97,690 research outputs found
Robust Controllers for Regular Linear Systems with Infinite-Dimensional Exosystems
We construct two error feedback controllers for robust output tracking and
disturbance rejection of a regular linear system with nonsmooth reference and
disturbance signals. We show that for sufficiently smooth signals the output
converges to the reference at a rate that depends on the behaviour of the
transfer function of the plant on the imaginary axis. In addition, we construct
a controller that can be designed to achieve robustness with respect to a given
class of uncertainties in the system, and present a novel controller structure
for output tracking and disturbance rejection without the robustness
requirement. We also generalize the internal model principle for regular linear
systems with boundary disturbance and for controllers with unbounded input and
output operators. The construction of controllers is illustrated with an
example where we consider output tracking of a nonsmooth periodic reference
signal for a two-dimensional heat equation with boundary control and
observation, and with periodic disturbances on the boundary.Comment: 30 pages, 3 figures, to appear in SIAM Journal on Control &
Optimizatio
Approximate robust output regulation of boundary control systems
We extend the internal model principle for systems with boundary control and
boundary observation, and construct a robust controller for this class of
systems. However, as a consequence of the internal model principle, any robust
controller for a plant with infinite-dimensional output space necessarily has
infinite-dimensional state space. We proceed to formulate the approximate
robust output regulation problem and present a finite-dimensional controller
structure to solve it. Our main motivating example is a wave equation on a
bounded multidimensional spatial domain with force control and velocity
observation at the boundary. In order to illustrate the theoretical results, we
construct an approximate robust controller for the wave equation on an annular
domain and demonstrate its performance with numerical simulations.Comment: 29 pages, 4 figure
Controller Design for Robust Output Regulation of Regular Linear Systems
We present three dynamic error feedback controllers for robust output
regulation of regular linear systems. These controllers are (i) a minimal order
robust controller for exponentially stable systems (ii) an observer-based
robust controller and (iii) a new internal model based robust controller
structure. In addition, we present two controllers that are by construction
robust with respect to predefined classes of perturbations. The results are
illustrated with an example where we study robust output tracking of a
sinusoidal reference signal for a two-dimensional heat equation with boundary
control and observation.Comment: 26 pages, 2 figures, to appear in IEEE Transactions on Automatic
Contro
The Internal Model Principle for Systems with Unbounded Control and Observation
In this paper the theory of robust output regulation of distributed parameter
systems with infinite-dimensional exosystems is extended for plants with
unbounded control and observation. As the main result, we present the internal
model principle for linear infinite-dimensional systems with unbounded input
and output operators. We do this for two different definitions of an internal
model found in the literature, namely, the p-copy internal model and the
-conditions. We also introduce a new way of defining an internal
model for infinite-dimensional systems. The theoretic results are illustrated
with an example where we consider robust output tracking for a one-dimensional
heat equation with boundary control and pointwise measurements.Comment: 38 pages, 2 figures, in revie
Reduced Order Controller Design for Robust Output Regulation
We study robust output regulation for parabolic partial differential
equations and other infinite-dimensional linear systems with analytic
semigroups. As our main results we show that robust output tracking and
disturbance rejection for our class of systems can be achieved using a
finite-dimensional controller and present algorithms for construction of two
different internal model based robust controllers. The controller parameters
are chosen based on a Galerkin approximation of the original PDE system and
employ balanced truncation to reduce the orders of the controllers. In the
second part of the paper we design controllers for robust output tracking and
disturbance rejection for a 1D reaction-diffusion equation with boundary
disturbances, a 2D diffusion-convection equation, and a 1D beam equation with
Kelvin-Voigt damping.Comment: Revised version with minor improvements and corrections. 28 pages, 9
figures. Accepted for publication in the IEEE Transactions on Automatic
Contro
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