Stabilization of Arbitrary Switched Nonlinear Fractional Order Dynamical Systems: Application to Francis Hydro-Turbine Governing System

  • Mona Faraji-Niri International Digital Laboratory, University of Warwick, Coventry CV4 7AL, United Kingdom
  • Vahid Asadzadeh Electrical Engineering Department, Pooyesh Institute of Higher Education, Qom 3713956331, Iran
  • Javad Rahmani Fard Electrical Engineering Department, Pooyesh Institute of Higher Education, Qom 3713956331, Iran
Keywords: Fractional Order System, Switched Dynamical System, Lyapunov Theory, Stabilization, Linear Matrix Inequality, Hydro-Turbine Governing System

Abstract

This paper is a theoretical and practical study on the stabilization of fractional order Lipschitz nonlinear systems under arbitrary switching. The investigated system is a generalization of both switched and fractional order dynamical systems. Firstly, a switched frequency distributed model is introduced as an equivalent for the system. Subsequently, a sufficient condition is obtained for the stabilizability of the system based on the Lyapunov approach. Finally, the results are extended to synthesis mode-dependent state feedback controller for the system. All the results are expressed in terms of coupled linear matrix inequalities, which are solvable by optimization tools and directly reducible to the conditions of the integer order nonlinear switching systems as well as the conventional non-switched nonlinear fractional order systems. The proposed method has various practical implications. As an example, it is utilized to control Francis hydro-turbine governing system. This system is represented as a switching structure and supposed to supply a load suffering abrupt changes driven by an arbitrary switching mechanism. The simulation results support the usefulness of the method.

Published
2019-09-24
Section
Articles