Analysis of transient oscillations in a nonlinear feedback system

In several recent papers [1]-[4] we established rigorous results which indicate when the describing function method is valid (i.e., under which conditions it predicts correctly the existence and the stability of a limit cycle). These results yield also estimates of bounds for limit cycles during transient time periods (i.e., during limit cycle build up or limit cycle build down). In the present paper we address the accuracy of our earlier results. In doing so, we analyzed several typical feedback systems by the method of [1] and we compared these results with those obtained via numerous simulations. Due to space limitations, the results of only one representative feedback system are included.