带有多种不确定的MIMO系统的自抗扰控制闭环稳定性研究

Decoupling the plant with multiple uncertainties is a hot topic in the process control. Recently, much work has been done for the ADRC decoupling problems, which performs excellently for the MIMO system. The related application research is fruitful. But, some applications are beyond the scope of the existing ADRC theoretical results, and need further theoretical support. So, with the mathematical tools, this project is on the ADRC decoupling problem for the MIMO system whose order, relative degree and parameters are uncertain: The mathematical description is made for the problems and the experiences found in the application research. Then, the closed-loop stability is proved for the open-loop-stable system and the minimum-phase system with ADRC, and the parameter tuning method and the closed-loop performance description are given. For more general plants, a quick method to design and adjust the ADRC is established based on the known PID controller, and the closed-loop performance is also described. This project is helpful for explaining the excellence of ADRC and revealing the general rule in the ADRC decoupling problem. It provides the theoretical support and the general guideline for designing and tuning ADRC for the MIMO system, and promotes the theoretical and application research on the ADRC.

带有不确定性的解耦控制问题是工业控制领域的研究热点。近来，对MIMO系统表现优秀的ADRC技术得到了许多关注，已有很多应用成果。一些应用研究已超出了现有ADRC 理论分析的适用范围，需要新的理论支持。本项目拟采用严格的数学工具，研究阶、相对阶和参数均不确定的MIMO 系统ADRC 解耦问题：对应用研究中积累的问题和经验给出严格的数学描述；证明开环稳定系统和最小相位系统的ADRC 闭环稳定性, 给出参数整定方法及闭环动态特性描述；分析更一般的对象；给出基于已知的PID 控制快速设计和整定ADRC 的流程，并分析此时的闭环动态特性。开展本项目有助于探明ADRC 优秀性能的成因，揭示ADRC 解耦问题的一般规律，为MIMO对象的ADRC 设计和整定提供理论支撑和一般思路，从而促进ADRC 理论与应用研究的发展。

本项目从理论上讨论了阶和相对阶未知的多变量系统的自抗扰控制(active disturbance rejection control，ADRC)设计，对线性情况做出了较为全面的分析，并通过为ALSTOM气化炉等若干工业过程的ADRC仿真实验检验了理论分析的有效性。具体而言，本项目主要贡献如下：.1. 讨论了多变量系统的ADRC设计方法与规律，所研究的被控对象，不仅具有参数不确定性，其阶和相对阶也是未知的。通过严格的理论分析，给出了ADRC闭环稳定的必要条件，证明了自抗扰控制可以对开环稳定对象实现闭环稳定，还证明了ADRC可以逐个通道取代既有的PID/PI控制器或其推广形式。.2. 通过一系列对工业过程的仿真实验，验证了上述理论结果的有效性，给出了理论结果对应的ADRC设计、整定方法；同时，在带时滞的线性对象、经典的非线性ALSTOM气化炉系统等更加广泛的对象上，研究了前述ADRC设计、整定方法的使用效果，展现了这些方法的实用性。