有零点二阶系统的动态性能分析

Dynamic Performance Analysis of Second-order Systems with a Zero

本文针对有零点的二阶系统,全面分析了零点对动态响应性能的影响,讨论了系统具有左半复平面实数或复数极点时对应的零点在负实轴或正实轴上四种情况,并推导了负实数零极点情况下产生超调的条件,准确地给出了不会产生超调的零点取值范围。结果表明:只有当系统具有实数极点时,恰当地配置一个负实数零点可以明显改善快速性,且不影响平稳性;对于其他情况,增加零点基本上都是弊大于利。

The influence of a system zero on dynamic performance is fully analyzed for the second-order systems.Four cases are discussed,i.e.system poles are real numbers or complex numbers in the left-half complex plane and the corresponding zero is either on the negative real axis or on the positive real axis.When the system has negative real zero and poles,a condition is also derived for producing overshoot and the accurate range of zero value is given for not producing overshoot.The results show that only when the system has real poles,a properly assigned zero of negative real number can significantly improve the responce speed without affecting its smooth-rise property.For other cases,increasing a zero basically produces no benefit or more harm.