Note on fractional-order proportional-integral-differential controller design

This study deals with the design of fractional-order proportional-integral-differential (PID) controllers. Two design techniques are presented for tuning the parameters of the controller. The first method uses the idea of the Ziegler-Nichols and the Astrom-Hagglund methods. In order to achieve required performances, two non-linear equations are derived and solved to obtain the fractional orders of the integral term and the derivative term of the fractional-order PID controller. Then, an optimisation strategy is applied to obtain new values of the controller parameters, which give improved step response. The second method is related with the robust fractional-order PID controllers. A design procedure is given using the Bode envelopes of the control systems with parametric uncertainty. Five non-linear equations are derived using the worst-case values obtained from the Bode envelopes. Robust fractional-order PID controller is designed from the solution of these equations. Simulation examples are provided to show the benefits of the methods presented.