Analyzing the transient response of a nonlinear servosystem by the phase-plane method

IT IS COMMON practice in college servomechanism laboratories to build a simple “linear” servomechanism system from which the student can determine the frequency and transient response. This simple system is generally composed of an error detector, electronic amplifier, and 2-phase servomotor as illustrated in Fig. 1. The student is immediately disturbed to discover that both the frequency and transient responses depend on the magnitude of the input signal. This is, of course, contrary to linear theory. The only conclusion that can be reached is that the apparently linear system just is not linear due to the characteristics of the 2-phase motor. In a previous publication it was shown why the Mp and resonant frequency of the frequency response characteristics varied with the magnitude of the input signal.1 It is the purpose of this paper to show how the nonlinear characteristics of the 2-phase motor influences the transient response of the system. This analysis is best carried out by means of the phase-plane method.