Nonlinear model predictive control of a hydraulic actuator

167 Pages·2010·4.87 MB·English

by  S. P. Hampson

Model Predictive Control of a
Theory and Implementation
thesis submitted in fulfillment of the requirements for the
Degree
of
Doctor of Philosophy in Engineering
~lechanical
in the
University of Canterbul'y
by
s.
P. Hampson
University of Canterbury
1995
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To Iny Parents
11
Abstract
The main objective of this thesis is the development and implementation of a
nonlinear optimal controller for a hydraulic positioning system. The controller is
able to respond rapidly as well as take care of the changing dynamics within the
hydraulic system.
The necessary attributes for a hydraulic actuator controller are deteffi1ined by
analysing the problems generally associated with hydraulic drives and reviewing
the control methods that have been applied in the past. It is concluded that while
significant advancements have been made in disturbance rejection, little effort has
been placed on the optimal, or minimum time specifications which are frequently
demanded by positioning systems. It is also noted that high perfoffi1ance
hydraulic drives are prone to cavitation and a controller must necessarily avoid
this.
The design of a hydraulic test rig is discussed and a novel valve drive circuit that
allows direct digital control is presented. The ability of the rig to demonstrate
typical control problems is established by experimental testing./ The purpose of
the test rig is to aid in the modelling process and for controller testing.
Power Bond Graphs are used to model the experimental rig and a companson
between a nonlinear model and experimental data shows good correlation. A linear
model is also considered and shown to be ineffective at representing the rig
dynamics over a range of inputs. By formulating an idealised model, valuable
insights into the dynamic characteristics are obtained and the directional dependent
gain of single ended rams explained.
The performance capabilities of the hydraulic rig are benchmarked by calculating
the minimum time response of the hydraulic system subject to constraints on the
111
actuator pressures, load velocity and position. A number of test cases are
examined.
The research objectives of high performance and flexible constraint handling make
model predictive control (MPC) an ideal approach. Model predictive controllers
have been successfully applied within the chemical process industry but their
application to robotics is hindered by the excessive computational requirements of
the algorithm. Furthermore they are typically linear and so in their present form
unsuitable. By simplifying the optimisation procedure involved in the MPC
algorithm an implementable, nonlinear version of the controller has been tested.
The controller is able to constrain the values of pressure, velocity and position
within prescribed boundaries, thus eliminating the need for extra hydraulic
components. Moreover, the speed of response is comparable to the theoretical
optimum.
The work reported in this thesis contributes to the field of hydraulic systems
control as it presents a novel, nonlinear optimal controJier for a hydraulic
positioning system. The controller differs from others reported in the literature in
that it allows for the plant nonlinearities and forces the system to operate within
prescribed boundaries on the state variables. As will be shown this eliminates the
need for extra hydraulic components.
IV
Acknowled
I would like to extend my appreciation to my fellow postgraduates, particularly
Colin McMurtrie and Kevin Hill, and all members of staff in the department of
mechanical engineering who have made the past few years so enjoyable. Colin also
for many late night discussions and for being brave enough to be present during
testing of the experimental apparatus.
I am indebted to my supervisor Dr. Reg Dunlop for his encouragement, patience
and expertise. Also Professor Sirisena of the electrical and electronic department
for many useful discussions and whose knowledge of control systems has been an
inspiration. Dr Paul Channon for his suggestions and tutelage on variational
calculus.
Thanks to Dr Paul Hodgson for his support to both myself and my wife during
these 'difficult' years.
A special thanks is due to my wife, Beryl, for her unquestioning support and
encouragement.
v
Contents
page
Abstract
II
Acknowledgements IV
Contents
V
Preface
Vlll
Nomenclature
Xl
1 Introduction 1
1.1 Background 1
1 Hydraulic Drives 3
1.3 Optimal Control of Hydraulic Actuators 9
1.4 Conclusions 10
2 Test Rig 11
