General Form of MIMO Type-1 Deadbeat Servo Systems by Using Virtual Command Signals

This paper shows the structure of the type-1 deadbeat servo system using virtual command signals, in which the output settles to a command signal in a finite number of control steps, for multiinput multi-output linear discrete-time systems. By using virtual command signals, new input is induced in the deviation system of the augmented system. The reachability indices of the deviation system are determined uniquely by the reachability indices of the controlled system and the number of the output. Then, the minimum settling time does not increase even when the integrator is added to the controlled system. Furthermore, two theorems are induced to obtain the general form of the type-1 deadbeat servo system. Finally, numerical examples are illustrated to show the effectiveness of using virtual command signals.