Robust H∞ performance of a two-degree-of-freedom servosystem

A two-degree-of-freedom servosystem for constant reference signals is considered, in which the integral compensation is effective only when there is a modeling error or a disturbance input. A condition on uncertain plants is presented, under which the servosystem achieves a specified robust H_∞ performance independently of the gain of the integral compensator. This result guarantees that if the plant uncertainty is in the permissible set defined by the condition, a high-gain integral compensation can be carried out, preserving the robust H_∞ performance, to suppress the influence of the plant uncertainties and disturbance inputs on the transient behavior of the servosystem. The transient behavior which is attainable by the limit of high-gain compensation is calculated using a singular perturbation approach