Mismatched Disturbance Rejection Control for Second-Order Discrete-Time Systems

This article is concerned with mismatched disturbance rejection control for the second-order discrete-time systems. Different from previous work, the controllability of the system is applied to design the disturbance compensation gain, which does not require any coordinate transformation. Via this new idea, it is shown that disturbance in the regulated output is immediately and directly compensated in the case that the disturbance is known. When the disturbance is unknown, an extra generalized extended state observer is applied to design the controller. Numerical simulation is used to demonstrate that the designed controller exhibits excellent disturbance rejection capabilities. Furthermore, by applying the proposed method to a permanent magnet synchronous motor servo system, the effectiveness and practicality of the proposed approach in eliminating unknown disturbances are illustrated.