Adaptive Control: Algorithms, Analysis and Applications

Cover
Communications and Control Engineering
Adaptive Control, 2nd Edition
ISBN 9780857296634
Preface
	Expected Audience
	About the Content
	Pathways Through the Book
	The Website
	Acknowledgments
Contents
	Abbreviations
Chapter 1: Introduction to Adaptive Control
	1.1 Adaptive Control-Why?
	1.2 Adaptive Control Versus Conventional Feedback Control
		1.2.1 Fundamental Hypothesis in Adaptive Control
		1.2.2 Adaptive Control Versus Robust Control
	1.3 Basic Adaptive Control Schemes
		1.3.1 Open-Loop Adaptive Control
		1.3.2 Direct Adaptive Control
		1.3.3 Indirect Adaptive Control
		1.3.4 Direct and Indirect Adaptive Control: Some Connections
		1.3.5 Iterative Identification in Closed Loop and Controller Redesign
		1.3.6 Multiple Model Adaptive Control with Switching
		1.3.7 Adaptive Regulation
		1.3.8 Adaptive Feedforward Compensation of Disturbances
		1.3.9 Parameter Adaptation Algorithm
	1.4 Examples of Applications
		1.4.1 Open-Loop Adaptive Control of Deposited Zinc in Hot-Dip Galvanizing
		1.4.2 Direct Adaptive Control of a Phosphate Drying Furnace
		1.4.3 Indirect and Multimodel Adaptive Control of a Flexible Transmission
		1.4.4 Adaptive Regulation in an Active Vibration Control System
		1.4.5 Adaptive Feedforward Disturbance Compensation in an Active Vibration Control System
	1.5 A Brief Historical Note
	1.6 Further Reading
	1.7 Concluding Remarks
Chapter 2: Discrete-Time System Models for Control
	2.1 Deterministic Environment
		2.1.1 Input-Output Difference Operator Models
		2.1.2 Predictor Form (Prediction for Deterministic SISO Models)
			Regressor Form
	2.2 Stochastic Environment
		2.2.1 Input-Output Models
		2.2.2 Predictors for ARMAX Input-Output Models
			Rapprochement with the Deterministic Case
			Rapprochement with the Kalman Predictor
			Regressor Form
		2.2.3 Predictors for Output Error Model Structure
	2.3 Concluding Remarks
	2.4 Problems
Chapter 3: Parameter Adaptation Algorithms-Deterministic Environment
	3.1 The Problem
	3.2 Parameter Adaptation Algorithms (PAA)-Examples
		3.2.1 Gradient Algorithm
			Improved Gradient Algorithm
		3.2.2 Recursive Least Squares Algorithm
		3.2.3 Choice of the Adaptation Gain
			A.1: Decreasing (Vanishing) Gain (RLS)
			A.2: Constant Forgetting Factor
			A.3: Variable Forgetting Factor
			A4: Constant Trace
			A.5: Decreasing Gain + Constant Trace
			A.6: Variable Forgetting Factor + Constant Trace
			A.7: Constant Gain (Gradient Algorithm)
			Choice of the Initial Gain F(0)
			Parameter Adaptation Algorithms with Scalar Adaptation Gain
		3.2.4 Recursive Least Squares and Kalman Filter
		3.2.5 Some Remarks on the Parameter Adaptation Algorithms
	3.3 Stability of Parameter Adaptation Algorithms
		3.3.1 Equivalent Feedback Representation of the Parameter Adaptation Algorithms and the Stability Problem
		3.3.2 Stability Approach for the Synthesis of PAA Using the Equivalent Feedback Representation
			Output Error Adaptive Predictor
		3.3.3 Positive Real PAA Structures
			\"Integral + Proportional\" Parameter Adaptation Algorithm
			Parameter Adaptation Algorithm with Leakage
			PAA for Systems with Time-Varying Parameters
		3.3.4 Parameter Adaptation Algorithms with Time-Varying Adaptation Gain
			A General Structure and Stability of PAA
			Interpretation of the Results
		3.3.5 Removing the Positive Real Condition
			Output Error with Extended Prediction Model
			Signal Dependent Condition
	3.4 Parametric Convergence
		3.4.1 The Problem
		3.4.2 Persistently Exciting Signals
		3.4.3 Parametric Convergence Condition
	3.5 Concluding Remarks
	3.6 Problems
Chapter 4: Parameter Adaptation Algorithms-Stochastic Environment
	4.1 Effect of Stochastic Disturbances
	4.2 The Averaging Method for the Analysis of Adaptation Algorithms in a Stochastic Environment
