Authors:
Markus Högberg,
Thomas R. Bewley,
Volume: 1, Page 3278 Paper number 2008
Abstract:
Optimal ((cal) H_2) linear feedback controllers are computed for
the Orr--Sommerfeld/Squire equations for an array of wavenumber pairs
k_x,k_z and then inverse-transformed to the physical domain, as recommended
by Bewleyamp; Liu (JFM 365, 1998) and using the general method outlined
therein. The feedback kernels so computed are effective at minimizing
both transient energy growth and the relevant input-output transfer
function norms in the controlled linear system representing small
perturbations to a laminar channel flow. The important new result
of the present paper is the demonstration that this calculation yields
feedback convolution kernels with localized support in the physical
domain. These localized kernels eventually decay exponentially with
distance from the actuator location, allowing them to be truncated
a finite distance from each actuator while retaining any desired
degree of accuracy in the feedback computation. The truncated, spatially
compact convolution kernels may then be used in decentralized control
implementations on the distributed flow system. Spatial localization
of (cal) H_2/(cal) H_(infinity) feedback for this type of system
was predicted theoretically by Bamieh, Paganini,amp; Dahleh (IEEE
TAC, submitted) and D'Andreaamp; Dullerud (IEEE TAC, submitted) in
related work. Spatial localization provides the critical link which
connects controllers designed for the (artificial) spatially periodic
model system to application on physical systems, which are spatially
evolving. Unfortunately, not all formulations of the present control
problem lead to physical-space controllers with localized spatial
support. The feedback convolution kernels so determined are then
implemented in direct numerical simulations of transitional flows
with both random and oblique finite-magnitude initial flow perturbations,
per the cases of particular physical significance enumerated by Reddy
et al. (JFM 365, 1998). The ability of the linear control feedback
to stabilize the nonlinear flow system is demonstrated for finite
initial flow perturbations with magnitudes well beyond the threshold
which induces transition to turbulence in the uncontrolled system.
Authors:
Necati Özdemir,
Stuart Townley,
Volume: 1, Page 3284 Paper number 1689
Abstract:
In this paper we present sampled-data low-gain I-control algorithms
for infinite-dimensional systems in which the sampling period is not
constant. The system is assumed to be exponentially stable with invertible
steady state gain. The choice of the integrator gain is based on steady
state gain information. In one algorithm the sampling time is divergent
and in the other it increases adaptively.
Authors:
Richard Rebarber,
Stuart Townley,
Volume: 1, Page 3290 Paper number 1977
Abstract:
We consider continuous-time, linear control systems for which a static
state feedback stabilizes the system. If we construct a sampled-data
controller by applying an idealized sample-and-hold process to the
continuous-time stabilizing feedback, it is known that if the state
and control spaces are finite dimensional, then this sampled-data controller
stabilizes the system for all sufficiently small sampling times. In
this paper we show that this robustness with respect to sampling times
is not true in general for infinite dimensional systems. We consider
systems where the state space X and the control space U are Hilbert
spaces, the system is of the form dx/dt = Ax + Bu, and A is the generator
of a strongly continuous semigroup on X. Suppose that the continuous
time feedback is u = Fx, where F is compact. Then it is known that
if either B is bounded, or if A generates an analytic semigroup on
X (in which case B s allowed to be unbounded in a general sense), then
the sampled-data controller stabilizes the system for all sufficiently
small sampling times. In this paper we show that the first condition
is sharp in the following sense: we give a counterexample to show that
this result is not true if B is barely unbounded, that is if B is unbounded
but A^-(delta) B is bounded for all (delta) > 0. We also give an easy
counterexample if F is not compact.
Authors:
Nicolas Guijarro,
Laurent Lefèvre,
Geneviève Dauphin-Tanguy,
Volume: 1, Page 3295 Paper number 1897
Abstract:
In this paper, we introduce a procedure to treat passive functional
nodes in bond graphs. This procedure is carried out in three steps.
First we approximate the initial infinite dimensional model by a finite
one with huge dimension. Then we reduce it to a lower dimension model.
Finally we realize this latter model by a lumped parameter electrical
network.
Authors:
Eric W. Justh,
Perinkulam S. Krishnaprasad,
Mikhail A. Vorontsov,
Volume: 1, Page 3301 Paper number 1968
Abstract:
A class of feedback systems for high-resolution optical wave-front
control (or adaptive optic wave-front distortion suppression) is modeled
and analyzed. Under certain conditions, the nonlinear dynamical system
models obtained are shown to be gradient systems, with energy functions
that also serve as Lyapunov functions. The approach taken here to a
problem of nonlinear control system design and analysis might also
be applicable to other problems involving high-resolution control of
physical fields, particularly if the field sensing is performed optically.
Authors:
Jih-Jenn Huang,
Daniel B. DeBra,
Volume: 1, Page 3307 Paper number 1648
Abstract:
The Smith-predictor is well known for its delay-free characteristic
and suitable for regulating systems with an excessively long time delay.
Previous studies have found that by introducing appropriate parametric
or temporal mismatch can significantly improve system performance.
In this paper, the previous theoretical results are summarized to
form an automatic tuning procedure based on optimal values obtained
from closed form integration solutions. The proposed procedure is
verified experimentally on a fluid temperature control system of Stanford's
quiet hydraulic precision lathe. Test results show good practical
feasibility and deserve more real world applications.
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