Open-loop frequency response method for nonlinear servomechanisms

This paper develops a useful graphical representation similar to the common Nyquist diagrams for the measured or calculated open-loop frequency response data of nonlinear systems.1,2,3,4 This representation indicates the frequency response characteristics and other phenomena such as limit cycles5 and response hysteresis, or jump phenomenon,6 of closed-loop systems. Likewise, this open-loop representation is convenient for the synthesis of linear filters, which can be inserted in the error amplifier to improve the closed-loop response of such nonlinear systems. In fact, the closed-loop frequency response of the nonlinear system with a linear filter in the error or forward section of the loop can be determined if both the transfer function of the linear filter and the open-loop frequency response of the nonlinear servo without the filter are known. Many who have measured the response of servo systems assumed to be linear have realized that the assumption of linearity is not always satisfactory. For very small input signals, backlash and coulomb friction cause nonlinear distortion, as does saturation when the input signal is large.7 It is hoped that the method used in this paper will help the servo engineer improve the response of nonlinear systems.