The frequency response of a servomechanism designed for optimum transient response

The frequency response of a mechanical system which is subjected to torque limitation and which, by the addition of nonlinear error processing, is designed to have an optimum response to step-function inputs, is evaluated qualitatively. This analysis is carried out to determine the effect on the frequency response of the error-processing element and, moreover, to determine whether this system has advantages in addition to optimum transient response. The closed-loop response of this system to a sinusoidal excitation signal is evaluated from a graphical representation of the open-loop frequency response. The latter takes into consideration the harmonics in the control signal. This closed-loop response is compared with that of the equivalent system subjected only to torque limitation. Both velocity feedback and derivative of error stabilization are considered. The mechanical system is simulated on an analogue computer and experimental verification of the analysis is obtained. Finally, the approximate frequency response of the optimum system is evaluated by neglecting the harmonics in the control signal. This approximate response is compared with that evaluated previously, and this comparison shows that the neglect of these harmonics is justifiable.