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Due to their fast response, high accuracy and non-friction force, piezo-actuators have been widely employed in multiple degree-of-freedom (DOF) stages for various nano-positioning applications. The use of flexible hinges in these piezo-actuator-driven stages allows the elimination of the influence of friction and backlash clearance, as observed in other configurations; meanwhile it also causes more complicated stage performance in terms of dynamics and the cross-coupling effect between different axes. Based on the system identification technique, this paper presents the development of a model for the 3-DOF piezo-actuator-driven stages with unknown configuration, with its parameters estimated from the Hankel matrix by means of the maximum a posteriori (MAP) online estimation. Experiments were carried out on a commercially-available piezo-actuator-driven stage to verify the effectiveness of the developed model, as compared to other methods. The results show that the developed model is able to predict the stage performance with improved accuracy, while the model parameters can be well updated online by using the MAP estimation. These capabilities allow investigation of the complicated stage performance and also provide a starting point from which the mode-based control scheme can be established for improved performance

State Space System Identification of 3-Degree-of-Freedom (DOF) Piezo-Actuator-Driven Stages with Unknown Configuration