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An integrating linearization method for Hammerstein models
Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Information Technology. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Information Technology, Automatic control. systemteknik.
Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Information Technology. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Information Technology, Automatic control. systemteknik.
Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Information Technology. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Information Technology, Automatic control. systemteknik.
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.

Place, publisher, year, edition, pages
2005. Vol. 41, no 10, 1825-1828 p.
Keyword [en]
Linearization; Hammerstein models; Static nonlinearities; Actuator nonlinearity control;
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:uu:diva-74724OAI: oai:DiVA.org:uu-74724DiVA: diva2:102634
Available from: 2005-11-07 Created: 2005-11-07 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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Samuelsson, PärNorlander, HansCarlsson, Bengt

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