Effective feedback control requires all state variable information of the system. However, in the translational flexible-link manipulator (TFM) system, it is unrealistic to measure the vibration signals and their time derivative of any points of the TFM by infinite sensors. With the rigid-flexible coupling between the global motion of the rigid base and the elastic vibration of the flexible-link manipulator considered, a two-time scale virtual sensor, which includes the speed observer and the vibration observer, is designed to achieve the estimation for the vibration signals and their time derivative of the TFM, as well as the speed observer and the vibration observer are separately designed for the slow and fast subsystems, which are decomposed from the dynamic model of the TFM by the singular perturbation. Additionally, based on the linear-quadratic differential games, the observer gains of the two-time scale virtual sensor are optimized, which aims to minimize the estimation error while keeping the observer stable. Finally, the numerical calculation and experiment verify the efficiency of the designed two-time scale virtual sensor.
Keywords: linear-quadratic differential games; rigid-flexible coupling; singular perturbation; translational flexible-link manipulator; vibration observation.