Practical Tracking Control via Discrete-Time Fractional-Order SMC

In this chapter, a novel discrete-time fractional-order sliding mode (DFSM) controller is proposed to guarantee the desired tracking performance of the linear motor control system. A discrete-time linear motor model is firstly presented by using Euler’s discretization method. By introducing a FO difference of the tracking error, a new FO sliding surface is proposed to obtain a better performance than integer-order counterparts due to the memory effect introduced by FO calculus. Then, a novel equivalent controller is introduced to drive the system to the newly proposed sliding surface in finite sampling steps. Meanwhile, a theoretical tracking error of the linear motor system is analyzed and the practical stability of the sliding surface is validated by numerical simulations. Finally, the effectiveness of the proposed control strategy is verified by a group of tracking experiments on the linear motor platform.