A structural model is significant for the verification of structural control algorithms. However, for nonlinear behavior, experiments are mostly destructive tests that are costly, and conducting repetitive structural experiments is difficult. Therefore, a repetitive structural vibration model is important for structural vibration control. In this study, a smart platform to realize different structural behaviors is developed based on the backstepping control algorithm. Lyapunov functions are used to derive the control law. Simulations show that the designed model can track the structural responses of different arbitrary linear structures very well. In addition, the proposed platform can track responses of different piecewise linear structures and desired models with various hysteresis very well. Numerical results verify the effectiveness of the proposed tracking controller through the backstepping method for the established platform. However, for nonlinear behavior, experiments are mostly destructive tests that are costly, and conducting repetitive structural experiments is difficult. Thus, a repetitive structural vibration model is important for structural vibration control. In this study, a smart platform to realize different structural behaviors is developed based on the backstepping control algorithm. Lyapunov functions are used to derive the control law. Simulations show that the designed model can track the structural responses of different arbitrary linear structures very well. In addition, the proposed platform can track responses of different piecewise linear structures and the desired models with various hysteresis very well. Numerical results verify the effectiveness of the proposed tracking controller through the backstepping method for the established platform.