非线性Markov跳变系统的几何控制及其在新能源电力系统中的应用研究

Based on the nonlinear control theory and its applications on the electrical power system, this project aims at establishing the geometric control theory for nonlinear Markovian jump systems, and then discusses the problems of stabilization control, passive control, dissipative control, H∞ control, and the application on several new energy power systems, respectively. Firstly, this project constructs the framework of geometric control theory for nonlinear Markovian jump systems through establishing several definitions and techniques, such as the coordinate transformation, the relative degree and feedback linearization, which sustains the conditions under which the system can be transformed into equivalent interconnected systems. Due to the specific interconnected structures, this project proposes the stabilization control design and the storage function method based on the geometric control theory for this class of systems. On the other hand, considering the stochastic characteristic of wind turbine power systems, we describe this class of systems with nonlinear Markovian jump systems, where the unified control of both variable-speed and variable-pitch modes is proposed based on the geometric control theory. From the viewpoint of control theory, this project tries to advance the basic theory and research method for new energy power systems, and promote the development of the related subjects.

深入分析了非线性控制及其在电力系统中的应用现状，以非线性Markov跳变系统为对象，研究其几何控制这一新问题，讨论此类系统基于几何控制方法的镇定控制、无源控制、耗散控制以及H∞控制等问题，并将相关结果运用到新能源电力系统的控制中来。本课题分别从非线性Markov跳变系统的坐标变换、相对阶定义、反馈线性化等方面构建几何控制理论的基本框架，讨论在何种条件下可将此类系统通过坐标变换和反馈补偿手段转换到特定的串联结构。本申请首次提出了非线性Markov跳变系统基于几何控制原理的镇定控制，以及直接构造能量函数的方法。针对风力发电系统本质上具有随机波动性的特点，首次使用非线性Markov跳变系统对其进行描述与研究，并运用几何控制方法实现其变速定桨/变速变桨运行模式的有效切换。项目的主要意义是从控制理论的角度探求新能源电力系统的基础理论与研究方法，总结科学问题，推动相关学科的发展与进步。

本课题以非线性Markov跳变系统为对象，研究其几何控制这一新问题，讨论此类系统基于几何控制方法的镇定控制、无源控制、耗散控制以及H∞控制等问题，并将相关结果运用到新能源电力系统的控制中来。分别从非线性Markov跳变系统的坐标变换、相对阶定义、反馈线性化等方面构建几何控制理论的基本框架，讨论在何种条件下可将此类系统通过坐标变换和反馈补偿手段转换到特定的串联结构。首次提出了非线性Markov跳变系统基于几何控制原理的镇定控制，以及直接构造能量函数的方法。针对风力发电系统本质上具有随机波动性的特点，首次使用非线性Markov跳变系统对其进行描述与研究，并运用几何控制方法实现其变速定桨/变速变桨运行模式的有效切换。