Optimal preview control based on quadratic performance index

This paper revisits the optimal preview tracking problem based on quadratic performance index. The reference signal is assumed to be step-type and previewable in a fixed interval of time ahead. Then, a reasonable performance index which quantifies the effect of the preview action on the transient response to the reference signal is proposed for this problem. The optimal preview control law is derived using optimal regulator theory. It consists of the feedback from the state of the plant and the feedforward from the reference signal within the previewable time interval. The relationship between the feedforward gains and the preview action is also investigated. Furthermore, a two-degree-of-freedom preview servosystem is proposed, in which the servo compensator is effective only when there exist modeling errors or disturbance inputs. This servosystem guarantees that designing the nominal transient response to the reference signal is independent of the gain of the servo compensator