【摘要】 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.更多还原

【Abstract】 A new kind of PID controller, fractional order PID (Proportional, Integral and Derivative) controller (involving 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 may have some superior performances compared with the classical integer order PID controller. A digital implementation of fractional order PID controller was given. Some limited terms of the definition of Grünwald-Letnicov fractional calculus are taken such that Z-transform method can be used to compute fractional order PID controller directly in the time domain. The simulation outcomes verify the effectiveness of the method proposed.更多还原