Correlation of transient and frequency responses by use of phase margin

Abstract

A linear automatic control system must be stable and yet meet certain specifications of accuracy. In general, both transient and frequency response are needed to guarantee satisfactory designs. The purpose of this investigation was to show that phase margin can be used to correlate transient and frequency response characteristics, primarily the resonant frequency peak and the transient peak overshoot. Using the electric analog computer, numerous servo systems were simulated. The resonant frequency peak and transient peak overshoot were plotted versus phase margin for various system gain settings. From the plots approximate equations relating the resonant frequency peak, the transient peak overshoot, and the phase margin were developed. Solutions to the equations are generally accurate to within a small percentage of the correct values.