fault conditions. In Chap. 7, well-known products of Independent Metering Control Valve or Systems are introduced and their representative features are discussed. Due to the limited level of the author and the short time, there may be omissions and inadequacies in the book. I hope the majority of readers and members of the academic and industrial affiliations can make criticisms and corrections. Nanchang, China November 2023

Ruqi Ding

Acknowledgments

This work was supported by the National Key Research and Development Program of China(Grant No.2020YFB2009703), the Natural Science Foundation of China(Grant No.52175050), and Major Scientific and Technological Research and Development Project of Jiangxi Province(No. 20233AAE02001).

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Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Independent Metering Control System (IMCS) . . . . . . . . . . . . . . . . . 1.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 4 6 7

2 Hardware Layout of Independent Metering Control . . . . . . . . . . . . . . . 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Valve Component . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Main-Stage Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Pilot Stage Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9 9 9 10 15 17 17

3 Multi-Mode Load Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Multiple Operating Modes for the Actuator . . . . . . . . . . . . . . . . . . . . . 3.3 Mode Switching Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Energy-Saving Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Force-Velocity Capability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.3 Mode Switching Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Mode Transition Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 Motivation for Bumpless Switch . . . . . . . . . . . . . . . . . . . . . . . 3.4.3 Continuous Switching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.4 Discrete Switching with the Bumpless Transfer . . . . . . . . . . . 3.4.5 Bidirectional Latent Tracking Loop . . . . . . . . . . . . . . . . . . . . . 3.5 Experiment Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21 21 22 24 24 26 29 30 31 33 33 35 41 44 46 47

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4 Multi-Variable Valve Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Independent Metering Valve Control Architecture . . . . . . . . . . . . . . . 4.2.1 Control Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Modelling of Independent Metering Control System . . . . . . 4.2.3 Analysis of Interactions Between the Different Loops . . . . . 4.2.4 Load-Independent Flow Control . . . . . . . . . . . . . . . . . . . . . . . . 4.2.5 Detailed Decentral Control Algorithm with Electronic PC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Damping Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Damping Control Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.3 Control Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.4 Self-Tuning Pressure-Feedback Control Based on Guaranteed Dominant Pole Placement . . . . . . . . . . . . . . . . 4.4 Experimental Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49 49 49 49 51 53 55 56 58 58 64 65 69 71 75 76

5 Pump-Valve Coordination Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 5.2 Pump Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 5.2.1 Pressure Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 5.2.2 Flow Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.2.3 Power Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.2.4 Hybrid Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.3 Configuration of Pump-Valve Coordinate Control . . . . . . . . . . . . . . . 82 5.4 Multi-Variable Control Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 5.4.1 Multi-Variable Controller Under Resistive Loads . . . . . . . . . 84 5.4.2 Multi-Variable Controller Under Overrunning Loads . . . . . . 85 5.4.3 Pressure Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 5.5 Energy-Saving Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.6 System Dynamic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 5.7 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 5.7.1 Startup Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 5.7.2 Single Actuator Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 5.7.3 Multi-Actuator Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 5.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 6 Fault-Tolerant Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Normal Controller (NC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 MIMO System in the IMCS . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.2 Normal Control Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Fault-Tolerant Control Against Valve Faults . . . . . . . . . . . . . . . . . . . .

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6.3.1 Valve Fault-Tolerant Control (VFTC) Principle . . . . . . . . . . . 6.3.2 Control Signal Reconfiguration (Parameter Degradation) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.3 Control Loop Reconfiguration (Functional Destruction) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.4 Operating Mode Reconfiguration (Flow Obstacle) . . . . . . . . 6.3.5 Design of the VFTC Decision Mechanism . . . . . . . . . . . . . . . 6.4 Fault-Tolerant Control Against Sensor Faults . . . . . . . . . . . . . . . . . . . 6.4.1 Sensor-Fault-Tolerant Control (SFTC) Principle . . . . . . . . . . 6.4.2 SFTC for the Supply Pressure Sensor . . . . . . . . . . . . . . . . . . . 6.4.3 SFTC for the Inlet Pressure Sensor . . . . . . . . . . . . . . . . . . . . . 6.4.4 SFTC for the Outlet Pressure Sensor . . . . . . . . . . . . . . . . . . . . 6.5 Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.1 Stability of Switching from the NC to FTC . . . . . . . . . . . . . . 6.5.2 Bumpless Transfer from NC to FTC . . . . . . . . . . . . . . . . . . . . 6.6 Experimental Verification Under Valve Faults . . . . . . . . . . . . . . . . . . 6.6.1 Test 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.2 Test 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.3 Test 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.4 Test 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.5 Test 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.6 Effect of BT in VFTC Under Test 2 . . . . . . . . . . . . . . . . . . . . . 6.6.7 Comparison with Classical VFTC Under Test 2 and 3 . . . . . 6.7 Experimental Verification Under Sensor Faults . . . . . . . . . . . . . . . . . 6.7.1 Experimental Results for the Sensor Fault Conditions . . . . . 6.7.2 Experimental Effects of the SFTC . . . . . . . . . . . . . . . . . . . . . . 6.7.3 Effects of the Bumpless Transfer Controller . . . . . . . . . . . . . . 6.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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7 Industrial Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Commercial Independent Metering Valve . . . . . . . . . . . . . . . . . . . . . . 7.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

143 143 143 148 149

111 113 114 115 116 118 118 119 121 123 124 124 126 128 128 128 129 130 131 132 134 135 136 136 139 140

Chapter 1

Introduction

1.1 Background Due to several advantages, such as a high power-weight ratio and high load capability, fluid power transmission technology has been used in all types of construction machinery [1]. These applications are often referred to as “mobile hydraulic systems.” High power is often required to precisely control the simultaneous motion of all of the actuators, which distinguishes mobile hydraulic systems from industrial hydraulic systems (Fig. 1.1a) [2]. The required flow and pressure vary continuously, and the load frequently alternates between resisting and overrunning to cover the four quadrants (Fig. 1.1b) [3]. Conventional electro-hydraulic control systems, such as HLS (Hydraulic Load Sensing) systems, are commonly used mobile hydraulic systems that make tradeoffs between energy efficiency and control characteristics. In Fig. 1.2, an adaptable flow and pressure control strategy, where the pump is pre-set to maintain a certain pressure margin beyond the highest load pressure is shown [4]. Hydro-mechanical pressure compensators (PC) makes the motion of actuator load-independent [5]. However, conventional systems have three typical disadvantages: (1) mechanical coupling between the inlet and outlet, (2) pressure feedback network via long pipelines, and (3) pressure compensation between different loads. The weaknesses arising from the three above constraints include the following: (1) Low energy efficiency Figure 1.3 displays the distribution of energy losses in an excavator. The heaviest energy losses, which consist of the three following aspects, reside in the valves [6]: Inlet throttling loss: the pump pressure margin pm is set to overcome losses across the hoses, directional valves, and pressure compensation valves. To satisfy the requirements of all operating points, the hydro-mechanical pump always considers the worst working conditions to preset the pressure margin, which causes unnecessary pressure losses.

© Shanghai Jiao Tong University Press 2024 R. Ding and M. Cheng, Independent Metering Electro-Hydraulic Control System, https://doi.org/10.1007/978-981-99-6372-0_1

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1 Introduction

(a)

(b)

Fig. 1.1 Distinct features of mobile machinery

Load 1

Load 2

Pb PL1

Pa

PL2 Pr

Ps

Fig. 1.2 Schematic diagram of the HLS system

Outlet throttling loss: due to the mechanical coupling of the inlet and outlet, the meter-out valve cannot open as large as possible under resisting loads, leading to a noticeable pressure loss. Under overrunning loads, the energy under lowering loads cannot be recuperated and is wasted by outlet throttling losses. Load difference: because multiple actuators are supplied by one pump, waste occurs in the pressure compensator owing to pressure differences between lower loads and higher load. (2) Insufficient compatibility Due to the complexity of hydro-mechanical systems, commissioning methods are often simplified to a combination of experience and trial-and-error, and the commissioning itself is inconveniently conducted by changing hardware, such as using meterin and meter-out orifices in valves, as well as adjusting springs, spool design, and

1.1 Background

3

Fig. 1.3 Energy consumption distribution of an excavator

hose volumes in the pump [7]. Such tedious commissioning with slow cycle time produces unnecessary waste, including time, manpower, and resources. Furthermore, the compatibility for various applications is limited due to the structure coupling, as depicted in Fig. 1.4. (3) Poor controllability By introducing the LS-pressure feedback, the system is often poorly damped with complex dynamics that oscillate. Additionally, pressure feedback via long pipelines causes a delay between the handle input and displacement regulator mechanism of the pump, decreasing the dynamic response [8].

Fig. 1.4 Commissioning process of the traditional system

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1 Introduction

Presently, construction machinery is increasingly confronted with the following challenges: (1) Rising energy costs and stringent emission regulations and standards [9], (2) Constant demands for higher productivity and enhanced flexibility, and (3) Tough requirements of operator comfort and safety [3]. Due to the complexity and inflexibility of conventional mobile hydraulic systems, they have difficulty meeting these requirements, which motivates the development of better components and creative circuits to overcome the three aforementioned weaknesses.

1.2 Independent Metering Control System (IMCS) The energy efficiency of mobile hydraulic systems has become an important topic in recent years. In mobile applications, controllability can be a secondary design objective. A good example of energy inefficient machine is the hydraulic excavator, whose total energy efficiency can be as low as 10%, contributing to approximately two hundred million tons of CO2 emissions in all construction machinery [10, 11]. Today, strict administrative regulations demand energy consumption and CO2 emissions reductions for the industry. In December 2017, 29 countries signed the Carbon Neutral Alliance Statement at the One Earth Summit, making a commitment to zero carbon emissions by the mid-twenty-first century [12]. As of 12 June 2020, 125 countries have committed to achieving carbon neutrality by the mid-twenty-first century [13]. To address the problem of low energy efficiency, the first approach is pump control, which can make the pump outlet pressure and flow automatically adjust with the load pressure and velocity without excess as possible. Benefiting from the absence of throttling losses, the direct pump control is highly energy efficient. There are two solutions to achieve pump control: variable displacement and variable speed [14]. The former achieves the purpose of pump control by changing pump displacement. Extensive research on this subject is conducted by Professor Ivantysynova et al. [15]. The latter acheives the purpose of pump control by changing motor speed, where the actuator and motor have their own pump, as shown in Fig. 1.5. Research on the characteristics and performance of speed variable pump circuits was carried out [16]. The main characteristics of these systems are lower energy consumption ratios, hence better fuel economy and fewer greenhouse gases. However, owing to the large inertia mass, leakages, and high nonlinearities, it is much more complicated to achieve accurate tracking performance and fast dynamic response of the actuator compared to the valve control systems. Moreover, compared to valve control, it needs a significant increase in the component effort: each cylinder needs to be coupled with a high dynamic variable pump unit.

1.2 Independent Metering Control System (IMCS)

5

Fig. 1.5 Individualization levels of pump control

When using valve control, the IMCS is an inevitable choice to increase energy efficiency. It is an abbreviation for systems where the meter-in orifice and the meterout orifice are independently controlled. The IMCS breaks the structural coupling of the spool, which changes from a single splool to twin spools, as shown in Fig. 1.6. After IMCS was proposed by Jansson and Palmberg [17], intensive investigations have been performed. Most research has focused on energy efficiency. Theoretically, a specific piston force f p can now be obtained with an infinite number of chamber pressure combinations. This enables a possibility for hydraulic actuators’ energy consumption reductions if such high-precision chamber pressure trackings can be designed for pa and pb , such that the pressures can be set as low as practically possible [18]. Moreover, independent control of inlet and outlet orifices increases energy efficiency by allowing individual control paths or modes. For example, the system can change flow paths during operation, i.e., recuperation and regeneration can be utilized to reduce energy consumption.

Fig. 1.6 Comparison of the structure of traditional multi-way valve and Independent Metering Valve (IMV)

6

1 Introduction

In addition to energy efficiency, high-precision motion, and force-tracking controls are vital functionalities for mobile hydraulic systems. Introducing mechanically decoupled orifices at the cylinder chambers increases the system’s degree of freedom (DOF) from 1 to 2 [6]. The additional DOF changes the system from Single Input Single Output (SISO) to Multiple Input Multiple Output (MIMO), making it possible to control both speed and pressure. Meanwhile, it changes the control system from the hydro-mechanical concept into an intelligent control system that relies on software. The improvement of energy efficiency and control controllability depends on the software programming. More advanced and complex control methods can now be applied to the hydraulic systems to adapt to various working conditions of different machines, such as an adaptive robust control (ARC) strategy by Yao et al. [19] and Virtual Decomposition Control (VDC) approach by Zhu etc. [20]. In addition, pressure feedback via sensitive sensors and electric circuits increases the dynamic stability. Famous companies such as Eaton and Husco have developed emedded integrated controllers with high-performance computing power and information transmission rate (the fastest 3 ms) [6]. To solve the uncertainty and nonlinear problems in IMCS, Li Chen et al. proposed a nonlinear valve flow model, which can capture the nonlinearity of valve flow well and achieve high control accuracy [21]. Moreover, the IMCS depends on software to determine performance, which improves hardware versatility and modularization simultaneously. It is convenient for manufacturer to efficiently programme software and tune parameters, instead of trial-and-error. This also greatly decreases the commissioning cycle and costs in practical application.

1.3 Conclusion In a summary, there are several advantages including higer energy efficiency, sufficient compatibility and better controllability in IMCS compared with conventional hydraulic control system. The core of IMCS is the improvement of energy efficiency and control controllability depending on the software programming, instead of hardware. Therefore, more advanced control strategies can be introduced to adapt to various working conditions of different machines. The book will introduce IMCS in detail from the following chapters: In this chapter, in terms of the conventional electro-hydraulic system, the background and motivation of IMCS are deeply analyzed. From the aspects of energy efficiency, compatibility, and controllability, the main characteristic of IMCS is presented. In Chap. 2, this chapter presents the representative hardware configurations of independent metering valves, including both the pilot and main stage, and analyzes their pros/cons. In Chap. 3, the system degree of freedom (DOF) increases from one to two in IMCS. It first benefits the flexible configuration of individual flow paths, including regeneration and recuperation. Multiple operating modes and the mode-switching

References

7

logic are established according to the achievable flow paths by the independent metering control, such that the most efficient operating mode without losing controllability can be automatically selected. In Chap. 4, the additional DOF restructures the system from SISO to MIMO. Therefore, the multi-variable valve control architecture is described, and a detailed decentral control algorithm is proposed. Meanwhile, to minimize the strong vibration generated by low damping, a hybrid control method combining dynamic pressurefeedback control with independent metering control is proposed for active damping compensation. In Chap. 5, the pump-valve coordinate control system is established by incorporating an electronically controlled pump (ECP) into the IMCS, such that higher energy efficiency and accurate motion control can be accomplished by different mode configurations and associated multi-variable control strategies. In Chap. 6, active VFTC (Valve fault-tolerant control) and SFTC (Sensor faulttolerant control) systems parallel to the normal controller are proposed to adapt to different valve or sensor faults. In Chap. 7, the application of the IMCS in construction machinery is discussed in detail.

