Robust disturbance rejection methodology for unstable non-minimum phase systems via disturbance observer

In this work, we propose a disturbance rejection methodology to deal with control problem of unstable non-minimum phase (NMP) systems. Firstly, we propose a two degrees-of-freedom control structure, which consists of an outer loop feedback controller and an inner loop disturbance observer (DOB). Specifically, the controller is designed for desired control performance, whereas the robust DOB is applied to deal with external disturbances and internal uncertainties. By analyzing the robust internal stability, several design requirements on both controller and DOB are presented for the control system. The H₂ theory is adopted for controller design. Then, we propose a systematic DOB optimization method for unstable NMP systems. The proposed method synthesizes the relative order, robust internal stability and mixed sensitivity optimization together to formulate the cost function. The standard H_∞ method is introduced to acquire the optimal solution that guarantying the design requirements. Simulations show that the proposed method can deal with the control system design for the unstable NMP systems, and it also has better performance comparing with the traditional method.