一种整数阶系统的分数阶(PID)<sup<<em<γ</em<</sup<控制方法

A Fractional Order (PID)<sup<<em<γ</em<</sup< Control Method for Integer-Order Systems

  • 摘要: 针对常见的1阶、2阶和1阶加积分系统,提出了一种分数阶(fractional order,FO)控制器设计方法. 基于内模控制(internal model control,IMC)原理,采用分数阶滤波器推导出了一种分数阶(PID)<sup<<em<γ</em<</sup<控制器,该控制器仅包含两个可调整参数,有效降低了分数阶控制器整定的难度,并基于系统相位裕量<em<φ</em<<sub<m</sub<和截止频率<em<ω</em<<sub<c</sub<,实现了分数阶(PID)<sup<<em<γ</em<</sup<控制器的参数整定. 仿真结果表明,所提出的方法不但设计简单,参数整定方便,而且可使系统获得良好的设定值跟踪特性和干扰抑制特性,以及克服系统参数摄动的鲁棒性.

     

    Abstract: For first-order, second-order, and first-order-plus-integrals systems, a design method for fractional order controllers is proposed. Based on the principle of internal model control, a fractional order (PID)<sup<<em<γ</em<</sup< controller is created by using the fractional order filter. This controller only contains two adjustable parameters, so the difficulty of the fractional order controller tuning is reduced. The parameter tuning of the fractional order (PID)<sup<<em<γ</em<</sup< controller is realized according to the phase margin, <em<φ</em<<sub<m</sub<, and the cutoff frequency, <em<ω</em<<sub<c</sub<, of the system. Simulation results show that the proposed method is not only simple in design and convenient in its parameter tuning, but also that it provides better performance in both command value tracking and disturbance rejection, as well as an increased robustness against system perturbation parameters.

     

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