High Performance Control of a Transmission Based Servo Actuator System

276 Pages·2016·1.97 MB·English

by  Renbin Zhou

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Doctoral Dissertations Graduate School
5-2006
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Renbin Zhou
University of Tennessee - Knoxville
Follow this and additional works at: https://trace.tennessee.edu/utk_graddiss
Part of the Mechanical Engineering Commons
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Zhou, Renbin, "High Performance Control of a Transmission Based Servo Actuator System. " PhD diss.,
University of Tennessee, 2006.
https://trace.tennessee.edu/utk_graddiss/1903
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To the Graduate Council:
I am submitting herewith a dissertation written by Renbin Zhou entitled "High Performance
Control of a Transmission Based Servo Actuator System." I have examined the final electronic
copy of this dissertation for form and content and recommend that it be accepted in partial
fulfillment of the requirements for the degree of Doctor of Philosophy, with a major in
Mechanical Engineering.
William R. Hamel, Major Professor
We have read this dissertation and recommend its acceptance:
Vijay S. Chellaboina, John Chiasson, Seddik M. Djouadi, Lynne E. Parker, Gary V. Smith
Accepted for the Council:
Carolyn R. Hodges
Vice Provost and Dean of the Graduate School
(Original signatures are on file with official student records.)
To the Graduate Council:

I am submitting herewith a dissertation written by Renbin Zhou entitled “High
Performance Control of a Transmission Based Servo Actuator System.” I have
examined the final electronic copy of this dissertation for form and content and
recommend that it be accepted in partial fulfillment of the requirements for the
degree of Doctor of Philosophy, with a major in Mechanical Engineering.

William R. Hamel
Major Professor

We have read this dissertation
and recommend its acceptance:

Vijay S. Chellaboina

John Chiasson

Seddik M. Djouadi

Lynne E. Parker

Gary V. Smith

Acceptance for the Council:

Anne Mayhew
Vice Chancellor and
Dean of Graduate Studies

(Original signatures are on file with official student records.)
High Performance Control of a Transmission
Based Servo Actuator System

A Dissertation
Presented for the Doctor of Philosophy Degree
The University of Tennessee, Knoxville

