Solution of the repetitive control circuit using W-transform

The principle of the repetitive control circuit is that the control deviation from the previous interval is added to the control signal of the current time interval. This process is carried out continuously and in this way an asymptotic equality of the output signal time course with the control signal can be achieved. But this process is not always successful. Ensuring convergence of such a process is analogous to ensure the stability of classical feedback control loop. Such system includes also the time-delay, which complicates the synthesis of a control circuit described by the differential equations. In the paper there are presented some results of using W-transform to solve the output responses and to investigate the stability of the repetitive control circuit.