Two-degrees-of-freedom dead-beat control system with robustness

This paper deals with the design of a two-degrees-of-freedom (TDF) dead-beat controller with both optimal robustness and minimum settling time. Based on the parametrization of all stabilizing TDF controllers, optimal robustness and minimum-time control are achieved simultaneously. The minimum-time dead-beat control is constructed for arbitrary real-rational reference input. At the same time, optimal robustness is achieved under the constraint that the error between reference input and output asymptotically vanishes for any plant perturbation that does not violate the internal stability. It is proved that under the same robustness criterion, irrespective of its length of settling time, the optimal robustness of the TDF system is always superior to that of the one-degree-of-freedom (ODF) system as long as its settling time is finite, and they become identical only when the settling time of the ODF system goes to infinity. A numerical example is given to illustrate the theoretical results.