335 research outputs found
Control and State Estimation of the One-Phase Stefan Problem via Backstepping Design
This paper develops a control and estimation design for the one-phase Stefan
problem. The Stefan problem represents a liquid-solid phase transition as time
evolution of a temperature profile in a liquid-solid material and its moving
interface. This physical process is mathematically formulated as a diffusion
partial differential equation (PDE) evolving on a time-varying spatial domain
described by an ordinary differential equation (ODE). The state-dependency of
the moving interface makes the coupled PDE-ODE system a nonlinear and
challenging problem. We propose a full-state feedback control law, an observer
design, and the associated output-feedback control law via the backstepping
method. The designed observer allows estimation of the temperature profile
based on the available measurement of solid phase length. The associated
output-feedback controller ensures the global exponential stability of the
estimation errors, the H1- norm of the distributed temperature, and the moving
interface to the desired setpoint under some explicitly given restrictions on
the setpoint and observer gain. The exponential stability results are
established considering Neumann and Dirichlet boundary actuations.Comment: 16 pages, 11 figures, submitted to IEEE Transactions on Automatic
Contro
Robust stabilization of first-order hyperbolic PDEs with uncertain input delay
A backstepping-based compensator design is developed for a system of
first-order linear hyperbolic partial differential equations (PDE)
in the presence of an uncertain long input delay at boundary. We introduce a
transport PDE to represent the delayed input, which leads to three coupled
first-order hyperbolic PDEs. A novel backstepping transformation, composed of
two Volterra transformations and an affine Volterra transformation, is
introduced for the predictive control design. The resulting kernel equations
from the affine Volterra transformation are two coupled first-order PDEs and
each with two boundary conditions, which brings challenges to the
well-posedness analysis. We solve the challenge by using the method of
characteristics and the successive approximation. To analyze the sensitivity of
the closed-loop system to uncertain input delay, we introduce a neutral system
which captures the control effect resulted from the delay uncertainty. It is
proved that the proposed control is robust to small delay variations. Numerical
examples illustrate the performance of the proposed compensator
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