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Singular perturbations for hyperbolic port-Hamiltonian and non-hyperbolic systems Scherpen, Jacqueline
Description
In this talk we explore the methodology of model order reduction based on singular perturbations for a fexible-joint robot within the port-Hamiltonian framework. The model is an ode model that is obtained after discretisation. We show that a fexible-joint robot has a port-Hamiltonian representation which is also a singularly perturbed ordinary differential equation. Moreover, the associated reduced slow subsystem corresponds to a port-Hamiltonian model of a rigid-joint robot. To exploit the usefulness of the reduced models, we provide a numerical example where an existing controller for a rigid robot is implemented. In addition, we provide ideas on how to expand this to planar slow-fast systems at a non-hyperbolic point. At these type of points, the classical theory of singular perturbations is not applicable and new techniques need to be introduced in order to design a controller that stabilizes such a point. We show for some class of nonlinear systems that using geometric desingularization (also known as blow up), it is possible to design, in a simple way, controllers that stabilize non-hyperbolic equilibrium points of slow-fast systems. Furthermore, we include controller design in the development.
Item Metadata
Title |
Singular perturbations for hyperbolic port-Hamiltonian and non-hyperbolic systems
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2017-07-20T13:34
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Description |
In this talk we explore the methodology of model order reduction based on singular
perturbations for a fexible-joint robot within the port-Hamiltonian framework. The model is an ode model that is obtained after discretisation.
We show that a fexible-joint robot has a port-Hamiltonian representation which is also a singularly perturbed
ordinary differential equation. Moreover, the associated reduced slow subsystem corresponds to
a port-Hamiltonian model of a rigid-joint robot. To exploit the usefulness of the reduced models,
we provide a numerical example where an existing controller for a rigid robot is implemented.
In addition, we provide ideas on how to expand this to planar slow-fast systems at a non-hyperbolic point.
At these type of points, the classical theory of singular perturbations
is not applicable and new techniques need to be
introduced in order to design a controller that stabilizes such
a point. We show for some class of nonlinear systems that using geometric desingularization (also
known as blow up), it is possible to design, in a simple way,
controllers that stabilize non-hyperbolic equilibrium points of
slow-fast systems. Furthermore, we include controller design in the development.
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Extent |
39 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: University of Groningen Netherlands
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Series | |
Date Available |
2018-01-17
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0363055
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International