Lecture Notes in Control and Information Sciences Edited by A.V. Balakrishnan and M.Thoma 33 Peter Dransfield Hydraulic Control Systems - Design and Analysis of Their Dynamics Springer-Verlag Berlin Heidelberg New York 1981
Series Editors h~ V. Balakrishnan - M. Thoma Advisory Board I D. Davisson A. G. J. MacFarlane. H. Kwakernaak J. I Massey Ya. 7_ Tsypkin A. J. Viterbi Author Peter Dransfield, Ph.D., Department of Mechanical Engineering Monash University, Australia ISBN 3-540-10890-4 Springer-Vertag Berlin Heidelberg NewYork ISBN 0-387-10890-4 Springer-Verlag NewYork Heidelberg Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under 54 of the German Copyright Law where copies are made for other than private use a fee is payable to 'Verwertungsgesellschaft Wort', Munich. Springer-Verlag Berlin Heidelberg 1981 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 9061020-543210
PREFACE The Text centres around the ideas that for hydraulic control systems the quality of their dynamic response is important to their proper operation, prediction of dynamic response capability is best obtained via the development of dynamic models, the inability of many designers to efficiently effect predictive dynamic analysis has its roots in a lack of confidence in the forming of models, the use of po~ bon~ ~aphs is a natural and superior approach to the development of reliable dynamic models, digital simulation provides the most appropriate method for extracting response information from dynamic models. Among these, the use of bond graphs (abbreviation for power bond graphs) is paramount to the Text. Therefore, bond graphs are introduced, explained, demonstrated, and utilized in substantial detail. The features of bond graphs which make them desirable in the hydraulic control system design situation include their structural affinity with the real system and its components, the formality in the assembly of a bond graph structure, their modular and re-usable nature, and the provision of a structure from which the set of equations which become the model can be formally prepared. It is assumed that the reader has a general appreciation of the nature and operation of hydraulic control systems and their major components. The Text is written mainly for those mechanical and control engineers who would like to be able to include predictive dynamic analysis among their techniques for the design of hydraulic control systems but who find existing approaches unsatisfying or inappropriate. The Text should be suitable also for up to twenty hours in appropriate graduate or senior undergraduate courses, and for specialized extensiontype courses. For full appreciation of the Text, the reader will need to make a "break through" by thoroughly understanding and using the symbols and structures of bond graphs. Such a break through was literally forced on me by a graduate student whom I was supervising for a research Master degree. I gladly acknowledge my debt to Bevis Barnard, Senior Lecturer at Caulfield Institute of Technology, for the gentle persuasion emanating from his own discovery and conviction that bond graphs offered something unique to the modelling, simulation and design of powered control systems. I acknowledge also the conceptions of Henry Paynter, the original and sustained developmental work of Dean Karnopp and Ron Rosenburg, the work of bond graph entrepreneur Jean Thoma, the assistance of colleague Jacek Stecki, and the contributing work of a small but steady stream of undergraduate and graduate students including Rob Winton, M.K. Teo, Roger LaBrooy, Kevin Duke, S. Ramachandran, V.K.L. Mai, and Merren Cliff. Many people contribute to the production of a text. I single out two for special thanks and appreciation; Lorry Ryan and John Millar, both of Monash University, for their excellent work in typing and drafting respectively. And there is an individual without whose encouragement this Text would not have been completed my wife Nevillie whose support was sustained, inspirational, and essential. To those willing to learn, and to those willing to try a new way, welcome aboard. P.D. March 1981
