Adaptive Vibration Control of Piezoactuated Euler-Bernoulli Beams Using Infinite-Dimensional Lyapunov Method and High-Order Sliding-Mode Differentiation

Abstract EN

This paper presents an adaptive control scheme to suppress vibration of flexible beams using a collocated piezoelectric actuator-sensor configuration.

A governing equation of the beams is modelled by a partial differential equation based on Euler-Bernoulli theory.

Thus, the beams are infinite-dimensional systems.

Whereas conventional control design techniques for infinite-dimensional systems make use of approximated finite-dimensional models, the present adaptive control law is derived based on the infinite-dimensional Lyapunov method, without using any approximated finite-dimension model.

Thus, the stability of the control system is guaranteed for all vibration modes.

The implementation of the control law requires a derivative of the sensor output for feedback.

A high-order sliding mode differentiation technique is used to estimate the derivative.

The technique features robust exact differentiation with finite-time convergence.

Numerical simulation and experimental results illustrate the effectiveness of the controller.