Dynamical analysis of the fractional-order centrifugal flywheel governor system and its accelerated adaptive stabilization with the optimality

摘要

This paper investigates the issues of dynamical analysis and accelerated adaptive stabilization of the fractional order (FO) centrifugal flywheel governor system with optimality. The dynamic behavior of the centrifugal fly-wheel governor system is revealed and its local stability is discussed in the fractional calculus (FC). A speed function is introduced to accelerate convergence rate within a pre-given time and a hierarchical type-2 fuzzy neural network (HT2FNN) is employed to play an approximating role for unknown nonlinear items. An extended state tracking differentiator which overcomes repetitive differentiation problem is used to approximate the derivative of virtual control input. Then, a stabilization controller is designed by integrating with the speed function, neural network and tracking differentiator in the framework of backstepping. It is proved that the proposed scheme guarantees the boundedness of all signals of the closed-loop system by using the frequency distributed model and makes the predefined cost function smallest. Finally, simulation results verify the effectiveness of the presented scheme.