For the systematic development of feedback flow controllers, a numerical model that captures the dynamic behaviour of the flow field to be controlled is required. This poses a particular challenge for flow fields where the dynamic behaviour is nonlinear, and the governing equations cannot easily be solved in closed form. This has led to many versions of low-dimensional modelling techniques, which we extend in this work to represent better the impact of actuation on the flow. For the benchmark problem of a circular cylinder wake in the laminar regime, we introduce a novel extension to the proper orthogonal decomposition (POD) procedure that facilitates mode construction from transient data sets. We demonstrate the performance of this new decomposition by applying it to a data set from the development of the limit cycle oscillation of a circular cylinder wake simulation as well as an ensemble of transient forced simulation results. The modes obtained from this decomposition, which we refer to as the double POD (DPOD) method, correctly track the changes of the spatial modes both during the evolution of the limit cycle and when forcing is applied by transverse translation of the cylinder. The mode amplitudes, which are obtained by projecting the original data sets onto the truncated DPOD modes, can be used to construct a dynamic mathematical model of the wake that accurately predicts the wake flow dynamics within the lock-in region at low forcing amplitudes. This low-dimensional model, derived using nonlinear artificial neural network based system identification methods, is robust and accurate and can be used to simulate the dynamic behaviour of the wake flow. We demonstrate this ability not just for unforced and open-loop forced data, but also for a feedback-controlled simulation that leads to a 90% reduction in lift fluctuations. This indicates the possibility of constructing accurate dynamic low-dimensional models for feedback control by using unforced and transient forced data only.

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3RESUMO -Apesar do grande potencial comercial da pitaia, ainda são escassos os estudos de caracterização físico-química de frutos da pitaia, principalmente considerando espécies nativas do Cerrado. Neste trabalho, objetivou-se analisar a caracterização físico-química, polifenóis e flavonoides amarelos totais de frutos de espécies de pitaia Hylocereus costaricensis, Hylocereus undatus, Selenicereus setaceus e Selenicereus megalanthus. Para as avaliações físico-químicas, foram realizadas as análises de sólidos solúveis, pH e acidez total titulável. Para a determinação dos compostos fenólicos, realizaram-se as análises de polifenóis extraíveis totais e flavonoides amarelos. Foram observadas diferenças significativas entre as espécies de pitaia e entre as partes basal, mediana e apical dos frutos, quanto às características físico-químicas e a concentração de compostos fenólicos. A espécie S. megalanthus apresentou maior quantidade de sólidos solúveis, apresentando, assim, a polpa mais doce. Tal característica foi mais pronunciada na parte mediana do fruto de todas as espécies. Houve diferença significativa entre o pH, com valores variando de 4,84 a 5,67, classificando-se como alimentos pouco ácidos. A acidez variou de 0,10 % a 0,15 % de ácido cítrico. H. costaricensis merece destaque pela presença de maior quantidade de polifenóis totais e de flavonoides amarelos, diferenciando-se significativamente das demais espécies. Termos para indexação: Cactaceae, variabilidade genética, melhoramento. PHYSICOCHEMICAL CHARACTERISTICS, POLYPHENOLS AND YELLOW FLAVONOIDS IN FRUITS OF COMMERCIAL AND WILD PITAYA SPECIES FROM THE BRAZILIAN SAVANNASABSTRACT -Although the high commercial potential of pitaya, there are yet few studies of physicochemical characterization of pitaya fruits, especially considering wild species from the Brazilian Savannas. This study was conducted with the objective to analyze the physico-chemical characterization, total polyphenols and yellow flavonoids of fruits of Hylocereus costaricensis, Hylocereus undatus, Selenicereus setaceus and Selenicereus megalanthus pitaya species. For the physico-chemical analyzes the percentage of soluble solids, pH value and total acidity. For the phenolic compounds quantification, total flavonoids and yellow polyphenols extractable were analyzed. Significant differences of chemical characteristics and the amount concentration of phenolic compounds were observed among pitaya species and basal, middle and apical portions of fruit. The species S. megalanthus had higher amounts of soluble solids. This characteristic is more pronounced in the middle part of the fruit of all species. There was significant difference of pH, with values ranging from 4.84 to 5.67. The pitaya fruits are classified as low acid fruits. The acid content ranged from 0.10% to 0.15% of citric acid. H. costaricensis presented higher amount of total polyphenols and yellow flavonoids, differing significantly from the other species.

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