Robust stabilization of a system with distributed pumping
Authors
Pedersen, Mikkel Schjøtt ; Johansen, Rasmus Vestergaard
Term
4. semester
Education
Publication year
2024
Submitted on
2024-05-30
Pages
102
Abstract
Dette projekt undersøger, om man kan garantere robust stabilitet i et køle-/HVAC-system med distribuerede pumper, hvor flere luftbehandlingsenheder deler den samme kølevandskreds med usikker hydraulisk kobling. Der udledes en dynamisk model af systemet, og usikkerheder i koblingen beskrives både som normindskrænkede og som polytopiske. Da hver pumpe kun har adgang til lokale målinger, pålægges regulatoren en blokdiagonal struktur; derfor anvendes LMI-baserede (optimeringsbaserede) metoder, som kan håndtere strukturelle begrænsninger. For tilstandsfeedback behandles robusthed via small-gain-teoremet og bounded real lemma, mens statisk output-feedback formuleres som et lineært parametervarierende (LPV) problem, hvor robust stabilitet sikres ved stabilitet i polytope hjørner. Derudover anvendes frekvensvægtet model matching for at opfylde specificerede responskrav. Arbejdet resulterer i designprocedurer og regulatorer, der kan garantere robust stabilitet over for de modellerede usikkerheder og samtidig leve op til de ønskede dynamiske egenskaber under modellens antagelser.
This project investigates whether robust stability can be guaranteed for a cooling/HVAC system with distributed pumping, in which multiple air handling units share the same cooling-water loop with uncertain hydraulic coupling. A dynamic model of the system is derived, and the coupling uncertainty is represented both as norm-bounded and as polytopic. Because each pump has access only to local measurements, the controller must have a block-diagonal structure; consequently, linear matrix inequality (LMI)-based optimization methods are used to enforce structural constraints. For state feedback, robustness is addressed via the small gain theorem and the bounded real lemma; for static output feedback, the problem is posed as a linear parameter-varying (LPV) system in which robust stability is ensured by guaranteeing stability at the vertices of a convex polytope. Frequency-weighted model matching is further used to meet specified response requirements. The study provides design procedures and synthesizes controllers that guarantee robust stability for the modeled uncertainties while achieving the desired dynamic behavior within the assumptions of the model.
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Keywords
LPV ; Robust control ; LMI
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