Design of a discrete-time sliding mode controller for a magnetic levitation system using multirate output feedback

The advent of highly efficient and superior digital computers and microprocessors in controller implementation has led to a significant interest in the field of discrete time controller design. Design of a discrete time sliding mode controller for a magnetic levitation system based on a multirate output feedback strategy is presented. The control objective is to precisely stabilize the position of a ferromagnetic ball above the ground by levitating it against the force of gravity using an electromagnet. For this application, we designed a discrete time sliding mode controller using the equivalent discrete time reaching law. Furthermore, we developed a new formulation on discrete time sliding mode control using multirate output feedback for this application, guaranteeing a system response close to that obtained through implementation of a continuous time sliding mode control. Simulation results show that for a magnetic levitation system the later, multirate output feedback based discrete time sliding mode controller is more robust than the former, discrete time sliding mode controller. Also, the phenomenon of chattering present in practical continuous time sliding mode controllers is significantly reduced in the discrete time counterparts.