This book introduces the reader to a novel method of mathematical description, analysis and design of digital control systems, which makes it possible to take into account, in the most complete form, specific features of interaction between continuous-time and discrete time processes.

Inhalt

I Operational transformations of functions of continuous and discrete arguments.- 1 Bilateral Laplace transforms.- 2 Operational transformations for discrete-time functions.- 3 Displaced pulse frequency response.- 4 Discrete LT for functions of a continuous argument.- II Linear periodic operators and systems.- 5 Linear time-invariant operators and systems.- 6 Linear periodic operators and systems.- 7 Analysis of linear periodic operators and systems.- 8 Stochastic analysis and H2-norm of LPO.- III Mathematical description of sampled-data systems in continuous time.- 9 Open-loop SD systems.- 10 Open-loop systems with a computer.- 11 Closed-loop systems with a single sampling unit.- 12 Systems with several sampling units.- IV Analysis of SD systems in continuous time.- 13 Open-loop systems under deterministic disturbances.- 14 Analysis of deterministic feedback SD systems.- 15 Analysis of SD systems under stochastic disturbances.- V Direct synthesis of SD systems.- 16 Quadratic optimization of open-loop SD systems.- 17 Direct design of feedback SD systems.- 18 Direct polynomial-design methods.- Appendices.- A Rational periodic functions.- A.1 Basic definitions.- A.2 Causal and limited rational periodic functions.- A.3 Zeros and poles of rational periodic functions.- A.4 Partial fraction expansion of limited rational periodic functions.- A.5 Boundedness of rational periodic functions.- A.6 Calculating integrals from rational periodic functions.- A.7 Integration of products of rational periodic functions.- A.8 Calculation of parameter integrals.- B DirectSD - a toolbox for direct design of SD systems.- B.1 Introduction.- B.2 Theoretical basis.- B. System description.- B.4 Optimal control under stochastic disturbances.- B.4.1 Optimal digital filtering.- B.5 Design of optimal tracking systems.- B.5.1 One degree of freedom systems.- B.5.2 Systems with two controllers.- B.6 Other possibilities.- B.6.1 Analysis of SD systems in continuous time.- B.6.3 Demonstration programs.- B.7 Numerical examples.- B.7.1 Design of optimal stabilizing system.- B.7.2 Redesign problem.- B.8 Conclusions.