Fractional Order Sliding Mode Control For A Class Of Fractional Order Systems With Mismatched Disturbance

With the improvement of control precision and the development of fractional order calculus,the problems of fractional order systems control have attracted more and more attention.The anti-interference of fractional order systems is an important research.Sliding mode control has well robustness in dealing with the matched disturbance.However,it is insufficient for the problem of mismatched interference.Therefore,in this paper,the fractional order calculus is applied to the traditional sliding mode control and a fractional order sliding mode control via a fractional order disturbance observer is proposed for a class of fractional order systems with the mismatched disturbance.Firstly,a class of commensurate fractional order systems with mismatched disturbance is studied.A new fractional order disturbance observer is proposed to estimate the mismatched disturbance of the system.Based on it,a new fractional order sliding mode controller is designed.Then,the proof of stability and finite time convergence is given.Finally,the simulations on Quad-Rotor UAV system and Maglev suspension system demonstrate the effectiveness of the proposed method.Secondly,a fractional order sliding mode control with disturbance observer is proposed for a class of noncommensurate fractional order systems.In this section,the noncommensurate fractional order system is decomposed into subsystems with commensurate order respectively.Then,the fractional order disturbance observer is designed for the subsystems,and the validity is proved.Then the fractional order sliding mode controller is designed based on the estimation information of the fractional order disturbance observers.The validity of the sliding mode control is proved and the parameter selection is given.Finally,the better control performance of the proposed method is verified by the simulation of a flexible link manipulator system.Compared with the traditional integer order sliding mode control method,the proposed fractional order sliding mode control method can deal with mismatched disturbance and has better control performance with faster response speed,lower overshoot,and less chattering effect.Meanwhile,the proposed method has a significant advantage in the rapidity of convergence and the reduction of overshoot compared with exsiting franctional order sliding mode control.