Frequency-tracking servocompensator to systems with sinusoidal disturbance/reference signals: realization of the internal model using exogenous synchronous signals

Robust servocompensators to systems with sinusoidal disturbance/reference signals are designed to accomplish asymptotic regulation even if the frequencies of the signals change from their nominal values. These compensators are developed based on the conventional servocompensator which has an internal model of the dynamics of the disturbance/reference signals. This model supplies transmission zeros to cancel the unstable poles of the disturbance/reference signals. When the frequencies of these exogenous signals vary, the unstable poles move from their original locations. Hence, for asymptotic tracking/regulation, the internal model must be altered according to the frequencies. In the developed compensators, control input is calculated based on convolution integral instead of state-space equation. In calculating the convolution, exogenous signals synchronized with the disturbance/reference signals are used as a weighting function. As a result, the transmission zeros of the closed-loop system are generated at the same locations as the unstable poles of the disturbance/reference signals. The developed compensator is applied to an active dynamic vibration absorber system. The performance of frequency tracking is certified experimentally