Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published December 2012 | metadata_only
Book Section - Chapter

PDE Boundary Control for Euler-Bernoulli Beam Using a Two Stage Perturbation Observer


A novel perturbation observer-based PDE boundary control law for beam bending is derived based on a combination of perturbation observers and polynomial trajectory planning. The perturbation observer consists of two components. The first stage employs the "particular" solution of the original dynamics with disturbances while its boundary conditions are set to zero. In contrast, the dynamics of the "homogeneous component" are independent of the beam dynamics, but its boundary conditions are identical to those of the beam. A tracking boundary control law, based on trajectory planning, is designed for the homogeneous component, and the same control signal is also applied to the beam. The stability of the adaptive perturbation-observer is proven by Lyapunov stability in the spatial L2 sense, while stability conditions are derived for a finite dimensional ODE analogue of the infinite dimensional closed loop PDE system. This paper also reports on one of the first experimental demonstrations of a controller designed entirely using a PDE boundary control formulation.

Additional Information

© 2012 IEEE. Date Added to IEEE Xplore: 04 February 2013. This project was supported by the U.S. Army Research Office (ARO) under Award No W911NF-10-1-0296.

Additional details

August 19, 2023
August 19, 2023