Observer-based Stabilization of an Unstable Parabolic PDE Using Pseudospectral Method and Sturm-Liouville Theory
C. Xu and E. Schuster
17th Mediterranean Conference on Control and Automation
Thessaloniki, Greece, June 24 - 26, 2009
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Abstract
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The stabilization of an unstable linear parabolic
partial differential equation (PDE) system with both Neumann
boundary control and interior control is considered in this
work. Point output measurement is available at one end of the
physical domain. The choice of a proportional output feedback
boundary control is justified by Lyapunov analysis while the
design of the interior control is carried out based on the Sturm-
Liouville theory. A proportional state feedback is proposed for
the interior control with a symmetric kernel function, and the
pseudospectral method is used to solve the stability conditions
governed by the Sturm-Liouville systems. In addition, an
observer is designed using the point measurement at one end
of the physical domain, and used to propose an observerñbased
feedback controller for the PDE system. Both controller and
observer gains are designed numerically to make the eigenvalues
of the associated Sturm-Liouville problems stable. Simulations
show the effectiveness of the proposed controller.
