Sampled-Data Control Systems

The first German edition of this book appeared in 1972, and in Polish translation in 1976. It covered the analysis and synthesis of sampled-data systems. The second German edition of 1983 ex tended the scope to design, in particular design for robustness of control system properties with respect to uncertainty of plant parameters. This book is a revised translation of the second Ger man edition. The revisions concern primarily a new treatment of the finite effect sequences and the use of nice numerical proper ties of Hessenberg forms. The introduction describes examples of sampled-data systems, in particular digital controllers, and analyzes the sampler and hold; also some design aspects are introduced. Chapter 2 reviews the modelling and analysis of continuous systems. Pole shifting is formulated as an affine mapping, here some n~w material on fixing some eigenvalues or some gains in a design step is included. Chapter 3 treats the analysis of sampled-data systems by state space and z-transform methods. This includes sections on inter sampling behavior, time-delay systems, absolute stability and non synchronous sampling. Chapter 4 treats controllability and reach ability of discrete-time systems, controllability regions for con strained inputs and the choice of the sampling interval primarily under controllability aspects. Chapter 5 deals with observability and constructability both from the discrete and continuous plant output. Full and reduced order observers are treated as well as disturbance observers.

Inhalt

1. Introduction.- 1.1 Sampling, Sampled-Data Controllers.- 1.2 Sampled-Data Systems.- 1.3 Design Problems for Sampled-Data Loops.- 1.4 Exercises.- 2. Continuous Systems.- 2.1 Modelling, Linearization.- 2.2 Basis of the State Space.- 2.3 System Properties.- 2.4 Solutions of the Differential Equation.- 2.5 Specifications.- 2.6 Pole Shifting.- 2.7 Exercises.- 3. Modelling and Analysis of Sampled-Data Systems.- 3.1 Discretization of the Plant.- 3.2 Homogeneous Solutions: Eigenvalues, Solution Sequences.- 3.3 Inhomogeneous Solutions: z-Transfer Function, Impulse and Step Responses.- 3.4 Discrete Controller and Control Loop.- 3.5 Root Locus Plots and Pole Specifications in the z-Plane.- 3.6. Time Domain Solutions and Specifications.- 3.7 Behavior Between the Sampling Instants.- 3.8 Time-Delay Systems.- 3.9 Frequency Response Methods.- 3.10 Special Sampling Problems.- 3.11 Exercises.- 4. Controllability, Choice of Sampling Period and Pole Assignment.- 4.1 Controllability and Reachability.- 4.2 Controllability Regions for Constrained Inputs.- 4.3 Choice of the Sampling Interval.- 4.4 Pole Assignment.- 4.5 Exercises.- 5. Observability and Observers.- 5.1 Observability and Constructability.- 5.2 The Observer of Order n.- 5.3 The Reduced Order Observer.- 5.4 Choice of the Observer Poles.- 5.5 Disturbance Observer.- 5.6 Exercises.- 6. Control Loop Synthesis.- 6.1 Design Methodology.- 6.2 Controller Structures.- 6.3 Separation.- 6.4 Construction of a Linear Function of the States.- 6.5 Synthesis by Polynomial Equations.- 6.6 Pole-Zero-Cancellations.- 6.7 Closed-loop Transfer Function and Prefilter.- 6.8 Disturbance Compensation.- 6.9 Exercises.- 7. Geometric Stability Investigation and Pole Region Assignment.- 7.1 Stability.- 7.2 Stability Region in P Space.- 7.3 Barycentric Coordinates, Bilinear Transformation.- 7.4 ?-Stability.- 7.5 Pole-Region Assignment.- 7.6 Graphic Representation in Two-dimensional Cross Sections.- 7.7 Exercises.- 8. Design of Robust Control Systems.- 8.1 Robustness Problems.- 8.2 Structural Assumptions and Existence of Robust Controllers.- 8.3 Simultaneous Pole Region Assignment.- 8.4 Selection of a Controller from the Admissible Solution Set.- 8.5 Stabilization of the Short-period Longitudinal Mode of an F4-E with Canards.- 8.6 Design by Optimization of a Vector Performance Criterion.- 8.7 Exercises.- 9. Multivariable Systems.- 9.1 Controllability and Observability Structure.- 9.2 Finite Effect Sequences (FESs).- 9.3 FES Assignment.- 9.4 Quadratic Optimal Control.- 9.5 Exercises.- Appendix A Canonical Forms and Further Results from Matrix Theory.- A.1 Linear Transformations.- A. 2 Diagonal and Jordan Forms.- A. 3 Frobenius Forms.- A.3.1 Controllability-Canonical Form.- A.3.2 Feedback-Canonical Form.- A.3.3 Observability-Canonical Form.- A.3.4 Observer-Canonical Form.- A.4 Multivariable Canonical Forms.- A. 4.1 General Remarks.- A.4.2 Luenberger Feedback-Canonical Form.- A. 4.3 Brunovsky Canonical Form.- A.5 Computational Aspects.- A.5.1 Elementary Transformations to Hessenberg Form.- A. 5. 2 HN Form.- A.6 Sensor Coordinates.- A.7 Further results from Matrix Theory.- A. 7.1 Notations.- A.7.2 Vector Operations.- A.7.3 Determinant of a Matrix.- A. 7.4 Trace of a Matrix.- A. 7.5 Rank of a Matrix.- A. 7.6 Inverse Matrix.- A. 7.7 Eigenvalues of a Matrix.- A.7.8 Resolvent of a Matrix.- A.7.9 Orbit and Controllability of (A, b).- A.7.10 Eigenvalue Assignment.- A. 7.11 Functions of a Matrix.- Appendix B The z-Transform.- B.1 Notation and Assumptions.- B.2 Linearity.- B.3 Right Shifting Theorem.- B.4 Left Shifting Theorem.- B. 5Damping Theorem.- B.6 Differentation Theorem.- B.7 Initial Value Theorem.- B.8 Final Value Theorem.- B.9 The Inverse z-Transform.- B.10 Real Convolution Theorem.- B.11 Complex Convolution Theorem, Parseval Equation.- B.12 Other Representations of Sampled Signals in Time and Frequency Domain.- B.13 Table of Laplace and z-Transforms.- Appendix C Stability Criteria.- C.1 Bilinear Transformation to a Hurwitz Problem.- C.2 Schur-Cohn Criterium and its Reduced Forms.- C.3 Necessary Stability Conditions.- C.4 Sufficient Stability Conditions.- Appendix D Application Examples.- D.1 Aircraft Stabilization.- D.2 Track-Guided Bus.- Literature.