Robust stability and high-gain compensation of a two-degree-of-freedom servosystem

In order to reject the steady-state tracking error, it is common to introduce integral compensators in servosystems for constant reference signals. However, the mathematical model of the plant is exact and no disturbance input exists, the integral compensation is not necessary. From this point of view, a two-degree-of-freedom (2DOF) servosystem has been proposed, in which the integral compensation is effective only when there is a modeling error or a disturbance input. The present paper considers robust stability and high-gain compensation of this 2DOF servosystem. A condition on uncertainties in the plant model is presented, under which the servosystem is robustly stable independent of the gain of the integral compensator. This result implies that if the plant uncertainty is in the allowable set defined by the condition, a high-gain integral compensation can be carried out preserving robust stability to accelerate the tracking response. The transient behavior attainable by the limit of the high-gain compensation is calculated using a singular perturbation approach