References 1. H. Shi, H.Y. Yang, G.F. Gong, H.Y. Liu, D.Q. Hou, Energy saving of cutterhead hydraulic drive system of shield tunneling machine. Autom. Constr. 37, 11–21 (2014). https://doi.org/10.1016/ j.autcon.2013.09.002 2. H. Murrenhoff, S.S. Milos, An overview of energy saving architectures for mobile applications, in 9th International Fluid Power Conference, ed. by H. Murrenhoff (RWTH Aachen University, Aachen, Germany, 2014), 978-3-9816480-0-3, pp. 24–26 3. B. Xu, M. Cheng, Motion control of multi-actuator hydraulic systems for mobile machineriesrecent advancements and future trends. Front. Mech. Eng. 13(2), 151–166 (2018). https://doi. org/10.1007/s11465-018-0470-5 4. J. Weber, B. Beck, E. Fischer, R. Ivantysyn, G. Kolks, M. Kunkis, et al., Novel system architectures by individual drives, in 10th InternationalFluid Power Conference, ed. by J. Weber, vol. 2 (Dresden University of Technology, Dresden, Germany, 2016), pp. 29–62. http://nbn-res olving.de/urn:nbn:de:bsz:14-qucosa-199972. Accessed 18 July 2018 5. B. Eriksson, J. Palmberg, Individual metering fluid power systems: challenges and opportunities, Proc. Inst. Mech. Eng. I J. Syst. Control Eng. (225), 196–211 (2011). https://doi.org/10. 1243/09596518JSCE1111 6. R. Ding, J. Zhang, B. Xu, et al., Programmable hydraulic control technique in construction machinery: status, challenges, and countermeasures. Autom. Constr. 95(NOV.), 172–192 (2018) 7. K. Abuowda, I. Okhotnikov, S. Noroozi, P. Godfrey, M. Dupac, A review of electrohydraulic independent metering technology. ISA Trans. 98, 364–381 (2020). https://doi.org/10.1016/j. isatra.2019.08.057. https://www.ncbi.nlm.nih.gov/pubmed/31522820 8. R. Ding, B. Xu, J. Zhang, et al., Self-tuning pressure-feedback control by pole placement for vibration reduction of excavator with independent metering fluid power system. Mech. Syst. Signal Process. (2017)

8

1 Introduction

9. T.A. Minav, L.I.E. Laurila, J.J. Pyrhonen, Analysis of electro-hydraulic lifting system’s energy efficiency with direct electric drive pump control. Autom. Constr. 30, 144–150 (2013). https:// doi.org/10.1016/j.autcon.2012.11.009 10. M. Vukovic, R. Leifeld, H. Murrenhoff, Reducing fuel consumption in hydraulic excavators—a comprehensive analysis. Energies 10(5), 687 (2017) 11. J. Chen, Q. Shi, W. Zhang, Structural path and sensitivity analysis of the CO2 emissions in the construction industry. Environ. Impact Assess. Rev. 92, 106679 (2022) 12. Carbon Neutrality Coalition. Plan of action: carbon neutrality coalition (2017) [2020-08-20]. https://www.carbon-neutrality.global/plan-of-action/ 13. Energy & Climate Intelligence Unit. Net zero emissions race (2020) [2020-08-20]. https://eciu. net/netzerotracker/map 14. A. Helbig, Energieeffizientes elektrisch-hydrostatisches Antriebssystem am Beispiel der Kunststoff-Spritzgießmaschine. Dissertation, TU Dresden (2007) 15. M. Ivantysynova, Quo Vadis fluid power? in ASME/BATH 2015 Symposium on Fluid Power and Motion Control, Chicago (USA) (2015) 16. E. Siemer, Variable-speed pump drive system for a 5000 kN ring expander, in 8th International Fluid Power Conference, Dresden, vol. 3, pp. 45–56 (2012) 17. A. Jansson, J.-O. Palmberg, Separate controls of meter-in and meter-out orifices in mobile hydraulic systems. SAE Trans. 377–383 (1990) 18. J. Koivumäki, J. Mattila, Energy-efficient and high-precision control of hydraulic robots. Control Eng. Pract. 85(2019), 176–193 (n.d.) 19. B. Yao, L. Xu, et al., Adaptive robust control of linear motors for precision manufacturing, in IFAC Proceedings Volumes (1999) 20. W.H. Zhu, Virtual decomposition control. Springer Tracts Adv. Robot. 60 (2012) 21. C. Li, L. Lyu, B. Helian et al., Precision motion control of an independent metering hydraulic system with nonlinear flow modeling and compensation. IEEE Trans. Ind. Electron. 69(7), 7088–7098 (2021)

Chapter 2

Hardware Layout of Independent Metering Control

2.1 Introduction The Independent Metering Valve (IMV) is a general term referring to a valve architecture class that allows for individual control of the inlet and outlet flow of hydraulic actuator working ports, as well as the flexible flow path for multiple operating modes [1]. For mechanical decoupling of the inlet and outlet, there are various valve arrangements according to the utilized components and different layouts. There is no common consensus about which arrangement of IMV is the preferred one because each arrangement presents distinguished features and performance. This chapter presents the representative hardware configurations of IMV, including both the pilot and main stage, and analyzes their pros/cons. The two-stage structure is considered because it is always utilized to address the increased flow force under the large flow rate condition.

2.2 Valve Component Proportional spool valve Spool valves have been widely used as proportional directional valves in both the mobile and industrial hydraulic fields [2, 3]. The flow of spool valve can be regulated accurately because the opening area is a linear function of the spool displacement. However, complicated spool structures with small valve displacements increase manufacturing costs. Other disadvantages include large leakage and poor resistance to contamination. Proportional poppet valve Compared with the spool valve, the flow forces and fluid inertance effects of the poppet valve are more significant, and the relationship between the open area and © Shanghai Jiao Tong University Press 2024 R. Ding and M. Cheng, Independent Metering Electro-Hydraulic Control System, https://doi.org/10.1007/978-981-99-6372-0_2

9

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2 Hardware Layout of Independent Metering Control

spool displacement is highly nonlinear [4, 5]. Traditionally, spool valves are suited to proportional control, and poppet valves are suited to on/off control. However, proportional poppet valves are still available, although the flow controlled by the poppet valve is less precise than a spool valve. In contrast, there are also many benefits with poppet valves compared to spool valves. Due to the seat structure, poppet valves have advantages including leakage-free and higher resistance to contaminants. Furthermore, Poppet valves are produced with lower manufacturing costs. For example, they have less demanding manufacturing tolerances [6]. Digital valve Both the proportional spool and poppet valves are controlled by an analogue method, which means that their spool displacements are continuous [7]. The digitally controlled valve distinguishes itself from them because the valve only has two states, i.e., on and off. The digital control manner includes Pulse Width Modulation (PWM), Pulse Number Modulation (PNM), pulse code modulation (PCM), etc. Numerous parallel connected on/off valves are used to form a DFCU (digital flow control unit), and a large number of unique flow rates to the chamber are achieved by opening a combination of valves. Therefore, the flow controlled by a DFCU is discrete [8, 9].

2.3 Main-Stage Layout The mechanical decoupling principle is based on changing the main-stage valve types from the traditional 4/3-valve into the 2-way valve, which leads to different configurations of IMV [10]. The functional decoupling relies on the switching and proportional valves, where the functionality depends on the switching valve. According to the valve component, the main-stage arrangements can be mainly classified into three types: two 3-way spool valves, four 2-way poppet valves, or numerous digital valves [11]. Some classifications also contain several varieties, especially for two 3-way spool types. Each type of IMV has its distinct characteristics. Their pros and cons are compared in Table 2.1 referring to the commercial products in the state of the arts. (1) Two 3-way spool valves Combinations of two industrial directional valves or a developed twin 3-way valves both belong to such an arrangement. It is a natural approach deriving from the conventional 4/3-valve of spool type, which is similar to the conventional technique [12, 13]. The individually controlled metering edges are introduced by adding a control input of the spool, such that an additional state variable can be controlled. Since they are 3-way valves, they must be spool valves. This layout can not be constructed with 2-way poppet valves unless increasing the number of valve components. One of the representative commercial products is the CMA from Eaton [14, 15]. Two spools both connect the supply and the drain lines, and the only work port of the two spools connects two cylinder ports respectively, which is a standard layout using two

Features

Products Mechanical decoupling Recuperation /regeneration Float Integrated pressure compensator Low leakage Control accuracy

Main-stage layout

Wessel PAS

Danfoss PVX

Two 3-way spool valves

anti-leakage

manufacture cost

redundancy

flow accuracy

flexibility

Husco/Caterpillar

Four 2-way poppet valves

sensitive to contamination

Eaton CMA

Table 2.1 Main valve configuration of independent control type hydraulic valve Numerous digital valves

2.3 Main-Stage Layout 11

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2 Hardware Layout of Independent Metering Control

3-way spools. This layout enables each cylinder port to connect to the pump or tank, but not to both simultaneously. Recuperation, regeneration, and float modes are all possible. Pros of the layout include that only two components are required at each cylinder to achieve separate metering control and free multi-operating mode. The spool valve technique is suitable for continuous and proportional metering control. However, leakage is inevitable in the spool valve, and certain safety features can be hard to achieve without the check valve functionality. Another con is a difficult task to integrate a pressure compensator, because of the bidirectional flow across the spool under regeneration and float modes. There are some variants in the two 3-way spool layout. Some traditional proportional multi-way valve also integrates the recuperation or regeneration flow path in the spool. These flow paths can be activated in a special spool position, which means the spool should be fabricated to a longer displacement. The representative commercial product utilized in his layout is the PVX multi-way valve from Danfoss [16]. The spool design in this layout usually complies with the machinery’s operating condition, losing certain flexibility compared to the standard two 3-way spool layout. Another alternative of the two 3-way spool layout is utilized in PAS multi-way valve from Wessel [17]. Instead of connecting one of the cylinder ports to either pump or tank, one of the valves connects the pump/tank to one or the other cylinder port, then the system cannot connect the cylinder chambers. Consequently, its cons contain not only all the cons of two 3-way spool layouts but also the absence of free operating modes. A pro is introduced by this layout—a possibility to partly distribute the system, e.g., have the meter-out valve distributed and the meter-in valve not distributed. (2) Four 2-way poppet valves This layout employs poppet valves because 2/2-valves are used, such that the advantages of the poppet valve can be inherited, including excellent sealing capabilities, higher resistance to contaminants, and lower manufacturing costs. With four 2-way poppet valves, it is possible to connect one cylinder port to both the pump and tank simultaneously. Since the objective is often to reduce energy consumption, such a connection is not preferable. Owing to accuracy limits and/or dynamic limits, there may be situations where the undesirable flow will occur from the pump directly to the tank. Nevertheless, the possibility to connect each cylinder port to both pump and tank simultaneously makes this layout more flexible than the two 3-way spool layout, since the dynamics of the system can be changed with the use of this connection. Therefore, the layout is a more flexible and redundant solution. What’s more, the integration of the pressure compensator can be achieved by a specially designed valve component, such as EHPV developed by Husco [18–20], and a Valvistor valve developed by Linkoping University [21]. However, more components are needed than two 3-way spool layout, and poppet valves can be difficult to control proportionally. The representative products with this layout can be seen in the INCOVA hydraulic control from Eaton [22] and Adaptive Control System (ACS) from Caterpillar [23]. Another four 2-way valve layout is a combination of the standard layout and an additional 2/2-valve that connects the cylinder chambers directly [24]. It has the same

2.3 Main-Stage Layout

13

properties as the system described in the previous paragraph, with the extension of the additional properties of the system due to the extra valve which connects the load ports. It is an even more flexible solution than the standard four 2-way valve layout. The extra valve can be used for example in regenerative and floating operations to reduce pressure losses. It is also conceivable to use the extra valve for dynamic improvements. Although more controlled components in the two layouts introduce higher flexibility and redundancy of the system, the risk of failure also increases accompanied by the number of components (an extra bypass valve makes this even worse). The safety issue is an important consideration in mobile applications. (3) Numerous digital valves This layout is similar to the aforementioned one, but numerous digital valves are utilized as a poppet proportional valve. For example, Linjama from Tampereen University proposed a “Digital Flow Control Unit (DFCU)”, which consists of several parallel-connected on/off valves [25]. Opening different combinations of parallel valves is employed to control the flow charged into or discharged from the cylinder. The on–off valves may be of the same flow capacity (pulse number modulation of bits with equal significance) or not (pulse code modulation of bits whose significance is set according to, e.g., binary series). Then, the flow rates can be achieved according to the number of on–off valves. A DFCU consisting of five valves is capable of producing unique flow rates (and zero flow). An increase in the number of bits results in greater resolution: in the case of ideal binary series, each bit doubles the resolution. Since the proportional control of the poppet valve is difficult, such a digital control method results in relatively good controllability for many applications. An IMV arranged by four or five DFCUs involves three main positive features: deterministic operation, fast response, and fault tolerance. (4) Other layouts using a combination of different valve types The aforementioned three layouts always utilized a single valve type, such as proportional spool valves, proportional poppet valves, or on–off switching valves. One of the biggest obstacles to applying independent metering control techniques in mobile machinery is the increased costs. The costs consist of not only the hardware, including more components and advanced sensors but also the sophisticated software control. For example, four metering edges are arranged in the system, and energy-saving regeneration/float modes mean that both two directional flows are required. Because the hydro-mechanical pressure compensator is difficult to integrate, an electrohydraulic pressure compensation must be designed based on the calibration of orifice flow characteristics, which requires sophisticated software control. There are several measures to overcome this challenge by a combination of different valve types. a. Reducing the number of high-tech components Generally, four metering edges are mounted because each actuator port may be charged or discharged by the supply and drain line, respectively. However, only two metering edges are responsible for a certain operation mode, and others are

14

2 Hardware Layout of Independent Metering Control

Fig. 2.1 Examples of incorporating directional on/ off valves into IMV to reduce the number of proportional valves

prepared for the next modes when the flow paths are changed. Due to the high costs of proportionally controlled units, As depicted in Fig. 2.1, some researchers proposed novel valve arrangements consisting of only two 2-way proportional valves combined with directional on/off valves [26, 27]. Another feasible solution is to replace all the proportional controlled valves in the IMV with digital control valves, as mentioned in Sect. 2.2. The costs of switching valves are much lower than proportional valves. Plockinger et al. adopt four fast-switching valves with the PWM control method [28]. Linjama and his co-worker developed a digitally controlled valve, which was a group of parallel-connected switching valves controlled by the PCM [29, 30]. b. Eliminating requirements for complex control strategy As depicted in Fig. 2.2, the utilization of individual PCs can reduce the complexity of the control strategy considerably by controlling a constant flow with a hydromechanical method. This approach requires a specifically designed bidirectional valve integrated with a PC or specific IMV structure. The decrease in electronic sensors also accompanies the simplification of the control strategy. Sitte and Weber proposed a layout in which two proportional valves are arranged with four on–off twoway directional valves and an individual pressure compensator is always configured in the inlet flow path, such that the reversing flow through the PC is avoided [27]. A novel control strategy using only one pressure sensor in the common supply pipe and spool stroke sensors at the individual PC [31]. The strategy uses the PC as a sensor for detecting the load situation and does not need any other pressure sensors, as shown in Fig. 2.2. Both the control software and sensor hardware are simplified. c. Simplifying the hardware layout Although the uses of proportional valves can be decreased, in the aforementioned studies, the circuit still includes both meter-in and meter-out edges. An interesting question is whether or not both these edges are necessary. Inspired by the findings of meter-out control, Vukovic and Murrenhoff further simplified the IMV system by utilizing a single-edge meter-out control circuit, in which the meter-in valve is no longer included [32], as shown in Fig. 2.3. Compared with the classic IMV arrangement with four proportional valves, at present, only one proportional valve

2.4 Pilot Stage Configuration

15

y1,ref

y

u

y2,ref

Fig. 2.2 Control schematic diagram of IMV using the IPC as a sensor Fig. 2.3 Single-edge meter-out control valve

and three switching valves are needed. Another advantage is the ability for simple integration of the pressure compensator.

