An Adaptive Self-Sensing Strategy for Dynamic Mass Estimation using Piezoelectrically-Driven Cantilevers

This paper presents an adaptive estimation strategy to dynamically balance a self-sensing capacitance bridge network for cantilever-based tip mass estimation. The system comprises of a cantilever beam with a piezoelectric patch actuator deposited on the beam surface, connected in a capacitance bridge network. The goal is to estimate the mass of a particle deposited on the cantilever tip by measuring the associated shift in the beam natural frequency. The piezoelectric patch behaves as a self-sensing actuator. Accurate balance of the capacitance bridge is a key requirement for the self-sensing network to function properly. In this paper, a prediction-error-based mechanism is presented to estimate the actuator capacitance and keep the bridge dynamically balanced. The adaptation law uses a generalized form of the gradient estimation method. Lyapunov-based stability analysis is carried out to prove the global stability of the law. A modified gradient estimation method, which is relatively easy to implement, is shown to be a special case of the generalized mechanism. Experimental results are presented to demonstrate the working of this estimation strategy.