CONTENTS PREFACE CHAPTER 1 INTRODUCTION 1.1 Introduction 1.2 A Design Philosophy 1.3 Dynamic Modelling 1.4 A Desirable Background 1.5 Arrangement of Text 1.6 Conclusion C~PTER2 2.1 2.2 NOTATION AND UNITS Introduction Notation 2.2.1 Symbols 2.2.2 Examples of Symbol Use 2.2.3 Operations 2.2.4 Equations 2.2.5 Comments 2.3 Units 2.3.i Comments 2.4 References CHAPTER 3 CONVENTIONAL MODELLING PROCEDURES 3.I Introduction 3.2 Conventional Model Forms 3.2.1 Informal Equation Set 3.2.2 Transfer Function 3.2.3 Vector-Matrix Models 3.2.4 Block Diagrams and Signal Flow Graphs 3.3 Deriving the Model 3.4 Selection of Relationships 3.5 Selection of Parameter Values 3.6 Another Example 3.7 Conclusion 3.8 References CHAPTER 4 POWER FLOW MODELLING 4.1 Introduction 4.2 Power Ports 4.3 Describing Power Flow 4.4 Getting Equations 4.5 An Example 4.6 Summary 4.7 References CHAPTER 5 POWER BOND GRAPHS 5.1 In troduction 5.2 Bond Graph Terms and Symbols 5.2.1 Effort and Flow Variables 5.2.2 Sources 5.2.3 Power Bonds 5.2.4 Power Transformers 5.2.5 Dynamic Effects 5.2.6 Resistive Power Dissipation 5.2.7 Capacitive Power Storage 5.2.8 Inertive Power Storage 5.2.9 Summing Junctions 5.2.10 Summary of Basic Terms and Symbols 1 1 2 7 ii ii 12 15 15 16 16 16 18 18 19 19 19 21 21 22 22 22 24 24 25 28 28 29 29 32 36 40 44 46 47 48 48 49 49 50 50 51 54 54 57 58 60 62
CHAPTER 5 (contd.} 5.3 Forming Power Bond Graph Structures 5.3.1 Inertia Load with Friction 5.3.2 Hydraulic Cylinder 5.3.3 Induction Electric Motor 5.3.4 A Simple System 5.4 Power Flow Directions, and Causality 5.4.1 Introduction 5.4.2 Directions of Power Flow 5.4.3 Causality 5.4.4 Exa/m~le: Hydraulic Cylinder 5.4.5 Example : Induction Electric Motor 5.4.6 Example: Simple cylinder-load System 5.4.7 Summary 5.5 Preparing Equation Set 5.5.1 In troduction 5.5.2 Example: A Simple Component 5.5.3 An Elementary System Example 5.5.4 A More Cc~plete System 5.5.5 Summary 5.6 Some Further Aspects of Bond Graphs 5.6.1 Modulation of Effects 5.6.2 Modulated Transformers 5.6.3 Fields and Junction Structures 5.6.4 Simplifications 5.7 Conclusion 5.8 References CHAPTER 6 SOLUTION OF POWER FLOW MODELS 6.i Introduction 6.2 Digital Simulation 6.3 Expression-Orientated CSSL' s 6.4 Conclusion 6.5 References CHAPTER 7 SELECTING EQUATIONS AND COEFFICIENTS 7.1 Introduction 7.2 Compliance 7.2.1 Introduction 7.2.2 Oil Compliance 7.2.3 Values for Bulk Modulus 7.2.4 Mechanical Compliance 7.3 Friction 7.4 Modelling Driven Loads 7.4.1 Inherent Load s 7.4.2 External Load Forces 7.5 Leakage Flowrate 7.5.1 Re laticn shlps 7.5.2 Coefficients 7.6 Relief Valve Flowrates 7.6.1 Relationships 7.6.2 Coefficients 7.7 Electric Induction Motor 7.7.1 Re lation ships 7.7.2 Model 7.7.3 Coefficients 7.7.4 Conclusion 7.8 Hydraulic Pumps 7.8.1 Relationships 7.8.2 Coefficients 62 62 64 66 68 70 70 7O 71 76 76 78 78 81 81 81 83 84 88 89 9O 9O 92 92 93 93 94 94 95 97 98 99 i01 101 102 102 102 106 106 109 110 ii0 112 112 112 114 116 116 118 118 118 120 120 121 121 121 125
VI CHAPTER 7 (contd.) 7.9 4-Way Control Valves 125 7.9.1 Introduction 125 7.9.2 The Basic Relationship 126 7.9.3 Valve Flow Nomenclature 129 7.9.4 The Closed-Centre Control Valve 129 7.9.5 The Open-Centre Control Valve 2 7.9.6 The Tandem-Centre Control Valve 6 7.9.7 Summary 8 7.10 Actuators 9 7.10.1 Introduction 9 7.10.2 Linear Actuator 9 7.10.3 Rotary Actuator (Hydraulic Motor) 142 7.10.4 Equations and Coefficients 142 7.11 Some Other Common Components 144 7.11.1 Hydraulic Lines 144 7.11.2 Filters 146 7.11.3 Accumulators 146 7.11.4 Some Other Valves (Check Valve, 148 Counterbalance Valve) 7.12 Conclusion 151 7. References 152 CHAPTER 8 APPLICATIONS OF BOND GRAPHS 153 8.1 Introduction 153 8.2 Closed-Centre Valve-Controlled Inertia Load 153 with Friction 8.3 Loaded Hydraulic Servosystem 155 8.4 Pump Sub-System 156 8.5 Pump-Controlled Hydrostatic Drive 164 8.6 Valve-Controlled Hydrostatic Drive 166 8.7 A Lifting System 169 8.7.1 Introduction 169 8.7.2 Development of Bond Graph 172 8.7.3 The Equations and Coefficients 173 8.7.4 Simulation 173 8.7.5 Conclusion 173 8.8 A Highly Dynamic Electrohydraulic Control System 173 8.8.1 Introduction 173 8.8.2 The Bond Graph 178 8.8.3 Conclusion 181 8.9 Conclusion 181 8.10 References 182 CHAPTER 9 OPTIMIZING DYNAMIC RESPONSE 183 9.1 Introduction 183 9.2 The Requirements 184 9.3 Error Criteria 185 9.4 Search Procedure 188 9.4.1 Introduction 188 9.4.2 Single-Parameter Optimization 188 9.4.3 Multi-Par~eter Optimization 189 9.4.4 Complex 190 9.5 Example 192 9.6 Conclusion 192 9.7 References 194 CHAPTER i0 PHENOMENA WHICH CAN AFFECT RESPONSE 196 10.1 Introduction 196
Vil CHAPTER i0 (contd.) 10.2 cavitation i0.2.1 General Discussion 10.2.2 Cavitation in Modelling and Simulation 10.3 Hydraulic Backlash 10.4 Flow Forces in Valves i0.5 Hydraulic Lock i0.6 Contaminated Fluid i0.7 Conclusion 10.8 References 197 197 200 201 204 205 210 212 212 CHAPTER ii APPENDIX 1 APPENDIX 2 CONCLUSION STATIC DESIGN APPROACHES SI CONVERSION FACTORS 215 217 221 APPENDIX 3 DYNAMIC RESPONSE --A BIBLIOGRAPHY INDEX 222 226