高阶系统闭环时域指标估算方法的实验研究

Experimental Study of Closed-loop Frequency Domain Index Estimation Methods for High Order System

针对目前＂自动控制原理＂教材中高阶系统时域指标与闭环频率指标之间的估算公式,使用了一个开环频率指标而不是完全的闭环频率指标,使得估算的调节时间不够准确,利用Matlab编程选取了满足估算公式要求的54个3~9阶的高阶系统,分别求出其时域性能指标、开环频率指标及闭环频率指标,并与估算公式进行对比。实验结果表明：使用系统带宽ωb（闭环频率指标）替换估算公式中的截止频率ωc（开环频率指标）求得的调节时间,其绝对误差最小,准确度更高;而谐振频率ωr（闭环频率指标）不适合用于估算调节时间。

There exists a problem in the commonly used estimation formula between time domain index and closed-loop frequency domain index of high order system in automatic control theory. An open-loop frequency domain index rather than completely closed-loop frequency domain index is used,and the regulation time may be caused inaccurate. 54 high order systems meeting the requirement of estimating formula are selected by using Matlab,there orders are 3 ~ 9. The time domain performance indeces,the open-loop and closed-loop frequency indeces are calculated and compared with the estimation formula. The experimental results show that the smallest absolute error and higher accuracy can be obtained with replacing the cut-off frequency（ closed loop frequency index） with the system bandwidth（ open loop frequency index）,the resonant frequency（ closed loop frequency index） is not suitable for the estimation of regulation time.