An IMC- PIλ Dμ controller design for fractional calculus system

This paper studies on fractional PI^λD^μ controller tuning, in particular, on controller tuning of processes described by fractional transfer function. Fractional PI^λ D^μ controller is a generalization of integer PID controller and has more advantages over integer controller, but the scarcity of tuning methods for the fractional PI^λ D^μ is still a problem to be resolved. In this paper, a random search optimization method is first introduced for fractional order model reduction. Then the parameters of fractional order controllers are tuned by internal model control (IMC) based method. Research results show that the reduced fractional order model has a better approximation to original system and much smaller error compared with the integer order approximation. And therefore through IMC method, an appropriate fractional PI^λ D^μ controller can be achieved based on the model. Experimental results are given to illustrate the effectiveness of this method.