Simultaneous suppression of badly damped vibrations and cross-couplings in a 2-DoF piezoelectric actuator by using feedforward standard H∞approach

This paper deals with the feedforward control of vibrations in a 2-axis piezoelectric actuator devoted to precise positioning. The actuator is very prized for high precision spatial positioning applications, but its positioning capability as well as the stability of the final tasks are compromised by badly-damped vibrations, especially during high-speed positioning operation. In addition to these vibrations, the presence of strong cross-couplings between different actuator axis poses challenge in the feedforward control scheme. This paper proposes a bivariable feedforward standard H1 approach to suppress the vibrations in the direct transfers and to reduce the amplitudes of the cross-couplings. The proposed approach is simple to handle and easy to implement, comparatively to the commonly used techniques for oscillations suppression. Experimental tests demonstrate the efficiency of the proposed approach.