2.4 Pilot Stage Configuration In the above section, only main-stage layouts of IMV have been discussed. The pilot stage associated with the valve arrangement of a specific topology is another issue. Generally, the main-stage valve is directly actuated by an electro-mechanical actuator or indirectly actuated by a pilot pressure. Preferably a directly actuated way

16

2 Hardware Layout of Independent Metering Control

can improve dynamical properties. However, current state-of-the-art electromechanical actuators do not provide enough force for handling the flow forces in spool valves, unless increasing electrical power and the cost of power electronics. This issue becomes significant for the large flow condition. The flow force compensation can be used with a specially designed sleeve, which is too expensive and less compact for the mobile application. Therefore, a main stage actuated via a pilot stage is necessary, especially for large flow rate valves. The primary requirement of the pilot stage to actuate the independent metering valve is a fast response. In the conventional proportional multi-way valve, the necessary pressure compensator is operated hydro-mechanically, making them very responsive with natural frequencies typically above 50 Hz [32]. The main stage should be actuated fast enough about the varied load pressure to reach similar response times using electro-hydraulic flow control. Second, the fail-safe state that all orifices of the main stage are closed must be obtainable if electrical power fails. This gives one restriction on the pilot actuation circuit that it must balance the pressures in pilot chambers facing the ends of the main stage if power fails. Four pilot actuation schemes whereby this is obtained are sketched. The 2-way valves of the three upper circuits are on–off valves but continuously controllable ones are also possible. As shown in other combinations of fixed and variable orifices are possible, but not all of these fulfill the fail-safe condition. Besides, the control performance, such as flexibility, accuracy, etc., is also to be taken into account for the precise adjustment of the main valve opening. A proportional directional spool has been employed in Eaton CMA [14, 15], in which the voice coil is used as the electro-mechanical actuator to improve the dynamic properties. The control of the two pilot pressure is coupled by a four-way spool, which provides precise displacement control and a sufficient fail-safe state of the main stage. However, a large dead zone and mass decrease the response time. Based on this pilot layout, a decoupled pilot layout is proposed by Zhejiang Table 2.2 The main configuration of the pilot drive of the high-flow hydraulic valve

References

17

University, in which a 4-way 3-position proportional spool is substituted by two independent 3-way 2-position spools [18]. This coupling contributes to a smaller dead zone and mass, such that a 20–40% increase in the frequency response can be obtained. The two proportional spools also can be replaced by a high-speed digital switching valve, which utilizes a PWM control method. Furthermore, the two 3-way 2-position spool valves can be decoupled to four 2-way poppet valves, which is the pilot layout of the Danfoss PVG multi-way valve. The comparison of different pilot layouts is depicted in the following Table 2.2 [16].

2.5 Conclusions This chapter started by presenting the different valve components utilized in the IMV. Proportional spool and poppet valves are mainly utilized in the state of the arts, while the digital on–off switching valve become more and more popular due to its distinct advantages. According to the three valve types, the standard hardware layouts of the main stage, as well as their variants, are all discussed in detail. The combination of the three valve types and other switching valves also attracts more attention to address the challenges of each standard layout, such as the difficult integration of pressure compensator, expensive cost, bidirectional flow, etc. In addition to the main stage, the possible layouts of the pilot stage are also analyzed.

References 1. R. Ding, et al., Programmable hydraulic control technique in construction machinery: status, challenges and countermeasures. Autom. Constr. 95, 172–192 (2018). https://doi.org/10.1016/ j.autcon.2018.08.001 2. E. Lisowski, G. Filo, P. Pluskowski, J. Rajda, Flow analysis of a novel, three-way cartridge flow control valve. Appl. Sci. 13(6) (2023). https://doi.org/10.3390/app13063719 3. K. Abuowda, I. Okhotnikov, S. Noroozi, et al., A review of electrohydraulic independent metering technology. ISA Trans. 364–381 (2019). https://doi.org/10.1016/j.isatra.2019.08.057 4. T.H. Nguyen, T.C. Do, V.H. Nguyen, K.K. Ahn, High tracking control for a new independent metering valve system using velocity-load feedforward and position feedback methods. Appl. Sci. 12(19) (2022). https://doi.org/10.3390/app12199827 5. P. Opdenbosch, N. Sadegh, W. Book, A. Enes, Auto-calibration based control for independent metering of hydraulic actuators, in 2011 IEEE International Conference on Robotics and Automation (ICRA) (IEEE, 2011), pp. 153–158 6. P. Opdenbosch, N. Sadegh, W. Book, Intelligent controls for electrohydraulic poppet valves. Control Eng. Pract. 21(6), 789–796 (2013). https://doi.org/10.1016/j.conengprac.2013.02.008. http://www.sciencedirect.com/science/article/pii/S0967066113000269 7. M.S.A. Laamanen, M. Vilenius, Is it time for digital hydraulics, in The Eighth Scandinavian International Conference on Fluid Power (2003) 8. M. Ketonen, M. Linjama, Simulation study of a digital hydraulic independent metering valve system on an excavator, in Proceedings of 15th Scandinavian International Conference on Fluid Power, June 7–9, 2017, Linköping, Sweden, no. 144 (Linköping University Electronic Press, 2017), pp. 136–146

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9. M. Karvonen, M. Heikkilä, M. Huova, M. Linjama, Analysis by simulation of different control algorithms of a digital hydraulic two-actuator system. Int. J. Fluid Power 15(1), 33–44 (2014) 10. R. Hippalgaonkar, M. Ivantysynova, A series-parallel hydraulic hybrid mini-excavator with displacement controlled actuators, in Linköping Electronic Conference Proceedings, Proceedings from the 13th Scandinavian International Conference on Fluid Power, June 3–5, 2013, Linköping, Sweden (2013). https://doi.org/10.3384/ecp1392a4 11. R. Zhang, A.G. Alleyne, E.A. Prasetiawan, Performance limitations of a class of two-stage electro-hydraulic flow valves. Int. J. Fluid Power 3(1), 47–53 (2014). https://doi.org/10.1080/ 14399776.2002.10781127 12. B. Eriksson, Mobile fluid power systems design: with a focus on energy efficiency (2010) 13. J.A. Crosser, Hydraulic circuit and control system therefor, US Patent 5, 138, 838 (1992) 14. EATON, CMA90 advanced independent-metering mobile valve (2016) 15. EATON, CMA200 advanced independent-metering mobile valve (2016). 16. Data sheet proportional valve PVX. Denmark, Danfoss (2016) 17. Proportional Valve with Autonomous Spools Proportional Directional Control Valve System. Wessel-Hydraulik, Wilhelmshaven, Germany (2013) 18. X. Yang, M.J. Paik, J.L. Pfaff, Pilot operated control valve having a poppet with integral pressure compensation mechanism, US Patent 6,745,992 (2004) 19. HUSCO International Inc., Electro-Hydraulic Poppet Valve. http://www.huscooffhighway. com/products/cartridg-e-valves-2/ehpv/?lang=en. Accessed June 8, 2018 20. D. Stephenson, M. Jahnke, P. Paik, Integrated valve assembly and computer controller for a distributed hydraulic control system. U.S. Patent 7,270,046 (2007) 21. B.R. Andersson, On the Valvistor a Proportionally Controlled Seat Valve (Linkoping University, Linkoping, Sweden,1984). https://ci.nii.ac.jp/naid/10015692657/. Accessed July 18, 2018 22. HUSCO International Inc., INCOVA hydraulic control system. http://www.huscooffhighway. com/incova-hydraulic-control-sysem/. Accessed June 8, 2018 23. Caterpillar Inc. Company, CAT 336E H hydraulic hybrid excavator delivers nocompromise, fuel-saving performance. https://www.cat.com/en_US/news/machine-press-releases/cat-sup174-sup-336ehhydraulichybridexcavatordeliversnocompromis.html. Accessed June 8, 2018 24. J. Weber, B. Beck, E. Fischer, 等. Novel system architectures by individual drives (2016) 25. M. Ketonen, M. Linjama, Simulation study of a digital hydraulic independent metering valve system on an excavator, in Proceedings of 15th Scandinavian International Conference on Fluid Power, June 7–9, 2017, no. 144 (Linköping University Electronic Press, Linköping, Sweden, 2017), pp. 136–146 26. A. Sitte, Design of independent metering control systems, in 9th International Fluid Power Conference, ed. by H. Murrenhoff (RWTH Aachen University, Aachen, Germany, 2014), pp. 429–441. 978-3-9816480-0-3 27. A. Sitte, J. Weber, Structural design of independent metering control systems, in 13th Scandinavian International Conference on Fluid Power, ed. by P. Krus (Linkoping University, Linkoping, Sweden, 2013), pp. 261–270. https://doi.org/10.3384/ecp1392a26 28. Simulation and experimental results of PWM control for digital hydraulics, in 5th Workshop on Digital Fluid Power, ed. by A. Plöckinger, M. Huova, R. Scheidl, A. Laamanen, M. Linjama (Tampere University of Technology, Tampere, Finland, 2012), pp. 133–152. 978-952-15-29429 29. M. Huova, M. Linjama, K. Huhtala, Energy efficiency of digital hydraulic valvecontrol systems, in SAE 2013 Commercial Vehicle Engineering Congress, SAE (Rosemont, USA, 2013), pp. 2347–2360. https://doi.org/10.4271/2013-01-2347 30. M. Linjama, M. Paloniitty, L. Tiainen, K. Huhtala, Mechatronic design of digitalhydraulic micro valve package. Proc. Eng. 106, 97–107 (2015). https://doi.org/10.1016/j.proeng.2015. 06.0123 31. D.-I.J. Lübbert, D.-I.A. Sitte, I.J. Weber, Pressure compensator control–a novel independent metering architecture, in 10th International Fluid Power Conference, vol. 1, pp. 231–245 (2016)

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32. M. Vukovic, H. Murrenhoff, Single edge meter out control for mobile machinery, in ASME/ BATH 2014 Symposium on FluidPower and Motion Control, ed. by D.N. Johnston, A.R. Plummer (ASME, Bath, UK, 2014), pp. 1–9. https://doi.org/10.1115/FPMC2014-7810

Chapter 3

Multi-Mode Load Control

3.1 Introduction Using the IMCS, the increased control DOFs in the hardware introduce many advantages including energy saving, functionality extension, etc. To make full of these advantages, more complex and intelligent control software attracts more attention than the hardware design. The improvements of the control software reside in three aspects, as shown in Fig. 3.1 [1]: (1) the control architecture is extended from the conventional one level to two or three levels by the separated meter-in and meter-out valves, as well as the electronically controlled pump; (2) the operating modes for each level are exploited from unicity to multiplicity regarding different load characteristics; (3) at least two control variables can be steered to achieve the first objective of actuator motion and simultaneously another secondary objective [2, 3]. In the electro-hydraulic control system, the upper level is always named the load control to regulate the flow paths (hydraulic circuits) [3, 4]. In the traditional electrohydraulic system, the flow paths of the actuator chambers are not individual due to the mechanical decoupling between the inlet and outlet. It means that the flow can only be charged into one chamber and discharged out from another chamber according to the direction of the velocity, which is referred to as “Normal mode” (Nor. mode). With the independent metering control, the flow paths of the actuator chambers become individual to perform more operating modes, such as regeneration and recuperation [5]. The upper level controls a group of flexible switching of flow paths according to the load condition. Therefore, it is also referred to as mode switching. Functions of the upper load control level first include the selection of high energyefficiency operating, and then control of the transfer from one mode to another. The former depends on the mode-switching logic, while the latter depends on the mode transition control. The operating mode decides the distribution of independent © Shanghai Jiao Tong University Press 2024 R. Ding and M. Cheng, Independent Metering Electro-Hydraulic Control System, https://doi.org/10.1007/978-981-99-6372-0_3

21

22

3 Multi-Mode Load Control

Fig. 3.1 Architecture of independent metering control system

metering valves to construct an energy-saving g hydraulic circuit and enable the controllability for precise motion tracking at the same time. Therefore, the upper level plays the most important role in the IMCS.

3.2 Multiple Operating Modes for the Actuator The load conditions of the hydraulic actuator (cylinder or motor) are described by the load quadrants. As shown in Fig. 3.2, four quadrants are distinguished by the combinations of load force directions and actuator velocity. The same directions of the force and velocity vectors define an overrunning load quadrant; otherwise is a resistive load quadrant [6, 7]. For the aforementioned load quadrants, the operation modes of the hydraulic actuator can be divided into four types in terms of flow paths, as shown in Fig. 3.3: Normal mode (Nor.): The flow is supplied by the pump, the inlet of the actuator is connected to the pump, and the meter-out chamber is connected to the drain line. This mode is the only one that can be realized by the traditional single-spool control valve. It is suitable for both resistive and overrunning loads among four load quadrants, with the high-pressure or low-pressure oils supplied by the pump respectively. Regeneration mode (Reg.): Two chambers are connected to the pump simultaneously, and the flows are regenerated from one chamber to another. With a resistive load in Qua.I, the actuator chambers are connected to the high-pressure supply together such that a light load with a large flow is transformed into a heavy load with a smaller flow. In this case, energy consumption is saved by diminishing the required flow of

3.2 Multiple Operating Modes for the Actuator

23

Fig. 3.2 Definition of the load quadrant + Rec.

Flo.

Reg.

Nor.

vc

FL Nor.

FL

vc

Reg.

FL

+

Nor.

vc

Nor.

FL

vc

Reg.

Flo.

v

Rec.

