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

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 ca...

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Bibliographic Details
Published in:Cybernetics and information technologies : CIT Vol. 20; no. 1; pp. 156 - 167
Main Authors: Shao, Pengyuan, Wu, Jin, Ma, Songhui
Format: Journal Article
Language:English
Published: Sofia Sciendo 01.03.2020
De Gruyter Brill Sp. z o.o., Paradigm Publishing Services
Subjects:
Bilinear-Matrix-Inequality (BMI)
gain scheduling
Linear-Matrix-Inequality (LMI)
Linear-Parameter-Varying (LPV) system
Proportional-Integration-Derivative (PID) control
Robust control
ISSN:1314-4081, 1311-9702, 1314-4081
Online Access:Get full text
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Summary: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.
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ISSN:1314-4081
1311-9702
1314-4081
DOI:10.2478/cait-2020-0011