multiple inner-loop control of an electro-hydrostatic actuator

250 Pages·2012·29.64 MB·English

MULTIPLE INNER-LOOP CONTROL OF AN
ELECTRO-HYDROSTATIC ACTUATOR
MULTIPLE INNER-LOOP CONTROL OF AN ELECTRO-HYDROSTATIC
ACTUATOR
By
Mohammed A. El Sayed, M.A.Sc, B.Sc.
A Thesis
Submitted to the School of Graduate Studies
in Partial Fulfilment of the Requirements
for the Degree
Doctor of Philosophy
McMaster University
(cid:13)c Copyright by Mohammed A. El Sayed, February 2012
DOCTOR OF PHILOSOPHY (2012) McMaster University
(Mechanical Engineering) Hamilton, Ontario
TITLE: Multiple Inner-Loop Control of an Electro-Hydrostatic Ac-
tuator
AUTHOR: Mohammed A. El Sayed, M.A.Sc (McMaster University)
SUPERVISOR: Dr. Saeid Habibi, Professor
Department of Mechanical Engineering
NUMBER OF PAGES: xxi; 228
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To my wife, my parents, and my children.
Abstract
Hydraulic systems are commonly used for actuation and manipulation of heavy loads.
They are found in a variety of different industries, such as in automotive, manufac-
turing, robotics, construction, and aerospace. Conventional hydraulic systems use a
centralized constant pressure supply system. Pressurized fluid is then channeled to
actuators using servo-valves. The advantages of these systems are their high torque
to mass ratio, and the ability to control speed and direction with relative precision.
However, there are also disadvantages such as the requirement of a bulky central-
ized supply, leakage, noise, and reduced energy efficiency due to orifice flow and the
requirement for maintaining a constant supply pressure.
Electro-Hydrostatic Actuation systems (EHA) alleviate many of the above
mentioned shortcomings of servo-valve controlled hydraulic systems. In the EHA po-
sition control is achieved by regulating the pumping action. Here, a fixed or a variable
displacement pump can be used to move oil from one chamber of the actuator to the
other. In these actuators, the presence of nonlinearities associated with pump/motor
static friction and backlash, pressure drop in the piping system, and nonlinear friction
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at the load have a significant effect on the performance and positional precision of
the system.
This research will focus on developing a multiple inner-loop control strategy
by implementing multiple inner-loops that utilize the differential pump/load position
and velocity. The main goal will be to decrease the effect of the pump backlash
as well as the nonlinear friction at the load; both of which negatively impact posi-
tional precision. Therefore, the main benefit of this method is an improvement in
trajectory tracking precision, which is particularly important for high precision hy-
drostatic systems. Furthermore, a sliding mode control strategy will be incorporated
into the design to suppress load oscillations reported in precision trajectory tracking
applications. The research hypothesis states that sliding mode control in conjunc-
tion with multiple inner-loops, will improve the trajectory tracking performance of a
hydrostatic actuation system by partially compensating the effects of static friction
at the load. Theoretical analysis, simulation supported by experimental results are
presented to demonstrate the effectiveness of the newly developed methods in sup-
pressing the effects of nonlinearities on the EHA performance, with the downside of
an increased complexity due to the increased number of controller parameters.
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Acknowledgements
I would like to express my gratitude to my supervisor Dr. Saeid Habibi for his valu-
able guidance and support throughout the course of this Ph.D. program. I would
also like to express my cordial appreciation to Mr. Andrew Gadsden, Mr. Kevin
McCullough, and Mr. Ryan Ahmed, for their technical help and support.
Furthermore,Iwouldliketothankallmyfriendsfortheircontinuoussupportthrough-
outthecourseofthisPh.D.program. Ialsowouldliketoexpressmysinceregratitude
to my parents, who have always provided me with solid support and encouragement
in all my endeavors. Last, but not least, I am very grateful to Noha, my wife and my
friend, for her help, patience, consideration, support and encouragement.
