Improving Equivalent-Input-Disturbance Approach via Modifying a Disturbance-Estimation Algorithm

The conventional equivalent-input-disturbance (EID) approach includes an estimation error. Suppressing the estimation error is an effective way to improve the disturbance-rejection performance. This article takes the estimation error as an artificial disturbance; thus, the estimation-error suppression is transformed into a disturbance-rejection problem. Next, studying the disturbance-rejection mechanism of the EID approach, we find that the EID approach estimates signals causing the observation error. If the observation error is caused by the disturbance and the estimation error, the EID approach compensates for them both. From this point of view, this article adds the estimation error into the control-input channel of the state observer to ensure the observation error is caused by the disturbance and estimation error. Summarizing this concept, this article modifies the disturbance-estimation algorithm and presents an improved EID (IEID) approach. Analyzing the disturbance-rejection mechanism and stability conditions of the IEID approach, this article transforms the design of the IEID approach into an optimization problem to achieve the best disturbance-rejection performance. The IEID approach removes the requirement for the highest angular frequency of exogenous disturbances, and thus, the application range of the IEID approach is wider than the methods of previous similar studies. Finally, simulation and experimental results show the validity and superiority of the presented method.