Adaptive non model-based piezoelectric control of flexible beams with translational base

An adaptive, nonmodel-based controller is proposed for the tracking control of a flexible cantilever beam with a translational base support. A piezoelectric (PZT) patch actuator is bonded on the top surface of the beam to apply a controlled moment for vibration suppression requirement. By selecting a Lyapunov function candidate based on a very simple energy relationship, an adaptive nonlinear feedback gain for the PZT input voltage and a simple PD controller for the moving base input force are designed to make the closed-loop system energy dissipative and hence stable. Due to the non model-based nature of the controller, some favorable features appear such as elimination of control spillovers, suppression of residual oscillations of the beam and simplicity of the control implementation. The feasibility of the controller is demonstrated using numerical simulations. Although the controller derivation is based on the original distributed partial differential model, a two-node finite element model is used for the numerical solution of the coupled PDE of the system.