Modeling and Adaptive Parameter Estimation for a Piezoelectric Cantilever Beam

This paper proposes a new adaptive estimation approach to online estimate the model parameters of a piezoelectric cantilever beam. The beam behavior is firstly modeled using partial differential equations (PDE) considering the Kelvin-Voigt damping. To facilitate the estimation of unknown model parameters, the Galerkin’s method is introduced to extract desired vibration modes by separating the time and space variables of the PDE. Then, considering two major vibration modes, the corresponding system model can be represented by a fourth-order ordinary differential equation (ODE). Finally, by using measured input and output information, a novel adaptive parameter estimation strategy is introduced to estimate the unknown parameters of the derived ODE model in real time. For the purpose of driving the parameter updating law, the estimation error is extracted by using an auxiliary variable and a time-varying gain. Consequently, the convergence of the parameter estimation error is rigorously proved based on the Lyapunov theory. Simulations and experimental results show the validity and practicability of the proposed estimation method.