Design of the Single-Input, Single-Output Type-1 Deadbeat Servo System by Minimizing the Deviation Input Energy

Abstract

This paper discusses the design of a type-1 deadbeat servo system for a single-input, single-output discrete-time linear time-invariant system when the settling time is larger than the order of the controlled system. The type-1 deadbeat servo system is transformed into the deviation system. First, a theorem which relates the general deadbeat input is obtained. By using this theorem, the fixed terminal state problem is transformed into the free new terminal state problem. Then, the problem of minimizing the deviation input energy for the specified settling time is formulated, and the optimal deviation input is obtained implicitly by using the special Riccati equation. Finally, the optimal deviation input is obtained explicitly. This optimal feedback gain is independent of the initial state of the controlled system, the step command signal and the step disturbance.