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On the impact of model accuracy for active damping of a viscoelastic beam
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
2011 (English)Report (Other academic)
Abstract [en]

How much do model errors influence the closed loop performance? This question is investigated for the control problem of designing active damping of vibrations in a viscoelastic cantilever beam. The beam is physically modeled using Fourier transformed Euler-Bernoulli beam equations. For control design the standard LQG technique is employed, and two different finite order models are used. One is based on truncated modal analysis of the system, and the other model is numerically fitted with respect to the frequency response of the physically theoretical model. The so obtained controllers are evaluated on the physical model with respect to disturbance attenuation and robustness for stability. It is found that all controllers stabilizes the system and attenuates the vibrations, but the controllers based on the numerically fitted model perform notably better than those based on truncated modal analysis.

Place, publisher, year, edition, pages
2011.
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2011-013
National Category
Control Engineering
Research subject
Electrical Engineering with specialization in Automatic Control
Identifiers
URN: urn:nbn:se:uu:diva-229593OAI: oai:DiVA.org:uu-229593DiVA: diva2:739725
Available from: 2014-08-21 Created: 2014-08-11 Last updated: 2015-01-23
In thesis
1. Modelling and Control Methods with Applications to Mechanical Waves
Open this publication in new window or tab >>Modelling and Control Methods with Applications to Mechanical Waves
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Models, modelling and control design play important parts in automatic control. The contributions in this thesis concern topics in all three of these concepts.

The poles are of fundamental importance when analyzing the behaviour of a system, and pole placement is an intuitive and natural approach for control design. A novel parameterization for state feedback gains for pole placement in the linear multiple input case is presented and analyzed. It is shown that when the open and closed loop poles are disjunct, every state feedback gain can be parameterized. Other properties are also investigated.

Hammerstein models have a static non-linearity on the input. A method for exact compensation of such non-linearities, combined with introduction of integral action, is presented. Instead of inversion of the non-linearity the method utilizes differentiation, which in many cases is simpler.

A partial differential equation (PDE) can be regarded as an infinite order model. Many model based control design techniques, like linear quadratic Gaussian control (LQG), require finite order models. Active damping of vibrations in a viscoelastic beam, modelled as a PDE, is considered. The beam is actuated by piezoelectric elements and its movements are measured by strain gauges. LQG design is used, for which different finite order models, approximating the PDE model, are constructed. The so obtained controllers are evaluated on the original PDE model. Minimization of the measured strain yields a satisfactory performance, but minimization of transversal deflection does not. The effect of the model accuracy of the finite order model approximations is also investigated. It turns out that a model with higher accuracy in a specified frequency interval gives controllers with better performance.

The wave equation is another PDE. A PDE model, with one spatial dimension, is established. It describes wave propagation in a tube perforated with helical slots. The model describes waves of both extensional and torsional type, as well as the coupling between the two wave types. Experimental data are used for estimation of model parameters, and for assessment of the proposed model in two different cases. The model is found adequate when certain geometrical assumptions are valid.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2014. 72 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1174
Keyword
automatic control, pole placement, linearization, vibration control, distributed parameter systems, wave propagation
National Category
Control Engineering
Research subject
Automatic Control
Identifiers
urn:nbn:se:uu:diva-229793 (URN)978-91-554-9023-2 (ISBN)
Public defence
2014-10-17, room 2446, ITC, Lägerhyddsvägen 2, Uppsala, 10:15 (English)
Opponent
Supervisors
Available from: 2014-09-26 Created: 2014-08-13 Last updated: 2015-01-23

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Norlander, Hans

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