Finite Time Control of a Fractional Order Hydro-Turbine Governing System With Load Rejection

Abstract

Abstract This study focuses on the finite time control of a fractional order hydro-turbine governing system (HGS) with load rejection. First, the hydraulic servo system has significant historical reliance. Since it is a powerful advantage for fractional calculus to describe the function which has significant historical reliance, the fractional order hydraulic servo system is adopted and the more actual fractional order hydro-turbine governing system is presented. Second, some definitions and properties are given, and the state trajectories of HGS with load rejection is observed. The simulation results show that the state trajectory of the system is not stable, so it is necessary to design a controller with better control effect. Third, based on the frequency distribution model, the equivalent transformation model of HGS is presented. A new finite time sliding mode control scheme is proposed for the stability control of the HGS with load rejection. Furthermore, the no chattering sliding mode controller and its detailed mathematical derivation are given. The system stability is proved, and the upper limit of HGS finite time stability is given. Finally, numerical simulations have verified the theoretical results. The controller can make the state trajectories of the HGS converge to zero in a finite time, and the control time is very short.