Multimodal active vibration suppression of a flexible structure by loop shaping

This paper reports multimodal vibration control of a flexible beam structure with piezoceramic actuators and sensors using the loop shaping method. These piezoceramic patch actuators and sensors are surface-bonded on the flexible beam. The non-parametric identification of the flexible beam structure is carried out using the Schroeder wave. The identified open loop model is then used for loop shaping based on the extended sensitivity charts. A loop shaping compensator is designed to achieve multimodal vibration suppression. Numerical results showed a reduction of 8 decibels for first mode, 12-14 decibels for second and third mode, respectively. Experimental results closely match the simulation results. Furthermore, the results of loop shaping method are compared with those of the methods of LQR (Linear Quadratic Regulator) and pole-placement control, which are designed using state space models. Comparisons show that the loop shaping method requires less control effort while maintaining the effectiveness in vibration suppression.