Abstract
This paper discuses the linear-quadratic optimal control problem of a type-1 deadbeat servo system for single-input linear time-invariant discrete-time system with fixed terminal atate. The fixed terminal state condition is called the state deadbeat condition. The type-1 servo system is transformed into the deviation system. first, the general deadbeat input of the deviation system is expressed by constant gain state problem is transformed into the deviation system. First, the general deadbeat input of the deviation system is expressed by constant gain state feedback and arbitrary input. By using this general deadbeat input, the fixed terminal state problem is transformed into the free new terminal state problem. Then, the problem of minimizing the quabratic performance function is solved, and the optimal deviation input is obtained by using the special Riccati equation. This optimal feedback gain is made up by the variable gains and the constant gain, which are independent of the initial state of the controlled system, the step command signal and the step disturbance.
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