Tilman Utz

Control of Parabolic Partial Differential Equations Based on Semi-Discretizations

ISBN:

978-3-8440-0932-3

Reeks:

Modellierung und Regelung komplexer dynamischer Systeme
Uitgegevens: Univ.-Prof. Dr. Andreas Kugi (TU Wien) en o. Univ.-Prof. Dr. Kurt Schlacher (JKU Linz)
Wien / Linz

Volume:

Trefwoorden:

feedforward control design; trajectory planning; parabolic partial differential equations; flatness; semi-discretization; finite differences; tracking control

Soort publicatie:

Dissertatie

Taal:

Engels

Pagina's:

164 pagina's

Gewicht:

243 g

Formaat:

24 x 17 cm

Prijs:

48,80 € / 97,60 SFr

Verschijningsdatum:

April 2012

Kopen:

Download:

Beschikbare online documenten voor deze titel:

U heeft Adobe Reader, nodig, om deze bestanden te kunnen bekijken. Hier vindt u ondersteuning en informatie, bij het downloaden van PDF-bestanden.

Let u er a.u.b. op dat de online-bestanden niet drukbaar zijn.


	Document		Samenvatting
	Soort bestand		PDF
	Kosten		gratis
	Acties		Het bestand tonen - 15 kB (14909 Byte)
	Acties		downloaden van het bestand - 15 kB (14909 Byte)


	Document		Document
	Soort bestand		PDF
	Kosten		12,20 EUR
	Acties		Tonen en kopen van het bestand - 2,6 MB (2758346 Byte)
	Acties		Kopen en downloaden van het bestand - 2,6 MB (2758346 Byte)


	Document		Inhoudsopgave
	Soort bestand		PDF
	Kosten		gratis
	Acties		Het bestand tonen - 85 kB (86912 Byte)
	Acties		downloaden van het bestand - 85 kB (86912 Byte)

Gebruikersinstellingen voor geregistreerde online-bezoekers

Hier kunt u uw adresgegevens aanpassen en uw documenten inzien.

Gebruiker:	niet aangemeld
Acties:	aanmelden/registreren Paswoord vergeten?

Aanbevelen:

Wilt u dit boek aanbevelen?

Recensie-exemplaar

Bestelling van een recensie-exemplaar.

Verlinking

Wilt u een link hebben van uw publicatie met onze online catalogus? Klik hier.

Samenvatting

This thesis is concerned with the model-based feedforward control design for systems governed by quasilinear parabolic partial differential equations in one- and two-dimensional spatial domains. The main focus is on the realization of setpoint transitions along predefined reference trajectories. The approach is based on the semi-discretization of the partial differential equation using suitable finite difference schemes. In the case of boundary control it is shown that the resulting system of ordinary differential equations is differentially flat for general nonlinearities. This system-theoretic property allows for the parametrization of the state and control input in terms of a so-called flat output and its time derivatives, which constitutes a systematic approach to the trajectory planning and feedforward control design for the considered transition problems. The particular appeal of this approach relies in its comparatively low computational demands especially for systems exhibiting significant nonlinear effects. The contributions of this thesis are two-fold. At first, it is shown by analytic considerations that the flatness-based parametrization of the semi-discretized approximation for vanishing discretization mesh widths approaches the flatness-based parametrization of the original infinite-dimensional system given in terms of an infinite series. Conditions for the convergence of this series are explicitly derived for some system classes. Second, tailored numerical methods are presented, which on the one hand provide an empirical test for the convergence of the parametrizations and which on the other hand extend the applicability of trajectory planning and feedforward control based on finite difference semi-discretization to a broader class of systems. Notably, the construction of admissible profiles is considered. Especially in two-dimensional spatial domains, where the reference trajectories have to be consistent with the boundary conditions, this a crucial task for the trajectory planning and feedforward control design. Both an optimization-based approach and an approach motivated by the regularization of inverse problems are presented and perform well also in cases where no analytical solutions are available. Furthermore, grid adaptation methods are introduced to make use of non-equidistant grids for state and control input parametrization, which can significantly reduce the necessary computational cost. Finally, both the problem of state reconstruction and tracking error stabilization are addressed. Integrating the flatness-based trajectory planning and feedforward control design, model-predictive tracking control and suitable state estimation within a two-degrees-of-freedom control scheme allows for the compensation of disturbances and modelling uncertainties as well as for the control of unstable PDEs.