Fractional Order Sliding Mode Control For Pmsm Speed Regulation System With Fractional Order Disturbance Observer

To improve the dynamic and static response performance,speed tracking performance and anti-disturbance performance of permanent magnet synchronous motor speed regulation system,fractional order calculus and sliding mode control method are combined,and a variety of fractional order sliding mode control methods are proposed in this paper.The research contents of this paper are:A fractional order linear sliding mode control method which has the same orders of differential and integration is proposed.The expression of controlled state variable is obtained by solving fractional order differential equation.Through mathematical analysis,it can be proved the convergence speed of the proposed fractional order sliding mode control is faster than that of corresponding integer order controller.By solving the boundary value problem of fractional differential equation,the fractional order terminal sliding mode control and fractional order nonsingular terminal sliding mode control can still achieve finite time control is proved in this paper.The exact expression of control time is given.Through mathematical analysis,it is proved that the control time of fractional order terminal sliding mode controller and fractional order nonsingular terminal sliding mode controller is less than the corresponding integer order controllers.The relationship between the control time and fractional order parameters is explained further.A fractional order improved fast terminal sliding mode controller is proposed,which can further increase the range of parameters setting.Furthermore,fractional order disturbance observer is designed in this paper to feedback the predicted disturbance to sliding mode controller,which can enhance the anti-disturbance performance and alleviate the sliding mode chattering problem.In order to cooperate with the proposed fractional order controllers,a fractional PI controller is designed in current loops.And an accurate fractional order relationship equation between the speed and reference q-axis current is derived.The proposed fractional order sliding mode controllers are designed in speed loop.The control laws of the designed integrated controllers are calculated by Lyapunov stability theory.The simulation and experimental results show that extending sliding mode control to fractional order sliding mode control and choosing the fractional order parameters reasonably can effectively improve control performance.In addition,the effectiveness of the designed fractional order disturbance observer is also proved.