Synthesis Methodology for Discrete MIMO PID Controller with Loop Shaping on LTV Plant Model via Iterated LMI Restrictions

Artem E. Konkov () and Yuri V. Mitrishkin
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Artem E. Konkov: Faculty of Physics, Lomonosov Moscow State University, 119991 Moscow, Russia
Yuri V. Mitrishkin: Faculty of Physics, Lomonosov Moscow State University, 119991 Moscow, Russia

Mathematics, 2024, vol. 12, issue 6, 1-38

Abstract: This paper presents a methodology for synthesizing discrete MIMO PID controllers through iterative solutions of LMIs. It justifies the necessity of direct synthesis of discrete controllers in digital control systems. The proposed methodology allows for synthesizing an LTI controller for an LTV plant model, ensuring the robust stability of the synthesized system. Robustness is further ensured by the small-gain theorem and a novel approach to loop shaping, enabling the use of arbitrary shape functions. As a result, this methodology provides a broad statement of the problem with performance criteria necessary for practical application in control systems. Numerical examples are used to illustrate the methodology, which is implemented using the MATLAB toolbox, freely available for use.

Keywords: discrete time; MIMO PID; LTV; PLV; loop shaping; LMI; convex-concave procedure (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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