FL

-

Fig. 3.3 Operating modes of the independent metering control system for four load quadrants

the actuator with a light load. This mode is also suitable for overrunning loads. In Qua.II and Qua.IV, the pump supplies low-pressure oil or operates as a motor respectively. The former saves energy in the same way as the resistive load in Qua.I, while the latter save energy through energy recuperation. Float mode (Flo.): With an overrunning load, both actuator chambers are connected to the tank, and pressure generated by the load itself can be pumped to generate flow. This mode can save energy by withdrawing flows from the pump. Recuperation mode (Rec.): With an overrunning load, the oil charges into the actuator without any flow from the tank. The load will subsequently pressurize the oil in the opposite actuator chamber and pump it into the system supply. The actuator thus is utilized as a pump to drive other loads or operates the system pump as a

24

3 Multi-Mode Load Control

motor. This mode must be operated accompanied by energy recuperation, storage, or transmission units.

3.3 Mode Switching Logic Although the mode classification and nomenclature are different in the state of the art, the layouts of flow paths involved in Fig. 3.3 can cover all the mentioned modes in different investigations [8–11]. Because Rec. mode and Reg. mode under overrunning load require extra energy recuperation units and circuits, they are not included in the general IMCS. Therefore, only Nor. mode, Flo. mode and Reg. mode under the resistive load is considered for utilizations here. A certain mode contains the following different hydraulic circuits according to different quadrants [8]. Nor. mode: Qua.I: Power extension (PE); Qua.II: Low Side Retraction (LSR); Qua.III: Power Retraction (PR); Reg. mode: Qua.I: High Side Regeneration Extension (HSRE); Qua.IV: High Side Regeneration Extension (HSRE); Flo. mode: Qua.II: Low Side Regeneration Retraction (LSRR); Qua.IV: Low Side Regeneration Extension (LSRE); In terms of such further definition of the operating modes, the targets of mode switching logic involve two aspects: (1) select the most energy-efficiency operating mode according to the load condition; (2) the selected mode can drive the actuator to complete the required motion. Therefore, the energy-saving characteristics, as well as the force–velocity limitations, should be both taken into account under a group of energy management strategies [12].

3.3.1 Energy-Saving Characteristics Omitting the pressure losses in the hoses and pipelines, the energy-saving characteristics of the IMCS are analyzed in comparison to the traditional valve-controlled system. The comparisons are conducted in the commonly used hydraulic system using a load-sensing (LS) control manner, in which the supply pressure of the pump is beyond the largest load pressure with a preset margin. A double-actuator condition is taken into account, of which Load 1, 3, 4 are featured as heavy resistive, light resistive, and overrunning respectively, such that Nor., Flo., and Reg. modes are covered. The energy-saving performances for typical three operating conditions are listed in Table 3.1:

3.3 Mode Switching Logic

25

Table 3.1 Energy consumption under different operating modes Inlet loss Load conditions

Fl

quadrant IV Fl

Fl

v

quadrant III quadrant IV Fl Fl

Load 2: Nor. (PE)

+

+v

pressure ps

Pm

pa1

Load 1: Nor. (PE)

pb2 Load 2

Load 1

pa2

pb1

v

Load 1: Nor. (PE) +v

Fl v

q2 flow

pressure ps pa1

pa2

Load 3: Reg. (HSRE)

Load 1 q1

Load 4

-

pb2 Load 2

Load 1 q2 flow

q2 flow

pressure ps

v

pa1

Loa -d 2

pb1

Fl

quadrant III Fl

ps pa2

q1

Load 1

Fl

pressure

pb1

v

-

v

+v

pb2 Load 2

q1

v

Fl

(b) IMCS Pm

Load 1

Load 1: Nor. (PE)

+ Load 1 & Load 3 Fl

Load 4

(a) LS

v

-

v

-

Fl

v

quadrant II Fl

Saved energy

pa1 Load 1

v

-

Operating mode

+

v Load 2

Outlet loss

pressure ps

quadrant II Fl -

Useful energy

pb2 Load 2

Load 1

Load 4: Flo. (LSRR/LSRE)

Pm

pa1

pb1 q1

flow

q1

flow

pressure ps pa1

pa2

Load 1 pb1 q1

q2 flow

pb1

(1) For Load 1 and Load 2 located in Qua.I and Qua.III, Nor. modes should be selected owing to the resistive loads, such that outlet pressure losses are both decreased by the decoupling of the inlet and outlet. (2) For heavy Load 1 located in Qua.I, the saved energy comes from the decrease of the outlet pressure loss. Although located in Qua.I, Load 3 is operated under the Reg. mode because it is the light one compared with Load 1. With a decreased supply flow into Load 3, energy consumption is reduced compared with the conventional system. Besides, the supply pressure is decreased by a smaller outlet pressure of Load 1, such that inlet losses caused by the difference between the two loads are diminished, which contributed to another energy-saving way. (3) For heavy Load 1 located in Qua.I, the saved energy comes from the decrease of the outlet pressure loss. Because Load 4 is located in Qua.II or Qua.IV, it is operated under Flo. mode to withdraw pump supply flow, so the energy consumption of Load 3, which exits in the conventional system, can be completely ignored.

26

3 Multi-Mode Load Control

3.3.2 Force-Velocity Capability Qua.I: Nor. mode (PE): Limits in load force F Nor and actuator velocity V Nor are given based on the pump maximum pressure and flow by Eq. (3.1): ( {FPE , vPE } =

ps,max · Aa ,

qs,max Aa

) (3.1)

Reg. mode (HSRE): The pump flow is reduced together with the increase of pressure. Therefore, the limits in load force F HSRE and actuator velocity V HSRE are given by Eq. (3.2): ( {FHSRE , vHSRE } =

qs,max ps,max · ( Aa − Ab ), Aa − Ab

) (3.2)

Qua.II: Flo. Mode (LSRR): When lowering an overrunning load, such as gravity load, both actuator chambers are charged from or discharged into the tank. The gravity load decreases with the downward motion of the actuator until it cannot overcome resistance caused by friction, inertia force, and back pressures [13]. Figure 3.4 is an example of the excavator boom driven by its gravity load. Actuators with different velocities all tend to stop when the gravity load decreases to a threshold value, which is defined as F l,lim to switch out from the Flo. mode. This threshold value is captured in terms of the force balance in the cylinder: m L v˙ = Fl,lim + pa Aa − pb Ab − B p v

(3.3)

Apart from force limitation, flow limitation also decides whether Flo. mode is feasible for the overrunning load [14]. Under this mode, the supply flow is sucked

Fig. 3.4 Experimental results of potential energy regeneration for excavator arm extension

3.3 Mode Switching Logic

27

from the drain line rather than the pump. However, the flow with a drain-line pressure should cross pipelines and valve orifices with a certain pressure loss. If the low-level drain-line pressure could not overcome the pressure loss, negative pressure in the actuator chamber would appear, causing cavitation or empty suction. Hence, the activation and inactivation of the Flo. mode depends on how much flow is available in the drain line. Such flow limitation is concerned with the valve throttling characteristics, which are calculated as: qLSRR

/ ( ) 2 · ( pr − pb ) = Cq Av u 2,max ρ

(3.4)

where pb usually is controlled to approximate 1~2 bar to avoid cavitation. Then, the force and velocity are limited by both force threshold F l,lim, and flow limitation qLSRR . ( ) qLSRR {FLSRR , vLSRR } = Fl,min , Ab

(3.5)

Nor. mode (LSR): Because Nor. the mode in Qua.II still utilizes the pump to supply, there is no force limitation, and the velocity is limited by the pump’s maximum flow. ) ( qs,max {FLSR , vLSR } = Fl , (3.6) Ab Qua.III: This quadrant is less complicated than the others because only Nor. mode (PR) can be chosen. The limits in load force F PE and actuator velocity V PE are also given based on the pump maximum pressure and flow by Eq. (3.7): ( {FPR , vPR } =

ps,max · Ab ,

qs, max Ab

) (3.7)

Qua.IV: Flo. mode (LSRE): As Flo. the mode in Qua.II, it only can be operated under strict conditions. First, the overrunning force should be high enough. The force threshold F l,lim can be given as: m L v˙ = Fl,lim + pb Ab − pa Aa − B p v

(3.8)

Second, sufficient drain line pressure pr must be built to overcome the pressure loss across the valve and pipelines.

28

3 Multi-Mode Load Control

qLSRE1

/ ( ) 2 · ( pr − pa ) = Cq Av u 1,max ρ

(3.9)

where pa usually is controlled to approximate 1~2 bar to avoid cavitation in this mode. Therefore, the force and velocity are limited by both force threshold F l,lim, and flow limitation qLSRE . )) ( ( qLSRE1 qLSRE2 {FLSRE , vLSRE } = Fl , min , Aa Ab

(3.10)

Reg. mode (HSRE): As depicted by Eq. (3.9), the threshold force between Flo. mode and Reg. mode in Qua.IV depends on the actuator velocity and drain-line pressure. If the actual load force F l is beyond the threshold value, it means the actuator cannot work in the Flo. mode. Then the Reg. mode should be chosen. In this condition, the energy-saving performance of Reg. mode is inferior to Flo. mode due to the required flow from the pump. The pump only provides low pressure and less regenerated flows to the actuator, such that the force is not strictly restricted for Reg. mode. Equation (3.11) exhibits the force–velocity capability: {

( ) } qs,max ∗ ∗ FHSRE = Fl , , vHSRE Aa − Ab

(3.11)

In summary, force–velocity capabilities for different modes can be depicted in the following Fig. 3.5. To avoid negative pressure under Flo. mode, the drain-line pressure pr should be increased to expand its operating range. A simple way of doing so is to mount a check valve with a certain cracking pressure before the tank, as shown in Fig. 3.6a. The cracking pressure determines the increased pr . However, the constant cracking pressure is not suitable for varied load conditions. A higher cracking pressure would vLSRR

Fig. 3.5 Mode selection for different load quadrants

Fl

LSRR

+

vLSR

(FPE ,vPE)

PE

(FHSRE ,vHSRE)

LSR HSRE

HSRE

PR (FPR ,vPR)

-

+v v*HSRE Threshold Fl LSRE

3.3 Mode Switching Logic

pr

29

pr

pr

pr

pr

(a)

pr

(b)

Fig. 3.6 Enhanced tank pressure by: a a check valve; b a low-pressure proportional relief valve

result in extra energy consumption under other operating modes, while a low cracking pressure has little effect on expanding the operating range. To address this problem, an electro-hydraulic proportional relief valve with low nominal pressure can be utilized to replace the checking valve, as shown in Fig. 3.6b. The drain line pressure can be regulated continuously to adapt to the required flow.

3.3.3 Mode Switching Logic Considering the energy-saving performance, the most efficient mode in each load quadrant is the optimal one. However, each mode contains its specific operating ranges due to the limits of the force–velocity capabilities. If the operating point exceeds the operating range, the most efficient mode is not available to actuate the required motion. In this case, a suboptimal switching logic using a less efficient mode has to substitute the most efficient one [15]. Taking the decreased overrunning load for instance, the actuator cannot be driven only by self-generated pressure oils under the Flo. mode. Then, the flow path should be switched to Nor. mode to continue the required motion with pump supplies. To address the complex switching problem, the aforementioned energy-saving characteristics for operating modes, together with their force capabilities, can be utilized to design a group of rules [10, 16–18]. Based on the designed rules, a rulebased mode-switching logic is constructed to achieve the dual objectives of saving energy and actuating required motion with no conflict, as depicted in Fig. 3.7. The actuator velocity and force are the key input variables to the rule-based switching logic. The velocity can be simply captured by the reference or desired one. The force should be captured by the desired force of the hydraulic actuator that is needed to deliver the required motion considering the dynamic forces to acceleration or

30

3 Multi-Mode Load Control

Fig. 3.7 Example of mode switch rules considering the dual purposes of saving energy and actuating required motion

deceleration. Thereby, measured chamber pressures along with the desired motion are both utilized to calculate the actuator force. The cost functions, which make tradeoffs between energy efficiency and motion control, are also employed to design switch rules. The representative investigation was presented by Linjama [19], in which a cost function containing velocity errors, pressure errors, and power loss items, was defined to control multi-mode switching.

3.4 Mode Transition Control Mode transfer after the mode selection is the next stage to complete the modeswitching control. Based on a rule-based switching logic, discrete mode transfer is usually employed, in which the hydraulic circuit in one mode is directly changed to another immediately [20]. Figure 3.8 shows an example of the mode-switching process for the arm actuator. With the extension of the arm, the applied force decreases from overrunning load to zero and then increases from zero to resistive load. There is a load-condition crossing from Qua.IV to Qua.I, such that the system is operated under Flo. mode at first, and then transferred to Nor. mode. The switch controls the inlet valve spool displacement from negative to positive, and thereby the head side of the actuator first connects to the drain line and then the supply line. Both changes in the hydraulic circuit and the valve controller are involved in this mode transition.

3.4 Mode Transition Control

31

Fig. 3.8 Mode switch of a typical motion

3.4.1 Problem Statement Unstable switching The mode switching for the aforementioned arm motion using the discrete way is tested in an excavator. The experimental result is exhibited in Fig. 3.9. It is seen that the actuator velocity is stable until the mode switching occurs. Severe oscillations begin at the switching instant, and the frequent switching between two modes appears, which means significant instabilities in the system. The unstable switching might be attributed to the discrete transfer way. According to the rule-based switching logic, the mode transition happens as soon as the load force crosses the threshold value. As a consequence, the switching dynamics are dependent on the load force data. However, the capture of the load force usually

Fig. 3.9 The experimental result of the unstable switch

32

3 Multi-Mode Load Control

relies on the pressures of the actuator chamber: F l = pa Aa − pb Ab , especially for the mobile hydraulic system. The mode switching processes in Fig. 3.10 compare the actual curve of the load force with the idea one. For an actual condition, there are pressure fluctuations caused by the fast transfer transient, which simultaneously feedback to the switching control logic and further exacerbates the frequent switching around the threshold value. As a consequence, the arm motion becomes unstable with severe oscillations in Fig. 3.9. Because the pressure fluctuations mainly come from the transient instability by the fast transfer, the stable switching in the IMCS is translated to the elimination of transient instability due to fast transfer. Unsmooth switch The modes switching changes the hydraulic circuits by deactivating/activating different valve components. Consequently, valve controllers in the two modes are also transferred with discrete gain scheduling or even different control algorithms. Therefore, the control system of the IMCS by the discrete switch is depicted as two individual control loops in Fig. 3.11. In the two individual control loops, C L1 and C L2 represent the online/offline controllers before and after the mode switching. C L2 is inactivated when the system is under mode 1 to prevent it from experiencing the anti-windup problem. However, Fig. 3.10 The cause analysis of instability during mode switch

3.4 Mode Transition Control

33

Mode 1 controller CL1

r + -

uA s1

Mode 2 controller uB CL2

Plant dynamic y

G

s2

Fig. 3.11 Schematic diagram of the discrete controller switch Fig. 3.12 Schematic diagram of control signals using discrete switch

output

Mode 1

uA

Mode 2 uB

t

a jump in controller output is inevitable during the switching instant, as depicted in Fig. 3.12. Such output jump leads to the discontinuity of valve control signals. The discontinuous switching in the closed-loop control system results in the flutter or fast reversing of valves, and thereby velocity fluctuations or pressure shocks appear after the switching.

