3,312 research outputs found
A fractional representation approach to the robust regulation problem for SISO systems
The purpose of this article is to develop a new approach to the robust
regulation problem for plants which do not necessarily admit coprime
factorizations. The approach is purely algebraic and allows us dealing with a
very general class of systems in a unique simple framework. We formulate the
famous internal model principle in a form suitable for plants defined by
fractional representations which are not necessarily coprime factorizations. By
using the internal model principle, we are able to give necessary and
sufficient solvability conditions for the robust regulation problem and to
parameterize all robustly regulating controllers.Comment: 13 pages, 1 figure, to appear in Systems & Control Letter
A fractional representation approach to the robust regulation problem for MIMO systems
The aim of this paper is in developing unifying frequency domain theory for
robust regulation of MIMO systems. The main theoretical results achieved are a
new formulation of the internal model principle, solvability conditions for the
robust regulation problem, and a parametrization of all robustly regulating
controllers. The main results are formulated with minimal assumptions and
without using coprime factorizations thus guaranteeing applicability with a
very general class of systems. In addition to theoretical results, the design
of robust controllers is addressed. The results are illustrated by two examples
involving a delay and a heat equation.Comment: 23 pages, 3 figures, submitted to International Journal of Robust and
Nonlinear Contro
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
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
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
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
Zero Dynamics for Port-Hamiltonian Systems
The zero dynamics of infinite-dimensional systems can be difficult to
characterize. The zero dynamics of boundary control systems are particularly
problematic. In this paper the zero dynamics of port-Hamiltonian systems are
studied. A complete characterization of the zero dynamics for a
port-Hamiltonian systems with invertible feedthrough as another
port-Hamiltonian system on the same state space is given. It is shown that the
zero dynamics for any port-Hamiltonian system with commensurate wave speeds are
well-defined, and are also a port-Hamiltonian system. Examples include wave
equations with uniform wave speed on a network. A constructive procedure for
calculation of the zero dynamics, that can be used for very large system order,
is provided.Comment: 17 page
Alternatives for jet engine control
The development of models of tensor type for a digital simulation of the quiet, clean safe engine (QCSE) gas turbine engine; the extension, to nonlinear multivariate control system design, of the concepts of total synthesis which trace their roots back to certain early investigations under this grant; the role of series descriptions as they relate to questions of scheduling in the control of gas turbine engines; the development of computer-aided design software for tensor modeling calculations; further enhancement of the softwares for linear total synthesis, mentioned above; and calculation of the first known examples using tensors for nonlinear feedback control are discussed
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