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Low‐order H ∞ controller design on the frequency domain by partial optimization
Author(s) -
Saeki Masami,
Ogawa Masashi,
Wada Nobutaka
Publication year - 2010
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1434
Subject(s) - multivariable calculus , control theory (sociology) , pid controller , monotonic function , frequency domain , norm (philosophy) , controller (irrigation) , mathematics , linear matrix inequality , sequence (biology) , mathematical optimization , computer science , control (management) , engineering , control engineering , temperature control , mathematical analysis , agronomy , genetics , artificial intelligence , law , political science , biology
In this paper, an optimization method of low‐order multivariable controllers for H ∞ control is proposed. Starting from a low‐order stabilizing controller, our method gives a sequence of controllers for which the H ∞ norm performance index is monotonically non‐increasing by tuning the numerator coefficient matrices of the low‐order controller. This controller class includes multivariable PID controllers. The proposed method is a descent method where the feasible direction is calculated by solving a linear matrix inequality that represents a sufficient condition for the H ∞ criterion for each frequency. Usefulness is shown by two numerical examples. Copyright © 2009 John Wiley & Sons, Ltd.