	4.3 The Martingale Approach for the Analysis of PAA in a Stochastic Environment
	4.4 The Frequency Domain Approach
	4.5 Concluding Remarks
	4.6 Problems
Chapter 5: Recursive Plant Model Identification in Open Loop
	5.1 Recursive Identification in the Context of System Identification
	5.2 Structure of Recursive Parameter Estimation Algorithms
	5.3 Recursive Identification Methods Based on the Whitening of the Prediction Error (Type I)
		5.3.1 Recursive Least Squares (RLS)
		5.3.2 Extended Least Squares (ELS)
		5.3.3 Output Error with Extended Prediction Model (OEEPM)
		5.3.4 Recursive Maximum Likelihood (RML)
		5.3.5 Generalized Least Squares (GLS)
	5.4 Validation of the Models Identified with Type I Methods
		5.4.1 Whiteness Test
	5.5 Identification Methods Based on the Decorrelation of the Observation Vector and the Prediction Error (Type II)
		5.5.1 Output Error with Fixed Compensator
		5.5.2 Output Error with Adjustable Compensator
		5.5.3 Filtered Output Error
		5.5.4 Instrumental Variable with Auxiliary Model
	5.6 Validation of the Models Identified with Type II Methods
		5.6.1 Uncorrelation Test
	5.7 Selection of the Pseudo Random Binary Sequence
		5.7.1 Pseudo Random Binary Sequences (PRBS)
	5.8 Model Order Selection
		5.8.1 A Practical Approach for Model Order Selection
			A Priori Choice of nA
			Initial Choice of d and nB
			Determination of Time Delay d (First Approximation)
			Determination of the (nA)max and (nB)max
			Initial Choice of nC and nD (Noise Model)
		5.8.2 Direct Order Estimation from Data
	5.9 An Example: Identification of a Flexible Transmission
	5.10 Concluding Remarks
	5.11 Problems
Chapter 6: Adaptive Prediction
	6.1 The Problem
	6.2 Adaptive Prediction-Deterministic Case
		6.2.1 Direct Adaptive Prediction
		6.2.2 Indirect Adaptive Prediction
	6.3 Adaptive Prediction-Stochastic Case
		6.3.1 Direct Adaptive Prediction
		6.3.2 Indirect Adaptive Prediction-Stochastic Case
	6.4 Concluding Remarks
	6.5 Problems
Chapter 7: Digital Control Strategies
	7.1 Introduction
	7.2 Canonical Form for Digital Controllers
	7.3 Pole Placement
		7.3.1 Regulation
			Choice of HR and HS-Examples
		7.3.2 Tracking
		7.3.3 Some Properties of the Pole Placement
			Time-Domain Design
			Alternative Expression of S and R in the Case of Auxiliary Poles
			Predictor Interpretation of the Pole Placement
			Youla-Kucera Parameterization
			Another Time-Domain Interpretation
			Regressor Formulation
		7.3.4 Some Particular Pole Choices
			Internal Model Control (IMC)
			Model Algorithmic Control
	7.4 Tracking and Regulation with Independent Objectives
		7.4.1 Polynomial Design
			Regulation (Computation of R(q-1) and S(q-1))
			Tracking (Computation of T(q-1))
			Controller Equation
		7.4.2 Time Domain Design
			Predictor Interpretation of the Tracking and Regulation with Independent Objectives
			Taking into Account Measurable Disturbances
	7.5 Tracking and Regulation with Weighted Input
	7.6 Minimum Variance Tracking and Regulation
		7.6.1 Design of Minimum Variance Control
			Direct Design
			Use of the Separation Theorem
			Rapprochement with Tracking and Regulation with Independent Objective
			Properties of the Tracking (Regulation) Error
			Rejection of Disturbances
		7.6.2 Generalized Minimum Variance Tracking and Regulation
	7.7 Generalized Predictive Control
		7.7.1 Controller Equation
		7.7.2 Closed-Loop Poles
		7.7.3 Recursive Solutions of the Euclidian Divisions
			Recursive Solution of the Euclidian Division (7.202)
			Recursive Solution of the Euclidian Division (7.204)
	7.8 Linear Quadratic Control
	7.9 Concluding Remarks
	7.10 Problems
Chapter 8: Robust Digital Control Design
	8.1 The Robustness Problem
	8.2 The Sensitivity Functions
	8.3 Robust Stability
		8.3.1 Robustness Margins
			Modulus Margin (DeltaM)
			Delay Margin (Deltatau)
