Change search
ReferencesLink to record
Permanent link

Direct link
Extremum seeking control of the CANON process-Existence of multiple stationary solutions
KTH, School of Electrical Engineering (EES), Automatic Control.ORCID iD: 0000-0003-3476-9849
KTH, School of Electrical Engineering (EES), Automatic Control.
2014 (English)In: Journal of Process Control, ISSN 0959-1524, Vol. 24, no 2, 348-356 p.Article in journal (Refereed) Published
Abstract [en]

The paper considers the use of extremum seeking control (ESC) for real-time optimization of the completely autotrophic nitrogen removal over nitrite (CANON) process. In particular, the feasibility of employing relatively fast estimation and control, compared to the open-loop dynamics, is considered. From simulations it is found that the ESC can lock onto stationary solutions far removed from the optimum and that, for some control parameters, multiple stationary solutions may exist. To verify the simulation results we analyze a general dynamic model for ESC and show that all stationary solutions can be characterized by simple conditions on the gain and phase lag of the frequency response of the locally linearized system. In order to relate the derived conditions to conditions for optimality, we consider characteristic dynamic properties of systems displaying extremum points and show that the phase lag condition implies that a stationary solution in the vicinity of the optimum is likely to exist even with relatively fast estimation and control. However, the phase lag condition can also be fulfilled at operating points with no relation to the optimum whatsoever. Thus, the ESC can yield multiple stationary solutions and for some initial conditions lock onto solutions far removed from the optimum. A simple stability analysis is presented to verify that multiple solutions can be locally asymptotically stable. A simple bioreactor model is considered to illustrate the results and we show that the ESC provides three stationary solutions, of which two are stable and one unstable, even for relatively slow estimation schemes. We also confirm that the stationary solutions of the CANON process, found through simulations, fulfill both the phase lag condition and the stability criterion derived in the paper.

Place, publisher, year, edition, pages
2014. Vol. 24, no 2, 348-356 p.
Keyword [en]
Wastewater, Extremum seeking control, Real time optimization, Bifurcation
National Category
Control Engineering
URN: urn:nbn:se:kth:diva-147074DOI: 10.1016/j.jprocont.2013.11.007ISI: 000336116100005ScopusID: 2-s2.0-84897108109OAI: diva2:728589

QC 20140624

Available from: 2014-06-24 Created: 2014-06-23 Last updated: 2014-06-24Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textScopus

Search in DiVA

By author/editor
Trollberg, OlleJacobsen, Elling W.
By organisation
Automatic Control
In the same journal
Journal of Process Control
Control Engineering

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 64 hits
ReferencesLink to record
Permanent link

Direct link