Step Response of Second Order Servo Incorporating Piecewise Linear Element : Case of Hysteresis

Abstract

An exact solution in mathematical sense for the step response of the second order servo incorporating a hysteresis element is obtained. It is made clear that the step responses are sorted out into three types according to the value which the system gain constant takes. And both the condition for the system to have a cycle and an elementary proof that the cycle is a limit cycle are given by the successor function method. Besides the approximate solution for the cycle obtained by the describing function method is studied in detail.