Tzafestas Multivariable Control

New Concepts and Tools
Erscheinungsjahr 2012
ISBN: 978-94-009-6478-5
Verlag: Springer Netherland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 504 Seiten, eBook

The foundation of linear systems theory goes back to Newton and has been followed over the years by many improvements such as linear operator theory, Laplace Transformation etc. After the World War II, feedback control theory has shown a rapid development, and standard elegant analysis and synthesis techniques have been discovered by control system workers, such as root-locus (Evans) and frequency response methods (Nyquist, Bode). These permitted a fast and efficient analysis of simple-loop control systems, but in their original "paper-and-pencil" form were not appropriate for multiple loop high-order systems. The advent of fast digital computers, together with the development of multivariable multi-loop system techniques, have eliminated these difficulties. Multivariable control theory has followed two main avenues; the optimal control approach, and the algebraic and frequency-domain control approach. An important key concept in the whole multivariable system theory is "ob servability and controllability" which revealed the exact relationships between transfer functions and the state variable representations. This has given new insight into the phenomenon of "hidden oscillations" and to the transfer function modelling of dynamic systems. The basic tool in optimal control theory is the celebrated matrix Riccati differential equation which provides the time-varying feedback gains in a linear-quadratic control system cell. Much theory presently exists for the characteristic properties and solution of this Riccati equation.

Zielgruppe

Research

Autoren/Hrsg.

Tzafestas, S.G.

Inhaltsverzeichnis

I General Topics.- 1 Applications of Algebraic Function Theory in Multivariable Control.- 2 The Theory of Polynomial Combinants in the Context of Linear Systems.- 3 The Occurrence of Non-Properness in Closed-Loop Systems and Some Implications.- 4 Skew-Symmetric Matrix Equations in Multivariable Control Theory.- 5 Feedback Controller Parameterizations: Finite Hidden Modes and Causality.- 6 Decompositions for General Multilinear Systems.- 7 Simplification of Models for Stability Analysis of Large-Scale Systems.- II Uncertain Systems and Robust Control.- 8 Representations of Uncertainty and Robustness Tests for Multivariable Feedback Systems.- 9 Additive,Multiplicative Perturbations and the Application of the Characteristic Locus Method.- 10 A Design Technique for Multi-Represented Linear Multi-Variable Discrete-Time Systems Using Diagonal or Full Dynamic Compensators.- 11 Minimizing Conservativeness of Robustness Singular Values.- III Algebraic and Optimal Controller Design.- 12 Frequency Assignment Problems in Linear Multivariable Systems:Exterior Algebra and Algebraic Geometry Methods.- 13 On the Stable Exact Model Matching and Stable Minimal Design Problems.- 14 Pole Placement in Discrete Multivariable Systems by Two and Three-Term Controllers.- 15 Linear Quadratic Regulators with Prescribed Eigenvalues for a Family of Linear Systems.- 16 Sensitivity Reduction of the Linear Quadratic Optimal Regulator.- 17 Design of Low-Order Delayed Measurement Observers for Discrete Time Linear Systems.- 18 Singular Perturbation Method and Reciprocal Transformation on Two-Time Scale Systems.- 19 Coordinated Decentralized Control with Multi-Model Representation (CODECO).- 20 Design of Two-Level Optimal Regulators with Constrained Structures.- IV Multidimensional Systems.- 21 A Canonical State-Space Model for m-Dimensional Discrete Systems.- 22 Eigenvalue Assignment of 3-D Systems.- 23 Feedback Deadbeat Control of 2-Dimensional Systems.- 24 State Observers for 2-D and 3-D Systems.- 25 Eigenvalue-Generalized Eigenvector Assignment Using PID Controller.