Generalized robust gain-scheduled PID controller design for affine LPV systems with polytopic uncertainty

In the paper a generalized guaranteed cost output-feedback robust gain-scheduled PID controller synthesis is presented for affine linear parameter-varying systems under polytopic model uncertainty. The controller synthesis is generalized in a sense that it covers robust, robust gain-scheduled, and robust switched (with arbitrary switching algorithm) PID controller design. The proposed centralized/decentralized controller method is based on Bellman–Lyapunov equation, guaranteed cost, and parameter-dependent quadratic stability. The proposed sufficient robust stability and performance conditions are derived in the form of bilinear matrix inequalities (BMI) which can efficiently be solved or further linearized. As the main result, the suggested performance and stability conditions without any restriction on the controller structure are convex functions of the scheduling and uncertainty parameters. Hence, there is no need for applying multi-convexity or other relaxation techniques and consequently the proposed solution delivers a less conservative design method. The viability of the novel design technique is demonstrated and evaluated through numerical examples

Robust Guaranteed Cost Output-Feedback Gain-Scheduled Controller Design

In the paper a new robust guaranteed cost output-feedback gain-scheduled PID controller design technique is presented for affine linear parameter-varying systems under polytopic model uncertainty, with the assumption that the scheduled parameters are affected with absolute uncertainty. The proposed centralized or decentralized method is based on the Bellman-Lyapunov equation, guaranteed cost, and parameter-dependent quadratic stability. The robust stability and performance conditions are translated to an optimization problem subject to bilinear matrix inequalities, which can be solved or further linearized. As the main result, the suggested stability and performance conditions without any restrictions on the controller structure are convex functions of the scheduling and uncertainty parameters. Hence, there is no need for applying multi-convexity or other relaxation techniques and consequently the proposed solution delivers a less conservative design method. The viability of the novel design technique is demonstrated and evaluated through numerical examples

Discrete gain-scheduled controller design: Variable weighting approach

Our paper deals with discrete gain-scheduled controller design which ensures closed-loop stability and guaranteed cost for all scheduled parameter changes. The novel procedure is based on Lyapunov theory of stability and BMI. To access the performance quality a quadratic cost function is used, where weighting matrices are time varying matrices which depends on scheduled parameter too. The class of control structure includes decentralized fixed order output feedback like PSD controller. Numerical examples illustrate the effectiveness of the proposed approach

PID robust gain-scheduled controller design

A novel methodology is proposed for robust gain-scheduled PID controller design for uncertain LPV systems. The proposed design procedure is based on the parameter-dependent quadratic stability approach. A new uncertain LPV system model has been introduced in this paper. To access the performance quality the notion of a parameter varying guaranteed cost is used. Numerical examples show the benefit of the proposed method

Gain-Scheduled PID Controller Design

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

Robust Controller Design with Input Constraints. Time Domain Approach.

A novel approach to robust controller design with hard input constraints is presented. The proposed design procedure is based on the robust stability condition developed using Affine or Parameter-Dependent Quadratic Stability approach. The obtained feasible design procedures are in the form of BMI or LMI. The obtained design results and their properties are illustrated in simulation examples

Observer-based output feedback gain-scheduled controller design

Our paper deals with the observer-based output feedback gain-scheduled controller design which ensures closed-loop stability and guaranteed cost for all scheduled parameter changes. The novel procedure is based on LPV paradigm, Lyapunov theory of stability and guaranteed cost from LQ theory. To access the performance quality a quadratic cost function is used. The obtained design procedures are in the form of BMI. The class of control structure includes decentralized fixed order observer-based output feedback like PID controller. Numerical examples illustrate the effectiveness of the proposed approach

Robust discrete gain-scheduled controller design for uncertain LPV systems

This paper deals with the robust discrete gain-scheduled controller design for uncertain linear parameter-varying (LPV) systems which ensures closed-loop stability and guaranteed cost for all scheduled parameter changes. The novel procedure is based on LPV paradigm, Lyapunov theory of stability and guaranteed cost from LQ theory. To access the performance quality a quadratic cost function is used, where weighting matrices are time varying matrices which depends on scheduled parameter. The obtained design procedures are in the form of bilinear matrix inequalities (BMI). The class of control structure includes decentralized fixed order output feedback like PID (PSD) controller. Numerical examples illustrate the effectiveness of the proposed approach

Robust gain–scheduled PID controller design for uncertain LPV systems

A novel methodology is proposed for robust gain-scheduled PID controller design for uncertain LPV systems. The proposed design procedure is based on the parameter-dependent quadratic stability approach. A new uncertain LPV system model has been introduced in this paper. To access the performance quality the approach of a parameter varying guaranteed cost is used which allowed to reach for different working points desired performance. Numerical examples show the benefit of the proposed method. \ua9 2015 Slovenska Technicka Univerzita. All rights reserved

Discrete Gain-Scheduled Controller Design: Guaranteed Cost and Affine Quadratic Stability Approach

Our paper deals with discrete gain-scheduled controller design which ensures closed-loop stability and guaranteed cost for all scheduled parameter changes which lie in closed set Ω. The novel procedure is based on Lyapunov theory of stability, guaranteed cost from LQ theory and BMI. The class of control structure includes decentralized fixed order output feedbacks like PSD controller. Numerical examples illustrate the effectiveness of the proposed approach