分数阶PID控制器及其数字实现

Fractional Order PID Controller and Its Digital Implementation

提出一种新的比例、积分、微分(PID)控制器——分数阶PID控制器(包含分数阶积分器和微分器),把传统的PID控制器的阶次推广到分数领域,它不但适合于分数阶系统,也适用于某些整数阶系统,并能够取得一些优于整数阶PID控制器的效果.给出了分数阶PID控制器的一种数字实现形式,运用Grünwald-Letnicov分数微积分定义,取有限项作近似处理,从而可以直接在时域中运用Z变换方法来计算分数阶PID控制器.仿真结果证明了所给方法的有效性.

The fractional order PID (proportional-integral-derivative) controller (including fractional order integrator and differentiator) was proposed, which is the generalization of classical integer order PID controller. It is useful not only for fractional order systems but also for some integer order systems, and has some superior performances as compared with the classical integer order PID controller. The digital implementation of fractional order PID controller was given. Some finite terms of the definition of Grunwald-Letnicov fractional calculus are taken so that Z-transform can be used to compute fractional order PID controller directly in the time domain. The simulation results verify the effectiveness of the proposed method.