On noise and period-time sensitivity in high order repetitive control

Repetitive control is useful if periodic disturbancesact on a control system. Perfect (asymptotic) disturbancerejection is achieved if the period-time is exactlyknown. The improved disturbance rejection at the periodicfrequency and its harmonics is achieved at the expense ofa degraded system sensitivity at intermediate frequencies. Aconvex optimization problem is defined for the design of highorderrepetitive controllers, where a trade-off can be madebetween robustness for changes in the period-time and forreduction of the error spectrum in-between the harmonicfrequencies. The high order repetitive control algorithms aresuccessfully applied in experiments with the tracking controlof a CD-player system.