3.4.2 Motivation for Bumpless Switch As summarized in Fig. 3.13, there are two discontinuities involved in the mode transition of the IMCS: (1) the hydraulic circuit and (2) the valve control signals, which arise unstable and unsmooth phenomena during the transition instant. To address these problems, multiple subsystems must weaken or eliminate the discontinuities to work as a single unit, which is the motivation of the bumpless transfer design in the next section.

3.4.3 Continuous Switching Continuously variable modes have been presented for a smooth transition. With three valves activated simultaneously, continuous system dynamics can be obtained during the mode transition. Figure 3.14 exhibits an example of continuously variable mode transition Nor. mode to Reg. mode. V1 and V2 valves are activated in Nor.

34

3 Multi-Mode Load Control

Fig. 3.13 The motivation for bumpless transfer

mode, while V1 and V4 valves are activated in Reg. mode. A discrete switching between the two modes requires the closing of V2 and the opening of V4. A new mode by the activation of V1, V2, and V4 valves is utilized between the Nor. and Reg. modes, such that the discrete switching is transferred to continuous switching. More energy consumption is accompanied by the continuous mode because of extra pressure losses in the third valve. The application of this approach is constrained by the hardware layout using four (five) 2-way valves. There are no extra valves in the two-spool layout to construct the hydraulic circuit of the continuous mode. Nor. mode

Reg. mode V4

V1 V2 V3

Fig. 3.14 Continuously variable modes by three valves from Nor. mode to Reg. mode

3.4 Mode Transition Control

35

3.4.4 Discrete Switching with the Bumpless Transfer Dwell-time switch Compared to the above continuous switching, discrete switching can be still utilized because of the compatibility for different hardware layouts and less energy consumption, but an alternative must be conducted to eliminate the transient instability due to fast transfer. To slower the fast transfer, each stabilizing subsystem in the loop is kept for a windowing period, such that the transient effects can dissipate for a sufficiently long time. In Fig. 3.15a, the pressure fluctuation during switch instants causes the instability of discrete switching. In comparison, a windowing period τ is added to implement the mode transfer in Fig. 3.15b. Then, there is enough time to decay the transient instability of pressure, and thereby prevent the infinitely fast switch. The windowing period τ is defined as the dwell time, which transfers the discrete switching to a dwell-time switch as: Fl (t) ≡ Fl [(k − 1) · τ ] t ∈ [(k − 1) · τ, k · τ ]

(3.12)

where k ∈ [1, 2, 3, …]. The principle of the dwell-time switch seems simple, but a new problem refers to how to dwell time τ: (1) If the value of τ is too small, the infinitely fast switch could not be relieved, and the mode switching is still unstable; (2) If the value of τ is too large, the mode is switched with a serious delay, and the system response decreases. Therefore, neither a smaller nor larger value of τ will be disabled to improve the dynamics performance of mode transition. To verify it, switching with a large dwell time τ is shown in Fig. 3.16. After approximately 5 s, the overrunning load decreases to a low level, which can not drive the actuator to move. The system switches to Nor. mode after a large dwell time, rather than immediate switching. With such a long waiting time to switch, the actuator velocity continues to decrease, which cannot meet the requirements of control performance.

Fig. 3.15 Effect of the dwell-time switch

36

3 Multi-Mode Load Control

Fig. 3.16 Actuator velocity with a large dwell time τ

Dynamic optimization of dwell time Dynamic dwell time design theorem A dwell-time design approach is presented to capture an optimal value for arbitrary switching instant dynamically. First, the state-space equation of the switched systems with N subsystems is defined as: x(t) ˙ = Aσ (t) x(t)

(3.13)

where σ:[0, ∞] → I = {1, 2, …, N} is the switching signal, state x ∈ Rn ; the matrices Ai ∈ Rn×n ; i ∈ I, {t 0 , t 1 , t 2 , … t k , …} denotes the switching sequence where t 0 is the initial time and t k denotes the kth switching instantly. The solution of the system (3.2) is assumed to exist and to be unique. Definition 3.1 Assuming each subsystem is stable, there exists a positive definite symmetric matrix Pi that solves the Lyapunov equation for each σth subsystem. Second, based on the switching signals σ(t), the positive definite symmetric matrices Pi are patched together to build a global Lyapunov function: Vσ (ti ) (x(ti )) = x T Pσ (ti ) x

(3.14)

AσT (ti ) Pσ (ti ) + Pσ (ti ) Aσ (ti ) = −Q

(3.15)

To analyze the stability with constrained switching, a very intuitive multiple Lyapunov functions (MLF) result is usually pursued [20–22]. As illustrated in Fig. 3.17, the switched system is asymptotically stable if the values of the Lyapunov function at the mode-switching instants form a decreasing sequence. Third, the dynamic dwell time for the switched system (3.2) is then designed in terms of the above MLF stability theorem.

3.4 Mode Transition Control

37

Fig. 3.17 MLF result for an asymptotically stable switched system

Definition 3.2 T(t k ) is called the dwell time of the switching signal σ for the kth switching instant, which stands for the time between the switching instants t k and t k+1 , i.e., τ(t k ) = t k+1 − t k . Accordingly, the following result is derived by assuming that all the subsystems are stable. Theorem 3.1 Considering switched system (3.2), if there is a collection of continuous positive scalar functions V i (x) and numbers λi > 0 satisfying: α1 (||x||) ≤ Vi (x) ≤ α2 (||x||)

(3.16)

Vi (x) ≤ −λi · V˙i (x)

(3.17)

where α 1 , α 2 are class K functions [23], then assume that the system switches from subsystem i to subsystem j at the switching instant t k , k = 1, 2, …., If the dwell time satisfies: ( τ (tk ) >

I n(u i ) λj

0

if V j (x(tk )) > Vi (x(tk )) V j (x(tk )) ui = Vi (x(tk )) if V j (x(tk )) ≤ Vi (x(tk ))

(3.18)

Then the switched system (3.2) is asymptotically stable. In this theorem, the sequences V(t k − ), k = 1, 2, …, are proved to be strictly decreasing [23]. In terms of Lyapunov’s second method, the Lyapunov function value for each subsystem itself decreases because all the subsystems are stable. As a consequence, the variations of Lyapunov function values are shown in Fig. 3.18, which infers that switched system (3.2) is stable in terms of the MLF stability theorem in Fig. 3.17. Dynamic dwell time design Theorem 3.1 provides an effective way to dynamically design the dwell time. However, the switched system in the IMCS must be linear and homogeneous, as formularized in the system (3.2). Owing to the typical nonlinear characteristic in the hydraulic system, it is necessary to linearize each subsystem in the independent

38

3 Multi-Mode Load Control

Fig. 3.18 The Lyapunov functions values at the switching instants in Theorem 3.1

metering control at first. Taking Nor. mode, for instance, the linearization of the electro-hydraulic control system is depicted in Fig. 3.19. When the meter-in valve is regulated by the flow mapping and pressure difference feedback, the flow-pressure gain of this valve is close to zero, such that a constant flow in the inlet could be considered [15]. Besides, the pressure of the rod chamber is controlled to a low value to save energy (approximately 2 bar), and thereby the meter-out valve is omitted to assume that the rod chamber is directly connected to the drain line [15]. At last, differential equations of the Nor. mode is derived as: m t v˙ c = Aa pa − Bp vc − Fl

(3.19)

Va p˙ a = Q a − Aa vc βe

(3.20)

The state-space equation is derived as: x(t) ˙ = A1 x(t) + B1 u(t)

Fig. 3.19 The linearization process of Nor. mode

(3.21)

3.4 Mode Transition Control

39

[ x(t) =

vc

]

[ x(t) ˙ =

v˙ c

]

[

, u(t) =

pa p˙ a ] [ [ B 0 − m1t − mpt mAat B1 = A1 = βe Aa βe 0 − Va 0 Va

Qa Fl ]

] (3.22)

(3.23)

Flo. and the Reg. modes both utilize differential hydraulic circuits, in which two chambers of the actuator are connected to the supply or drain line simultaneously. Thus, the asymmetric actuator, such as a cylinder, can be considered a discrete transformer with two possible states of operation. Taking Flo. mode, for instance, the linearization of the system is depicted in Fig. 3.20. A plunger cylinder is employed to simplify the actual asymmetric one, and its inlet is also regarded as a constant flow. Referring to Nor. mode, the linearized state-space equations of Flo. mode is derived by: [ u(t) = [ A6 =

B

− mpt mAdt − AVd dβe 0

Qa Fl

]

] (3.24) [

B6 =

0 (1−κ)βe Vd

1 mt

] (3.25)

0

where the effective pressurized area and the compressible fluid volume in the control volume will change according to the: Ad = Aa − Ab , Vd = Va + Vb , Q d = Q a − Q b = (1 − κ)Q a

(3.26)

A similar approach is taken to derive the state-space equation of Reg. mode: [ A2 =

B

− mpt mAdt − AVd dβe 0

]

[ B2 =

Fig. 3.20 The linearization process of Flo. mode

0 (1−κ)βe Vd

− m1t 0

] (3.27)

40

3 Multi-Mode Load Control

Remark The following unified formula is proposed for linearized expressions of a multi-mode IMCS: x(t) ˙ = Aσ (t) x(t) + Bσ (t) u(t)

(3.28)

After linearization, input vectors u(t) /= 0 in Eq. (3.28) become another obstacle to designing the dwell time by employing Theorem 3.1. The control input u(t) is utilized to achieve system stability or certain performances. Here a state feedback u(t) = K σ(t) x(t) is considered, where K p , ∀ σ(t) = i ∈ {1, 2, …, N}, is the control gain to be determined. Then, the resulting closed-loop system is given by: x(t) ˙ = Aσ (t) x(t)

(3.29)

where Aσ (t) = Aσ (t) + Bσ (t) K σ (t) . To solve the control gain K p , the following theorem is derived. Theorem 3.2 Consider the switched linear systems (3.2), λi > 0, u i > 0, I = {1, 2, . . . , N }, If there exist matrices Ui > 0, Ti > 0, i ∈ I, j ∈ I, I /= j, Ai Ui + Bi Ti + Ui AiT + TiT BiT + λi Ui ≤ 0

(3.30)

U j ≤ u i Ui

(3.31)

Then, for any switching signal, there is a set of stabilizing controllers to guarantee a global, uniformly, and exponential for system (3.2). In addition, control gains can be obtained if Eqs. (3.30) and (3.31) have a solution: K i = Ti · Ui−1

(3.32)

where Ui = Pi−1 U j = P j−1 Ti = K i · Pi−1 The demonstration of Theorem 3.2 refers to Ref. [24]. Summary: following steps are listed to dynamically design a dwell time for multi-mode switching: (1) Referring to Eqs. (3.19)–(3.33), formulate the IMCS before and after mode switching as the standard expression: x(t) ˙ = Aσ (t) x(t) + Bσ (t) u(t)

(3.33)

(2) Seek the state feedback of controller gain K p and Pi , Pj until the matrices satisfy the conditions of Eqs. (3.30) and (3.32). (3) Calculate λi using Eqs. (3.16)–(3.17). (4) Compute dwell time τ(t k ) for switching instant t k according to Eqs. (3.18) and (3.31).

3.4 Mode Transition Control Table 3.2 The parameters of the switching instant

41

Parameters

Value

mt (kg)

550

Aa (m2 )

0.003849

(m2 )

0.002592

Ab

β e (MPa)

700

V a0 (m3 )

0.01

(m3 )

0.01

V b0

Bp (N s/m)

10,000

vc (m/s)

0.05

pa (MPa)

0.4

Qa (L/min)

11.547

F l (N)

−1800

The arm motion in Fig. 3.10 is employed again to verify the presented dwell time design approach. A dwell time of 0.25 s is set based on the parameters of the switching instant in Table 3.2. Figure 3.21 compares the actuator velocities using three switching methods: discrete, long dwell-time, and the presented approach. The results verify that the frequent mode switch is eliminated, and few velocity oscillations or sharp decreases occur using the presented approach. A minor drop in the velocity can be put down to the crossing of the neutral spool position during mode switching. The comparison also depicts that a stable mode switching, together with an increase in the system response, can be guaranteed by the presented dwell-time design approach.

3.4.5 Bidirectional Latent Tracking Loop To avoid discontinuity in valve control, the control signal of the switched mode must smoothly take over the previous mode when the switching happens. To achieve a such smooth transition, a latent tracking loop is employed, which is similar to Graebe and Ahlen’s [25]. Because the mode switching of the IMCS is bidirectional, two latent tracking loops in this chapter are also considered for bidirectional switching. Figure 3.22 shows the framework of latent tracking for the multi-mode IMCS. Compared with conventional unidirectional switching, an extension is made to make the latent tracking suitable for the bidirectional mode switch. To make mode 1 active, switch S 1 is shifted to C L1 : y=

C L1 G r 1 + C L1 G

(3.34)

42

3 Multi-Mode Load Control

Fig. 3.21 Actuator velocity comparison by different switch approach

Mode 1 latent tracking s3 + TL1

r

+ +

+

s1

FL1

Plant dynamic G

+ +

uA

CL1

-

-

CL2

s2

uB

TL2

FL2

Mode 2 latent tracking Fig. 3.22 Bidirectional latent tracking diagram

+

y

3.4 Mode Transition Control

43

Meanwhile, S 2 is activated although mode 2 is on standby. The control loop connected by S 2 adds a feedback loop, as highlighted by the gray background in Fig. 3.21, such that the transfer function subjected to uB becomes a complex form: uB =

C L2 TL2 C L2 FL uA + (r − y) 1 + TL2 C L2 1 + TL2 C L2

(3.35)

It is seen that the online control signal uA acts as a reference signal to the latten tracking loop of mode 2, such that subsequent output uB is forced to track the online uA . Because both reference signal r and plant output y are imported to the latent tracking loop as disturbance generators, the asymptotic tracking between the output uB of the offline controller and the output uA of the online controller can be achieved [26]. The convergence of the latent tracking loop depends on the design of the tracking controller triplet (F L2 and T L2 ). If the mode switching is implemented, S 1 shifts to C L2 , while S 2 is deactivated and S 3 is activated simultaneously. Meanwhile, T L2 and F L2 will not affect the control loop of mode 2 and uA will start tracking uB in preparation to take over C L2 when the next mode switch happens. At this moment, Eqs. (3.34) and (3.35) are transformed into the following equations. y= uA =

C L2 G r 1 + C L2 G

(3.36)

C L1 TL1 C L1 FL uB + (r − y) 1 + TL1 C L1 1 + TL1 C L1

(3.37)

With the help of latent bidirectional tracking, the abrupt jump is eliminated and the transition of this control signal is smoothed, as depicted in Fig. 3.23. The tracking controller triplet has the following settings: F L = 1; T L = 10. Fig. 3.23 Schematic diagram of control signals using latent tracking diagram

