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PID control for multivariable processes. (English) Zbl 1181.93004

Lecture Notes in Control and Information Sciences 373. Berlin: Springer (ISBN 978-3-540-78481-4/pbk). xii, 264 p. (2008).
In the monograph PID Control algorithms for finite-dimensional, linear, continuous-time dynamical systems are studied. Mathematical models of such systems both using differential state equations and matrix transfer functions are presented and discussed. Next, PID control formulas are introduced and analysed. Special cases as P, PI and PD control algorithms are discussed and compared. The procedures for optimal control algorithms in closed-loop control systems are proposed and verified using numerical methods. Different types of feedback gains are proposed and compared using algebraic and optimization methods. For example static feedback with point delays is also considered. Design methods for multivariable PID control using Linear Matrix Inequality (LMI) approach are also presented and suboptimal control problems are solved. Pole placement problems are also stated and practically solved using algebraic methods. In the last chapter multivariable process identification is studied. Integral identification method is proposed both for single input – single output control systems with time delay and for multi input – multi output systems with multiple point delays in control variables. Finally, it should be pointed out, that the monograph contains many remarks and fruitful comments on PID control problems for linear systems. Moreover, it contains relationships to the similar results existing in the literature. The list of references has 229 positions, mainly published in the few last years. Summarizing the presented monograph contains comprehensive and detailed treatment of PID control for multivariable, continuous-time, finite-dimensional dynamical systems with constant coefficients. Both decentralized and centralized forms of PID controllers are discussed. Illustrative examples of different complexity are also presented.

MSC:

93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory
93A30 Mathematical modelling of systems (MSC2010)
93B10 Canonical structure
93B30 System identification
93B50 Synthesis problems
93B51 Design techniques (robust design, computer-aided design, etc.)
93B52 Feedback control
93B55 Pole and zero placement problems
93C35 Multivariable systems, multidimensional control systems
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