Abstract: The first order vibration mode is used in the mathematic modeling of the Galfenol cantilever beam. The frequency dependences of the model parameters are found by analyzing the experimental displacement data. It is found that when the excitation frequency is higher than 220 Hz, the divergences of the model parameters are obvious. In order to solve the frequency dependence problem, a robust adaptive control strategy is proposed based on state observer. The performance of the control can be improved by estimating the model parameters adaptively. Numerical simulation and experimental researches are conducted by comparing the proposed method with the Luenberger observer. It is found that the adaptive observer can predict the state variable of the beam effectively. The aberrant disturbance resulted from the high order vibration modes of the beam can be suppressed by using the proposed dead zone adaptive law. The model parameters also can be estimated to effective values. It is found from the tracking experiments that effective control performance can be obtained by using the same initial model parameters, even when the cantilever beam is excited at 100 Hz and 500 Hz, respectively.

Key words: Adaptive, Cantilever beam, Control, Galfenol, Observer