We investigate the limits of localized linear control
in spatially extended, nonlinear systems.
Spatially extended, nonlinear systems can be found in virtually
every field of engineering and science.
An important category of such systems are fluid flows.
Fluid flows play an important role in many commercial applications,
for instance in the chemical, pharmaceutical and food-processing industries.
Other important fluid flows include
air- or water flows around cars, planes or ships.
In all these systems, it is highly desirable to control the flow of the
respective fluid.
For instance control of the air flow around an airplane or car
leads to better fuel-economy and reduced noise production.
Usually, it is impossible to apply control everywhere.
Consider an airplane: It would not be feasibly to cover the
whole body of the plane with control units.
Instead, one can place the control units at localized regions,
such as points along the edge of the wings,
spaced as far apart from each other as possible.
These considerations lead to an important question:
For a given system, what is the minimum number of localized controllers
that still ensures successful control?
Too few controllers will not achieve control,
while using too many leads to unnecessary expenses and wastes resources.
To answer this question, we study localized control
in a class of model equations.
These model equations are good representations
of many real fluid flows.
Using these equations,
we show how one can design localized control that renders the system stable.
We study the properties of the control
and derive several expressions that allow
us to determine the limits of successful control.
We show how the number of controllers
that are needed for successful control
depends on the size and type of the system, as well as the way control is
implemented. We find that especially the nonlinearities and the amount
of noise present in the system play a crucial role.
This analysis allows us to determine under which circumstances
a given number of controllers can successfully stabilize a given system.
| Identifer | oai:union.ndltd.org:GATECH/oai:smartech.gatech.edu:1853/5025 |
| Date | 08 July 2004 |
| Creators | Handel, Andreas |
| Publisher | Georgia Institute of Technology |
| Source Sets | Georgia Tech Electronic Thesis and Dissertation Archive |
| Language | en_US |
| Detected Language | English |
| Type | Dissertation |
| Format | 1267064 bytes, application/pdf |
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