基于ADRC思想的几类非线性随机系统的PID控制理论研究

实际系统往往会受到各种各样干扰的影响，如何有效地消除或抑制干扰的影响，是控制科学中的核心问题。PID控制，由于其具备结构简单、鲁棒性好以及可靠性高等优点，在大量的应用研究中表现出了良好的品质，但其理论研究仍有很多关键问题需要突破。ADRC的核心思想是可以将系统中所有不确定因素都视为扩张状态而加以观测，将其引入PID控制器的设计中可以很大程度上提高系统的鲁棒性。.本项目基于ADRC的思想，结合随机系统稳定性理论，研究几类具有复杂不确定对象的非线性随机系统的PID控制器设计问题、闭环系统的稳定性问题以及输出跟踪问题，并结合数值实验进行仿真验证。在此过程中开发新算法，利用计算机语言对算法进行编程实现，将其在实际系统模型中进行应用验证。本项目欲从理论上拓展PID控制技术的适用范围，进一步促进PID控制理论与实际问题的紧密结合。本项目的研究是PID控制领域的前沿课题之一，具有重要的科学意义。

Actual systems are often effected by various kinds of disturbances. How to effectively eliminate or suppress the influence of the disturbances is the key problem in control science. Because of the simple structure, good robustness and high reliability, PID control has shown promising performance in a large number of applications, but there are still many key problems to be solved in its theoretical research. The core idea of ADRC is that all the uncertain factors in the system can be observed as extended states, which can be introduced into the design of PID controller to greatly improve the robustness of the system..Based on the idea of ADRC and the stability theory of stochastic systems, the designs of controllers for several classes of nonlinear stochastic systems, the stability analysis of the closed-loop control systems and the output tracking problems are investigated, also the numerical simulations are given. In addition, some new algorithms are developed, which are implemented by computer language and verified in the actual system models. This project intends to theoretically expand the application scope of PID and further promotes the close integration of PID theory and practical problems. The research is one of the cutting-edge topics in the theory field of PID, which has important scientific significance.