		8.3.2 Model Uncertainties and Robust Stability
		8.3.3 Robustness Margins and Robust Stability
	8.4 Definition of \"Templates\" for the Sensitivity Functions
	8.5 Properties of the Sensitivity Functions
		8.5.1 Output Sensitivity Function
			Design of the Resonant Pole-Zero Filter HSi/PFi
		8.5.2 Input Sensitivity Function
		8.5.3 Noise Sensitivity Function
	8.6 Shaping the Sensitivity Functions
	8.7 Other Design Methods
	8.8 A Design Example: Robust Digital Control of a Flexible Transmission
	8.9 Concluding Remarks
	8.10 Problems
Chapter 9: Recursive Plant Model Identification in Closed Loop
	9.1 The Problem
		9.1.1 The Basic Equations
	9.2 Closed-Loop Output Error Algorithms (CLOE)
		9.2.1 The Closed-Loop Output Error Algorithm (CLOE)
		9.2.2 Filtered Closed-Loop Output Error Algorithm (F-CLOE)
		9.2.3 Extended Closed-Loop Output Error Algorithm (X-CLOE)
	9.3 Filtered Open-Loop Recursive Identification Algorithms (FOL)
		9.3.1 Filtered Recursive Least Squares
		9.3.2 Filtered Output Error
	9.4 Frequency Distribution of the Asymptotic Bias in Closed-Loop Identification
		9.4.1 Filtered Open-Loop Identification Algorithms
		9.4.2 Closed-Loop Output Error Identification Algorithms
	9.5 Validation of Models Identified in Closed-Loop
		9.5.1 Statistical Validation
			Uncorrelation Test
			Whiteness Test
		9.5.2 Pole Closeness Validation
		9.5.3 Time Domain Validation
	9.6 Iterative Identification in Closed-Loop and Controller Redesign
	9.7 Comparative Evaluation of the Various Algorithms
		9.7.1 Simulation Results
		9.7.2 Experimental Results: Identification of a Flexible Transmission in Closed-Loop
	9.8 Iterative Identification in Closed Loop and Controller Redesign Applied to the Flexible Transmission
	9.9 Concluding Remarks
	9.10 Problems
Chapter 10: Robust Parameter Estimation
	10.1 The Problem
	10.2 Input/Output Data Filtering
	10.3 Effect of Disturbances
	10.4 PAA with Dead Zone
	10.5 PAA with Projection
	10.6 Data Normalization
		10.6.1 The Effect of Data Filtering
		10.6.2 Alternative Implementation of Data Normalization
		10.6.3 Combining Data Normalization with Dead Zone
	10.7 A Robust Parameter Estimation Scheme
	10.8 Concluding Remarks
	10.9 Problems
Chapter 11: Direct Adaptive Control
	11.1 Introduction
	11.2 Adaptive Tracking and Regulation with Independent Objectives
		11.2.1 Basic Design
			Analysis
			Alternative Direct Adaptive Control Design via Adaptive Prediction
		11.2.2 Extensions of the Design
			Filtering of the Measurement Vector and of the Adaptation Error
			Taking into Account Measurable Disturbances
	11.3 Adaptive Tracking and Regulation with Weighted Input
	11.4 Adaptive Minimum Variance Tracking and Regulation
		11.4.1 The Basic Algorithms
			Exact Adaptive Minimum Variance Tracking and Regulation
				The case d=0
			Approximate Adaptive Minimum Variance Tracking and Regulation
				The case d=0
				The case d>0
			Adaptive Minimum Variance Regulation
		11.4.2 Asymptotic Convergence Analysis
			Exact Adaptive Minimum Variance Tracking and Regulation
			Approximate Adaptive Minimum Variance Tracking and Regulation
		11.4.3 Martingale Convergence Analysis
	11.5 Robust Direct Adaptive Control
		11.5.1 The Problem
		11.5.2 Direct Adaptive Control with Bounded Disturbances
		11.5.3 Direct Adaptive Control with Unmodeled Dynamics
	11.6 An Example
	11.7 Concluding Remarks
	11.8 Problems
Chapter 12: Indirect Adaptive Control
	12.1 Introduction
	12.2 Adaptive Pole Placement
		12.2.1 The Basic Algorithm
			Step I: Estimation of the Plant Model Parameters
			Step II: Computation of the Controller Parameters and of the Control Law
		12.2.2 Analysis of the Indirect Adaptive Pole Placement
		12.2.3 The \"Singularity\" Problem
			The Modification Algorithm
		12.2.4 Adding External Excitation
	12.3 Robust Indirect Adaptive Control
