Analysis and Control of Chaos and Bifurcation in Power Electronic Control Systems

本课题旨在发展电力电子控制系统中混沌与分岔现象的分析与控制方法。我们开发了几种分析方法和计算机辅助方法来研究电力电子系统中混沌和分岔现象的发生机制。首先，提出了一种电力电子系统稳定性的计算机辅助确定方法。其次，我们开发了高效的计算机算法来确定分岔值，即发生分岔的系统参数值。所开发的算法不仅可以检查系统的稳定性，而且可以直接确定引起系统分岔或混沌的系统参数的值。第三，讨论了工作模式分析问题，这是电力电子电路中由于功率半导体器件的开关行为而存在的一个特殊问题。提出了一种确定电力电子系统参数空间上工作模式边界的通用计算机方法。在上述所有计算机算法的开发中，如何以合理的精度和效率计算系统的参数灵敏度成为一个关键。为此，还开发了一种高效、准确的灵敏度计算算法。在此基础上，提出了一种简单实用的脉冲调频混合反馈系统稳定性检验方法。本研究项目所开发的方法和算法可作为研究电力电子系统中混沌和分岔现象发生原因的有效工具，也可用于确定稳定系统的控制参数。

The purpose of this research project is to develop analysis and control methods of chaos and bifurcation phenomena in power electronic control systems. We developed several analytical and computer-aided methods for investigating the mechanisms of occurrence of chaos and bifurcation phenomena in power electronic systems.First a computer-aided method to determine stability of power electronic systems was developed. Second, we developed efficient computer algorithms to determine bifurcation values, that is, values of system parameters where bifurcations occur. The developed algorithms make it possible not only to check the stability of the systems but also to directly determine values of the system parameters which cause bifurcations or chaos in the systems. Third, the problem of operating mode analysis, which is a specific problem in power electronic circuits due to the switching behaviors of power semiconductor devices, was took up. We developed a general computer method for determining operating-mode boundaries on a parameter space of power electronic systems. In developing all the computer algorithms stated above, it becomes a key how to compute parameter sensitivities of the systems with reasonable accuracy and efficiency. For this purposed an efficient and accurate algorithm for computing those sensitivities was also developed. Furthermore we developed a simple and practical method to check stability of hybrid feedback systems with PFM (pulse frequency modulation) mechanisms.The methods and algorithms developed in this research project can be effective tools for investigating the causes of occurrence of chaos and bifurcation phenomena in power electronic systems and also can be utilized to determine control parameters that stabilize the systems.