Research Initiation: A Passivity-Based Control Methodology for Distribution Parameter Systems (SGER Supplement)

这个项目的目的是开发工具来分析具有对象不确定性的闭环系统分布参数控制系统的稳定性，并将这些工具应用于鲁棒镇定控制器的设计。在机械系统的控制中，分布参数对象模型由于具有集总参数模型所不具备的主要优点而被广泛使用。然而，由于分布参数模型的自由度非常多，加上实际计算资源的限制，控制问题面临着基于不准确的开环对象信息的低维控制器来维持整个对象的稳定性的挑战性任务。该项目建议扩展无源方法以解决与此场景相关的鲁棒稳定性分析和鲁棒控制器设计问题。无源系统被定义为具有并置的传感器和执行器的系统。该方法的优点是结合了时域分析(以推断稳定性)和频域分析。本课题研究的四个问题包括：(1)在无源性方法中引入参数稳健性要求；(2)将无源性方法推广到无界输入输出算子；(3)利用最优乘子技术降低基于无源性的稳健性分析中的保守性；(4)通过仿真和实验室实验验证理论结果。

The intent of this project is to develop tools to analyze stability of a closed loop distributed parameter control system with plant uncertainties, and to apply these tools to the design of robustly stabilizing controllers. In the control of mechanical systems, distributed parameter plant models are often used because of major advantages over lumped parameter models. However, with the very large number of degrees of freedom in distributed parameter models and the practical limitation of computational resources, the control problem faces the challenging task of maintaining stability of the entire plant with a low dimensional controller based on inexact open loop plant information. This project proposes to extend the passivity approach to address the robust stability analysis and robust controller design problems related to this scenario. A passive system is defined as one having colocated sensors and actuators. The approach has the advantage of combining the time domain analysis (to infer stability), and the frequency domain analysis. The four topics investigated in this project include (1) incorporating the parameter robustness requirement in the passivity method, (2) generalizing the passivity approach to unbounded input and output operators, (3) reducing conservatism in the passivity based robustness analysis by using the optimal multiplier technique, and (4) validating the theoretical results through simulation and laboratory experiments.