How the bandwidth of a servo affects its saturated response

The transient response of a servomechanism to a very large step may be quite oscillatory because of saturation of the power member in acceleration. By making certain idealized yet reasonable assumptions, this paper shows that the number of overshoots of the response to a step large enough to drive the system to velocity saturation is related quite simply to the maximum acceleration, maximum velocity, and the gain crossover frequency (bandwidth) of the primary servoloop. To limit the number of overshoots in certain applications, the maximum velocity and/or bandwidth of the servo may have to be excessively lowered. However, it is possible to remedy this difficulty with nonlinear compensation, which varies the gain crossover frequency inversely with the output velocity, so as to allow a stable transient for a large step input yet maintain high gain and a wide bandwidth for small inputs.