In writing this monograph my aim has been to present a "geometric" approach to the structural synthesis of multivariable control systems that are linear, time-invariant and of finite dynamic order. The book is addressed to graduate students specializing in control, to engineering scientists engaged in control systems research and development, and to mathemati cians with some previous acquaintance with control problems. The present edition of this book is a revision of the preliminary version, published in 1974 as a Springer-Verlag "Lecture Notes" volume; and some of the remarks to follow are repeated from the original preface. The label "geometric" in the title is applied for several reasons. First and obviously, the setting is linear state space and the mathematics chiefly linear algebra in abstract (geometric) style. The basic ideas are the familiar system concepts of controllability and observability, thought of as geometric properties of distinguished state subspaces. Indeed, the geometry was first brought in out of revulsion against the orgy of matrix manipulation which linear control theory mainly consisted of, not so long ago. But secondly and of greater interest, the geometric setting rather quickly suggested new methods of attacking synthesis which have proved to be intuitive and econo mical; they are also easily reduced to matrix arithmetic as soon as you want to compute.
Reihe
Auflage
Sprache
Verlagsort
Verlagsgruppe
ISBN-13
978-1-4684-0068-7 (9781468400687)
DOI
10.1007/978-1-4684-0068-7
Schweitzer Klassifikation
0 Mathematical Preliminaries.- 0.1 Notation.- 0.2 Linear Spaces.- 0.3 Subspaces.- 0.4 Maps and Matrices.- 0.5 Factor Spaces.- 0.6 Commutative Diagrams.- 0.7 Invariant Subspaces. Induced Maps.- 0.8 Characteristic Polynomial. Spectrum.- 0.9 Polynomial Rings.- 0.10 Rational Canonical Structure.- 0.11 Jordan Decomposition.- 0.12 Dual Spaces.- 0.13 Tensor Product. The Sylvester Map.- 0.14 Inner Product Spaces.- 0.15 Hermitian and Symmetric Maps.- 0.16 Well-Posedness and Genericity.- 0.17 Linear Systems.- 0.18 Transfer Matrices. Signal Flow Graphs.- 0.19 Rouché's Theorem.- 0.20 Exercises.- 0.21 Notes and References.- 1 Introduction to Controllability.- 1.1 Reachability.- 1.2 Controllability.- 1.3 Single-Input Systems.- 1.4 Multi-Input Systems.- 1.5 Controllability is Generic.- 1.6 Exercises.- 1.7 Notes and References.- 2 Controllability, Feedback and Pole Assignment.- 2.1 Controllability and Feedback.- 2.2 Pole Assignment.- 2.3 Incomplete Controllability and Pole Shifting.- 2.4 Stabilizability.- 2.5 Exercises.- 2.6 Notes and References.- 3 Observability and Dynamic Observers.- 3.1 Observability.- 3.2 Unobservable Subspace.- 3.3 Full Order Dynamic Observer.- 3.4 Minimal Order Dynamic Observer.- 3.5 Observers and Pole Shifting.- 3.6 Detectability.- 3.7 Detectors and Pole Shifting.- 3.8 Pole Shifting by Dynamic Compensation.- 3.9 Observer for a Single Linear Functional.- 3.10 Preservation of Observability and Detectability.- 3.11 Exercises.- 3.12 Notes and References.- 4 Disturbance Decoupling and Output Stabilization.- 4.1 Disturbance Decoupling Problem (DDP).- 4.2 (A, B)-Invariant Subspaces.- 4.3 Solution of DDP.- 4.4 Output Stabilization Problem (OSP).- 4.5 Exercises.- 4.6 Notes and References.- 5 Controllability Subspaces.- 5.1 Controllability Subspaces.- 5.2 SpectralAssignability.- 5.3 Controllability Subspace Algorithm.- 5.4 Supremal Controllability Subspace.- 5.5 Transmission Zeros.- 5.6 Disturbance Decoupling with Stability.- 5.7 Controllability Indices.- 5.8 Exercises.- 5.9 Notes and References.- 6 Tracking and Regulation I: Output Regulation.- 6.1 Restricted Regulator Problem (RRP).- 6.2 Solvability of RRP.- 6.3 Extended Regulator Problem (ERP).- 6.4 Example.- 6.5 Concluding Remarks.- 6.6 Exercises.- 6.7 Notes and References.- 7 Tracking and Regulation II: Output Regulation with Internal Stability.- 7.1 Solvability of RPIS: General Considerations.- 7.2 Constructive Solution of RPIS: ??= 0.- 7.3 Constructive Solution of RPIS: ?? Arbitrary.- 7.4 Application: Regulation Against Step Disturbances.- 7.5 Application: Static Decoupling.- 7.6 Example 1: RPIS Unsolvable.- 7.7 Example 2: Servo-Regulator.- 7.8 Exercises.- 7.9 Notes and References.- 8 Tracking and Regulation III: Structurally Stable Synthesis.- 8.1 Preliminaries.- 8.2 Example 1: Structural Stability.- 8.3 Well-Posedness and Genericity.- 8.4 Well-Posedness and Transmission Zeros.- 8.5 Example 2: RPIS Solvable but Ill-Posed.- 8.6 Structurally Stable Synthesis.- 8.7 Example 3: Well-Posed RPIS: Strong Synthesis.- 8.8 The Internal Model Principle.- 8.9 Exercises.- 8.10 Notes and References.- 9 Noninteracting Control I: Basic Principles.- 9.1 Decoupling: Systems Formulation.- 9.2 Restricted Decoupling Problem (RDP).- 9.3 Solution of RDP: Outputs Complete.- 9.4 Extended Decoupling Problem (EDP).- 9.5 Solution of EDP.- 9.6 Naive Extension.- 9.7 Example.- 9.8 Partial Decoupling.- 9.9 Exercises.- 9.10 Notes and References.- 10 Noninteracting Control II: Efficient Compensation.- 10.1 The Radical.- 10.2 Efficient Extension.- 10.3 Efficient Decoupling.- 10.4 Minimal Order Compensation: d(??) = 2.- 10.5 Minimal Order Compensation: d(??) = k.- 10.6 Exercises.- 10.7 Notes and References.- 11 Noninteracting Control III: Generic Solvability.- 11.1 Generic Solvability of EDP.- 11.2 State Space Extension Bounds.- 11.3 Significance of Generic Solvability.- 11.4 Exercises.- 11.5 Notes and References Chapter.- 12 Quadratic Optimization I: Existence and Uniqueness.- 12.1 Quadratic Optimization.- 12.2 Dynamic Programming: Heuristics.- 12.3 Dynamic Programming: Rigor.- 12.4 Matrix Quadratic Equation.- 12.5 Exercises.- 12.6 Notes and References.- 13 Quadratic Optimization II: Dynamic Response.- 13.1 Dynamic Response: Generalities.- 13.2 Example 1: First-Order System.- 13.3 Example 2: Second-Order System.- 13.4 Hamiltonian Matrix.- 13.5 Asymptotic Root Locus: Single Input System.- 13.6 Asymptotic Root Locus: Multivariable System.- 13.7 Upper and Lower Bounds on P0.- 13.8 Stability Margin. Gain Margin.- 13.9 Return Difference Relations.- 13.10 Applicability of Quadratic Optimization.- 13.11 Exercises.- 13.12 Notes and References.- References.- Relational and Operational Symbols.- Letter Symbols.- Synthesis Problems.
