A Finite Settling Time Response of the 2nd Discrete-Data Control System with a Dead Zone Element

In general, the settling time is infinite in continuous control systems which have the transient response without overshoots. However, in a discrete-data control system, we can obtain a finite settling time response. In this paper, the nonlinear discrete-data control system having 2nd order linear transfer function was considered about the response to a step-function input, and the state-transition method, which is more available for complicated problems, was used in the analysis or synthesis of the control system instead of the classical method with the aid of the Z-transform. The dead zone which has a general characteristic was picked up as an example of nonlinear elements, and the compensating method by a digital controller which was treated as a variable gain element with the nonlinear element, was used to settle the transient response in the minimum sampling numbers. In consequence, it is shown that the gain of a system has no effect on the transient response, but has an effect on the pulse-transfer function of the digital controller.