Control signal Mode 1

uA

Mode 2

uB t

44

3 Multi-Mode Load Control

3.5 Experiment Research To verify the proposed mode-switching control strategy, the experiment was conducted in a 2-ton excavator through three motion trajectories in Table 3.3. Figure 3.24 shows the experimental results including actuator velocities/pressures, valve control signals, as well as the estimated energy consumptions. It is seen that the expected most efficient operating mode can be automatically selected by the proposed controller. The comparisons are conducted between the IMCS and the traditional proportional directional valve control system (marked as “PDV”). In Case A and B, although mode switchings are involved in the IMCS, their velocities transfer very smoothly without any oscillations, such that their motion control performances are consistent with that of PDV. In Case C, there are two different mode switching: PR mode to LSRE mode owing to the variation of the velocity direction, and LSRE mode to HSRE mode owing to the variation of load direction. The motion control performance of the former mode switching remains perfect. However, a relatively large peak velocity appears during the latter mode switching, which decreases from 50 mm/s to approximately 0 mm/s. Such a decrease in velocity can be explained that both the inlet and outlet valve spool must cross the neutral position of the 3-position and 3-way directional valves, which is needed by switching from LSRE to HSRE mode. On account of the crossing through a neutral position, both two valves shut off all the ports, and thereby the decrease in velocity is inevitable. Furthermore, the mode switching also involves a supply transformation from the overrunning load to the pump, and thereby a process for pressure charging is required in the actuator chamber. After this temporary switching instant, the actuator velocity promptly tracks to the reference one without any instabilities. Moreover, there is little performance degradation on the actuator displacement. Experimental results of pressures verify that under Nor. mode (PE and PR), the IMCS is much lower than PDV, of which the outlet pressure is always close to a drain-line pressure—a preset pressure of 0.2 MPa—to overcome pipeline losses and avoid cavitation [15]. Decreases in pressure losses benefit from the decoupling between the inlet and outlet of the actuator. Meanwhile, as depicted in Case A, dynamic performances of the pressure are not influenced by the mode switching, which appears even better than that of those in PDV. Table 3.3 Experimental motion trajectories Actuator

Boom

Arm

Case A

Lifting (v1,ref = 80 mm/s) → lowering (v1,ref = −50 mm/s) → lifting (v1,ref = 80 mm/s)

/

Case B

Lifting (v1,ref = 40 mm/s)

Retraction (v2,ref = 100 mm/s)

Case C

Lifting (v1,ref = 40 mm/s)

Extension (v2,ref = 80 mm/s) → arm retraction (v2,ref = 50 mm/s)

3.5 Experiment Research

45

-80mm/s 50mm/s

-50mm/s s

m/

m 80

Case A

100mm/s s

m/

m 40

Case B

Case C 20000

PDV

IMS

energy (J)

16000

9. 5%

12000 8000

IMS

PDV

4000 0 4000

Case A

IMS PDV

3500

power (w)

3000 2500 2000 1500 1000 500 0 0

2

4

6

time (s)

8

20000

energy (J)

16000 PDV IMS

12000 8000

50. 6%

PDV

4000

IMS

0

Case B

5000 PDV IMS

power (w)

4000 3000 2000 1000 0

0

1

2 time (s)

3

4

20000 PDV IMS

energy (J)

16000 12000 8000

56. 8%

PDV 4000

IMS

0 3000

Case C

IMS PDV

power (w)

2500

`

2000 1500 1000 500 0 0

2

4

time (s)

6

8

Fig. 3.24 Experiment concentrates on the comparison between the IMS and PDV including the energy consumption and control performance

46

3 Multi-Mode Load Control

To calculate energy and power consumptions, the supply pressure and flow rate of the hydraulic system are multiplied under the condition that the pressure margin in the load sensing system is set as 1.5 MPa. They are given respectively as Power: P = ps Q s

(3.38)

Energy: ʃt1 E=

ps Q s dt

(3.39)

t0

Defining E 1 and E 2 as the energy consumption for IMCS and PDV, respectively, the energy saving ratio is given as rE =

E2 − E1 × 100% E2

(3.40)

By the analysis in Sect. 3.3.1, energy savings for the IMCS in experiments also contains three aspects: (1) under Nor. modes, the actuator pressures are decreased, such as the boom lifting in Case A and B (2) under Reg. modes, supply flows are reduced owing to the regeneration flow paths from one chamber to another, such as the arm retractions in Case B and C. (3) under Flo. modes, no pump energies are utilized, which is replaced by the self-generated pressure oils by overrunning loads. It is inferred by the power consumption that energy-saving contributions from the three aspects are different. Generally speaking, the first way is relatively low because pressure differences between IMS and PDV are limited (in this experiment, pressure differences range from 0.1 MPa to 0.8 MPa). In contrast, the second and third ways of energy savings are remarkable.

3.6 Conclusions The decoupled inlet and outlet using the IMCS first benefits the flexible configuration of individual flow paths. The energy-saving functions, including regeneration and recuperation, can be realized. Multiple operating modes are established according to the achievable flow paths by the independent metering control. Energy-saving characteristics and force–velocity capability are analyzed to design the mode-switching logic, such that the most efficient operating mode without losing controllability for precise motion tracking can be automatically selected. A discrete transfer based on the mode switching logic arises the discontinuities during the switching instant, which leads to dynamic problems including instability and un-smoothness. Therefore, a novel bumpless mode transfer method based on

References

47

discrete switching is presented, which employs the dwell time and bidirectional latent tracking loop to make multi-mode subsystems transfer as a single one. Experiments in a 2-ton excavator demonstrate that the proposed mode-switching strategy can increase energy efficiency by automatically selecting the optimal operating mode, and simultaneously guarantee the stability and smoothness of the switching. Consequently, a good motion control performance of the IMCS can be obtained. Therefore, the bumpless mode switching strategy can achieve the dual objectives of saving energy in comparison with traditional valve-controlled systems and improving motion control performance.

References 1. R. Ding, et al. Programmable hydraulic control technique in construction machinery: status, challenges and countermeasures. Autom. Constr. 95, 172–192. https://doi.org/10.1016/j.aut con.2018.08.001 2. M. Cheng, B. Sun, R. Ding, B. Xu, A multi-mode electronic load sensing control scheme with power limitation and pressure cut-off for mobile machinery. Chin. J. Mech. Eng. (English Edition), 36(1), Article 29 (2023). https://doi.org/10.1186/s10033-023-00861-1 3. C. Meyer, D. Weiler, Optimal nominal pressurization generation-a novel idea for a discrete logic control using an independent metering valve configuration, in ASME 2011 Dynamic Systems and Control Conference, ASME, Arlington, VA, USA, pp. 351–354 (2011).https://doi.org/10. 1115/DSCC2011-5947 4. R. Madau, A. Vacca, F. Pintore, Energy saving on a full-size wheel loader through variable load sense margin control. J. Dyn. Syst. Meas. Control Trans. ASME 144(3), Article 031003 (2022). https://doi.org/10.1115/1.4052821 5. K. Abuowda, I. Okhotnikov, S. Noroozi, et al., A review of electrohydraulic independent metering technology. ISA Trans. 364–381 (2019). https://doi.org/10.1016/j.isatra.2019.08.057 6. B. Eriksson, Control Strategy for Energy Efficient Fluid Power Actuators: Utilizing Individual Metering, Linkoping University, Linkoping, Sweden (2007). http://www.diva-portal. org/smash/get/diva2:443/FULLTEXT01.pdf. Accessed July 18, 2018 7. B. Eriksson, Mobile Fluid Power Systems Design: With a Focus on Energy Efficiency, Linkoping University, Linkoping, Sweden (2010). http://www.divaportal.org/smash/get/diva2:370276/ FULLTEXT01.pdf. Accessed July 18, 2018 8. K. Heybroek, Saving Energy in Construction Machinery Using Displacement Control Hydraulics—Concept Realization and Validation, Linkoping University, Linkoping, Sweden (2008). http://www.diva-portal.org/smash/get/diva2:126676/FULLTEXT01.pdf. Accessed July 18, 2018 9. A. Shenouda, Quasi-Static Hydraulic Control Systems and Energy Savings Potential Using Independent Metering Four-Valve Assembly Configuration, Georgia Institute of Technology, Atlanta, USA (2006). https://smartech.gatech.edu/handle/1853/11553. Accessed July 18, 2018 10. K.A. Tabor, A novel method of controlling a hydraulic actuator with four valve independent metering using load feedback. SAE Tech. Paper 1, 3639–3681 (2005). https://doi.org/10.4271/ 2005-01-3639 11. G. Kolks, J. Weber, Modiciency—efficient industrial hydraulic drives through independent metering using optimal operating modes, in 10th International Fluid Power Conference, Dresden University of Technology, Dresden, Germany, ed. by J. Weber, pp. 105–120 (2016). http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-199423. Accessed July 18, 2018 12. Y.J. Liu, B. Xu, H.Y. Yang, Modeling of separate meter in and Separate Meter out control system, in 2009 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (IEEE, Singapore, 2009), pp. 227–232. https://doi.org/10.1109/AIM.2009.5230009

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3 Multi-Mode Load Control

13. R. Ding, B. Xu, J. Zhang, M. Cheng, Bumpless mode switch of independent metering fluid power system for mobile machinery. Autom. Constr. 68, 52–64 (2016) 14. D.I.G. Kolks, J. Weber, Modiciency—Efficient industrial hydraulic drives through independent metering using optimal operating modes 15. B. Xu, R. Ding, J. Zhang, M. Cheng, T. Sun, Pump/valves coordinate control of the independent metering system for mobile machinery. Autom. Constr. 57, 98–111 (2015) 16. A. Shenouda, W. Book, Optimal mode switching for a hydraulic actuator controlled with fourvalve independent metering configuration. Int. J. Fluid Power 9(1), 35–43 (2008). https://doi. org/10.1080/14399776.2008.10781295 17. K. Heybroek, J. Larsson, J.O. Palmberg, Mode switching and energy recuperation in open circuit pump control, in 10th Scandinavian International Conference on Fluid Power, Tampere University of Technology, Tampere, Finland, ed, by J. Vilenius, K.T. Koskinen, pp. 197–209 (2007). https://www.diva-portal.org/smash/get/diva2:133010/FULLTEXT01.pdf. Accessed July 18, 2018 18. H. Yuan, Y. Shang, M. Vukovic, S. Wu, H. Murrenhoff, Z.X. Jiao, Characteristics of energy efficient switched hydraulic systems. JFPS Int. J. Fluid Power Syst. 8(2), 90–98 (2014). https:// doi.org/10.5739/jfpsij.8.90 19. M. Linjama, V. Matti, Energy-efficient motion control of a digital hydraulic jointactuator, in 6th JFPS International Symposium on Fluid Power, ed. by T. Tsukiji, vol. 6 (Japan Fluid Power System Society, Tsukuba, Japan, 2005), pp. 640–645. https://doi.org/10.5739/isfp.2005.640 20. H. Lin, P.J. Antsaklis, Stability and stabilizability of switched linear systems: a survey of recent results. IEEE Trans. Autom. Control 54(2), 308–322 (2009) 21. R.A. Decarlo, M.S. Branicky, S. Pettersson, Perspectives and results on the stability and stabilizability of hybrid systems. Proc. IEEE Spec. Issue Hybrid Syst. 1069–1082 (2000) 22. D. Liberzon, A.S. Morse, Basic problems in stability and design of switched systems. IEEE Control. Syst. 19(5), 59–70 (1999) 23. Z.R. Xiang, W.M. Xiang, Stability analysis of switched systems under dynamical dwell time control approach. Int. J. Syst. Sci. 40(4), 347–355 (2009) 24. X. Zhao, L. Zhang, P. Shi, Stability and stabilization of switched linear systems with modedependent average dwell time. IEEE Trans. Autom. Control 57(7), 1809–1815 (2011). https:// doi.org/10.1109/tac.2011.2178629 25. S.F. Graebe, A. Ahlen, Dynamic transfer among alternative controllers and its relation to antiwindup controller design. IEEE Trans. Control Syst. Technol. 4(1), 92–99 (1996) 26. Y. Zhang, A.G. Alleyne, D. Zheng, A hybrid control strategy for active vibration isolation with electrohydraulic actuators. Control. Eng. Pract. 13(3), 279–289 (2004). https://doi.org/ 10.1016/j.conengprac.2004.03.009

Chapter 4

Multi-Variable Valve Control

4.1 Introduction The multiway valve is a key component of the hydraulic system of construction machinery. A conventional control valve adopts a single spool structure with coupling of inlet and outlet areas. Due to mechanically coupled orifices, it only has one control signal (spool position), and thereby only controls a variable (position, velocity, acceleration, or pressure in one of the chambers). Hence, even if a high-performance control strategy is employed, a conventional control valve still performs worse. By introducing mechanically decoupled orifices at the cylinder chambers in IMCS, the inlet and outlet areas can be adjusted independently. As a result, the system degree of freedom (DOF) increases from one to two, which is possible to improve the control performance of construction machinery. In Fig. 3.1, for example, the control strategies of valves include flow control and pressure control. In IMCS, the additional DOF changes the system from SISO to MIMO, making it possible to control the velocity of cylinder without changing the system preset pressure level and vice versa. Hence, the IMCS can obtain higher efficiency and better dynamic performance simultaneously compared to the conventional electro-hydraulic system.

4.2 Independent Metering Valve Control Architecture 4.2.1 Control Structure In Fig. 4.1, the control structures of independent metering valves can be divided into three categories.

© Shanghai Jiao Tong University Press 2024 R. Ding and M. Cheng, Independent Metering Electro-Hydraulic Control System, https://doi.org/10.1007/978-981-99-6372-0_4

49

50

4 Multi-Variable Valve Control Controller Controller Controlled system

vref

pref

K1

K2

u1(s)

u2(s)

G11

v

vref

Controlled system

u1(s)

K11

G11

G21

K21

G21

G12

K12

G12

G22

Controller

v

vref

Controlled system

u1(s)

G11

v

G21 K(s)

p

pref

(a) Decentral control

K22

u2(s)

G22

(b) Decoupling control

G12

p

pref u2(s)

G22

p

(c) Multivariable control

Fig. 4.1 Control structure of IMV

Decentral control A decentral control system is an extension of the typical SISO system. The meterin and meter-out areas are regulated by the individual velocity loop and pressure loop. The aim of the velocity loop is to track the desired trajectory of motion, while the pressure loop keeps outlet losses as low as possible, thereby reducing the required supply pressure. This control structure has been investigated by Shi et al. [1], Helian et al. [2], Choi et al. [3], Zhou et al. [4], Nielsen [5], Linjama et al. [6], Liu et al. [7], Pedersen et al. [8, 9], and Yao et al. [10]. Decoupling control Although the use of IMV breaks the structural coupling of the spool, two output variables are still because of the interference between the pressure of two chambers through its velocity. To eliminate disturbances caused by interactions, the decoupling control block must be introduced into the simple decentral controller. Nielsen [5], Jansson et al. [11] and Elfving [12] provided an overview of this decoupling control approach, in which the signal of the velocity sensor needs to be introduced. In view of a physical point, the approach decouples the system by feeding velocity and pressure signals back into the valves. Multivariable control Regarding the IMCS as a typical MIMO system, the input is the control signals of the meter-in and meter-out orifices, while the output involve the motion (velocity or position) and pressure of the cylinder. There were related investigations involving different multivariable control laws. For instance, Virvalo [13] and Liu et al. [14] proposed a multivariable I/O feedback linearization implementation to eliminate the non-linear interference between force and velocity. Yuan adopted a multiple sliding surface mode control method to control the motion while adjusting the back pressure [15]. Eriksson et al. [16] and Meyer et al. [17] have also attempted to use LQR-configured multivariable state-feedback controller approaches. These multivariable control laws are all model-based, which makes the control performance extremely sensitive to the accuracy of the dynamic models. However, many time-varying and uncertain parameters, such as fluid temperature, bulk modulus, and cylinder capacitances, are difficult to be dealt with in the control design.

