Optimal controls of SISO type-1 digital servo systems using virtual command signals

Describes linear-quadratic optimal controls of type-1 servo systems by using virtual command signals for discrete-time systems. The problem of designing a type-1 servo system is transformed into a regulator problem by using a deviation system of an augmented system with an integrator. Since the virtual command signal works as the new input, the deviation system becomes a two-input system. Then, the optimal control with infinite control time, the free-end-point optimal control, and the fixed-endpoint optimal control are obtained. The transient responses can be improved by the effect of the virtual command signal