This paper proposes a model-free real-time optimization and control strategy for CO2 transcritical refrigeration plants that assures covering the cooling demand and continuous tracking of conditions for maximum efficiency. Our approach obtains the feedback with only three measurements, and controls the opening degree of a back-pressure valve and the speed of the compressor. The strategy minimizes the power consumption of the compressor instead of maximizing the coefficient of performance, which avoids several sensors, and we demonstrate mathematically that both approaches are equivalent. We implemented the strategy with an algorithm that includes two independent auto tuned controllers, one devoted to regulate the high-pressure and another to regulate the outlet temperature of the secondary fluid of the evaporator. It also incorporates a real time perturb and observe procedure to locate on-line the optimum high-pressure that minimizes the compressor power consumption. The paper presents the experimental evaluation of the control strategy, verifying the stable operation of the algorithm and the energy optimization of the plant. KEYWORDS
Abstract. Combining ideas of Troallic [20] and Cascales, Namioka, and Vera [3], we prove several characterizations of almost equicontinuity and hereditarily almost equicontinuity for subsets of metric-valued continuous functions when they are defined on aČech-complete space. We also obtain some applications of these results to topological groups and dynamical systems.
We extend to metrizable locally compact groups Rosenthal's theorem describing those Banach spaces containing no copy of ℓ 1 . For that purpose, we transfer to general locally compact groups the notion of interpolation (I 0 ) set, which was defined by Hartman and Ryll-Nardzewsky [25] for locally compact abelian groups. Thus we prove that for every sequence {g n } n<ω in a locally compact group G, then either {g n } n<ω has a weak Cauchy subsequence or contains a subsequence that is an I 0 set. This result is subsequently applied to obtain sufficient conditions for the existence of Sidon sets in a locally compact group G, an old question that remains open since 1974 (see [32] and [20]). Finally, we show that every locally compact group strongly respects compactness extending thereby a result by Comfort, Trigos-Arrieta, and Wu [13], who established this property for abelian locally compact groups.
Let X and K be aČech-complete topological group and a compact group, respectively. We prove that if G is a non-equicontinuous subset of CHom(X, K), the set of all continuous homomorphisms of X into K, then there is a countably infinite subsetis canonically homeomorphic to βω, the Stone-Čech compactifcation of the natural numbers. As a consequence, if G is an infinite subset of CHom(X, K) such that for every countable subset L ⊆ G and compact separable subset Y ⊆ X itGiven a topological group G, denote by G + the (algebraic) group G equipped with the Bohr topology. It is said that G respects a topological property P when G and G + have the same subsets satisfying P. As an application of our main result, we prove that if G is an abelian, locally quasiconvex, locally k ω group, then the following holds: (i) G respects any compact-like property P stronger than or equal to functional boundedness; (ii) G strongly respects compactness. M X . This property, or its absence, has deep implications on the topological structure of G as a set of continuous functions on X and has found many applications in different settings (for instance, see [20,22,17,25] where there are applications to topological groups, dynamical systems, functional analysis and harmonic analysis, respectively).
Let M be a compact smooth manifold of dimension m (without boundary) and G be a finite-dimensional Lie group, with Lie algebra g. Let H > m 2 (M, G) be the group of all mappings γ : M → G which are H s for some s > m 2 . We show that H > m 2 (M, G) can be made a regular Lie group in Milnor's sense, modelled on the Silva spaceas a Lie group (where H s (M, G) is the Hilbert-Lie group of all Gvalued H s -mappings on M ). We also explain how the (known) Lie group structure on H s (M, G) can be obtained as a special case of a general construction of Lie groups F(M, G), whenever function spaces F(U, R) on open subsets U ⊆ R m are given, subject to simple axioms.
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