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Table of Contents
Abstract iv
Acknowledgements vi
Table of Contents vii
List of Tables xi
List of Figures xii
Nomenclature xvii
1 Introduction 1
1.1 The Electro-Hydrostatic Actuator . . . . . . . . . . . . . . . . . . . . 2
1.2 Multiple Inner-Loop Control Strategy . . . . . . . . . . . . . . . . . . 3
1.3 Multiple Sliding Mode Control Strategy . . . . . . . . . . . . . . . . . 4
1.4 Research Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.5 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
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2 Literature Review 12
2.1 High Precision Manufacturing . . . . . . . . . . . . . . . . . . . . . . 12
2.2 High Precision Actuation Systems . . . . . . . . . . . . . . . . . . . . 16
2.2.1 Linear Motors . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.2 Friction Drive . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.3 Membrane-Type Hydraulic Actuator . . . . . . . . . . . . . . 18
2.2.4 Dual Actuators . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.5 Electro-Hydrostatic Actuator . . . . . . . . . . . . . . . . . . 18
2.3 Friction Modeling and Compensation . . . . . . . . . . . . . . . . . . 19
2.3.1 Friction Induced Limit Cycle Oscillations . . . . . . . . . . . . 20
2.3.2 Friction Mathematical Models . . . . . . . . . . . . . . . . . . 23
2.3.3 Friction Compensation Techniques . . . . . . . . . . . . . . . 26
2.4 Backlash Modeling and Compensation . . . . . . . . . . . . . . . . . 27
2.4.1 Backlash Mathematical Models . . . . . . . . . . . . . . . . . 28
2.4.2 Backlash Compensation Techniques . . . . . . . . . . . . . . . 33
2.5 Variable Structure Systems and Sliding Mode Control . . . . . . . . . 35
2.5.1 SMC Brief History . . . . . . . . . . . . . . . . . . . . . . . . 39
2.5.2 SMC Literature Review . . . . . . . . . . . . . . . . . . . . . 43
2.5.3 SMC Applications . . . . . . . . . . . . . . . . . . . . . . . . 46
2.5.4 Lyapunov Stability Function . . . . . . . . . . . . . . . . . . . 49
2.5.5 Continuous Sliding Mode Control . . . . . . . . . . . . . . . . 53
2.5.6 Discrete Sliding Mode Control . . . . . . . . . . . . . . . . . . 61
2.5.7 Chattering Phenomenon and Elimination . . . . . . . . . . . . 70
2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
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3 Electro-Hydrostatic Actuator (EHA) 93
3.1 Hydraulic Actuation Systems . . . . . . . . . . . . . . . . . . . . . . 93
3.2 Electro-Hydrostatic Actuation System (EHA) . . . . . . . . . . . . . 95
3.2.1 Load Friction Model . . . . . . . . . . . . . . . . . . . . . . . 97
3.2.2 Pump Backlash Model . . . . . . . . . . . . . . . . . . . . . . 99
3.3 EHA Mathematical Model . . . . . . . . . . . . . . . . . . . . . . . . 101
3.3.1 EHA Transfer Function Representation . . . . . . . . . . . . . 102
3.3.2 Overall System Model . . . . . . . . . . . . . . . . . . . . . . 106
3.3.3 EHA State Space Model . . . . . . . . . . . . . . . . . . . . . 110
3.4 EHA Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . 113
3.5 PID Controller Design . . . . . . . . . . . . . . . . . . . . . . . . . . 114
3.5.1 PID Tuning Process . . . . . . . . . . . . . . . . . . . . . . . 117
3.5.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . 120
4 Multiple Inner-Loop Control Strategy 126
4.1 The Proposed Inner-Loop . . . . . . . . . . . . . . . . . . . . . . . . 127
4.1.1 Motor/Pump Velocity Inner-Loop . . . . . . . . . . . . . . . . 127
4.1.2 Inner-Loop Control for Backlash Compensation . . . . . . . . 128
4.1.3 Overall EHA Dynamics With Multiple Inner-Loop Control . . 132
4.2 Controller Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
4.2.1 Conventional Control Strategy . . . . . . . . . . . . . . . . . . 134
4.2.2 Multiple Inner-Loop Control Strategy . . . . . . . . . . . . . . 135
4.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
4.4 Experimental Validation of MIL Control . . . . . . . . . . . . . . . . 138
4.5 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
4.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
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