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**Fractional order [proportional derivative] controller for a class of fractional order systems.**
*(English)*
Zbl 1183.93053

Summary: Recently, Fractional Order Systems (FOS) have attracted more and more attention in various fields. But the control design techniques available for the FOS suffer from the lack of direct systematic approaches. In this paper, we focus on a given type of simple model of FOS. A Fractional Order [Proportional Derivative] (FO-[PD]) controller is proposed for this class of FOS, and a practical and systematic tuning procedure has been developed for the proposed FO-[PD] controller synthesis. The fairness issue in comparing with other controllers such as the traditional integer order PID (IO-PID) controller and the fractional order proportional derivative (FO-PD) controller has been addressed under the same number of design parameters and the same specifications. Fair comparisons of the three controllers (i.e., IO-PID, FO-PD and FO-[PD]) via the simulation tests illustrate that, the IO-PID controller designed may not always be stabilizing to achieve flat-phase specification while both FO-PD and FO-[PD] controllers designed are always stabilizing. Furthermore, the proposed FO-[PD] controller outperforms FO-PD controller for the class of fractional order systems.

### MSC:

93B50 | Synthesis problems |

93B51 | Design techniques (robust design, computer-aided design, etc.) |

93D15 | Stabilization of systems by feedback |

34A08 | Fractional ordinary differential equations |

### Keywords:

fractional calculus; integer order PID controller; fractional order PD controller; fractional order [PD] controller; fractional order system; robustness; controller tuning
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\textit{Y. Luo} and \textit{Y. Chen}, Automatica 45, No. 10, 2446--2450 (2009; Zbl 1183.93053)

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