Finite-Time Stability of a Time-Delay Fractional-Order Hydraulic Turbine Regulating System

Finite-time terminal sliding mode control of a time-delay fractional-order hydraulic turbine regulating system (HTRS) is studied. First, an improved Adams-Bashforth-Moulton algorithm is introduced to solve the fractional-order nonlinear system with a time delay. Then, given the unique advantage of fractional calculus and the great influence that time delay has on system stability, a time-delay fractional-order HTRS is introduced. Moreover, by means of a frequency distribution model, the transformation of the fractional-order HTRS is realized. To stabilize the system under the influence of a random disturbance, a novel terminal sliding surface and a controller are proposed, and the detailed mathematical deduction for system stability is given. Finally, the simulation results, compared with traditional proportional-integral-derivative control and the conventional sliding mode control in the existing literature, demonstrate the validity and significant advantages of the proposed finite-time control scheme.