Digital redesign methods based on plant input mapping and a new discrete-time model

The digital redesign approach is to obtain discrete-time controllers which realize a digital control system approximating some characteristics of the predesigned continuous-time control system. This paper describes a digital redesign method for linear time-invariant continuous-time control systems of the 1-DOF type and the state-feedback type. It is a closed-loop method that takes account of the closed-loop characteristics of the predesigned continuous-time control system. Generally, such methods provide better closed-loop stability and closer approximation to the underlying continuous-time control system for a wider range of sampling periods. The proposed method is based on mapping of the closed-loop control inputs and the transfer function matrix from external inputs to control inputs is discretized as a discrete-time model which generates average continuous-time system outputs for constant inputs. The discrete-time controller or the feedback/feedforward gain matrix is determined so that the discretized closed-loop transfer function matrix can be realized. The redesign is carried out using the state-space approach; thereby the method can be applicable to MIMO systems. To illustrate the method's effectiveness, numerical examples are shown.