Model Predictive Control of Piecewise Affine System with Constrained Input and Time Delay

Zhilin Liu,Jun Zhang,Lutao Liu,Yuan Xing

doi:10.1155/2013/937274

Zhilin Liu, Jun Zhang + Show 2 more

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https://doi.org/10.1155/2013/937274

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Abstract

A model predictive control (MPC) is proposed for the piecewise affine (PWA) systems with constrained input and time delay. The corresponding operating region of the considered systems in state space is described as ellipsoid which can be characterized by a set of vector inequalities. And the constrained control input of the considered systems is solved in terms of linear matrix inequalities (LMIs). An MPC controller is designed that will move the PWA system with time delay from the current operating point to the desired one. Multiple objective functions are used to relax the monotonically decreasing condition of the Lyapunov function when the control algorithm switches from a quasi-infinite horizon to an infinite horizon strategy. The simulation results verify the effectiveness of the proposed method. It is shown that, based on LMI constraints, it is easy to get the MPC for the PWA systems with time delay. Moreover, it is suitable for practical application.

Highlights

In engineering practice, there are many hybrid systems described by piecewise affine systems (PWA) which are composed of linear subsystems and convex polytopic regions
We propose a MPC control algorithms for the discrete polytopic time-delay PWA systems
To stabilize the PWA system (2), a state feedback control law is solved by defining a quadratic

Summary

Introduction

There are many hybrid systems described by piecewise affine systems (PWA) which are composed of linear subsystems and convex polytopic regions. MPC has become the control strategy of choice in industrial applications that typically involve linear systems subject to linear inequality constraints. The use of piecewise models in a control structure necessitates a means of switching among the available models to the one that best describes the current process dynamics. A closely related work is the stability analysis of piecewise linear systems by [16] in which piecewise quadratic Lyapunov functions were constructed using convex optimization in terms of linear matrix inequalities (LMIs) as an alternative to a globally quadratic Lyapunov function. Few works on control algorithms development for time delay PWA system have been reported [17, 18] Based on this concept, we propose a MPC control algorithms for the discrete polytopic time-delay PWA systems.

Problem Formulation

Main Result

Simulation Result

Conclusion