二阶系统的瞬态响应性能指标分析与应用

设计二阶系统时,在允许系统有适度的振荡情况下,为了获得较短的过渡过程,通常使系统在欠阻尼状态下工作(通常取ζ=0.4～0.8)。但是在系统设计和实验中,为了使学生直观、深入了解3种不同状态下(ζ<1,ζ=1,ζ>1),系统瞬态响应性能指标随阻尼比改变而改变的情况,本文对临界阻尼和过阻尼情况做了深入的理论分析,并进行了实验研究,获得了求取以上2种情况的调整时间ts的理论公式。

Analysis and application of performance index for transient response of second-order system

When design a second - order system, in order to get a shorter transitional stage (if moderate oscillation is allowed for the system), we usually make the system work under the circumstances of underdamped condition (ζ=0 4～0 8). But in the system design and experiment, in roder to make students directly perceive and thoroughly understand the circumstances of three different kinds of system conditions (ζ<1,ζ=1,ζ>1), deep-going theory analysis is made on the circumstances of critically damped and overdamped conditions in this paper. In addition, two theory formulas of the settling time on the above two different conditions are obtained