Fuzzy generalised predictive control for a fractional-order nonlinear hydro-turbine regulating system

This study focuses on a fuzzy generalised predictive control method for a fractional-order hydro-turbine regulating system (HTRS). Based on the Grunwald–Letnikov (G–L) definition of fractional calculus and discretisation, the fractional-order hydraulic servo system is transformed into the standard controlled autoregressive integrating moving average (CARMA) model. With the help of fuzzy linearisation theory, the fuzzy predictive model of the integer-order part of the HTRS is presented. Furthermore, by using the fourth-order Runge–Kutta algorithm, the obtained fuzzy predictive model can be easily transformed into the CARMA model. Then, based on the overall CARMA model and the generalised predictive control theory, a novel nonlinear fuzzy generalised predictive controller is designed for the fractional-order HTRS. Finally, numerical simulations are implemented to verify the validity and superiority of the proposed method. It also provides a reference for relevant hydropower systems.