An extension of the root locus method to obtain closed-loop frequency response of feedback control systems

THE root locus method for analyzing feedback control systems has become increasingly popular over the last few years. However, the great potentialities of the method have yet to be realized. The method has had the drawback of presenting only the transient response of the system under study. An ideal method of analysis and synthesis would allow the engineer to arrive at both the transient and the steady-state sinusoidal response without any large amount of extra work involved for either. The work would progress in two stages. The first stage would take a relatively short time to complete and would yield approximations to both the closed-loop transient response and the frequency response. At this point, various design features could be compared. The second stage would be an extension of the work done in the first stage - not a more detailed rework of the problem. This second stage of the problem would yield exact and complete transient and sinusoidal solutions.