Comparison of stabilization of current-actuated and voltage-actuated piezoelectric beams

Current controlled piezoelectric beams have become increasingly popular recently. The authors have used a variational approach derive the model for a single piezoelectric beam actuated by a current source at the electrodes, and similarly for the voltage-controlled case. Magnetic effects are included. In addition to the Euler-Bernoulli displacement assumptions for the mechanical part, electrical and magnetic vector potential terms are assumed to be quadratic-through thickness, not linear. Inclusion of magnetic effects significantly changes the stabilizability properties of the model. The voltage-controlled beam leads to a control operator that is unbounded in the energy space, while the current-controlled case leads to a bounded control operator. The two situations are compared from a control perspective.