An observer-based piezoelectric control of flexible Cartesian robot arms: theory and experiment

摘要

An observer-based control strategy is proposed for regulating problem of a Cartesian robot arm, which is modeled as a flexible cantilever beam with a translational base support. The base motion is controlled utilizing an electrodynamic shaker, while a piezoelectric (PZT) patch actuator is bonded on the surface of the flexible beam for suppressing residual arm vibrations. Taking into account both electrical and mechanical fields for the PZT patch actuator, a full-order model is developed using assumed mode model expansion and the Lagrangian approach. Utilizing three measurable quantities (i.e., the base displacement, arm tip deflection and the strain at the root end of the arm), a reduced-order observer is designed to estimate the velocity related variables, which are not directly measurable for the truncated model. A simple PD controller is selected for the moving base regulation, while a Lyapunov-based controller is utilized for the PZT input voltage to make the closed-loop system energy dissipative and hence stable. The PZT input voltage control uses the velocity related signals estimated by the reduced-order observer, which simplifies the control implementation in practice. The feasibility of the controller is validated through both numerical simulations and experimental testing. Significant matching between experimental results and numerical simulation is observed.