Nonlinear Fractional Active Disturbance Rejection Speed Control for Stabilization of Hydraulic Turbine Regulating Systems With Mechanical Delay

An improved fractional-order nonlinear active disturbance rejection speed control (FO-NADRC) method is proposed for hydraulic turbine regulating systems (HTRSs) with a mechanical delay. First, the mathematical model of an HTRS with a mechanical time delay is established. Based on the principle of coordinate transformation, the state space equation of an HTRS with a time delay is transformed into the controllable normative mathematical model. Second, a new nonlinear function is proposed for the extended state observer ESO) that improves the observation accuracy and suppresses the high-frequency oscillation of the HTRS. Third, a new fractional-order state error feedback law (FO-SEFL) is proposed by introducing double adjustable parameters. Fourth, according to the improved ESO and the FO-SEFL, a novel FO-NADRC is designed for the HTRS. Furthermore, the Popov-Lyapunov robust stability analysis method is used to analyze the stability of the hydraulic turbine regulating control systems with mechanical delay. Finally, numerical simulation experiments demonstrate the effectiveness and superiority of the proposed control scheme.