Applications of robust control to nonlinear systems

This book offers a three-step approach to generating a robust nonlinear controller: modeling, synthesis and robustness analysis. The publication is targeted to practicing engineers and graduate-level students working in guidance, information command and control systems, and CAD/CAM. The methods covered in this book allow the user to design and analyze nonlinear controllers for nonlinear systems with several important and unique characteristics: the ability to specify the closed loop system's frequency response via requirements on the sensitivity (S) and complementary sensitivity (T), the ability to directly minimize an undesirable resonance or peak in the frequency response while simultaneously closing all loops from the input to the output vector in essentially one single design step, and the ability to analyze the stability characteristics for multiple independent and dependent problem variables. The approach uniquely allows the user to achieve stable and robust performance for systems which are both unstable and contain discontinuous nonlinearities using adaptive nonlinear controllers.

Author Notes

Richard D. Colgren is an associate professor in aerospace engineering at the University of Kansas

Preface	p. ix
Acknowledgments	p. xi
Volume Nomenclature	p. xiii
Chapter 1. Introduction to Robust Control	p. 1
Chapter 2. Describing Function	p. 3
I. Definition of Describing Function	p. 3
II. General Describing Function Evaluation Methods	p. 5
Chapter 3. H[subscript infinity] Optimal Controlis	p. 17
I. Performance Specification	p. 18
II. H[subscript infinity] Control Synthesis	p. 20
III. H[subscript infinity] Riccati Solution for Augmented Plant Containing Describing Function	p. 29
Chapter 4. Robustness Analysis via Simplicial Algorithms	p. 41
I. Analytic Geometry	p. 41
II. Simplicial Mapping	p. 44
III. Simplex Nulling	p. 46
IV. Integer Labeling	p. 47
V. Vector Labeling	p. 50
Chapter 5. Nonlinear H[subscript infinity] Control	p. 53
I. Nonlinear H[subscript infinity] Control Approach	p. 53
II. H[subscript infinity] Control of System with Relay Element via Loo-Shifting	p. 53
III. Control via Adaptive Perturbation Filter	p. 64
IV. Nonlinear Robustness Analysis of Relay Element via Simplicial Algorithms	p. 79
Chapter 6. Direct Approach to Nonlinear H[subscript infinity] Control	p. 93
I. Riccati Equation Solution Initialization	p. 93
II. Hamiltonian Matrix H[subscript infinity] Solution	p. 94
III. Solution to H[subscript infinity] Riccati Equation	p. 96
IV. Hamiltonian Matrix J[subscript infinity] Solution	p. 101
V. Solution to J[subscript infinity] Riccati Equation	p. 103
VI. Optimal H[subscript infinity] Controller	p. 105
Chapter 7. Nonlinear H[subscript infinity] Control of a UAV	p. 111
I. UAV Plant Model	p. 111
II. UAV Roll Axis Control	p. 114
III. Closed Loop UAV Response	p. 129
Chapter 8. Computer Algorithms	p. 133
I. H[subscript infinity] Optimization	p. 133
II. FORTRAN Simulation	p. 136
III. Variable Dimension Restart Algorithm	p. 137
Chapter 9. Hardware Implementation Example	p. 139
I. Circuit Design	p. 139
II. Circuit's Dynamic Response	p. 144
Chapter 10. Piloted Aircraft Performance	p. 155
I. [mu]-Synthesis Design Procedure	p. 155
II. Weightings and Uncertainty Models	p. 157
III. Conceptual [mu]-Synthesis Design	p. 160
IV. Iterated [mu]-Synthesis Design	p. 161
V. Maneuvers	p. 163
VI. Conclusions	p. 163
References	p. 165
Index	p. 171
Supporting Materials	p. 175

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