Abstract
This paper discusses the linear-quadratic optimal control problem of a type-1 deadbeat servo system for a multi-input, multi-output linear time-invariant discrete-time system. The type-1 servo system is formulated by using the augmented system and its deviation system. By using the deadbeat principle, the deviation system is transformed into the new time-variant system with the time-variant structure of the new inputs. The performance index is transformed into the new one, and the new terminal state is free. The optimal deviation inputs are made up of three phases, and they are given by linear combinations of the constant gain state feedback and the variable gain state feedback. The variable gains are obtained by using the special nonstationary Riccati equation. The optimal gains are independent of the initial state of the controlled system, the step command signal and the step disturbance.
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