Mittag–Leffler stability and finite-time control for a fractional-order hydraulic turbine governing system with mechanical time delay: An linear matrix inequalitie approach

Abstract

This article mainly studies the Mittag–Leffler stability and finite-time control of a time-delay fractional-order hydraulic turbine governing system. First, properties of the Riemann–Liouville derivative and some important lemmas are introduced. Second, considering the mechanical time delay of the main servomotor, the mathematical model of a fractional-order hydraulic turbine governing system with mechanical time delay is presented. Then, based on Mittag–Leffler stability theorem, a suitable sliding surface and finite-time controller are designed for the hydraulic turbine governing system. The system stability is confirmed, and the stability condition is given in the form of linear matrix inequalities. Finally, the traditional proportional–integral–derivative control method and an existing sliding mode control method are selected to verify the effectiveness and robustness of the proposed method. This study also provides a new approach for the stability analysis of the time-delay fractional-order hydraulic turbine governing system.