Improve Disturbance-Rejection Performance for an Equivalent-Input-Disturbance-Based Control System by Incorporating a Proportional-Integral Observer

This paper presents a new configuration of a linear control system that provides a superior disturbance-rejection performance. The concept of equivalent input disturbance (EID) is used to estimate the influence of an exogenous disturbance on the system. Compared with the Luenberger observer, an extra integrating term from a proportional-integral observer (PIO) helps to introduce a relaxing variable to the system design. This increases the flexibility of system design and enables the robustness of the system. Moreover, the integrating term improves the estimation precision of the system state. Taking advantages of these merits, the combination of an EID estimator and a PIO is used to produce an EID. Then, a new control law, which incorporates the EID estimate, is designed to ensure good control performance. A stability condition of the closed-loop control system is derived in terms of linear matrix inequalities (LMIs). Further, the gains of the state-feedback controller and PIO are designed based on the LMIs. Comparisons with related methods demonstrate the validity of the developed method.