Active vibration control of a sandwich plate by non-collocated positive position feedback

The active vibration control of a free rectangular sandwich plate by using the Positive Position Feedback (PPF) algorithm was experimentally investigated in a previous study. Four normal modes were controlled by four nearly collocated couples of piezoelectric sensors and actuators. The experimental results of the control showed some limitation, especially in the Multi-Input Multi-Output (MIMO) configuration. This was attributed to the specific type of sensors and their conditioning, as well as to the phase shifts present in the vibration at different points of the structure. An alternative approach is here undertaken by abandoning the configuration of quasi-perfect collocation between sensor and actuator. The positioning of the piezoelectric patches is still led by the strain energy value distribution on the plate; each couple of sensor and actuator is now placed on the same face of the plate but in two distinct positions, opposed and symmetrical with respect to the geometric center of the plate. Single-Input Single-Output (SISO) PPF is tested and the transfer function parameters of the controller are tuned according to the measured values of modal damping. Then the participation matrices necessary for the MIMO control algorithm are determined by means of a completely experimental procedure. PPF is able to mitigate the vibration of the first four natural modes, in spite of the rigid body motions due to the free boundary conditions. The amplitude reduction achieved with the non-collocated configuration is much larger than the one obtained with the nearby collocated one. The phase lags were addressed in the MIMO algorithm by correction phase delays, further increasing the performance of the controller.