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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Vydané v:Cybernetics and information technologies : CIT Ročník 20; číslo 1; s. 156 - 167
Hlavní autori: Shao, Pengyuan, Wu, Jin, Ma, Songhui
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Sofia Sciendo 01.03.2020
De Gruyter Brill Sp. z o.o., Paradigm Publishing Services
Predmet:
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
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Abstract 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.
AbstractList 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.
Author Shao, Pengyuan
Ma, Songhui
Wu, Jin
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Snippet 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...
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StartPage 156
SubjectTerms Bilinear-Matrix-Inequality (BMI)
gain scheduling
Linear-Matrix-Inequality (LMI)
Linear-Parameter-Varying (LPV) system
Proportional-Integration-Derivative (PID) control
Robust control
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