Direct Adaptive Control Algorithms

Suitable either as a reference for practising engineers or as a text for a graduate course in adaptive control systems, this is a self-contained compendium of readily implementable adaptive control algorithms. These algorithms have been developed and applied by the authors for over fifteen years to a wide variety of engineering problems including flexible structure control, blood pressure control, and robotics. As such, they are suitable for a wide variety of multiple input-output control systems with uncertainty and external disturbances. The text is intended to enable anyone with knowledge of basic linear multivariable systems to adapt the algorithms to problems in a wide variety of disciplines. Thus, in addition to developing the theoretical details of the algorithms presented, the text gives considerable emphasis to designing algorithms and to representative applications in flight control, flexible structure control, robotics, and drug-infusion control. This second edition makes good use of MATLAB programs for the illustrative examples; these programs are described in the text and can be obtained from the MathWorks file server.

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.