迟后时滞系统Pade等效式的最佳阶次分析研究

Analysis to the Optimal Order of the Pade Equivalent about Time Delay

时滞现象是生产过程中常见的现象,是影响系统稳定性的一个重要因素;因此研究时滞环节对于解决工程中的时延问题,提高控制系统性能有着重要意义。现建立一种求延时环节的对称Pade展开式最佳等效阶次的简便方法。首先,阐述了开环传递函数中的最小相位环节和延时常数部分,对延时环节最佳Pade等效阶次的影响;其次,建立相对均方根误差指标,分析了Pade等效阶次、延时时间参数及Pade展开式中极点与虚轴的距离三者之间的关系,并确定控制系统中延时环节的Pade等效最佳阶次的方法;最后,验证了求Pade最佳等效阶次方法的准确性,表明该方法能快速有效地求出延时环节的Pade等效的最佳等效阶次。

Delay phenomenon is a common phenomenon in the production process. It is a crucial factor to affect system stability. Thus, it is necessary to research delay block for solving the delay problem in engineering. Aims to establish a method to solve the best equivalent order of symmetrical Pade expansion in delay block, first of all,the thesis elaborates the influence of minimum phase part and delay constant part on the best equivalent order of sym- metrical Pade expansion. In the next place, the relative root mean square error is established, and the relationship between Pade equivalent order and delay time parameter is analyzed, and the method to determine Pade equivalent best order in control system is proposed. Finally, the accuracy of the optimal order of law is verified, and rapidity and validity of the method to determine the best equivalent order of symmetrical Pade expansion is proved.