Robust Gain-Scheduled PID Control: A Parameter Dependent BMI Solution

Cybernetics and Information Technologies

Wu Jin¹  Ma Songhui²  Shao Pengyuan³ 

[1] Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Hong Kong, China;Northwetern Polytechnical University, Xi’an, China;School of Aircraft, Xi’an Aeronautical University, Xi’an, China;

关键词: robust control;    gain scheduling;    proportional-integration-derivative (pid) control;    bilinear-matrix-inequality (bmi);    linear-matrix-inequality (lmi);    linear-parameter-varying (lpv) system;   

DOI  :  10.2478/cait-2020-0011

来源: DOAJ

【 摘 要 】

In control practices, problems of parametric or time-varying uncertainties must be dealt with. Robust control based on norm theory and convex and non-convex optimization algorithms is a powerful tool to solve these problems in theory, but it is employed rarely in applications. In most engineering cases, Proportional-Integration-Derivative (PID) control is still the most popular method for its easy-to-tune and controllable properties. The control method proposed in this paper integrates the PID control into robust control formulation as a robust Structured Static Output Feedback (SSOF) problem of Linear-Parameter-Varying (LPV) systems, which can be converted into a Parameter Dependent Bilinear-Matrix-Inequality (PDBMI) optimization problem. A convex-concave decomposition based method is given to solve the proposed PDBMI problem. The proposed solution has a simple structure in PID form and can guarantee stability and robustness of the system being controlled in the whole operation range with less conservativeness than existing solution.

【 授权许可】

Unknown