Design of an optimal controller for a discrete-time system subject to previewable demand

This paper is concerned with a method of designing a type one servomechanism for a discrete-time system subject to a time-varying demand and an unmeasurable constant disturbance. It is assumed that the time-varying demand is previewable in the sense that some finite future as well as present and past values of the demands are available at each time. A controller with state feedback plus integral and preview actions is derived by applying a linear quadratic integral (LQI) technique due to Tomizuka and Rosenthal (1979). It is shown under the stabilizability and detectability conditions that the closed-loop system achieves a complete regulation in the presence of small perturbations in system parameters, eliminating the effect of disturbance. An example of power plant control is presented to show the flexibility of the design method and the effectiveness of the preview action for improving the transient responses of the closed-loop system.