Robust vibration control of two-mass resonant systems in state space

In this paper, a novel robust position controller is proposed for two-mass resonant systems. It is designed by using Differential Flatness (DF) and Disturbance Observer (DOb) in state space. Firstly, DF-based trajectory tracking controller is designed by neglecting plant uncertainties and external disturbances. Since a two-mass resonant system is controllable, state and control input references are generated in terms of differentially flat output. However, the trajectory tracking controller is sensitive so the stability and performance may significantly change due to the robustness issues in practice. Secondly, the robustness is achieved by treating estimated disturbances, which are obtained via DOb, in the design of the controller. A two-mass resonant system includes matched and mismatched disturbances; therefore, the robustness cannot be achieved by directly feeding-back their estimations. The states of the system are re-constructed by using estimated disturbances so that the mismatched disturbance is automatically cancelled via state feed-back control. The matched disturbance is simply cancelled by feeding-back its estimation. Hence, the robust trajectory tracking controller is designed for two-mass resonant systems. The validity of the proposal is verified by giving simulation results.