The Describing-Function Analysis of a Non-Linear Servo Mechanism subjected to Stochastic Signals and Noise

A technique is presented for evaluating the response of a specific type of non-linear servo mechanism to random signals, to sinusoidal signals contaminated by noise and to random signals contaminated by noise. In particular, a second-order servo mechanism incorporating derivative-of-error stabilization and subjected to torque limitation is considered. Theoretical responses are evaluated for a wide range of parameters, and experimental verification is included. The analysis presented is basically an extension of the describing-function technique and can be applied to any second-order servo mechanism incorporating, either by design or inherently, a simple amplitude-dependent frequency-insensitive non-linearity.