Introduction to the nonlinear PIλDμ control

In this paper, the nonlinear fractional-order PID (N-FO-PID) controller, which can be considered as a combination of the nonlinear and the fractional-order PID controllers, is introduced for the first time. It is shown that the proposed structure, which has eight parameters to tune, provides us with a powerful framework to control complicated processes by using smaller control effort compared to the PID controllers. Tuning the parameters of the proposed N-FO-PID controller is discussed and the challenges are presented. Application of the N-FO-PID controller to control a first-order plus time delay process, a process with nonlinear valve and the nonlinear magnetic levitation system is studied and the results are compared with the conventional PID, nonlinear PID and fractional-order PID controllers.