Optimal Sampled-Data Control Systems

Among the many techniques for designing linear multivariable analogue controllers, the two most popular optimal ones are H2 and H-infinity optimization. The fact that most new industrial controllers are digital provides strong motivation for adapting or extending these techniques to digital control systems. This book, now available as a corrected reprint, attempts to do so. Part I presents two indirect methods of sampled-data controller design: These approaches include approximations to a real problem, which involves an analogue plant, continuous-time performance specifications, and a sampled-data controller. Part II proposes a direct attack in the continuous-time domain, where sampled-data systems are time-varying. The findings are presented in forms that can readily be programmed in, e.g., MATLAB.

Contenu

1 Introduction.- 1.1 Sampled-Data Systems.- 1.2 Approaches to SD Controller Design.- 1.3 Notation.- Exercises.- Notes and References.- 1 Indirect Design Methods.- 2 Overview of Continuous-Time H2- and H?-Optimal Control.- 2.1 Norms for Signals and Systems.- 2.2 H2-Optimal Control.- 2.3 H?-Optimal Control.- Notes and References.- 3 Discretization.- 3.1 Step-Invariant Transformation.- 3.2 Effect of Sampling.- 3.3 Step-Invariant Transformation Continued.- 3.4 Bilinear Transformation.- 3.5 Discretization Error.- Exercises.- Notes and References.- 4 Discrete-Time Systems: Basic Concepts.- 4.1 Time-Domain Models.- 4.2 Frequency-Domain Models.- 4.3 Norms.- 4.4 Multivariable Systems.- 4.5 Function Spaces.- 4.6 Optimal Discretization of Analog Systems.- Exercises.- Notes and References.- 5 Discrete-Time Feedback Systems.- 5.1 Connecting Subsystems.- 5.2 Observer-Based Controllers.- 5.3 Stabilization.- 5.4 All Stabilizing Controllers.- 5.5 Step Tracking.- Exercises.- Notes and References.- 6 Discrete-Time H2-Optimal Control.- 6.1 The LQR Problem.- 6.2 Symplectic Pair and Generalized Eigenproblem.- 6.3 Symplectic Pair and Riccati Equation.- 6.4 State Feedback and Disturbance Feedforward.- 6.5 Output Feedback.- 6.6 H2-Optimal Step Tracking.- 6.7 Transfer Function Approach.- Exercises.- Notes and References.- 7 Introduction to Discrete-Time H?-Optimal Control.- 7.1 Computing the H?-Norm.- 7.2 Discrete-Time H?-Optimization by Bilinear Transformation..- Exercises.- Notes and References.- 8 Fast Discretization of SD Feedback Systems.- 8.1 Lifting Discrete-Time Signals.- 8.2 Lifting Discrete-Time Systems.- 8.3 Fast Discretization of a SD System.- 8.4 Design Examples.- 8.5 Simulation of SD Systems.- Exercises.- Notes and References.- II Direct SD Design.- 9 Properties of S and H.- 9.1 Review of Input-Output Stability of LTI Systems.- 9.2 M. Riesz Convexity Theorem.- 9.3 Boundedness of S and H.- 9.4 Performance Recovery.- Exercises.- Notes and References.- 10 Continuous Lifting.- 10.1 Lifting Continuous-Time Signals.- 10.2 Lifting Open-Loop Systems.- 10.3 Lifting SD Feedback Systems.- 10.4 Adjoint Operators.- 10.5 The Norm of SG.- 10.6 The Norm of GH.- 10.7 Analysis of Sensor Noise Effect.- Exercises.- Notes and References.- 11 Stability and Tracking in SD Systems.- 11.1 Internal Stability.- 11.2 Input-Output Stability.- 11.3 Robust Stability.- 11.4 Step Tracking.- 11.5 Digital Implementation and Step Tracking.- 11.6 Tracking Other Signals.- Exercises.- Notes and References.- 12 H2-Optimal SD Control.- 12.1 A Simple ?2 SD Problem.- 12.2 Generalized ?2 Measure for Periodic Systems.- 12.3 Generalized ?2 SD Problem.- 12.4 Examples.- Exercises.- Notes and References.- 13 H?-Optimal SD Control.- 13.1 Frequency Response.- 13.2 H?-Norm in the Frequency Domain.- 13.3 H?-Norm Characterization.- 13.4 H? Discretization of SD Systems.- 13.5 Computing the L2(0,h)-Induced Norm.- 13.6 Computing the Matrices in G eq,d.- 13.7 H? SD Analysis.- 13.8 H? SD Synthesis.- Exercises.- Notes and References.- A State Models.