Quick methods for evaluating the closed-loop poles of feedback control systems

An evaluation of the closed-loop poles of a feedback control system is almost necessary if one desires an accurate knowledge of its time response. If these poles are known, the response of the system to any kind of input can be determined fairly simply. However, evaluation of the closed-loop poles has long been a stumbling block in feedback control design, because it often requires finding the roots of a polynomial of high order. In 1947 Evans1 presented the root-locus method which facilitates this evaluation, but yet is still quite cumbersome. In 1951 Kusters and Moore2 simplified Evans' approach by utilizing generalized frequency-response plots. This paper extends this method of Kusters and Moore, and supplements it with a method for estimating by inspection approximate values of the closed-loop poles from the open-loop transfer function, and a numerical method for evaluating the closed-loop poles exactly.