Multi-Mode Vibration Suppression in MIMO Systems by Extending the Zero Placement Input Shaping Technique: Applications to a 3-DOF Piezoelectric Tube Actuator

Piezoelectric tube actuators are extensively used in scanning probe microscopes to provide dynamic scanning motions in open-loop operations. Furthermore, they are employed as micropositioners due to their high bandwidth, high resolution and ease of excitation. However, these piezoelectric micropositioners exhibit badly damped vibrations that occur when the input excites the dynamic response, which tends to degrade positioning accuracy and performance. This paper deals with vibrations' feedforward control of a multi-degrees of freedom (DOF) piezoelectric micropositioner in order to damp the vibrations in the direct axes and to reduce the cross-couplings. The novelty in this paper relative to the existing vibrations feedforward controls is the simplicity in design approach, the minimal number of shaper impulses for each input required to damp all modes of vibration at each output, and the account for the strong cross-couplings which only occur in multi-DOF cases. A generalization to a multiple degrees of freedom actuator is first proposed. Then simulation runs on a 3-DOF piezoelectric tube micropositioner have been effectuated to demonstrate the efficiency of the proposed method. Finally, experimental tests were carried out to validate and to confirm the predicted simulation.