State Feedback Repetitive Control: Robustness and Load Disturbance Conditions

Robust and load disturbance conditions for state feedback Repetitive Control (RC) are investigated for linear time-invariant system. The Conditions found sets either an upper limit or lower limit weighting parameter depending on the case investigated in the design. The repetitive design investigated is a development of previously reported work, where the new design incorporates both past error feedforward and current error feedback rather than a current error feedback alone. The design idea is to include a pure delay model acting on the system input representing periodic disturbances. Isolating the delay model, finding the overall transfer function around the delay model, and using the small gain theorem, a stability condition is obtained that assures overall system stability and periodic disturbances accommodation. The conditions found, as the simulation results obtained show, had suppressed the uncertainty effect in the case where a weighting parameter is used compared to the case where the weighting parameter is omitted.