4.2 Independent Metering Valve Control Architecture

51

Fig. 4.2 The control structure of the IMCS

Lu and Yao [18] and Cao [19] employed an adaptive robust control (ARC) method to reduce the influence of parameter uncertainties and modeling errors in IMCS. Li et al. [20] proposed a nonlinear valve flow model, which can capture the nonlinearity of valve flow well and achieve high control accuracy. Additionally, the inherent characteristic of IMCS is the lack of damping at the outlet. However, the above-mentioned control strategies don’t refer to this issue. As depicted in Fig. 4.2, an active damping solution in IMCS is developed to overcome the problem. The system breaks the mechanical coupling between the inlet and outlet so that the position control signal and the vibration control signal can be decoupled. It permits individual operation of the position controller and the active damping controller.

4.2.2 Modelling of Independent Metering Control System The hydraulic cylinder and proportional directional valve determine the dynamic characteristics of the system. The system structure depicted in Fig. 4.3 is analysed. Without considering the dynamics of the valve, the flows across the valve are characterized as: q A = Kq A 'u1 − Kq p A ' p A

(4.1)

qB = Kq B 'u2 − Kq p B ' pB

(4.2)

where K q A ' and K q B ' are flow coefficients of the IMCS, K q p A ' and K q p B ' are flowpressure coefficients of the IMCS. The continuity equation may be used to explain the pressure in the two chambers as follows

52

4 Multi-Variable Valve Control

Fig. 4.3 Transfer block of the IMCS

p˙ A =

1 1 (q A + A A v), p˙ B = (q B − A B v) CA CB

(4.3)

VA VB , CB = βea βeb

(4.4)

CA =

where βea and βeb are the bulk modulus of the chambers. The hydraulic cylinder’s force balance can be calculated by M v˙ = p A A A − p B A B − FL

(4.5)

The transfer block of the IMCS is shown in Fig. 4.3. The system has two outputs, including position and pressure, to accommodate the need for the position control and the active damping control of a construction machinery. In MIMO system, the decouping effects vary with different variable pairs. Supposing that u1 controls the position and u2 controls the pressure, the transfer function matrix of the system may be represented as. [ [

x pB

] =

x pB

]

[ =G

u1 u2

]

[ ][ ] 1 K q A ' G b A A /s −K( q B ' G a A B /s ) u 1 u2 P(s) K q A ' Aa A B K q B ' M G a s + A2A

(4.6)

G A (s) = K q p A ' + C A s

(4.7)

G B (s) = K q p B ' + C B s

(4.8)

R(s) = M G A G B s + A2A G B + A2B G A

(4.9)

4.2 Independent Metering Valve Control Architecture

53

4.2.3 Analysis of Interactions Between the Different Loops The relative gain array (RGA) approach is utilized to analyze the interactions between the various control loops, and accordingly to choose the optimal variable pair of the IMCS [21]. The definition of the RGA of a transfer function matrix is: )T ( RG A(G) = Ʌ(G) ≜ G × G −1

(4.10)

The RGA element can be stated as follows: λi j ≜

ki j

(4.11)

Ʌ

ki j

| | ∂ yi || ∂ yi || 1 = k = , = kˆi j = [G] ij ij ∂u j |u k =0,k/= j ∂u j | yk =0,k/= j [G] ji

(4.12) Ʌ

where ki j is the gain from input uj to output yi with other control loops opening; k i j is the gain from input uj to output yi with other control loops uk closing. The interactions between the different loops can be estimated by the relative gain λi j . Other loops have less interaction with the loop from ui to yi when the relative gain λii is near to 1. Therefore, the coupling degree between different loops can be acquired by calculating the relative gain array. With the above analysis, the gain array can be obtained as: [ ] 1 K q A ' K q p B ' A A −K q B ' K q p A ' A B (4.13) k= Kq B ' A A2 A A2 Kq p B ' + A B 2 Kq p A' Kq A' A A A B The relative gain is expressed as: λ11 = λ22 =

1 1−

k21 k12 k11 k22

(4.14)

Using the parameters provided in Table 4.1, the relative gain λ11 when u1 controls the position and u2 controls the pressure, is computed as 0.7075. It is relatively close to 1, indicating that there is little interaction between the various control loops. In contrast, the relative gain λ11 is 0.2925 when u1 controls pressure and u2 controls position. The interaction between various loops increases. Therefore, the optimal variable pair for the IMCS is that u1 controls position and u2 controls the pressure. The absolute value of the factor κ(s) gives information on the extent of couplings in accordance with the characteristics of the RGA [5]. The value of κ(s) close to or greater than one implies strong couplings. To obtain the smallest factor κ(s), there is some advice about the preferred design option. For instance, Nielsen concluded that the valve corresponding to the high pressure side should always control the velocity, as the one associated with the low pressure side controls the velocity, which will result

54

4 Multi-Variable Valve Control

Table 4.1 Parameters of the IMCS Parameters

Symbol

Value

Unit

Flow coefficients

K q B ' /K q A '

2 × 10−4 /2.3 × 10−4

m2 /s

Flow-pressure coefficients

K q p B ' /K q p A '

6.9 × 10−12 /6.1 × 10−12

m3 /(Pa · s)

The bulk modulus of the chambers

βeb /βea

7000

bar

in a higher coupling according to the coupling [5] factor in Fig. 4.4. Sitte explained that the addition of a pressure compensator significantly reduces couplings between two primary control lines [22]. In spite of these advices, strong couplings cannot be avoided due to the varying operating conditions. Therefore, it needs to introduce decoupling control to acquire the preferable dynamic performance. However, it is not very practical for the present decoupling control methods, proposed by Elfving [12] and Eriksson [23], due to the need for velocity feedback. Velocity sensors are usually excluded in construction machinery owing to the high cost and excessive sensitivity for practical applications. Consequently, it is necessary for the researcher to provide a novel strategy without velocity feedback. Such a strategy requires combinations of advanced multivariable decoupling control algorithms, including adaptive feedforward, neural networks, and model prediction.

Fig. 4.4 Comparison of coupling factor by different valve control

4.2 Independent Metering Valve Control Architecture

55

4.2.4 Load-Independent Flow Control During operating the construction machinery, load situations always change randomly with many factors, such as the external load decided by different digging actions and circumstances, together with the inertia mass and the geometry in a mobile crane application. To make the operator handle load changes adaptively without disturbances among different loads, the output velocity or the flow should be load-independent. However, the flow across the valve relies on more than just one parameter, such as spool displacement, pressure drops across the orifice, and fluid temperature, which appears an apparent challenge. As previously mentioned, the position or velocity feedback is seldom applied to construction machinery. Furthermore, the extra cost and high failure likelihood of sensors in such harsh circumstances are prohibitive, which makes the scheme of precise motion control without additional sensors very attractive. To substitute for the velocity feedback, it is recommended to adopt a pressure compensation control to keep the flow across the orifice independently from a time-varying pressure drop. This control strategy is divided into partly hydro-mechanical and fully electronic concepts. As shown in Fig. 4.5, the individual pressure compensator (PC) is incorporated at the pilot stage in partly hydro-mechanical concepts. The PC not only makes the flow independent of the load but also is practical and easier to implement. Meanwhile, it has a better dynamic performance with natural frequencies beyond 50 Hz [24]. However, a significant challenge to introducing the PC into IMV is the unidirectional flow function of the PC, which conflicts with regeneration or recuperation modes. There are two solutions to solve the issue. The first solution is employing a specifically designed valve. Bidirectional proportional poppet valves with a pressurecompensated pilot valve were introduced by Andersson [25] as the “Valvistor valve” and HUSCO Inc. as the “Electro-Hydraulic Poppet Valve” (EHPV) [26, 27]. The second solution is proposed by Sitte et al. [22] and Liu et al. [28] which adopts a specific IMV structure. The novel IMV structure employs on/off directional valves, which ensures that the PC always regulates the flow through the meter-in edge into the inlet cylinder chamber by throttling the flow from the pump. As seen in Fig. 4.5b, fully electronic concept moves the pressure compensation functional feature into the software. Naturally, the concept needs additional sensors, such as pressure and even spool position sensors. Meanwhile, high bandwidth valves and a complex programmable control strategy are required owing to the absence of the PC. Nielsen [5], Hansen et al. [8], Pedersen et al. [9], Yao et al. [29] and Shenouda [30] have all published overviews of the studies in this field. The known desired flow pertaining to pressure drops across a valve is involved in these investigations. The required command voltage is calculated backward through an inverse nonlinear valve model, usually in the form of flow mapping or gain. However, the calibration of the inverse valve model poses a new challenge. The offline calibration is a timeconsuming and expensive task. Additionally, the actual valve flow is sensitive to some

56

4 Multi-Variable Valve Control

v

v

v

-

U P

-

vref

vref

+

Inverse flow mapping

uv U P

(a) using individual PC

(b) Feedforward electronic PC

U P

+

Flow mapping

uv

-

+ vref

G(s) U P

(c) Feedback electronic PC

Fig. 4.5 Schematic diagram of load-independent velocity control

inevitable uncertain parameters (e.g., the fluid effective bulk modulus) and timevarying parameters (e.g., the fluid temperature) in different operating circumstances. Therefore, online calibration is a better alternative than offline calibration. Liu and Yao proposed an automated online calibration for poppet valve flow mapping based on the pressure dynamics of the hydraulic cylinder [31]. With the aid of a Nodal Link Perceptron Network (NLPN), Opdenbosch adopted the adaptive learning method to automatically calibrate the inverse input-state map of the poppet valve [32]. Another electrical pressure compensation strategy converts the feedforward method to the feedback method as seen in Fig. 4.5c, this closed-loop control is performed without the measured velocity. Instead of an inverse valve model, a forward non-linear valve model is used to estimate the calculated flow, from which the required command voltage is further obtained. Liu et al. [7] and Gu [33] provide examples of this study. Due to the demands of regulator G(s) (e.g., a PID regulator), such strategy is more complicated than the feedforward method. However, the dynamic properties of system may be tuned by adjusting PID parameters, which increases the flexibility for motion control and brings some advantages. For instance, it is beneficial to reduce the oscillations by setting a special proportional gain or integration gain to obtain larger damping during the settle time.

4.2.5 Detailed Decentral Control Algorithm with Electronic PC As shown in Fig. 4.6, there are the velocity and pressure tracking loops in the presented decentral control system. Due to the high cost and sensitivity to practical use, the closed-loop flow or velocity control has been excluded via flow or velocity sensors. Therefore, the section applies electronic pressure compensation based on the pressure drops across the valve to track the required velocity. As discussed above,

4.2 Independent Metering Valve Control Architecture

57

Fig. 4.6 Independent control schematic of pressure and velocity

there are two types of electronic pressure compensation techniques: open-loop feedforward and closed-loop feedback [34]. Using the valve flow mapping, they both conduct constant flows at varying operating pressures across the valves. Taking the close-loop electronic pressure compensation as an example, the flow mapping of proportional directional is tested to estimate the actual flow. The control signal of the meter-in valve is related to the difference between the required flow and the actual flow, as expressed by Eq. (4.15). The pressure compensation eliminates the non-linear dependence on load pressure so that the flow-pressure gain of the valve approaches zero. ∫t1 u 1 = K p · Q e (t) + K i

Q e (t)dt + K d

d Q e (t) dt

(4.15)

t0

Q e = Q r e f − Q actual

(4.16)

The meter-out valve must be opened fully to reduce the energy consumption of the outlet. Nonetheless, the issue of cavitation must also be considered. Therefore, the backpressure should be increased to roughly 2 bar to reduce the valve opening area. The equation for the closed-loop pressure controller is as follows: ∫t1 u 2 = K p · pb,e (t) + K i

pb,e (t)dt + K d t0

where pb,e = pb,r e f − pb .

dpb,e (t) dt

(4.17)

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4 Multi-Variable Valve Control

4.3 Damping Control Due to mechanically decoupled orifices, the area of the inlet and outlet no longer relies on each other. The meter-out valve can open as much as possible to reduce pressure loss at the outlet significantly. Although the energy consumption of the IMCS is lower compared with the conventional system, it also weakens the original controllability due to the lack of damping at the outlet. It will intensify the vibration of machine structure, which reduces the operator’s comfort and safety, as well as machinery life. These facts motivate the development of an enhanced independent metering system to suppress the vibrations. There are various methods to damp the vibrations in hydraulic system, classified into hydraulic, mechanical and electronic types. The electronic method relies on feedback to calculate a compensation and then adjust the area of the valve to further reduce the actuators oscillations. So there are no extra energy losses. The acceleration feedback is not apreferable choice owing to the high cost of acceleration sensors, although the magnitude of cylinder oscillations is directly correlated with the acceleration. Additionally, it is difficult to guarantee reliability in the complex operation conditions of mobile applications. Pressure feedback is a better alternative since pressure sensors are cheap and easy to install in the hydraulic system. Moreover, cylinder chamber pressure indirectly reflects the magnitude of oscillations. Hence, this section will introduce the active damping control method into the decentral controller, such that the damping can be optimized to suppress the oscillations for the IMCS. High stability and fast response should also be balanced to obtain the best overall dynamic response.

