Adaptive Control

Adaptive Control provides techniques for automatic, real-time adjustments in controller parameters with a view to achieving and/or maintaining a desirable level of system performance in the presence of unknown or variable process parameters.

Many aspects of the field are dealt with in coherent and orderly fashion, starting with the problems posed by system uncertainties and moving on to the presentation of solutions and their practical significance. Within the general context of recent developments, the book looks at:

. synthesis and analysis of parameter adaptation algorithms;

. recursive plant-model identification in open and closed loop;

. robust digital control for adaptive control;

. direct and indirect adaptive control; and

. practical aspects and applications.

To reflect the importance of digital computers for the application of adaptive control techniques, discrete-time aspects are emphasized. To guide the reader, the book contains various applications of adaptive control techniques.

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Contenu

to Adaptive Control.- Adaptive Control - Why?.- Adaptive Control Versus Conventional Feedback Control.- Basic Adaptive Control Schemes.- Examples.- Open Loop Adaptive Control of Deposited Zinc in Hot-Dip Galvanising.- Direct Adaptive Control of a Phosphate Drying Furnace.- Indirect Adaptive Control of a Flexible Transmission.- A Brief Historical Note.- Concluding Remarks.- Discrete Time System Models for Control.- Deterministic Environment.- Input-Output Difference Operator Models.- Predictor Form for Deterministic SISO Models.- Stochastic Environment.- Input-Output Models.- Predictors for ARMAX Input-Output Models.- Predictors for Output Error Model Structure.- Concluding Remarks.- Problems.- Parameter Adaptation Algorithms - Deterministic Environment.- The Problem.- PAA - Examples.- Gradient Algorithm.- Recursive Least Squares Algorithm.- Choice of the Adaptation Gain.- Recursive Least Squares and Kaiman Filter.- Some Remarks on the Parameter Adaptation Algorithms.- Stability of Parameter Adaptation Algorithms.- Equivalent Feedback Representation of the Parameter Adaptation Algorithms and the Stability Problem.- Stability Approach for the Synthesis of PAA using the Equivalent Feedback Representation.- Positive Real PAA Structures.- Parameter Adaptation Algorithms with Time-Varying Adaptation Gain.- Removing the Positive Real Condition.- Parametric Convergence.- The Problem.- Persistently Exciting Signals.- Parametric Convergence Condition.- Concluding Remarks.- Problems.- Parameter Adaptation Algorithms - Stochastic Environment.- Effect of Stochastic Disturbances.- The Averaging Method.- The Martingale Approach.- The Frequency Domain Approach.- Concluding Remarks.- Problems.- Recursive Plant Model Identification in Open Loop.- Recursive Identification in the Context of System Identification.- Structure of Recursive Parameter Estimation Algorithms.- Identification Methods (Type I).- Recursive Least Squares.- Extended Least Squares.- Output Error with Extended Prediction Model.- Recursive Maximum Likelihood.- Generalized Least Squares.- Validation of the Models Identified with Type I Methods.- Identification Methods (Type II).- Output Error with Fixed Compensator.- Output Error with Adjustable Compensator.- Filtered Output Error.- Instrumental Variable with Auxiliary Model.- Validation of the Models Identified with Type II Methods.- Selection of the Pseudo Random Binary Sequence.- Pseudo Random Binary Sequences.- Model Order Selection.- A Practical Approach for Model Order Selection.- Direct Order Estimation from Data.- An Example: Identification of a Flexible Transmission.- Concluding Remarks.- Problems.- Adaptive Prediction.- The Problem.- Adaptive Prediction - Deterministic Case.- Direct Adaptive Prediction.- Indirect Adaptive Prediction.- Adaptive Prediction - Stochastic Case.- Direct Adaptive Prediction.- Indirect Adaptive Prediction - Stochastic Case.