Theory and Experiments on Tracking of the Repetitive Signals

The work presented here is a simple feedback controller methodology that allows for exact tracking of the sinusoidal input signals and rejection of the sinusoidal disturbances in a closed loop control system. The control method is motivated by a mathematical inequality that expresses the tracking and disturbance rejection requirements for a closed loop system. The exact tracking of the input command at a particular frequency requires an infinite loop gain for the system at the frequency of the input command. A second order undamped transfer function is cascaded to teach input channel to increase the loop transfer function gain at the frequency of the input command. A feedback controller is then designed via the LQG/LTR method to stabilize the system while the loop gain remains large at the frequency of the input. The method is experimentally verified on a single axis servo system and extended to multivariable systems.