Design of Internal-model-based Disturbance Observers for Achieving Asymptotic Disturbance Rejection

This paper presents a design method for internal-model-based disturbance observers for first-order uncertain linear plants to achieve asymptotic disturbance rejection. Conventional disturbance observers typically attenuate the effect of disturbances on the closed-loop system, but do not guarantee asymptotic rejection of disturbances. By contrast, inspired by the internal model principle, we explicitly embed a disturbance model into the disturbance observer structure, thereby enabling asymptotic disturbance rejection. The disturbance is assumed to be generated by the output of a second-order linear exosystem that may include unstable modes. Accordingly, it can be sinusoid or polynomial-in-time of degree less than two. A robust stability condition for the resulting closed-loop system is also derived, based on singular perturbation theory. Finally, simulation results for motor control system are provided to validate the effectiveness of the proposed disturbance observer design.