Composite Nonlinear Feedback-Based $N$-Order Equivalent-Input-Disturbance Approach

The equivalent-input-disturbance (EID) approach is effective to suppress the influences of disturbances. However, an EID-based control system suffers from severe fluctuations when an exogenous disturbance appears and disappears, which degrades the transient performance. This article uses the composite nonlinear feedback (CNF) to deal with such a problem and is the first time to do that. Moreover, an $n$-order low-pass filter is designed for the EID approach to improving the disturbance-rejection performance. Combining the $n$-order EID estimator with the CNF, a CNF-based $n$-order EID approach is presented, which not only improves the disturbance-rejection performance but also degrades the fluctuations of the system output when the disturbance appears and disappears. Analyzing the configuration of the $n$-order low-pass filter, this article finds and proves its general mathematical express using the mathematical induction method. Next, the stability analysis is broken into stability conditions of two subsystems. Then, the design of the $n$-order EID estimator is transformed into an optimization problem based on the stability conditions. Finally, the simulation results show the validity and superiority of the presented method.