Direct Adaptive Control Algorithms

1 Introduction.- 1.1 Definition of the Problem.- 1.2 Prologue to Simple Adaptive Control.- 1.3 Background on Adaptive Control Algorithms.- 1.4 Objectives and Overview.- 1.4.1 Objectives.- 1.4.2 Relation with Other Texts.- 1.4.3 Overview of Text.- 1.5 Software Availability for Example Problems.- 2 Basic Theory of Simple Adaptive Control.- 2.1 Model Following.- 2.2 Output Model Following.- 2.2.1 Command Generator Tracker Description.- 2.2.2 Modifications for the Tracking of A Larger Class of Input Commands.- 2.2.3 The General Tracking Problem.- 2.3 Stability and Positivity Concepts.- 2.3.1 Introduction: Stability with Fixed Controllers Versus Nonlinear Adaptive Controllers.- 2.3.2 Basic Stability Concepts.- 2.3.3 Positive Real Analysis.- 2.4 Adaptive Control Based on CGT.- 2.4.1 Controller Structure.- 2.4.2 Stability Analysis.- 2.4.3 System Constraints.- 2.4.4 An Illustrative Example.- 2.5 The Adaptive Algorithm with General Input Commands.- 2.5.1 Controller Structure.- 2.5.2 Stability Analysis.- 2.5.3 An Illustrative Example.- 2.6 Summary of Adaptive Algorithms.- Appendix 2A Proof of Theorem 2.1.- Appendix 2B Proof of Theorem 2.2.- Appendix 2C Poles, Zeros, and Relative Degree in Multivariable Systems.- 3 Extensions of the Basic Adaptive Algorithm.- 3.1 Parallel Feedforward and Stability Considerations.- 3.2 Feedforward Around Plant.- 3.2.1 Adaptive Control with Basic Feedforward Augmentation.- 3.2.2 Summary of MRAC Using Plant Feedforward.- 3.2.3 Illustrative Examples.- 3.3 Feedforward in Both Plant and Model.- 3.3.1 Modifications to Insure Asymptotic Model Following.- 3.3.2 Stability Proof.- 3.3.3 Summary of Constraints and Design Rules.- 3.3.4 Illustrative Examples.- 3.3.5 Conclusions and Recommendations.- 3.4 A Unified Approach to Supplementary Dynamics.- 3.4.1 Theory.- 3.4.2 Summary of Constraints and Design Rules.- 3.4.3 Illustrative Examples.- 3.5 Adaptive Control in the Presence of Nonlinearities.- 3.5.1 Adaptation for Nonlinearity of Known Form.- 3.5.2 Adaptation When the Linear Part Is not ASPR.- 3.6 Summary.- Appendix 3A Proof of Positivity Lemmas.- Appendix 3B Proof of Theorem 3.1.- Appendix 3C Proof of Theorem 3.2.- Appendix 3D Proof of Theorem 3.3.- Appendix 3E Proof of Theorem 3.4.- Appendix 3F Outline of Proof of Theorem 3.5.- 4 Robust Design Procedures.- 4.1 Introduction.- 4.2 Robust Redesign of the Basic Adaptive Algorithm.- 4.2.1 Algorithm Description.- 4.2.2 Illustrative Examples.- 4.3 Robustness Considerations with Feedforward in the Reference Model.- 4.3.1 Algorithm Description.- 4.3.2 Illustrative Examples.- 4.4 Robust Redesign for Supplementary Dynamics.- 4.4.1 Algorithm Description.- 4.4.2 Error System Equations.- 4.4.3 Stability Analysis.- 4.4.4 Illustrative Examples.- 4.5 Bursting Phenomena and Their Elimination.- 4.6 Summary.- Appendix 4A Proof of Robust Stability, Theorem 4.1.- Appendix 4B Development of Lyapunov Function Derivative.- Appendix 4C Proof of Theorem 4.2.- 5 Adaptive Control of Time-Varying and Nonlinear Systems.- 5.1 Introduction.- 5.2 Passivity and Almost Passivity of Nonstationary Systems.- 5.3 Adaptive Control of ASP Plants.- 5.4 The “Almost Passivity” Lemmas.- 5.5 Passivity and Almost Passivity of Nonlinear Systems.- 5.6 Simple Adaptive Control for a Class of Nonlinear Systems.- 5.7 Simple Adaptive Control of Rigid Robotic Manipulators.- 5.8 Summary.- Appendix 5A Proof of Stability for the Algorithm (5.27)-(5.32).- Appendix 5B Strictly Causal Almost Passive Systems.- Appendix 5C Proof of Lemma 5.1.- Appendix 5D Proof of Almost Passivity Lemma in Nonlinear Systems.- Appendix 5E Almost Passivity with Application to Manipulators.- Appendix 5F The Proof of Stability of the Adaptive Control Algorithm.- Appendix 5G Adaptive Control of Strictly Causal Almost Passive Systems.- 6 Design of Model Reference Adaptive Controllers.- 6.1 Algorithm Overview.- 6.2 Constraint Satisfaction.- 6.2.1 Feedforward Compensator Design for SISO Plants.- 6.2.2 Feedforward Compensator Design for MIMO Plants.- 6.3 Weight Selection.- 6.4 Reference Model Selection.- 6.5 Digital Implementation.- 6.6 Time-Varying Commands.- 6.6.1 Command Generated as Output of Linear System.- 6.6.2 Command Variations Slow Compared with Reference Model.- Appendix 6A Proof of Theorem 6.1.- Appendix 6B Proof of Theorem 6.2.- Appendix 6C Proof of Lemma 6.1.- Appendix 6D Proof of Theorem 6.3.- 7 Case Studies.- 7.1 Direct Model Reference Adaptive Control of a PUMA Manipulator.- 7.1.1 Introduction.- 7.1.2 Puma Model Development.- 7.1.3 Implementation Issues.- 7.1.4 Simulation Results.- 7.1.5 Experimental Results.- 7.1.6 Conclusions and Recommendations.- 7.2 Model Reference Adaptive Control of Large Structures.- 7.2.1 Introduction.- 7.2.2 Large Flexible Structures Dynamics.- 7.2.3 The ASPR Condition for Flexible Structures.- 7.2.4 Adaptive Control Algorithm.- 7.2.5 Experimental Set-Up.- 7.2.6 Experiment Results and Discussion.- 7.2.7 Summary and Conclusions.- 7.3 Adaptive Drug Delivery Control.- 7.3.1 Introduction.- 7.3.2 Problem Statement.- 7.3.3 Controller Design.- 7.3.4 Operation of the Complete Hierarchical Controller.- 7.3.5 Experimental Results.- 7.3.6 Conclusions.- 7.4 Adaptive Control for a Relaxed Static Stability Aircraft.- 7.4.1 Introduction.- 7.4.2 Model Development.- 7.4.3 Control Law Development.- 7.4.4 Conclusions.- 7.5 Liquid Level System Emulation.- 7.5.1 Emulation Background and Instructions.- 7.5.2 System Background.- 7.5.3 Illustrative Example.- References.