4.3.1 Problem Statement In Fig. 4.7, the results show the comparison of the oscillations of the cylinder velocity and chambers pressures, where conventional system and independent metering system are marked as “PDV” and “IMCS” respectively. They both employ the velocity/pressure compound dcentral controller, as shown in Eqs. (4.15–4.17). According to all four results, the oscillations of the cylinder velocity in IMCS are more severe than those in PDV. Fig. 4.7c and d depcit the cylinder velocity and pressure subject to different reference velocity. They show that the comparisons of oscillations between the two systems are more remarkable when the cylinder velocity is lower. Fig. 4.7a and b demonstrate the results of boom and arm respectively, which implies that a higher mass of load raises severer oscillations. It is noted that violent oscillations in mobile applications are caused by low damping [35]. Hence the results in Fig. 4.7 will be explained by analyzing the damping of the hydraulic system. Since the hydraulic system is a typical non-linear system, so it is primary to carry out linearization. In Fig. 4.8, the linearization procedure of the normal mode is illustrated, where the inlet and outlet are connected to the pump and drain line respectively. The nonlinearity of hydraulic system resides

4.3 Damping Control

59

Fig. 4.7 The results using Independent pressure and velocity control

Fig. 4.8 Linearization process of normal mode

in the flow pertaining to pressure and orifice area. The nonlinear equations of inlet and outlet flows are expressed as: / Q a = C q Av

2( ps − pa ) Q b = C q Av ρ

/ 2 pb ρ

The system is linearized under the following assumptions:

(4.18)

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4 Multi-Variable Valve Control

(1) The flow-pressure gain of the meter-in valve is set as 0 since the inlet flow of the meter-in valve is controlled by electronic PC and the flow across the valve is independent of pressure drops. (2) Valve dynamics are ignored since its response is much faster than the rest of the system. Consequently, the inlet flow is transferred to a constant flow Qa which eliminates the nonlinearity of inlet. There are some investigations to prove the validity of this simplified model, such as Heybroek from Linkoping University [36], have proved the validity of this simplified model. The outlet flow Qb is linearized by multiplying the pressure pb and the flow-pressure gain K cb , of which the flow-pressure gain is pertaining to pressure and orifice area as follows: K cb =

C q Av ∂qb =√ ∂ pb 2ρ · pb

(4.19)

Under these reasonable assumptions, the derivations of the equations are provided by Eqs. (4.20)–(4.24). Ab = κ Aa

(4.20)

Va spa βe

Q a − Aa Vc =

m t s 2 X c = Aa pa − κ Aa pb − Bp s X c − F1 κ Aa s X c − Q b =

Vb spb βe

Q b = K cb pb

(4.21) (4.22) (4.23) (4.24)

Defining the three parameters listed below: / Va γ = 1 + κ 2 , ωo = Aa Vb

βe βe K cb , ωb = m t Va Vb

(4.25)

Then the transfer function is given by: (

) Bp Va 2 s3 s2 γs BP Va Vc + + + 1 + s + s ωo2 ωb A2a βe ωb Aa2 βe ω02 ωb )( ) ( 1 Va s Q a − 2 s F1 = 1+ ωb Aa Aa βe

(4.26)

4.3 Damping Control

61

The denominator polynomials of the system transfer function may be factored. The interesting case is when the system has a resonance and a break frequency [35, 37], see Eq. (4.27). ) 2 ) ( ( Bp Va s γ 1 BP Va s3 · 2+ s+1 + + Dp = 2 + ωb A2a βe A2a βe ωb ω0 ωb ω02 ω0 ( )( 2 ) s s 2ξh s = 1+ + + 1 ωn ωh ωh2

(4.27)

Eqs. (4.26) and (4.27), can also be applied to the conventional system, but the difference resides in the value of flow-pressure gain K cb . Due to the larger opening area of the meter-out valve in the IMCS, this parameter is substantially higher in the IMCS than that of the traditional system. It is concluded that the system has a pair of conjugate poles, a real pole and two zeros. In general, the locations of the poles and zeros determine the dynamic performance of the system. Taking the boom motion system as an example, the pole locations pertaining to the opening area of meter-out valve are depicted in Fig. 4.9 by solving Eq. (4.26) with the parameters from Table 4.1. The studied system has provided global parameters. State variables are constantly changing during the control process. They are evaluated by measured data or calculated by the input and output of controller. Here, for theoretical analysis, the state variables are provided directly. The locations of poles are acquired in in MATLAB platform based on the two types of parameters simultaneously. To represent different orifice areas, the pressures are supposed to rise from 0.2 MPa, with a gradient of 0.02 MPa for each evaluation. The three poles are placed on the left half-plane of the pole-zero map, as shown in Fig. 4.9. Then, their definitions are as follows: p1,2 = −a ± bj, a > 0, b > 0

(4.28)

p3 = −c, c > 0

(4.29)

It is inferred that the influence of negative real pole p3 on the system dynamic can be ignored because: (1) As the opening of the meter-out valve increases, this real pole moves away from the imaginary axis. When the ratio of the real part of this pole to –a (e.g., c/a) exceeds l, which is typically between 3 and 5 [38], it could be defined that the pole is far away from the imaginary axis and conjugate poles; (2) As the opening area of the valve is not large enough, this real pole is not far away from the conjugate poles. Nevertheless, it should be noted according to Eq. (4.27) that there exists a real zero (z1 = −ωb ), and the zero z1 is near to the pole p3 according to Eq. (4.28). This indicates that they achieve pole-zero cancellation;

62

4 Multi-Variable Valve Control

Fig. 4.9 Pole locations with respect to valve area

Consequently, the real pole p3 does not affect the dynamics of the system, and thus conjugate poles p1,2 become the dominated poles, whose locations actually affect the system response including overshoot and settling time the system damping ξ h is calculated by the angle between the conjugate poles and the negative real axis as Eq. (4.30). The angle, marked as θ, is easy to obtain by the movement of the poles in the pole-zero map. / θ = arccosζh = arctan

1 − ζh2 ζh

a ⇒ ζh = √ 2 a + b2

(4.30)

According to Eq. (4.30), a larger angle θ leads to a high damping. With the parameters listed in Table 4.1, the relationship between damping and flow-pressure gain K cb is illustrated in Fig. 4.10. As the opening area of the valve increases, the system damping of the system firstly increases and then continually decreases. The damping of IMCS is located in the lowest region, while that of the conventional system is nearby located in the highest region. Therefore, it can explains that the reason that the oscillations of cylinder velocity in the former system are more violent than the latter one, as the results shown in Fig. 4.7c and d. The relationship between the pole location and the equivalent load mass mt in IMCS is exhibited in Fig. 4.11. As the equivalent load mass mt increases, the real pole p3 is also far away from the imaginary axis. Moreover, the ratio of the real pole p3 to −a (formulated as c/a) exceeds 10. Consequently, conjugate poles p1,2 are always the dominated poles, and the damping as function of the equivalent load mass mt is depicted in Fig. 4.12. It is concluded that the damping of heavy load systems

4.3 Damping Control

63

Fig. 4.10 Damping as a function of the flow-pressure gain

is lower than that of light load systems, which would explain the comparison results between boom and arm in Fig. 4.7a and b.

Fig. 4.11 Pole locations with respect to equivalent load mass

64

4 Multi-Variable Valve Control

Fig. 4.12 Damping as a function of the equivalent load mass

4.3.2 Damping Control Design Noted the fact that the cylinder pressure is associated with the derivative of cylinder velocity, so a dynamic pressure feedback(DPF) is introduced to suppress the oscillations: mt s + Bp pa = Vc Aa

(4.31)

In fact, the introduction of pressure feedback on the meter-in side (high-pressure side) has the biggest influence and also contributes to the suppression of the pressure vibrations on the meter-out side. It is noted that two pressures are coupled through the cylinder velocity. The signal from the pressure sensor is fed to the control valve as a compensation variable. To extract the oscillating signal of the component, a control unit with a high-pass filter process is employed, as shown in Fig. 4.13a. Gr refers to the flow control by close-loop electronic pressure compensation. The form of the pressure feedback loop is given by Eq. (4.32). This pressure-feedback controller is individual and does not relys on the main controller (the flow controller illustrated in Sect. 4.3). The output of the pressure-feedback controller is superimposed on the output of the flow controller. The block diagram of the control system is shown in Fig. 4.13b. u com τc s s = K com = K com pa τc s + 1 s + ωc

(4.32)

4.3 Damping Control

65

Fig. 4.13 Pressure feedback control schematics

4.3.3 Control Parameters In the design of the pressure-feedback controller, it is a challenge to tune the following two important parameters: (1) Cut-off frequency of the high-pass filter ωc . It ought to be configured lower than the system resonance frequency [39]. In this study, it is noted that the IMCS differs from the conventional system. In detail, the IMCS could change the the hydraulic circuit to save energy in regeneration and recuperation modes, where both the inlet and outlet are connected to pump or drain line simultaneously. The regeneration and recuperation circuits also refer to differential mode instead of the normal one. Therefore, their resonance frequency should be caculated respectively. In normal mode, the backpressure pb can be ignored since it is close to the drain line pressure, and the hydraulic resonance frequency of the normal mode is acquired by Eq. (4.33). / ωh =

Aa2 βe = m t Va

/

A2a βe m t (Aa · xc + Vdead )

(4.33)

Meanwhile, the linearization process of differential mode is illustrated in Fig. 4.14. In the differential hydraulic circuits, the two chambers are connected to each other hydrualically. Thus, the asymmetric cylinder can be regarded as a discrete transformer with two potential operation. The cylinder is considered to be a plunger cylinder and the only inlet is assumed to have a constant flow, where the effective pressurized area and the compressible fluid volume in the control volume will be replaced in terms

66

4 Multi-Variable Valve Control

Fig. 4.14 Linearization process of differential mode

of Eqs. (4.34) and (4.35). Adiff = Aa − Ab Q diff = Q a − Q b

(4.34)

( ) Vdiff = Aa · xc + Ab xc,max − xc + 2Vdead

(4.35)

Then, the hydraulic resonance frequency of the differential mode is calculated referring to the normal mode: / ωdiff =

A2diff βe = m t Vdiff

/

( Aa − Ab )2 βe ( ) ) m t Aa · xc + Ab xc, max − xc + 2Vdead (

(4.36)

In terms of Eqs. (4.32)–(4.35), it is concluded that the resonance frequency relies on the following parameters: the oil chamber volume (V a , V b ), cylinder displacement (x c ) and equivalent load mass (mt ). Fig. 4.15 exhibits the comparison of the resonance frequencies ωh and ωdiff with a range of parameters suitable for the boom and arm of excavator applications. In the normal mode, ωh varies only with changes in piston displacement. lt is mainly affected by equivalent load mass. In the differential mode, the resonance frequency ωdiff is changes little with cylinder displacement, but significantly with equivalent load mass two parameters. Additionally, ωdiff is much lower than ωh at all working points. Thus, the cut-off frequency of the high-pass filter ωc in the differential mode should be configured much lower than the normal mode, as well as they are restricted to below the system resonance frequency corresponding to ωdiff and ωh respectively. (2) Feedback gain Kcom. The gain significantly affects the reasonable stability margins. As depicted in Ref. [8], the constant gain will not yield an acceptable response when there are very large variations in the dynamics. To accommodate the large variations, a gain tuning approach should be used. Thus, a gain tuning approach should be used to accommodate the large variations. As the pressure feedback is introduced, the denominator polynomials of the system transfer function change from third order to fourth order as:

4.3 Damping Control

67

Fig. 4.15 Hydraulic resonance frequency for boom and arm

(

( ) ) 1 1 ωc K com · m t 3 4 + + + s s ωo2 ωb ωo2 ωo2 ωb ωb A2a ) ) ( ( γ ωc K com · m t 2 γ · ωc s s + ωc + + 2+ + 1 + ωb ωo A2a ωb

Dpf =

(4.37)

Despite the high order in denominator polynomials, the pole locations method in Sect. 4.3 still can analyze the effect of the gain Kcom on system dynamics. Figure 4.16 exhibits the poles location variations of boom system pertaining to the gain K com when the meter-out flow-pressure gain of IMCS is approximately 3.53429e−9. A real pole is added compared with the conventional system. It is also in the left plane and marked as p4 = −d (d > 0). With the increase of K com , the real poles p3 and p4 both move towards the imaginary axis, and conjugate poles p1,2 are gradually far away from the imaginary axis. Meanwhile, the conjugate poles p1,2 gradually move away from the imaginary axis, and the angle θ between p1,2 and the negative real axis decreases. It should be noted that the conjugate poles p1,2 may no longer be guaranteed to dominate system dynamic arising from the following reasons: (1) The newly added real pole p4 is very close to the imaginary axis, and obviously the ratio of d to a is smaller than 3; (2) The original real pole p3 gradually approaches p1,2 , leading to the ratio of c to a being possibly smaller than 3; In view of the above two aspects, it is confusing to tune the gain via the pole locations to improve the system damping. 1 the ratio of c to a larger than 3. On the other hand, the poles in the feedback path will become the closed-loop zero as well. From Eq. (4.31), and Fig. 4.13b, there is concluded that there is a new zero in the closed-loop system, which is generated by the pole (-ωc ) in the pressure-feedback loop. The newly added zero is defined as z2 (z2 = −ωc ), whose location relies on the cut-off frequency of high-pass filter. Additionally, when it is located nearby the added pole p4 , then they can achieve pole-zero cancellation [40, 41]. In this case,

68

4 Multi-Variable Valve Control

Fig. 4.16 Pole locations with respect to feedback gain K com

the poles p3 and p4 can be enforced to be non-dominant poles for getting rid of their influence to system dynamic. Consequently, the conjugate poles p1,2 become dominated poles. As shown in Fig. 4.16, the system damping, which presents a negative correlation relationship with angle θ, increases gradually with the trending up of K com . If K com is too small. The poles p1,2 change little when K com is too small, such that the controller has little effect on performance improvement. Accordingly, a large K com value should be set to damp violent oscillations in the cylinder velocity. However, while increasing damping, another issue appears: a time delay between input and output, so-called “phase-lag” increases. Besides, if K com exceeds an upper threshold, the added negative real pole p4 may become dominated pole because with its moving toward the imaginary axis, it is no longer close to the added zero z2 . On this occasion, system stability may even become poor because pole p4 is located near the imaginary axis to make system stability margin excessively low. Remark Variations of feedback gain have the following effects on the close-loop system: 1. A smaller value of K com has little effect on the improvement of controllability; 2. With the increase of K com , system damping increases but the fast response is sacrificed simultaneously; 3. An overlarge value of K com will reduce the stability margin, even causing more severe oscillations rather than decreasing them.

4.3 Damping Control

69

Fig. 4.17 Damping variation as a function of the feedback gain K com

4.3.4 Self-Tuning Pressure-Feedback Control Based on Guaranteed Dominant Pole Placement According to Fig. 4.16, the damping increases with the trending up of K com , where the flow-pressure gain is approximately 3.53429e-9, as shown in Fig. 4.17. To make a trade-off between fast response and high stability, the damping should be optimized to 0.707 to obtain the best overall dynamic response. Based on this criterion, the optimal K com is set to be 0.045. However, with variation of operating parameters including flow-pressure gain and equivalent load mass as the control variables involved in displacement, velocity, and pressure always change in mobile applications, the operating parameters always change involved in flow-pressure gain and equivalent load mass. Thus, the K com needs to be tuned online to adapt these variations. Inheriting the above method by pole-zero location, a parameter optimization algorithm based on pole assignment is developed, and the complete controller with selftuning pressure-feedback control is established in Fig. 4.18. The optimum pair of K com and ωc is directly related to the following parameters: flow-pressure gain, inlet and outlet volume, equivalent load mass, and the operating mode. The former three are incorporated to map pole-zero locations. In detail, the flow-pressure gain is evaluated by the reference flow and pressure difference, and the equivalent load mass can be estimated by transforming the dynamic equation of the hydraulic arm in the joint space. The last parameter is involved to represent the upper thresholds of the cut-off frequency ωc in different modes. In Fig. 4.18, the control parameters in the pressure-feedback loop, including ωc and K com , should be tuned and matched according to the following algorithm. (1) Keep the pole p3 = −c away from imaginary axis (l = 3); (2) Endeavour the pole p4 = −d close to zero z2 (|d − ωc |