A series method of calculating control-system transient response from the frequency response

THE methods of calculating the closed-loop frequency response (control ratio C/R) of a linear control system are well known and straightforward.1 To calculate the transient response to a step reference input, which in some cases may be more important, is more difficult. Of the various methods1¿4 for calculating this transient response, the Laplace transformation is perhaps the most rigorous and also the most laborious, especially if the control ratio C/R has numerous poles. Partly because of this difficulty, the frequency response has predominated over the transient response in analysis and design. There is need for a simple, fast method of calculating the step transient response, preferably from the frequency response.