The residual vibration is a very universal problem in flexible manipulators which are widely used in robot technology. This paper focuses on the soft measurement of the vibration signals for a translational flexible-link manipulator (TFLM) system. A vibration observer based on the improved Luenberger observer, which only requires the practical measurement values of the boundary positions, is designed to obtain the vibration signals of the TFLM. The main contribution of the vibration observer is its ability to simplify system structure and get the vibration signals of any point of the TFLM which is unrealistic by infinite sensors in practice. Furthermore, the improved part of the Luenberger observer is the added feedback coefficients for the tip vibration signals which can correct the observed mode and reduce the observation error markedly. And according to the stable conditions of observer, the added feedback coefficients are designed by Lyapunov technique and multiple population genetic algorithms (MPGA). Finally, the efficiency of the designed vibration observer is verified by combined-simulation
