Adaptive Control

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 Interconnected Systems.- Hyperstability and Small Gain.- Martingales.