On the Nonlinear Modeling and Identification of Piezoelectric Inertial Actuators

Active counter-force vibration control has significant advantages over the more traditional motion-based active vibration suppression schemes. A piezoelectric ceramic (PZT) inertial actuator is an efficient and inexpensive solution for this type of structural vibration control. In order to properly tune the control parameters of the absorber subsection, an accurate mathematical model is necessary. For this, a nonlinear model for the PZT inertial actuators is presented. In particular, a polynomial form of non-linearity in the dynamical model of the actuator is assumed. An inverse problem is then formed to identify the model parameters of the actuator (absorber). The model parameters consist of the effective mass, damping and stiffness of the actuator as well as the polynomial form of the non-linearity. Using Lyapunov’s second method, the stability conditions for the proposed nonlinear model are established. An experimental setup is developed to validate the proposed nonlinear model. The results of the model identification using the actual experimental data demonstrate that the nonlinear model would better fit the experimental data, when compared to the linear model.