Optimal Control: Linear Quadratic Methods

Overview


This augmented edition of a respected text teaches the reader how to use linear quadratic Gaussian methods effectively for the design of control systems. It explores linear optimal control theory from an engineering viewpoint, with step-by-step explanations that show clearly how to make practical use of the material.
The three-part treatment begins with the basic theory of the linear regulator/tracker for time-invariant and time-varying systems. The ...
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Optimal Control: Linear Quadratic Methods

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Overview


This augmented edition of a respected text teaches the reader how to use linear quadratic Gaussian methods effectively for the design of control systems. It explores linear optimal control theory from an engineering viewpoint, with step-by-step explanations that show clearly how to make practical use of the material.
The three-part treatment begins with the basic theory of the linear regulator/tracker for time-invariant and time-varying systems. The Hamilton-Jacobi equation is introduced using the Principle of Optimality, and the infinite-time problem is considered. The second part outlines the engineering properties of the regulator. Topics include degree of stability, phase and gain margin, tolerance of time delay, effect of nonlinearities, asymptotic properties, and various sensitivity problems. The third section explores state estimation and robust controller design using state-estimate feedback.
Numerous examples emphasize the issues related to consistent and accurate system design. Key topics include loop-recovery techniques, frequency shaping, and controller reduction, for both scalar and multivariable systems. Self-contained appendixes cover matrix theory, linear systems, the Pontryagin minimum principle, Lyapunov stability, and the Riccati equation. Newly added to this Dover edition is a complete solutions manual for the problems appearing at the conclusion of each section.
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Product Details

  • ISBN-13: 9780486457666
  • Publisher: Dover Publications
  • Publication date: 2/27/2007
  • Series: Dover Books on Engineering Series
  • Pages: 464
  • Product dimensions: 6.10 (w) x 9.10 (h) x 1.00 (d)

Table of Contents


Preface     ix
Basic Theory of the Optimal Regulator
Introduction     1
Linear Optimal Control     1
About This Book in Particular     4
Part and Chapter Outline     5
The Standard Regulator Problem-I     7
A Review of the Regulator Problem     7
The Hamilton-Jacobi Equation     12
Solution of the Finite-Time Regulator Problem     20
Discrete Time Systems     28
The Standard Regulator Problem-II     35
The Infinite-Time Regulator Problem     35
Stability of the Time-Invariant Regulator     45
Summary and Discussion of the Regulator Problem Results     51
Cross-Product Terms and Second Variation Theory     56
Regulator with a Prescribed Degree of Stability     60
Tracking Systems     68
The Problem of Achieving a Desired Trajectory     68
Finite-Time Results     71
Infinite-Time Results     84
A Practical Design Example     95
Properties and Application of the Optimal Regulator
Properties of Regulator Systems with a Classical Control Interpretation     101
The Regulator from an Engineering Viewpoint     101
Return Difference Equality and RelatedFormulas     104
Some Classical Control Ideas: Sensitivity, Complementary Sensitivity, and Robustness     110
Gain Margin, Phase Margin, and Time-Delay Tolerance     116
Insertion of Nonlinearities     127
The Inverse Optimal Control Problem     131
Return Difference Equality for Discrete-Time Regulators     134
Asymptotic Properties and Quadratic Weight Selection     139
Single Input Systems     139
Multivariable Systems     148
Further Issues in Q, R Selection     156
State Estimator Design     164
The Nature of the State Estimation Problem     164
Deterministic Estimator Design     168
Statistical Estimator Design (The Kalman-Bucy Filter)     178
System Design Using State Estimators     207
Controller Design-Basic Versions and Variations     207
The Separation Theorem and Performance Calculation     218
Loss of Passband Robustness with Observers     228
Loop Recovery     236
Robustness Improvement via Residual Feedback     251
Frequency Shaping     262
Blending Classical and Linear Quadratic Methods     262
State Estimate Feedback with Frequency Shaping      268
Proportional Plus Integral State Feedback     272
Proportional Plus Integral State Estimate Feedback     282
Controller Reduction     289
Introduction: Selection of Frequency Weighting     289
Frequency-Weighted Balanced Truncation     294
Approaches to Controller Reduction via Fractional Representations     304
Direct Design of Low-Order Controllers     317
Digital Controllers     323
Controller Implementation     323
Sampling Time Selection     325
Anti-Aliasing Analog Prefilter     328
The Discrete-Time Transfer Function     330
State-Variable Implementation of the Discrete-Time Transfer Function     334
Appendices     336
Brief Review of Some Results of Matrix Theory     336
Brief Review of Some Major Results of Linear System Theory     353
The Pontryagin Minimum Principle and Linear Optimal Control     363
Lyapunov Stability     367
The Riccati Equation     370
Author Index     375
Subject Index     377
Solutions     381
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