Zeros of the Closed-Loop Transfer Function from Disturbance to Its Estimation Error via Disturbance Observers Based on Minimal-Order State Estimators

In this paper, a synthesis method is proposed for locating the zeros of the closed-loop transfer function Gdd~(s) from disturbance to its estimation error using a disturbance observer based on a minimal-order state observer. The basic idea involves distinguishing assignable and unassignable zeros by transforming the system matrix of Gdd~(s) into a block lower-triangular form. The observer gain matrix is then designed to enable the placement of desired zeros and poles of Gdd~(s). By applying the synthesis procedure for the observer gain matrix, Gdd~(s) is made to satisfy the following design conditions: 1) The direct current (DC) gainGdd~(0) can be selected as a real value within the range [0, 1). 2) All poles of Gdd~(s) can be located in the left half of the complex plane. The significance of the proposed approach is illustrated through its application to an angle control system of a DC motor.