Sensitivity reduction of adaptive repetitive control system with asymptotical rejection against uncertain periodic disturbance

This paper deals with a repetitive control problem for the cases where the period of periodic disturbances to be rejected is uncertain but is within known lower and upper bound. A new adaptive repetitive control system with on-line estimation of the period is proposed not only to guarantee stability of the overall system but also both to reject any periodic disturbances with the uncertain period and to reduce sensitivity against any disturbances, for example, non-periodic persistent ones. The design problem is reduced to a simple and feasible l₁ norm minimization problem. The controller can be obtained easily by solving a simple linear programming problem. Simulations show the effectiveness of the proposed controller for rejection of periodic disturbances and sensitivity reduction.