Gain-scheduled PID controller design

• This paper addresses the problem of the design of a gain-scheduled controller (GSC).
• In this paper we have proposed two GSC design procedures.
• GSC design procedure guarantees parameter dependent quadratic stability.
• GSC design procedure ensures the guaranteed cost.
• The proposed procedure is based on the Lyapunov theory and BMI.

Gain scheduling (GS) is one of the most popular approaches to nonlinear control design and it is known that GS controllers have a better performance than robust ones. Following the terminology of control engineering, linear parameter-varying (LPV) systems are time-varying plants whose state space matrices are fixed functions of some vector of varying parameters. Our approach is based on considering that the LPV system, scheduling parameters and their derivatives with respect to time lie in a priori given hyper rectangles. To guarantee the performance we use the notion of guaranteed costs. The class of control structure includes centralized, decentralized fixed order output feedbacks like PID controller. Numerical examples illustrate the effectiveness of the proposed approach.