Fractional Order Fixed-Time Nonsingular Sliding Mode Control of a Fractional Hydro-Turbine Governing System

The fixed-time nonsingular sliding mode control of fractional-order hydro-turbine governing system (HTGS) is studied. First, a fractional-order HTGS model with better stability is presented. Next, it is found that the system has chaotic oscillation by dynamics analysis and numerical simulation. Then, a novel fractional order terminal sliding mode control method is applied to guarantee the fixed-time convergence of HTGS states. Moreover, there is no chattering phenomenon on the control curve and the sliding surface. Furthermore, the fixed-time stability and the robustness of the control scheme are proved using the fractional Lyapunov stability theory. Finally, the simulation results verify the effectiveness of the control method in this paper.