		12.3.1 Standard Robust Adaptive Pole Placement
			Step I: Estimation of the Plant Model Parameters
			Step II: Computation of the Control Law
		12.3.2 Modified Robust Adaptive Pole Placement
		12.3.3 Robust Adaptive Pole Placement: An Example
	12.4 Adaptive Generalized Predictive Control
	12.5 Adaptive Linear Quadratic Control
	12.6 Adaptive Tracking and Robust Regulation
	12.7 Indirect Adaptive Control Applied to the Flexible Transmission
		12.7.1 Adaptive Pole Placement
		12.7.2 Adaptive PSMR Generalized Predictive Control
	12.8 Concluding Remarks
	12.9 Problems
Chapter 13: Multimodel Adaptive Control with Switching
	13.1 Introduction
	13.2 Principles of Multimodel Adaptive Control with Switching
		13.2.1 Plant with Uncertainty
		13.2.2 Multi-Estimator
		13.2.3 Multi-Controller
		13.2.4 Supervisor
	13.3 Stability Issues
		13.3.1 Stability of Adaptive Control with Switching
		13.3.2 Stability of the Injected System
			Stability with Common Lyapunov Matrix
			Stability by Minimum Dwell-Time
	13.4 Application to the Flexible Transmission System
		13.4.1 Multi-Estimator
		13.4.2 Multi-Controller
		13.4.3 Experimental Results
			Experiment 1
			Experiment 2
			Experiment 3
		13.4.4 Effects of Design Parameters
			Number of Fixed and Adaptive Models
			Parameter Adaptation Algorithm
	13.5 Concluding Remarks
	13.6 Problems
Chapter 14: Adaptive Regulation-Rejection of Unknown Disturbances
	14.1 Introduction
	14.2 Plant Representation and Controller Design
	14.3 Robustness Considerations
	14.4 Direct Adaptive Regulation
	14.5 Stability Analysis
	14.6 Indirect Adaptive Regulation
	14.7 Adaptive Rejection of Multiple Narrow Band Disturbances on an Active Vibration Control System
		14.7.1 The Active Vibration Control System
		14.7.2 Experimental Results
			Plant Identification and Central Controller Design
			Direct Adaptive Regulation Under the Effect of Two Sinusoidal Disturbances
			Comparison Between Direct and Indirect Adaptive Regulation
	14.8 Concluding Remarks
	14.9 Problems
Chapter 15: Adaptive Feedforward Compensation of Disturbances
	15.1 Introduction
	15.2 Basic Equations and Notations
	15.3 Development of the Algorithms
	15.4 Analysis of the Algorithms
		15.4.1 The Deterministic Case-Perfect Matching
		15.4.2 The Stochastic Case-Perfect Matching
		15.4.3 The Case of Non-Perfect Matching
			Boundedness of the Residual Error
			Bias Distribution
		15.4.4 Relaxing the Positive Real Condition
	15.5 Adaptive Attenuation of Broad Band Disturbances on an Active Vibration Control System
		15.5.1 System Identification
		15.5.2 Experimental Results
	15.6 Concluding Remarks
	15.7 Problems
Chapter 16: Practical Aspects
	16.1 Introduction
	16.2 The Digital Control System
		16.2.1 Selection of the Sampling Frequency
		16.2.2 Anti-Aliasing Filters
		16.2.3 Digital Controller
		16.2.4 Effects of the Digital to Analog Converter
		16.2.5 Handling Actuator Saturations (Anti-Windup)
		16.2.6 Manual to Automatic Bumpless Transfer
		16.2.7 Effect of the Computational Delay
		16.2.8 Choice of the Desired Performance
	16.3 The Parameter Adaptation Algorithm
		16.3.1 Scheduling Variable alpha1(t)
		16.3.2 Implementation of the Adaptation Gain Updating-The U-D Factorization
	16.4 Adaptive Control Algorithms
		16.4.1 Control Strategies
		16.4.2 Adaptive Control Algorithms
	16.5 Initialization of Adaptive Control Schemes
	16.6 Monitoring of Adaptive Control Systems
	16.7 Concluding Remarks
Appendix A: Stochastic Processes
Appendix B: Stability
Appendix C: Passive (Hyperstable) Systems
	C.1 Passive (Hyperstable) Systems
	C.2 Passivity-Some Definitions
	C.3 Discrete Linear Time-Invariant Passive Systems
	C.4 Discrete Linear Time-Varying Passive Systems
	C.5 Stability of Feedback Interconnected Systems
	C.6 Hyperstability and Small Gain
Appendix D: Martingales
References
Index