Tuning Fractional-Order PIλDμ Controllers for a Solid-Core Magnetic Bearing System

This brief presents the design of a fractional-order (FO) (PID mu)-D-lambda controller and its application to stabilizing an FO solid-core magnetic bearing (MB) system. A practical numerical search method of designing the FO (PID mu)-D-lambda controller is proposed. By presearching the orders lambda and mu in their calculated ranges, the remaining three undetermined controller parameters can be first analytically solved based on three given basic specifications, and thus, a series of controllers are obtained. Then, a relative optimal FO (PID mu)-D-lambda controller is achieved by evaluating exact performance indexes. In addition, an integer order (IO) PID controller based on the same specifications is derived and the corresponding feasible control zone consisting of specifications is calculated. The performance comparisons between the IO PID and the FO (PID mu)-D-lambda controllers are implemented by simulation and experiments. The results show that this tuning method is effective, and the FO (PID mu)-D-lambda controller can achieve more favorable dynamic performance than the IO PID controller for this FO MB system.