Ou Linlin, Zhang Weidong, Gu Danying
Department of Automation, Shanghai Jiaotong University, People's Republic of China.
ISA Trans. 2006 Jul;45(3):361-71. doi: 10.1016/s0019-0578(07)60218-3.
In recent decades, several optimization-based methods have been developed for the proportional-integral-derivative (PID) controller design, and the common feature of these methods is that the controller has only one adjustable parameter. To keep the closed-loop systems stable is an essential requirement for the optimization-based PID controllers. In almost all these methods, however, no exact stability region for the single adjustable parameter was sketched. In this paper, using the proposed analytical procedure based on the dual-locus diagram technique, explicit stability regions of the optimization-based PID controllers are derived for stable, integrating, and unstable processes with time delay in the nominal and perturbed cases, respectively. It is revealed that the proposed analytical procedure is effective for the determination of the nominal and robust stability regions and it offers simplicity and ease of mathematical calculations over other available stability analysis methods. The results in this paper provide some insight into the tuning of the optimization-based PID controllers.
近几十年来，已经开发了几种基于优化的方法来设计比例积分微分（PID）控制器，这些方法的共同特点是控制器只有一个可调参数。保持闭环系统稳定是基于优化的PID控制器的基本要求。然而，在几乎所有这些方法中，都没有画出单个可调参数的确切稳定区域。在本文中，使用基于双轨迹图技术提出的解析程序，分别针对标称和扰动情况下具有时滞的稳定、积分和不稳定过程，推导了基于优化的PID控制器的显式稳定区域。结果表明，所提出的解析程序对于确定标称和鲁棒稳定区域是有效的，并且与其他可用的稳定性分析方法相比，它具有简单性和易于数学计算的优点。本文的结果为基于优化的PID控制器的整定提供了一些见解。
