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Article Dans Une Revue Systems and Control Letters Année : 2019

A quadratic matrix inequality based PID controller design for LPV systems

Yan Wang
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Rajesh Rajamani
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Ali Zemouche

Résumé

This paper develops a robust gain-scheduled proportional–integral–derivative (PID) controller design method for a linear-parameter-varying (LPV) system with parametric uncertainty. It is recognized in the literature that the robust fixed-order controller design can be formulated as a feasibility problem of a bilinear matrix inequality (BMI) constraint. Unfortunately, the search for a feasible solution of a BMI constraint is an NP hard problem in general. Previous researchers have applied a linearization method, such as a variable change technique or a congruence transformation, to transform the BMI into a LMI. The applicability of the linearization method depends on the specific structure of the problem at hand and cannot be generalized. This paper instead formulates the gain-scheduled PID controller design as a feasibility problem of a quadratic matrix inequality (QMI) constraint, which covers the BMI constraint as a special case. An augmented sequential LMI optimization method is proposed to search for a feasible solution of the QMI constraint iteratively. As an illustrative application, a vehicle lateral control problem is presented to demonstrate the applicability of the proposed algorithm to a real-world output feedback control design system.

Dates et versions

hal-02054215 , version 1 (01-03-2019)

Identifiants

Citer

Yan Wang, Rajesh Rajamani, Ali Zemouche. A quadratic matrix inequality based PID controller design for LPV systems. Systems and Control Letters, 2019, 126, pp.67-76. ⟨10.1016/j.sysconle.2019.02.006⟩. ⟨hal-02054215⟩
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