An improved electromechanical model and parameter identification technique for piezoelectric actuators

Piezoelectric actuators are often modeled as a lumped mass system in the mechanical domain and as a capacitive element in the electrical domain. Based on a real-time capacitance measurement, it is observed that the piezoelectric capacitance is a function of voltage. This leads to a modification of the traditional piezoelectric actuator model where the capacitance is usually considered constant. A voltage-dependent capacitance term is introduced in the constitutive equations in the electrical domain, and it is demonstrated that this term satisfies a power balance. Then, a novel parameter identification technique is proposed for the modified constitutive equations. The advantage of this identification technique lies in its simplicity that requires only a single experiment to identify all pertinent model parameters. In addition, the hysteresis voltage is conveniently extracted from the applied voltage for a large frequency range. In comparison to the traditional parameter identification procedure and electromechanical models, the proposed technique along with the modified model provides an improved fitting of the parameters. The new model and its identification technique can be applied to sensorless position control applications where exact models are the basis for robust control system designs.