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Fully parameterized fixed‐order controller design for H ∞ loop shaping method using frequency responses—extension to MIMO systems
Author(s) -
Usami Tomohiro,
Yubai Kazuhiro,
Yashiro Daisuke,
Komada Satoshi
Publication year - 2018
Publication title -
electrical engineering in japan
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.136
H-Index - 28
eISSN - 1520-6416
pISSN - 0424-7760
DOI - 10.1002/eej.23110
Subject(s) - control theory (sociology) , robustness (evolution) , weighting , transfer function , parameterized complexity , open loop controller , controller (irrigation) , mimo , multivariable calculus , robust control , frequency response , control system , mathematics , computer science , control engineering , engineering , closed loop , algorithm , control (management) , channel (broadcasting) , artificial intelligence , computer network , chemistry , biology , biochemistry , agronomy , radiology , medicine , electrical engineering , gene
Robust control is often applied to systems with uncertainties and disturbances. Above all, the H ∞ loop shaping method is known to achieve good control performance and robustness. In this method, the final controller consists of weighting functions and a stabilizing controller. The stabilizing controller is derived for the shaped plant to suppress the H ∞ norm of the transfer matrix consisting of a sensitivity function, a complementary sensitivity function, and so on. In addition, the stabilizing controller improves robust stability margin while keeping gain characteristic of the shaped plant if weighting functions are suitable. As a result, the closed‐loop system is well‐balanced between good tracking and robustness. However, a final controller tends to be high‐order. For this problem, reduction techniques are often applied to the final controller. In this case, performance and stability is not always adequately evaluated due to errors by the controller reduction. This paper proposes a fully parameterized fixed‐order controller design method using frequency responses of the plant. We formulate a design problem for multi‐input–multi‐output systems as an optimization problem. Therefore, we can directly design a low‐order controller from frequency responses using the iterative LMI optimization. Accordingly, we can avoid to deteriorate the evaluation of performance and stability.