Bhattacharyya / Datta / Keel Linear Control Theory

Structure, Robustness, and Optimization
Erscheinungsjahr 2018
ISBN: 978-1-4200-1961-2
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 924 Seiten

Reihe: Automation and Control Engineering

Successfully classroom-tested at the graduate level, Linear Control Theory: Structure, Robustness, and Optimization covers three major areas of control engineering (PID control, robust control, and optimal control). It provides balanced coverage of elegant mathematical theory and useful engineering-oriented results.

The first part of the book develops results relating to the design of PID and first-order controllers for continuous and discrete-time linear systems with possible delays. The second section deals with the robust stability and performance of systems under parametric and unstructured uncertainty. This section describes several elegant and sharp results, such as Kharitonov’s theorem and its extensions, the edge theorem, and the mapping theorem. Focusing on the optimal control of linear systems, the third part discusses the standard theories of the linear quadratic regulator, Hinfinity and l1 optimal control, and associated results.

Written by recognized leaders in the field, this book explains how control theory can be applied to the design of real-world systems. It shows that the techniques of three term controllers, along with the results on robust and optimal control, are invaluable to developing and solving research problems in many areas of engineering.

Zielgruppe

Control systems engineers and students.

Autoren/Hrsg.

Bhattacharyya, Shankar P.

Datta, Aniruddha

Keel, Lee H.

Fachgebiete

• Technische Wissenschaften Elektronik | Nachrichtentechnik Elektronik Überwachungstechnik

Inhaltsverzeichnis

Preface
THREE TERM CONTROLLERS
PID Controllers: An Overview of Classical Theory
Introduction to Control
The Magic of Integral Control
PID Controllers
Classical PID Controller Design
Integrator Windup
PID Controllers for Delay-Free LTI Systems
Introduction
Stabilizing Set
Signature Formulas
Computation of the PID Stabilizing Set
PID Design with Performance Requirements
PID Controllers for Systems with Time Delay
Introduction
Characteristic Equations for Delay Systems
The Padé Approximation and Its Limitations
The Hermite–Biehler Theorem for Quasipolynomials
Stability of Systems with a Single Delay
PID Stabilization of First-Order Systems with Time Delay
PID Stabilization of Arbitrary LTI Systems with a Single Time Delay
Proofs of Lemmas 3.3, 3.4, and 3.5
Proofs of Lemmas 3.7 and 3.9
An Example of Computing the Stabilizing Set
Digital PID Controller Design
Introduction
Preliminaries
Tchebyshev Representation and Root Clustering
Root Counting Formulas
Digital PI, PD, and PID Controllers
Computation of the Stabilizing Set
Stabilization with PID Controllers
First-Order Controllers for LTI Systems
Root Invariant Regions
An Example
Robust Stabilization by First-Order Controllers
Hinfinity Design with First-Order Controllers
First-Order Discrete-Time Controllers
Controller Synthesis Free of Analytical Models
Introduction
Mathematical Preliminaries
Phase, Signature, Poles, Zeros, and Bode Plots
PID Synthesis for Delay-Free Continuous-Time Systems
PID Synthesis for Systems with Delay
PID Synthesis for Performance
An Illustrative Example: PID Synthesis
Model-Free Synthesis for First-Order Controllers
Model-Free Synthesis of First-Order Controllers for Performance
Data-Based Design vs. Model-Based Design
Data-Robust Design via Interval Linear Programming
Computer-Aided Design
Data-Driven Synthesis of Three Term Digital Controllers
Introduction
Notation and Preliminaries
PID Controllers for Discrete-Time Systems
Data-Based Design: Impulse Response Data
First-Order Controllers for Discrete-Time Systems
Computer-Aided Design
ROBUST PARAMETRIC CONTROL
Stability Theory for Polynomials
Introduction
The Boundary Crossing Theorem
The Hermite–Biehler Theorem
Schur Stability Test
Hurwitz Stability Test
Stability of a Line Segment
Introduction
Bounded Phase Conditions
Segment Lemma
Schur Segment Lemma via Tchebyshev Representation
Some Fundamental Phase Relations
Convex Directions
The Vertex Lemma
Stability Margin Computation
Introduction
The Parametric Stability Margin
Stability Margin Computation
The Mapping Theorem
Stability Margins of Multilinear Interval Systems
Robust Stability of Interval Matrices
Robustness Using a Lyapunov Approach
Stability of a Polytope
Introduction
Stability of Polytopic Families
The Edge Theorem
Stability of Interval Polynomials
Stability of Interval Systems
Polynomic Interval Families
Robust Control Design
Introduction
Interval Control Systems
Frequency Domain Properties
Nyquist, Bode, and Nichols Envelopes
Extremal Stability Margins
Robust Parametric Classical Design
Robustness under Mixed Perturbations
Robust Small Gain Theorem
Robust Performance
The Absolute Stability Problem
Characterization of the SPR Property
The Robust Absolute Stability Problem
OPTIMAL AND ROBUST CONTROL
The Linear Quadratic Regulator
An Optimal Control Problem
The Finite Time LQR Problem
The Infinite Horizon LQR Problem
Solution of the Algebraic Riccati Equation
The LQR as an Output Zeroing Problem
Return Difference Relations
Guaranteed Stability Margins for the LQR
Eigenvalues of the Optimal Closed Loop System
Optimal Dynamic Compensators
Servomechanisms and Regulators
SISO Hinfinity AND l1 OPTIMAL CONTROL
Introduction
The Small Gain Theorem
L Stability and Robustness via the Small Gain Theorem
YJBK Parametrization of All Stabilizing Compensators (Scalar Case)
Control Problems in the Hinfinity Framework
Hinfinity Optimal Control: SISO Case
l1 Optimal Control: SISO Case
Hinfinity Optimal Multivariable Control
Hinfinity Optimal Control Using Hankel Theory
The State Space Solution of Hinfinity Optimal Control
Appendix A: Signal Spaces
Vector Spaces and Norms
Metric Spaces
Equivalent Norms and Convergence
Relations between Normed Spaces
Appendix B: Norms for Linear Systems
Induced Norms for Linear Maps
Properties of Fourier and Laplace Transforms
Lp/lp Norms of Convolutions of Signals
Induced Norms of Convolution Maps
EPILOGUE
Robustness and Fragility
Feedback, Robustness, and Fragility
Examples
Discussion
References
Index
Exercises, Notes, and References appear at the end of each chapter.