Design of an optimal preview servomechanism for discrete-time systems in a multirate setting

This paper presents an LQ optimal preview servomechanism design method for linear discrete-time systems with time-delay in the multirate control setting. By making use of the discrete-time lifting technique, we reduce the multirate preview control problem to the single-rate one for a certain augmented system. Applying the standard LQ optimal preview control method to this augmented system, we characterize the optimal multirate preview controller in terms of a certain algebraic Riccati equation. The resulting optimal controller is a time-varying controller with periodic feedback gain matrices. It is show that the above Riccati equation has a positive semi-definite stabilizing solution under the standard assumptions for the optimal servomechanism design of the original system. A numerical example is included to illustrate the applicability of the present results.