A correlation between the transient and frequency responses in servomechanisms

The need is stressed for simple correlation between the time and frequency responses in servomechanisms in order to rationalize synthesis procedures. Some existing methods of correlating features of the unit step response with frequency response parameters are examined and their shortcomings noted. Statistical evidence, obtained from the responses of a large number of servo systems of various types, is employed to set up empirical relations between selected parameters of the time and frequency responses, i.e. delay time, rise time, overshoot, settling time, and period of oscillation on the one hand, and 6 db bandwidth, peak magnification, etc., on the other. A new theoretical relation for the delay time is also obtained. These relations make it possible to sketch the step response with reasonable accuracy, when the open-loop frequency response is given. In some cases, in which the closed-loop amplitude response departs considerably from the more typical form, the step response is shown to consist of two sub-transients, each of which can be determined separately.