Renbin Zhou
May, 2006
Copyright © 2006, by Renbin Zhou
All rights reserved

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Acknowledgement
I would like to thank Dr. William R. Hamel for his support and guidance
throughout my graduate study in the Robotics and Electromechanical Systems
Laboratory of the Department of Aerospace, Mechanical, and Biomedical
Engineering at the University of Tennessee, Knoxville. I would like to thank him
for his help in rewrite most of the dissertation draft, it is a rewarding experience
which I will benefit from for the years ahead.
I would like to thank our TBA team, of which I was a member. It is this
team’s work that built the TBA prototype, on which my dissertation research is
developed. The TBA team includes Dr. William Hamel, Dr. Arnold Lumsdaine,
Dr. Spivey Douglass, Dr. Sewoong Kim, Kelley P. Brown, Sriram Sridharan,
Kalyana Ganti, and many others.
I would like to thank Heather Humphreys for her kind help to edit the first
draft of the dissertation. I would like to thank Ge Zhang for the technical
discussions during my initial transition to real time Linux world. I would like to
thank Dr. Reid Kress for his help during my initial transition to the university. I
would also like to thank my committee members for their time and guidance in
making this dissertation possible.
My greatest thanks go to my family: my parents, my wife and my daughter.
It is their love that leads me through all the difficulties and makes all my effort
meaningful, and here I humbly dedicate this work to them.
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Abstract
High performance actuation is a key factor in the industrial robot area. The
transmission based servo actuator system (TBA) is a new type of robot actuator
with a brushless DC servo motor and a three speed discrete variable
transmission (DVT). The proposed TBA design can match the performance of a
typical hydraulic actuator with compact size and weight.
The TBA is a typical hybrid dynamic system consisting of three continuous
dynamic systems and a discrete state controller. This dissertation addresses the
fundamental problems associated with the TBA system control from a hybrid
system point of view.
A detailed dynamic model of the TBA is developed. Due to the complexity
of the TBA system, an exact model is unwieldy for control design and analysis
purposes. In this research, the TBA system is simplified into a hybrid system with
three second order linear time invariant systems, on which all the controls are
developed.Dynamic stability of the TBA is critical for its function as a
servoactuator. For a hybrid system, the stability problem has much broader
range of issues than a purely continuous system.
In general, the plant stability and the subsystem stability are independent.
For example, a hybrid system with stable subsystems can be unstable for certain
switch sequences; on the other hand, a hybrid system with unstable subsystems
can be stabilized by proper switch signals. In this dissertation, a sufficient
condition is established for stability of the TBA system. It is proven that the hybrid
system is stable under asynchronous switching if there exists a common
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Lyapunov function for all subsystems. It is proven that the TBA subsystems can
have a common Lypunov function by designing appropriate feedback controller.
The feedback controller to stabilize the TBA can be transformed into a PID
equivalent controller because the subsystems are second order linear time
invariant systems (LTI). The PID controller was then implemented and high
performance in terms of position error and transient suppression has been
achieved. The discrete state controller should be stable, which means that its
output should be consistent if the hybrid system is subjected to disturbances. A
common phenomenon is that the state changes back and forth very frequently
near the switch boundary, which is referred to as transition instability. This
research proposes a switch strategy consisting of two boundaries to achieve the
transition stability, and it is proved that the proposed switch strategy is transition
stable.
An optimal controller is designed and difficulties associated with
implementation are generated.
Based on the proposed control methods, a multithread real time control
software has been developed to achieve a deterministic control loop sampling.
The control software is developed in C/C++ under Real Time Application
Interface (RTAI), which provides a real time programming environment in a
normal Linux operating system.
With the proposed controller and a prototype TBA test system, TBA
stability and control performance was demonstrated and evaluated. The following
results were observed:
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1. Steady state error of 0.005 degrees at the emulated robust manipulator
shoulder pitch joint
2. Control loop sampling period of 1 millisecond with negligible delay
3. Transient disturbances associated with the gear shifting of ~20% in most
cases.
4. The methods and applications used in this dissertation can be extended to
a large range of hybrid dynamic systems in terms of control system
design, analysis and implementation.
This research contributes to the literature and research knowledge base in
the following ways:
1. Exploration and solution of the control problems of TBA’s in the hybrid
system control context.
2. Expansion of the fundamental understanding of the practical control
issues of TBA’s.
3. Analysis, design, and implementation of a real time TBA control system,
and identification of the most suitable control strategy for the TBA.
4. The development of analysis and control methods that can be extended to
a much broader range of hybrid dynamic systems.
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TABLE OF CONTENTS
CHAPTER 1 BACKGROUND AND INTRODUCTION..........................................1
HISTORY OF INDUSTRY ROBOT –ACTUATOR AND CONTROL...................1
AN INTRODUCTION OF TBA – IDEAS, DESIGN, AND INTEGRATION.........10
TBA Prototype and the Experimental System....................19
SCOPE AND ORGANIZATION OF THE DISSERTATION.............................22
CHAPTER 2 MATHEMATICAL MODELING......................................................24
BLDC MODEL.................................................................................24
THREE SPEED DVT MODEL - A HYBRID DYNAMIC SYSTEM.................29
A Single Planetary Gear Model..........................................33
A Three Speed DVT Model................................................36
A ROBOT ARM MODEL.....................................................................40
THE TBA PROTOTYPE MODEL..........................................................41
CHAPTER 3 TBA CONTROLS...........................................................................45
BACKGROUND.................................................................................45
SUPERVISORY CONTROL..................................................................54
Switch Strategy- Transition Stability...................................54
HYBRID SYSTEM STABILITY - TBA......................................................65
CONTROLLER DESIGN AND IMPLEMENTATION.....................................72
State Feedback Control......................................................73
Optimal Control and Robust Control Discussion................85
SUMMARY.......................................................................................93
CHAPTER 4 CONTROL SYSTEM SOFTWARE................................................95
TBA DESIGN REQUIREMENT.............................................................96
OPERATING SYSTEM - INTRODUCTION...............................................98
GPOS and RTOS...............................................................98
RTAI/Linux........................................................................105
TBA SOFTWARE DESIGN................................................................109
A Windows/LabVIEW Implementation..............................110
Multithread Design with RTAI...........................................111
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