随机系统中具有结构不确定性的扩展PID控制的理论与设计
Theory and Design of Extended PID Control for Stochastic Systems with Structural Uncertainties
AI总结：
本文提出了一种针对具有结构不确定性的非线性随机系统的扩展PID控制器设计方法，证明其在均方意义下的全局稳定性及跟踪误差可控性。
摘要：
由于经典比例-积分-微分（PID）控制器至今仍是最广泛使用的反馈方法之一，在工程系统中持续占据主导地位，因此有必要研究PID在处理非线性、不确定性和随机噪声方面的机制。最近，赵和郭（2022）已经建立了PID控制在一类具有相对阶数为二的不确定非线性控制系统中的全局稳定性，而无需随机扰动。在本文中，我们将考虑更一般的非线性随机系统，其相对阶数为任意n，并讨论扩展PID控制器（PID的自然扩展）的稳定性与设计。我们证明，只要扩展PID参数从一个(n+1)维无界集合中选取，闭环控制系统在均方意义下将全局稳定，并且跟踪误差有界。即使系统非线性漂移和扩散项包含广泛结构不确定性，这一结论仍然成立。此外，稳态跟踪误差被证明与设定点的噪声强度成正比，通过适当选择控制器参数，这一误差可以被任意减小。
英文摘要：
Since the classical proportional-integral-derivative (PID) controller has continued to be the most widely used feedback methods in engineering systems by far, it is crucial to investigate the working mechanism of PID in dealing with nonlinearity, uncertainty and random noises. Recently, Zhao and Guo (2022) has established the global stability of PID control for a class of uncertain nonlinear control systems with relative degree two without random perturbations. In this paper, we will consider a more general class of nonlinear stochastic systems with an arbitrary relative degree $n$, and discuss the stability and design of extended PID controller (a natural extension of PID). We demonstrate that, the closed-loop control systems will be globally stable in mean square with bounded tracking errors provided the extended PID parameters are selected from an $(n+1)$-dimensional unbounded set, even if both the system nonlinear drift and diffusion terms contain a wide range of structural uncertainties. Moreover, the steady-state tracking error is proved to be proportional to the noise intensity at the setpoint, which can also be made arbitrarily small by choosing the controller parameters suitably large.
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