Open AccessSynthesis of low‐coefficient sensitivity controllers with respect to multiplicative controller coefficient variations
Author(s) -
Guo XiangGui,
Gao Qiang,
Xu Zhe
Publication year - 2015
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2014.0272
Subject(s) - control theory (sociology) , multiplicative function , sensitivity (control systems) , mathematics , transfer function , norm (philosophy) , controller (irrigation) , mathematical optimization , computer science , mathematical analysis , engineering , control (management) , agronomy , electrical engineering , artificial intelligence , electronic engineering , law , political science , biology
In this study, a set of optimal state‐space descriptions with minimum H ∞ ‐sensitivity to multiplicative controller coefficient variations and a desirable disturbance attenuation level is synthesised for discrete‐time linear systems. The first aim is to present a new strategy to evaluate the H ∞ ‐sensitivity of the transfer function to multiplicative controller coefficient variations. The H ∞ norm of the sum of coefficient sensitivity functions is regarded as an H ∞ ‐sensitivity measure. The second contribution is to present less conservative conditions to design low‐sensitivity controllers via minimisation of the H ∞ ‐sensitivity measure. In addition, a linear matrix inequality‐based algorithm is developed to obtain the controller gain matrices. Finally, two numerical examples which demonstrate the effectiveness and advantages of the proposed method are presented.