受有色噪声干扰的切换系统的建模与控制问题

This project is intended to investigate the modeling and control problems for switched systems with non-white noise. Based on Lyapunov technique, we establish the stability and passivity theory of random switched systems for the foundation of controller design. Because the energy of the physical system is finite, non-white noise is more reasonable to describe random disturbances than white noise. In order to obtain a ideal structure and universal results, the focus of our research is the modeling of random Lagrange systems driven by non-white noise. By the aid of energy shaping and passivity, the switched controllers are designed such that the closed-loop systems reach the expected objective. Finally, as applications, the control problems are discussed in the practical switched models such as electrical systems, power systems. The project synthesizes some features such as modeling correctness, analysis strictness and control practicability. Therefore, this research of the project has a great challenge and meaning.

本项目将研究受有色噪声干扰的切换系统的建模和控制问题. 基于Lyapunov函数技术, 研究随机切换系统的稳定性和无源性理论, 为控制器的设计奠定基础. 其次, 由于实际物理系统的能量是有限的, 选取有色噪声作为随机扰动更为合理. 为了获得较为理想的结构和普适性的成果, 重点研究受有色噪声干扰的随机拉格朗日系统的建模. 基于能量整形和无源性, 设计切换控制器使得闭环系统达到预期目标. 最后, 作为应用, 讨论电路系统、电力系统等实际切换模型的控制问题. 该项目综合了建模的正确性, 分析的严密性和控制的实用性等特点, 因此, 研究本项目具有很大的挑战和意义.

该项目围绕着受噪声干扰的切换系统的建模与控制问题进行了深入的探索研究.建立了具有未知参数的随机切换系统的自适应跟踪切换控制, 作为应用, 给出了悬挂在随机振动天花板上的平面双摆的数学模型, 设计自适应切换控制器, 使得平面双摆模型跟踪到给定的参考信号以达到预期目标. 首次提出了基于PWM控制的开关功率变换器的轨迹跟踪问题, 其中系统输入是一个数字化控制. 针对以数字开关控制为输入、参数未知的开关降压功率变换器, 建立了一个基于PWM的自适应轨迹跟踪框架. 讨论了机电系统的数字化控制问题, 给出了机电系统的建模与PWM控制器设计. 本项目所获得的成果在机械系统、电路系统、机电系统等实际系统中得到了应用, 以切换控制的观点对系统进行建模、分析和设计. 目前仅处于理论阶段, 用虚拟现实软件Simulink的Simscape (多域)模块验证了所提策略的有效性. 所获得成果具有重要的理论意义与实际价值.