Multi-variable Generalized Minimum Variance Control with Time-delay Using Interactor Matrix

This paper proposes a generalized minimum variance controller for multivariable systems with time-delays. The controller is derived by the following procedure to avoid the difficulty caused by time-delays; First the design problem for single-input single-output (SISO) systems with time-delay is considered. The problem is modified for systems without time-delay in appearance but equivalent to the original problem. Then the SISO case is extended to multi-input multi-output(MIMO) case by replacing time-delay steps in SISO case with an interactor matrix of MIMO plants. That is, the outputs of the MIMO plants are shifted forward by the steps of the degrees of the interactor matrix, then the MIMO plants with time-delays is modified to the plants without time-delay and a controller for plants with time-delay are obtained by applying the method for no time-delay plants to the modified MIMO plants.