A robust state-space controller design for multi-mass resonant systems

This paper proposes a new state-space controller for the robust trajectory tracking control problem of multi-mass resonant systems. It is designed in state-space by combining Differential Flatness (DF) and a higher order Disturbance Observer (DOb). The former systematically generates the control input and state references of a state feed-back controller so that not only regulation but also trajectory tracking control can be performed in state-space. They are obtained in terms of differentially flat output variable in DF. The latter estimates disturbances and their successive time derivatives. Its order depends on the resonant modes of the system. The proposed controller has a two-degrees-of-freedom motion control structure. Its performance and robustness can be independently adjusted by tuning the state feed-back controller and DOb, respectively. It is designed in two steps. In the first one, the state feed-back controller is tuned by only considering the nominal plant model of the system. The nominal performance is adjusted by using pole placement; e.g., all poles of the nominal system are placed on the real axis so as to suppress the vibration at tip. The state and control input references of the state feed-back controller are obtained by using DF. In the second step, the robustness of the system is achieved by reconstructing the state vector via the estimations of disturbances and their successive time derivatives. Thanks to the proposed new state variables, mismatched disturbances are automatically cancelled by the state feed-back controller. The matched disturbances are cancelled by feeding-back their estimations through control input. Hence, the robustness of the multi-mass resonant systems is achieved. Without losing generality, the proposal is verified by considering three-mass resonant systems. Its simulation results are given to validate the proposal.