Fractional and Distributed Order PID Controllers for PMSM Drives

This paper investigates fractional- and distributed-order proportional-integral-derivative (FOPID and DOPID) controllers for permanent magnet synchronous motors. The design of FOPID controllers requires the setting of four parameters, i.e. the gains of the three different actions and the non-integer order of differentiation, because the non-integer order of integration is fixed to an optimal value. An efficient particle swarm optimization (PSO) sets the parameters in two steps: firstly for an inner loop, secondly for an outer loop. The DOPID controller is characterized by seven different orders of integration or differentiation. In this second case, the tuning is also performed by PSO in two steps. In both cases, the feedback transfer function of the inner loop is a non-integer order plant for the outer loop, then the outer controller should be of fractional order to obtain the best performance/robustness indexes, as shown by simulation