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

Repetitive control is useful if periodic disturbances act on a control system. Perfect (asymptotic) disturbance rejection is achieved if the period-time is exactly known. The improved disturbance rejection at the periodic frequency and its harmonics is achieved at the expense of a degraded system sensitivity at intermediate frequencies. A convex optimization problem is defined for the design of high-order repetitive controllers, where a trade-off can be made between robustness for changes in the period-time and for reduction of the error spectrum in-between the harmonic frequencies. The high order repetitive control algorithms are successfully applied in experiments with the tracking control of a CD-player system.