Modeling and stabilization of current-actuated piezoelectric beams

Current controlled piezoelectric beams have been very popular recently due to the substantial reduction of hysteresis between the input and output. Even though there are many different PDE models for the voltage and charge controlled piezoelectric beams, there is no thoroughly derived PDE model in the literature for current controlled piezoelectric beams. A variational approach is utilized to derive the boundary value problem which models a single piezoelectric beam actuated by a current source at the electrodes. Magnetic effects are included. In addition to the Euler-Bernoulli displacement assumptions for the mechanical part, we assume that electrical and magnetic vector potential terms are quadratic-through thickness. Since current controller at the electrodes can control only the stretching equations, only the stretching equations are considered. Unlike the voltage or the charge actuation cases, a bounded control operator in the natural energy space is obtained.