409 research outputs found
Boundary Control of Coupled Reaction-Advection-Diffusion Systems with Spatially-Varying Coefficients
Recently, the problem of boundary stabilization for unstable linear
constant-coefficient coupled reaction-diffusion systems was solved by means of
the backstepping method. The extension of this result to systems with advection
terms and spatially-varying coefficients is challenging due to complex boundary
conditions that appear in the equations verified by the control kernels. In
this paper we address this issue by showing that these equations are
essentially equivalent to those verified by the control kernels for first-order
hyperbolic coupled systems, which were recently found to be well-posed. The
result therefore applies in this case, allowing us to prove H^1 stability for
the closed-loop system. It also shows an interesting connection between
backstepping kernels for coupled parabolic and hyperbolic problems.Comment: Submitted to IEEE Transactions on Automatic Contro
Control of Homodirectional and General Heterodirectional Linear Coupled Hyperbolic PDEs
Research on stabilization of coupled hyperbolic PDEs has been dominated by
the focus on pairs of counter-convecting ("heterodirectional") transport PDEs
with distributed local coupling and with controls at one or both boundaries. A
recent extension allows stabilization using only one control for a system
containing an arbitrary number of coupled transport PDEs that convect at
different speeds against the direction of the PDE whose boundary is actuated.
In this paper we present a solution to the fully general case, in which the
number of PDEs in either direction is arbitrary, and where actuation is applied
on only one boundary (to all the PDEs that convect downstream from that
boundary). To solve this general problem, we solve, as a special case, the
problem of control of coupled "homodirectional" hyperbolic linear PDEs, where
multiple transport PDEs convect in the same direction with arbitrary local
coupling. Our approach is based on PDE backstepping and yields solutions to
stabilization, by both full-state and observer-based output feedback,
trajectory planning, and trajectory tracking problems
Feedback control of bilinear distributed parameter system by input-output linearization
International audienceIn this paper, a control law that enforces the tracking of a boundary controlled output for a bilinear distributed parameter system is developed in the framework of geometric control. The dynamic behavior of the system is described by two weakly coupled linear hyperbolic partial differential equations. The stability of the resulting closed-loop system is investigated based on eigenvalues of the spatial operator of a weakly coupled system of balance equations. It is shown that, under some reasonable assumptions, the stability condition is related to the choice of the tuning parameter of the control law. The performance of the developed control law is demonstrated, through numerical simulation, in the case of a co-current heat exchanger. The control objective is to control the outlet cold fluid temperature by manipulating its velocity. Both tracking and disturbance rejection problems are considered
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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