对PID控制器参数整定中T_I=4T_D的解释

Explanation for T_I=4T_D of PID Controller Tuning

在一些PID控制器参数设置中,通常做如下假设:TI=δTD(默认值δ=4),从而使参数整定变得简单有效。但并没有文献对此做出明确解释。本文在对上述假设做出明确解释的同时,给出一种简单的PID控制器设计构架,得到TI=4TD。这一关系式在齐格勒-尼科尔斯(ZN)整定方法中首次出现并且至今仍在广泛采用。本设计构架还给出了解析的性能优于ZN法的PID参数整定公式。仿真实例揭示了这一设计构架的有效性。

For some PID parameter settings, an assumption of TI = δTD （ default ） is often employed so that the PID controller tuning becomes simple and effective. However, no reference has given an analytical explanation for it. An analytical explanation to this assumption is given in this paper; and a simple framework for PID controller design is presented which leads to the popular setting, TI =4TD. This setting first appeared in the Ziegler and Nichols （ZN） tuning and has been widely adopted so far. The framework also provides analytical PID tuning formulas with improved performance over the ZN tuning. A simulation example indicates the effectiveness of the proposed method.