2.1 Introduction 11
Rig Layout 12
Hydraulic Circuits 14
2.4 ElectricallElectronic Circuits 16
2.5 Software 27
2.6 System Performance 30
Conclusions 34
3 System I\1odelli and Identification 36
1 Introduction 36
3.2 Power bond graphs 37
3.3 System Model 40
VI
3.1.1 Equations and Relationships
3.4 Mathematical Models 49
3.5 Model Verification 51
3.6 Linear Model 53
3.7 Idealised Transfer Function 57
3.8 System Analysis 61
3.9 Conclusions 65
4 Optimal State ectories 66
4.1 Introduction 66
4.2 Performance Criteria 68
4.3 Functional Minimisation with Equality Constraints 69
4.4 Pontryagin's Equations and the Minimum Principle 74
4.5 Inclusion of Inequality Constraints 76
4.6 Techniques for solving the TPBVP 77
4.7 Application to the Hydraulic System 80
4.8 Results 84
4.9 Conclusions 94
5 Model Predictive Control 96
5.1 Introduction 96
5.2 The Model Predictive Control Algorithm 98
5.3 Simplified MPC Algorithm 101
5.3.1 Optimisation Routine 101
5.3.2 Integrators 106
5.3.3 Velocity, Spool Position and Load Estimation 107
Vll
5.4 Simulated Results 107
5.5 Experimental Testing 113
5.5.1 Implementation 113
5.5.2 Results 115
5.6 Conclusions 128
6 Conclusions snd Recommendations l30
6.1 Introduction l30
6.2 Recommendations for Extending the Work l31
6.3 Future Work l33
6.4 Conclusion l37
APPENDIX Rig Components l38
APPENDIX B Direction Dependent Gain l39
APPENDIX C Power Bond Graphs 144
APPENDIX Necessary Conditions for a Minimum (Variational Approach) 147
APPENDIX E Golden Search Ratio 149
References
VI11
Interest in closed loop hydraulic drives has increased dramatically since the early
seventies and, in particular, interest has grown with regard to their control. This is
due, at least in part, to the development of low cost microprocessors that have
made possible the implementation of complex control algorithms to improve the
performance of the hydraulic drive. However, despite a large number of actuators
being utilised in tasks where rapid positioning is imperative, little work has been
reported on the performance capabilities of these hydraulic drives.
Hydraulic systems are always required to operate within constraints. These are
generally handled at the design stage by limiting variables such as supply pressure,
actuator dimensions and valve sizing and response. Controllers are then designed
for worst case conditions. However, a common feature of hydraulic system
applications is the variable nature of the drive. Constraints imposed at the design
stage can often compromise the performance of the system, remaining sluggish
despite favourable conditions. Removing the constraints from the design stage
means they must now be handled by the control system, permitting greater
flexibility .
Controllers that are capable of combining optimal control and at the same time
imposing constraints on the state variables are not Ullcommon. They have become
popular in the chemical process industry but typically only for fixed systems
with large time constants. The computational requirements of the algorithm has
precluded their use with robotic positioning systems.
This thesis examines the optimal control of linear hydraulic actuators subject to
constraints on the state space and suggests a novel way by which constraint on
the state variables may be handled by the controller. Simulation and experimental
testing verify the pelfomlance of the control algorithm.
IX
Papers prepared during the course of this thesis:
Hampson S P and Dunlop G 1992 Design ofa hydraulic system for
advanced control teaching, Proc. IPENZ Conf., Christchurch, Vol. pp
363-370.
Dunlop R and Hampson S P 1993 Bond graphs for nonlinear
modelling ofa ll electro-hydraulic system. Proc. of the Int. Congress
MV2 - Active Control in Mechanical Engineering, Lyon, France, Tome 1,
pp 62-72.
Hampson S P and Dunlop G R 1993 Hydraulic control and vibrations.
Proc. New Zealand Vibrations Association 4th Annual Conference,
Christchurch, New Zealand, pp 1-5.
Hampson S P and Dunlop G 1993 Ivfodelhl1g techniques applied to an
electro-hydraulic system, Proc. IPENZ Conf., Hamilton, pp 233-242.
G R Dunlop, S P Hampson and R K Rayudu 1994 Design teclmiquesfor
hydraulic systems. Proc. IPENZ Conf., Nelson, Feb. 18-21, Vol. 1 pp
70-73.
Dunlop GRand Hampson S P 1994 All integrated digital control
::;ystemfor hydraulic actuators. Presented at the Seventh Bath
International Fluid Power Workshop, Bath, UK, Sept. 21-23. pp 177-186.
Dunlop R and Hampson S P 1995 Bond graphsfor nonlinear
modelling qfa n electro-hydraulic .system. Active Control in Mechanical
Engineering, Ed. L Jezequel, Editions Hermes, ISBN 2-86601-450-2,
Paris, France, pp 57-68.