Engineering
Model Predictive Control of Parabolic PDE Systems with Dirichlet Boundary Conditions via Galerkin Model Reduction
In this paper, we propose a framework to solve a closed-loop, optimal tracking control problem for a nonlinear parabolic partial differential equation (PDE) via diffusivity, interior, and boundary actuation. The approach is based on model reduction via proper orthogonal decomposition (POD) and Galerkin projection methods. A conventional integration-by-parts approach during the Galerkin projection fails to effectively incorporate the considered Dirichlet boundary control into the reduced-order model (ROM). To overcome this limitation we use a spatial discretization of the interior product during the Galerkin projection. The obtained low dimensional dynamical model is bilinear as the result of the presence of the diffusivity control term in the nonlinear parabolic PDE system. We propose a closed-loop optimal controller based on a nonlinear model predictive control (MPC) scheme aimed at bating the effect of disturbances with the ultimate goal of tracking a nominal trajectory. A quasi-linear approximation approach is used to solve on-line the quadratic optimal control problem subject to the bilinear reduced-order model associated with the MPC scheme. Based on the convergence properties of the quasi-linear approximation algorithm, the symptotical stability of the closed-loop nonlinear MPC scheme is discussed. Finally, the proposed approach is applied to the current profile control problem in tokamak plasmas and its effectiveness is demonstrated in simulations.
Raman and UV-Vis Spectroscopy Study of Vanadium-Containing Heteropoly Acids in Aqueous Solutions
To advance liquid phase spectroscopic techniques, we have selected two types of heteropoly acids (HPAs) in aqueous solutions to serve as our experimental catalysts: H3PW12O40, (TPA-tungstophosphoric acid) and H3PMo12O40, (MPA-molybdophosphoric acid). The cage-like structure that these HPAs assume is called the Keggin structure [1,2]. Distorted forms of the Keggin structure are also known to exist. For example, the Dawson structure is composed of two Keggin anions which have each expelled three WO3 or MoO3 units and joined together as a dimeric unit [1,3].
The initial objectives of this investigation were (1) to compare the ambient and aqueous solution spectra of the HPAs and (2) to determine differences or similarities in their structures between their ambient and aqueous states. Varying levels of vanadium were introduced into the primary and secondary structure of each HPA in order to investigate the influence of vanadium when the HPAs are in solution. TPA and MPA samples containing vanadium in the primary structure are denoted as TPAVx and MPAVx. The chemical formulas for solid TPAVx and MPAVx are H3+xPW12-xVxO40 and H3+xPMo12-xVxO40 (where x=1, 2, and 3). TPA and MPA which contain vanadia on the secondary structure are denoted as VOTPA and VOMPA. › Continue reading
Retention and Release of Cryptosporidium parvum Oocysts by Experimental Biofilms Composed of Natural Stream Microbial Communities
Cryptosporidium is a group of waterborne protozoan parasites that cause significant gastrointestinal disease in humans. The potential exists for these parasites to accumulate in stream or pipe surface biofilms and to be subsequently released to contaminate the water supply. Natural microbial assemblages were collected from three streams for three seasons (fall, winter, and spring) and used to grow biofilms in laboratory microcosms. These biofilms were then exposed to Cryptosporidium parvum oocysts via continuous inflow to determine daily influx, efflux, and biofilm retention and sloughing. Daily oocyst counts showed that oocysts attached to the biofilm quickly (within hours) and released slowly (within days). In these experiments, at least 40% of the oocysts added to the system attached to the biofilm in the first 72 hours, and at least 20% of the oocysts remained attached to the biofilm beyond 72 hours after the oocyst supply was removed. Although variation across site and season exists, likely as a result of variable microbial communities, all biofilms captured at least 40% of the oocysts and retained some of those oocysts for at least five days. The biofilm attachment and detachment dynamics of C. parvum oocysts have important implications for public health and suggest that biofilm monitoring should be included in routine water supply monitoring.
Influence of ZrO2 Nanoligands on the Catalytic Performance of Supported Pt/ZrO2/SiO2 Catalysts
A series of double-supported Pt/ZrO2/SiO2 catalysts were prepared to determine the influence of ZrO2 nanoparticle (NP) domain size on the reactivity of the catalytic active Pt component. The catalysts were synthesized by first impregnating zirconium tert-butoxide, Zr[OC(CH3)3]4, in toluene, drying and then calcining at 500 C to form ZrO2. In a second step, aqueous platinum tetra-ammine nitrate, Pt(NH3)4(NO3)2, was impregnated, dried and calcined in air at 500 C to form the final double-supported Pt/ZrO2/SiO2 catalyst. The ZrO2 loading was varied between 1% and 50% and the Pt loading was maintained constant at 0.1%. In situ Raman and UV-vis spectroscopy and TEM microscopic characterization revealed that the supported ZrO2 phase varied its domain size from isolated surface species to polymeric surface species to NPs (1-3 nm). TEM microscopy revealed that the supported Pt phase was present as 10-70 nm NPs for 1-20% ZrO2/SiO2, where the surface ZrOx species was present (1-12%) and a combination of surface ZrOx species and ZrO2 NPs (15-20%). The Pt NPs, however, were completely absent for higher zirconia loading where ZrO2 NPs are present and reflect the presence of a highly dispersed Pt phase on the ZrO2 NPs. The reactivity of the supported Pt phase was chemically probed with CH3OH oxidation (both steady-state and CH3OH-temperature programmed surface reaction (TPSR) spectroscopy). The reactivity of the methanol oxidation reaction was found to increase with the dimension of the Pt NPs, which also corresponds to lower ZrO2 domain size. Thus, the reactivity of the Pt catalytic active sites could be tuned by the domain size of the ZrO2 nanoligands.