NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK ...
NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK ... NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK ...
BRIGHAM YOUNG UNIVERSITY As chair of the candidate's graduate committee, I have read the thesis of J. Willard Curtis III in its nal form and have found that (1) its format, citations, and bibliographical style are consistent and acceptable and ful ll university and department style requirements (2) its illustrative materials including gures, tables, and charts are in place and (3) the nal manuscript is satisfactory to the graduate committee and is ready for submission to the university library. Date Randy W. Beard Chair, Graduate Committee Accepted for the Department Accepted for the College A. Lee Swindlehurst Graduate Coordinator Douglas M. Chabries Dean, College of Engineering and Technology
ABSTRACT NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK SYSTEM J. Willard Curtis III Department ofElectrical and Computer Engineering Master of Science The quest for practical, robust, and e ective nonlinear feedback controllers has been an area of active research in recent years. One of the challenges in this research ishowtoevaluate the performance of new nonlinear control strategies, given that the set of nonlinear systems is so varied. A benchmark problem for nonlinear systems has been proposed, in order to provide a standard testbed for newly devel- oped, nonlinear control algorithms. This benchmark problem is an ideal system on which to apply the Successive Galerkin Approximation to the optimal nonlinear full- state feedback problem. The Successive Galerkin Approximation (SGA) technique provides an approximation to the solution of the Hamilton-Jacobi equations associ- ated with optimal nonlinear control theory. The main contribution of this thesis is the comparison of the SGA algorithm to four other control methodologies, each of which is implemented on a hardware system that can be modeled as the nonlinear benchmark problem. The results show that the SGA algorithms provide excellent performance and good robustness properties when applied to this benchmark system, outperforming a simple passivity-based control, two standard linearized controls, and a simpli ed backstepping control.
- Page 1 and 2: NONLINEAR CONTROLLER COMPARISON ON
- Page 3: BRIGHAM YOUNG UNIVERSITY GRADUATE C
- Page 7 and 8: Contents Acknowledgments vi List of
- Page 9: List of Tables 4.1 Tabular Comparis
- Page 12 and 13: 4.19 SGA: Nonlinear H1 vs. Linear O
- Page 14 and 15: Figure 1.1: TORA System One of the
- Page 16 and 17: 1.3 Literature Review In surveying
- Page 19 and 20: Chapter 2 Plant Speci cations and M
- Page 21 and 22: Figure 2.2: Mechanical Model of Fle
- Page 23 and 24: Figure 2.4: Translational Oscillati
- Page 25 and 26: 2.3 Software Set-up All of the cont
- Page 27 and 28: Chapter 3 Overview of Control Strat
- Page 29 and 30: The optimal gain matrix was given b
- Page 31 and 32: 3.3 Passivity-Based Control Certain
- Page 33 and 34: limitations, k 1 and k 2 are tuning
- Page 35 and 36: Now we regard as the control variab
- Page 37 and 38: where V satis es the well known Ham
- Page 39 and 40: ecause one can quickly adjust the Q
- Page 41 and 42: Chapter 4 Simulation Results 4.1 Th
- Page 43 and 44: disturbances, whereas the hardware
- Page 45 and 46: Response in cm 4 3 2 1 0 −1 −2
- Page 47 and 48: Response in cm Response in cm 4 3 2
- Page 49 and 50: Response in cm Response in cm 5 4 3
- Page 51 and 52: Response in cm 4 3 2 1 0 −1 −2
- Page 53 and 54: Response in cm Response in cm 4 3 2
ABSTRACT<br />
<strong>N<strong>ON</strong>LINEAR</strong> <strong>C<strong>ON</strong>TROLLER</strong> <strong>COMPARIS<strong>ON</strong></strong> <strong>ON</strong> A <strong>BENCHMARK</strong> SYSTEM<br />
J. Willard Curtis III<br />
Department ofElectrical and Computer Engineering<br />
Master of Science<br />
The quest for practical, robust, and e ective nonlinear feedback controllers<br />
has been an area of active research in recent years. One of the challenges in this<br />
research ishowtoevaluate the performance of new nonlinear control strategies, given<br />
that the set of nonlinear systems is so varied. A benchmark problem for nonlinear<br />
systems has been proposed, in order to provide a standard testbed for newly devel-<br />
oped, nonlinear control algorithms. This benchmark problem is an ideal system on<br />
which to apply the Successive Galerkin Approximation to the optimal nonlinear full-<br />
state feedback problem. The Successive Galerkin Approximation (SGA) technique<br />
provides an approximation to the solution of the Hamilton-Jacobi equations associ-<br />
ated with optimal nonlinear control theory. The main contribution of this thesis is<br />
the comparison of the SGA algorithm to four other control methodologies, each of<br />
which is implemented on a hardware system that can be modeled as the nonlinear<br />
benchmark problem. The results show that the SGA algorithms provide excellent<br />
performance and good robustness properties when applied to this benchmark system,<br />
outperforming a simple passivity-based control, two standard linearized controls, and<br />
a simpli ed backstepping control.
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