Prescribed performance sliding mode control for the bursting oscillation of a fractional-order hydro-turbine governing system based on time-varying tangent barrier Lyapunov function

Abstract

A dynamic model for a hydro-turbine governing system is established that accounts for the periodic excitation caused by the dynamic transfer coefficient. The dynamic analysis shows that the turbine regulation system produces bursting oscillatory behaviors when its transmission coefficient changes. The bursting oscillation behavior can adversely affect its stable operation. In response to this challenge, a prescribed performance sliding mode controller based on the time-varying tangent barrier Lyapunov function is proposed. Specifically, a time-varying constraint function of the exponential decay type is initially established. This function is then combined with the prescribed performance constraint function and the dynamic sliding surface to construct the time-varying tangent barrier Lyapunov function. In addition, to ensure that the system output exhibits a slight overshoot and fast-tracking speed at the initial time while satisfying the steady-state index, the relevant parameters of the time-varying constraint function are presented. Finally, the stability of the proposed controller is rigorously proven, verifying the effectiveness of the controller under five working conditions. The simulation results demonstrate that the prescribed performance sliding mode control based on the time-varying tangent barrier Lyapunov function can enable the hydro-turbine governing system to quickly break away from the bursting oscillation state. The proposed control strategy achieves faster convergence times for the rotor angle and generator speed (0.3 s) as well as the guide vane opening (0.3 s) than the ordinary sliding mode controller. The proposed strategy is also superior in controlling the steady-state error, which means that the proposed controller has a faster response speed, higher control accuracy, and optimized transient performance of the system than the traditional controller.