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Modelling and Control Methods with Applications to Mechanical Waves
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.
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 [en]
automatic control, pole placement, linearization, vibration control, distributed parameter systems, wave propagation
National Category
Control Engineering
Research subject
Automatic Control
Identifiers
URN: urn:nbn:se:uu:diva-229793ISBN: 978-91-554-9023-2 (print)OAI: oai:DiVA.org:uu-229793DiVA: diva2:742318
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
List of papers
1. Parameterization of state feedback gains for pole assignment
Open this publication in new window or tab >>Parameterization of state feedback gains for pole assignment
2001 (English)Licentiate thesis, monograph (Other scientific)
Abstract [en]

The pole assignment problem has been subject for research for a long time. For single-input single-output systems this problem is well understood but for multi-input multi-output systems the pole assignment problem is more complex.

In this thesis a parameterization of state feedback gains for pole assignment is characterized with respect to completeness, redundancy and existence. In order to make a systematic examination of this parameterization a number of classes are introduced.

This parameterization depends on two matrices that can be regarded as design parameters. In the thesis it is shown how the degree of freedom in the pole assignment problem for multi-input systems is characterized by these two matrices.

It turns out that the properties of the parameterization depends on whether the characteristic polynomials of the open and the closed loop systems are coprime or not. It is shown in the thesis that if the characteristic polynomials are coprime, every possible feedback gain can be parameterized in this way, and in this sense the parameterization is complete. If the characteristic polynomials have factors in common the parameterization is not complete. In the thesis the shortcomings of the parameterization for this case are characterized.

The design parameters seem to offer a greater degree of freedom than what can be offered in the pole assignment problem. This indicates a certain degree of overparameterization. This redundancy in the design parameters is characterized in the thesis.

The parameterization implies that a certain matrix is invertible. Necessary conditions for when this matrix is invertible are given in terms of the two design parameters. It is shown that this matrix is invertible for almost every value of the design parameters when the characteristic polynomials are coprime, and hence that the parameterized gains are generally applicable.

The parameterization and its properties are illustrated on a linear model of the military aircraft JAS Gripen.

Place, publisher, year, edition, pages
Uppsala University, 2001
Series
Information technology licentiate theses: Licentiate theses from the Department of Information Technology, ISSN 1404-5117 ; 2001-007
National Category
Control Engineering
Research subject
Automatic Control
Identifiers
urn:nbn:se:uu:diva-86017 (URN)
Supervisors
Available from: 2001-05-20 Created: 2005-05-05 Last updated: 2017-08-31Bibliographically approved
2. An integrating linearization method for Hammerstein models
Open this publication in new window or tab >>An integrating linearization method for Hammerstein models
2005 (English)In: Automatica, ISSN 0005-1098, Vol. 41, no 10, 1825-1828 p.Article in journal (Refereed) Published
Abstract [en]

This paper considers a method for linearization of models containing

static input nonlinearities in series with a linear model, so called

Hammerstein models. The method linearizes the system exactly, and is

performed by differentiating the nonlinearity

with respect to the input signal. Using this approach, an integration

is added in the loop gain of the linearized system via the internal

feedback. The method presented here is an equivalent alternative

to the standard method that utilizes the

inverse of the static nonlinearity complemented with an

integration. Particularly, in cases when

analytic inversion is

difficult, the presented method provides an attractive alternative.

Keyword
Linearization; Hammerstein models; Static nonlinearities; Actuator nonlinearity control;
National Category
Control Engineering
Identifiers
urn:nbn:se:uu:diva-74724 (URN)
Available from: 2005-11-07 Created: 2005-11-07 Last updated: 2015-01-23
3. Modeling and control of a viscoelastic piezolaminated beam
Open this publication in new window or tab >>Modeling and control of a viscoelastic piezolaminated beam
2005 (English)In: Proc. IFAC 16th World Congress, 2005Conference paper, Published paper (Refereed)
Identifiers
urn:nbn:se:uu:diva-71411 (URN)
Available from: 2005-05-06 Created: 2005-05-06 Last updated: 2015-01-23
4. On the impact of model accuracy for active damping of a viscoelastic beam
Open this publication in new window or tab >>On the impact of model accuracy for active damping of a viscoelastic beam
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.

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:nbn:se:uu:diva-229593 (URN)
Available from: 2014-08-21 Created: 2014-08-11 Last updated: 2015-01-23
5. Parameter estimation from wave propagation tests on a tube perforated by helical slots
Open this publication in new window or tab >>Parameter estimation from wave propagation tests on a tube perforated by helical slots
2013 (English)In: Mechanical systems and signal processing, ISSN 0888-3270, E-ISSN 1096-1216, Vol. 40, no 1, 385-399 p.Article in journal (Refereed) Published
Abstract [en]

For a tube with doubly symmetric cross section and perforations by helical slots there is a coupling between extension and torsion. In this paper a one dimensional (1D) model structure for a tube with such a helical slot segment (HSS) is established, and parameters accounting for the coupling between extension and torsion are estimated from wave propagation experiments. In these experiments incident extensional waves were generated through axial impact by strikers of different lengths, causing reflected and transmitted waves of extensional and torsional type which were measured in terms of surface strains on either side of the HSS part of the tube. A statistical test on the experimental data shows that the output residuals (the difference between modeled and experimental output) cannot be explained by measurement noise alone. This is not surprising since the 1D model structure is based on some simplifying assumptions concerning the geometry of the HSS. Parameters for two different geometries of the HSS are estimated, and the models are assessed in terms of model fa, simulations and wave energy distribution. It turns out that for one case, where the geometrical assumptions are valid, the 1D model is adequate, while for another case, where the validity of the assumptions is questionable, it is not. It is concluded that the 1D model structure provides a simple and efficient description of the HSS if the geometrical assumptions are valid.

Keyword
Tube, Helical slots, Elastic wave, Extension, Torsion, Parameter estimation
National Category
Control Engineering Applied Mechanics
Research subject
Engineering science with specialization in Applied Mechanics
Identifiers
urn:nbn:se:uu:diva-208351 (URN)10.1016/j.ymssp.2013.04.011 (DOI)000323803100024 ()
Available from: 2013-10-01 Created: 2013-09-30 Last updated: 2017-12-06Bibliographically approved

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