Two degree of freedom fractional order PID controllers design for fractional order processes with dead time.
Recently, fractional order (FO) processes with dead time have attracted more and more attention of many researchers in control field, but FO PID controllers design techniques available for the FO processes with dead time suffer from lack of direct systematic approaches. In this paper, a simple design and parameters tuning approach of two degree of freedom (2 DOF) FO PID controller based on internal model control (IMC) is proposed for FO processes with dead time, conventional one degree of freedom control exhibited the shortcoming of coupling of robustness and dynamic response performance. 2 DOF control can overcome the above weakness which means it realizes decoupling of robustness and dynamic performance from each other. The adjustable parameter e2 of FO PID controller is directly related to the robustness of closed loop system, and the analytical expression is given between the maximum sensitivity specification Ms and parameters e2. In addition, according to the dynamic performance requirement of the practical system, the parameters e1 can also be selected easily. By approximating the dead time term of the process model with the first order Pade or Taylor series, the expressions for 2 DOF FO PID controller parameters are derived for three classes of FO processes with dead time. Moreover, compared with other methods, the proposed method is simple and easy to implement. Finally, the simulation results are given to illustrate the effectiveness of this method.
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