Two-degree-of-freedom design method of LQI servo systems: performance deterioration by the introduction of an observer and optimal observer design

This paper studies a two-degree-of-freedom design method of robust servo systems for step references and disturbances in the setting of output feedback. Specifically, we consider the introduction of a state observer, and show that the fundamental desirable properties (i.e., two-degree-of-freedom nature) attained in the state feedback case are inherited, qualitatively speaking, to the output feedback case. On the other hand, we quantitatively clarify the performance deterioration of disturbance rejection caused by the introduction of an observer. Furthermore, a design method of the optimal observers for such servo systems that minimize this deterioration is given. Separation property is shown to hold also in the two-degree-of-freedom servo problem, and connections of the optimal observers with the technique of loop transfer recovery and with perfect control of disturbances are discussed