Empirical Correlations between Time Domain and Closed Loop Frequency Domian Parameters for Type 1 Linear Feedback Control Systems

Abstract

The paper presents the results of certain studies¹ exploring the existence of possible correlations between the significant features of the step transients, such as overshoot (Ω) rise time (tr) and settling time (ts) and the closed loop frequency domain parameters, namely resonance peak (M_p), resonant frequency (W_p) and bandwidth (W_b) for type 1 linear feedback systems. The complex gain plot² is made use of for the determination of the closed loop frequency domain parameters. The step responses of a large number of different systems all of type 1 third and higher orders were determined by analogue computation and possible correlations among the parameters examined. Certain significant correlations found to exist are presented. These correlations can be used for the approximate predictions of the step transient characteristics from a knowledge of the closed loop frequency domain parameters, and also for the frequency domain synthesis of systems to meet the given time domain specifications.