Design of an optimal preview controller for linear discrete-time multirate systems with state-delay

Designing a preview controller for discrete-time muhirate input systems was considered. At first, by making use of the lifting technique to eliminate the muhirate characteristic and the state time-delay of the sampled system, the problem was converted into a controller design problem for a single-rate no-delay sampled system. Because of the existence of state time-delay, the historical values of input data would be introduced during the lifting process. However, the historical values and the state delay were put into the state vector of the expanding system so that no error was introduced during the lifting process. For the lifted system, the problem was changed into an adjust problem via the standard method of dealing the optimal preview control and by constructing an expanded-error system, and finally an optimal controller with preview compensation was derived subsequently. Through transformation a preview controller was then obtained for the original system. The existence condition of the preview controller was discussed. Numerical simulations proved the effectiveness of the preview controller designed in the paper.