基于模型降阶的分数阶系统动态性能研究

Research on Dynamic Performance of Fractional Order Control System Based on Model Reduction

由于大多数分数阶系统阶次过高,使得系统的控制器设计变得非常困难,会造成系统控制精度变差且动态性能降低等不利因素,而模型降阶技术是解决这一问题的有效工具。首先简要介绍了H2范数模型降阶的一般方法,并提出一种新的降阶模型结构,可以使降阶后的模型扩展到分数阶并且更加精确地逼近各种高阶系统。仿真结果证明,采用改进型H2范数模型降阶方法不仅保持了原有分数阶模型系统的动态性能而且还提升了原有整数阶模型系统的动态性能。

For most of fractional order systems, the design of controllers would be very difficult due to high order, which may lead to low control accuracy and bad dynamic characters, and the model order reduction technique is an effective tool to solve the problem. First, this paper briefly introduced the common methods of H2 norm model reduc- tion, then a new model reduction based on that was proposed, which extends to the fractional order after the mode reduction and models a large variety of higher order systems with greater accuracy. The simulation experiments prove that the modified H2 norm model reduction method not only retains the original fractional model dynamic performance but also improves the dynamic performance of the original integer order model.