- Concluding Remarks.- Problems.- Digital Control Strategies.- Canonical Form for Digital Controllers.- Pole Placement.- Regulation.- Tracking.- Some Properties of the Pole Placement.- Some Particular Pole Choices.- Tracking and Regulation with Independent Objectives.- Polynomial Design.- Time Domain Design.- Tracking and Regulation with Weighted Input.- Minimum Variance Tracking and Regulation.- Design of Minimum Variance Control.- Generalized Minimum Variance Control.- Generalized Predictive Control.- Linear Quadratic Control.- Concluding Remarks.- Problems.- Robust Digital Control Design.- The Robustness Problem.- The Sensitivity Functions.- Robust Stability.- Robustness Margins.- Model Uncertainties and Robust Stability.- Robustness Margins and Robust Stability.- Definition of "Templates" for the Sensitivity Functions.- Properties of the Sensitivity Functions.- Output Sensitivity Function.- Input Sensitivity Function.- Noise Sensitivity Function.- Shaping the Sensitivity Functions.- The Iterative Method.- Other Design Methods.- Example: Robust Digital Control of a Flexible Transmission.- Concluding Remarks.- Problems.- Recursive Plant Model Identification in Closed Loop.- The Problem.- Closed Loop Output Error Algorithms.- Closed Loop Output Error Algorithm.- Filtered Closed Loop Output Error Algorithm.- Extended Closed Loop Output Error Algorithm.- Filtered Open Loop Recursive Identification Algorithms.- Filtered Recursive Least Squares.- Filtered Output Error.- Frequency Distribution of the Asymptotic Bias in Closed Loop Identification.- Filtered Open Loop Identification Algorithms.- Closed Loop Output Error Identification Algorithms.- Validation of Models Identified in Closed Loop.- Statistical Validation.- Pole Closeness Validation.- Time Domain Validation.- Comparative Evaluation of the Various Algorithms.- Simulation Results.- Closed Loop Identification of a Flexible Transmission.- Concluding Remarks.- Problems.- Robust Parameter Estimation.- The Problem.- Input/Output Data Filtering.- Effect of Disturbances.- PAA with Dead Zone.- PAA with Projection.- Data Normalization.- A Robust Parameter Estimation Scheme.- Concluding Remarks.- Problems.- Direct Adaptive Control.- Adaptive Tracking and Regulation with Independent Objectives.- Basic Design.- Extensions of the Design.- Adaptive Tracking and Regulation with Weighted Input.- Adaptive Minimum Variance Tracking and Regulation.- The Basic Algorithms.- Asymptotic Convergence Analysis.- Martingale Convergence Analysis.- Adaptive Generalized Minimum Variance Control.- Robust Direct Adaptive Control.- The Problem.- Direct Adaptive Control with Bounded Disturbances.- Direct Adaptive Control with Unmodelled Dynamics.- An example.- Concluding Remarks.- Problems.- Indirect Adaptive Control.- Adaptive Pole Placement.- The basic Algorithm.- Analysis of the Indirect Adaptive Pole Placement.- The "Singularity" Problem.- Adding External Excitation.- Robust Indirect Adaptive Control.- Standard Robust Adaptive Pole Placement.- Modified Robust Adaptive Pole Placement.- Adaptive Generalized Predictive Control.- Adaptive Linear Quadratic Control.- Iterative Identification in Closed Loop and Controller Redesign.- An Example.- Concluding Remarks.- Practical Aspects and Applications.- The Digital Control System.- The Parameter Adaptation Algorithm.- Adaptive Control Algorithms.- Initialization of Adaptive Control Schemes.- Supervision.- Iterative Identification in Closed Loop and Controller Redesign.- Adaptive Tracking and Robust Regulation.- Indirect Adaptive Control.- Adaptive Pole Placement.- Adaptive PSMR generalized predictive control.- Concluding Remarks.- A Perspective View and Further Reading.- Stochastic Processes.- Stability.- Passive (Hyperstable) Systems.- Passive (Hyperstable) Systems.- Passivity - Some Definitions.- Discrete Linear Time-Invariant Passive Systems.- Discrete Linear Time-Varying Passive Systems.- Stability of Feedback Intercon…