Applied Nonlinear Control

Transcription

1 Applied Nonlinear Control JEAN-JACQUES E. SLOTINE Massachusetts Institute of Technology WEIPING LI Massachusetts Institute of Technology Pearson Education Prentice Hall International Inc. Upper Saddle River, New Jersey 07458

2 Contents Preface xi 1. Introduction Why Nonlinear Control? Nonlinear System Behavior An Overview of the Book Notes and References 13 Part I: Nonlinear Systems Analysis 14 Introduction to Part I Phase Plane Analysis Concepts of Phase Plane Analysis Phase Portraits Singular Points Symmetry in Phase Plane Portraits Constructing Phase Portraits Determining Time from Phase Portraits Phase Plane Analysis of Linear Systems Phase Plane Analysis of Nonlinear Systems Existence of Limit Cycles Summary Notes and References Exercises 38 Vll

3 viii 3. Fundamentals of Lyapunov Theory Nonlinear Systems and Equilibrium Points Concepts of Stability Linearization and Local Stability Lyapunov's Direct Method Positive Definite Functions and Lyapunov Functions Equilibrium Point Theorems Invariant Set Theorems System Analysis Based on Lyapunov's Direct Method Lyapunov Analysis of Linear Time-Invariant Systems Krasovskii's Method The Variable Gradient Method Physically Motivated Lyapunov Functions Performance Analysis Control Design Based on Lyapunov's Direct Method Summary Notes and References Exercises Advanced Stability Theory Concepts of Stability for Non-Autonomous Systems Lyapunov Analysis of Non-Autonomous Systems Lyapunov's Direct Method for Non-Autonomous Systems Lyapunov Analysis of Linear Time-Varying Systems The Linearization Method for Non-Autonomous Systems * Instability Theorems * Existence of Lyapunov Functions Lyapunov-Like Analysis Using Barbalat's Lemma Asymptotic Properties of Functions and Their Derivatives Barbalat's Lemma Positive Linear Systems PR and SPR Transfer Functions The Kalman-Yakubovich Lemma Positive Real Transfer Matrices The Passivity Formalism Block Combinations Passivity in Linear Systems 137

4 4.8 Absolute Stability 4.9 * Establishing Boundedness of Signals 4.10 * Existence and Unicity of Solutions 4.11 Summary 4.12 Notes and References 4.13 Exercises 5. Describing Function Analysis 5.1 Describing Function Fundamentals An Example of Describing Function Analysis Applications Domain Basic Assumptions Basic Definitions Computing Describing Functions Common Nonlinearities In Control Systems 5.3 Describing Functions of Common Nonlinearities 5.4 Describing Function Analysis of Nonlinear Systems The Nyquist Criterion and Its Extension Existence of Limit Cycles Stability of Limit Cycles Reliability of Describing Function Analysis Summary 5.6 Notes and References 5.7 Exercises Part II: Nonlinear Control Systems Design Introduction to Part II Feedback Linearization 6.1 Intuitive Concepts Feedback Linearization And The Canonical Form Input-State Linearization Input-Output Linearization Mathematical Tools 6.3 Input-State Linearization of SISO Systems

5 X 6.4 Input-Output Linearization of SISO Systems * Multi-Input Systems Summary Notes and References Exercises Sliding Control Sliding Surfaces A Notational Simplification * Filippov's Construction of the Equivalent Dynamics 7.13 Perfect Performance - At a Price Direct Implementations of Switching Control Laws Continuous Approximations of Switching Control Laws The Modeling/Performance Trade-Offs * Multi-Input Systems Summary Notes and References Exercises Adaptive Control Basic Concepts in Adaptive Control Why Adaptive Control? What Is Adaptive Control? How To Design Adaptive Controllers? Adaptive Control of First-Order Systems Adaptive Control of Linear Systems With Full State Feedback Adaptive Control of Linear Systems With Output Feedback Linear Systems With Relative Degree One Linear Systems With Higher Relative Degree Adaptive Control of Nonlinear Systems Robustness of Adaptive Control Systems * On-Line Parameter Estimation Linear Parametrization Model Prediction-Error-Based Estimation Methods The Gradient Estimator The Standard Least-Squares Estimator 370

6 8.7.5 Least-Squares With Exponential Forgetting Bounded-Gain Forgetting Concluding Remarks and Implementation Issues 8.8 Composite Adaptation 8.9 Summary 8.10 Notes and References 8.11 Exercises 9. Control of Multi-Input Physical Systems 9.1 Robotics as a Prototype Position Control Trajectory Control Adaptive Robot Trajectory Control The Basic Algorithm * Composite Adaptive Trajectory Control Putting Physics in Control High-Frequency Unmodeled Dynamics Conservative and Dissipative Dynamics Robotics as a Metaphor Spacecraft Control The Spacecraft Model Attitude Control Summary 9.6 Notes and References 9.7 Exercises BIBLIOGRAPHY INDEX