Design of the low-order controllers by the \(H_{\infty }\) criterion: a parametric approach. (English. Russian original) Zbl 1125.93343

Gryazina, E. N.; Polyak, B. T.; Tremba, A. A.

Autom. Remote Control 68, No. 3, 456-466 (2007); translation from Avtom. Telemekh. 68, No. 3, 94-105 (2007).

Summary: Consideration was given to the problem of describing all stabilizing controllers of a given structure (for example, the PID-controllers) satisfying the \(H_{\infty }\) criterion. Controllers of a certain family were defined by the parameters \(k\), and in the parameter space a domain corresponding to the desired criteria was specified. Two approaches were proposed where (i) the desired domain is represented as an intersection of the admissible sets or (ii) its boundary is determined analytically. The two-parameter case is of special importance because it allows one to make use of the graphical mathematics.

MSC:

93B36	\(H^\infty\)-control
93D99	Stability of control systems
93B51	Design techniques (robust design, computer-aided design, etc.)

Keywords:

stabilizing controllers; controller design; fixed order of controllers

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