Feedback control of unstable steady states of flow past a flat plate using reduced-order estimators

We present an estimator-based control design procedure for flow control, using reduced-order models of the governing equations, linearized about a possibly unstable steady state. The reduced models are obtained using an approximate balanced truncation method that retains the most controllable and observable modes of the system. The original method is valid only for stable linear systems, and we present an extension to unstable linear systems. The dynamics on the unstable subspace are represented by projecting the original equations onto the global unstable eigenmodes, assumed to be small in number. A snapshot-based algorithm is developed, using approximate balanced truncation, for obtaining a reduced-order model of the dynamics on the stable subspace. The proposed algorithm is used to study feedback control of 2-D flow over a flat plate at a low Reynolds number and at large angles of attack, where the natural flow is vortex shedding, though there also exists an unstable steady state. For control design, we derive reduced-order models valid in the neighborhood of this unstable steady state. The actuation is modeled as a localized body force near the leading edge of the flat plate, and the sensors are two velocity measurements in the near-wake of the plate. A reduced-order Kalman filter is developed based on these models and is shown to accurately reconstruct the flow field from the sensor measurements, and the resulting estimator-based control is shown to stabilize the unstable steady state. For small perturbations of the steady state, the model accurately predicts the response of the full simulation. Furthermore, the resulting controller is even able to suppress the stable periodic vortex shedding, where the nonlinear effects are strong, thus implying a large domain of attraction of the stabilized steady state.Comment: 36 pages, 17 figure

Density Matrix Renormalization for Model Reduction in Nonlinear Dynamics

We present a novel approach for model reduction of nonlinear dynamical systems based on proper orthogonal decomposition (POD). Our method, derived from Density Matrix Renormalization Group (DMRG), provides a significant reduction in computational effort for the calculation of the reduced system, compared to a POD. The efficiency of the algorithm is tested on the one dimensional Burgers equations and a one dimensional equation of the Fisher type as nonlinear model systems.Comment: 12 pages, 12 figure

Repeatable method of thermal stress fracture test of brittle materials

Method heats specimens slowly and with sufficient control so that the critical temperature gradient in the specimens cannot occur before temperature equilibrium is reached

Quantum control via a genetic algorithm of the field ionization pathway of a Rydberg electron

Quantum control of the pathway along which a Rydberg electron field ionizes is experimentally and computationally demonstrated. Selective field ionization is typically done with a slowly rising electric field pulse. The $(1/n^*)^4$ scaling of the classical ionization threshold leads to a rough mapping between arrival time of the electron signal and principal quantum number of the Rydberg electron. This is complicated by the many avoided level crossings that the electron must traverse on the way to ionization, which in general leads to broadening of the time-resolved field ionization signal. In order to control the ionization pathway, thus directing the signal to the desired arrival time, a perturbing electric field produced by an arbitrary waveform generator is added to a slowly rising electric field. A genetic algorithm evolves the perturbing field in an effort to achieve the target time-resolved field ionization signal.Comment: Corrected minor typographic errors and changed the titl

Reduced-Order Modeling of Channel Flow Using Traveling

Reduced-order models of the flow in a plane channel flow are constructed in two regimes: a minimal flow unit in which turbulence is sustained, and a transitional flow linearized about the laminar profile. Proper orthogonal decomposition (POD) of data from a direct numerical simulation of a channel flow in a minimal flow unit is performed in order to examine the coherent structures and their dynamical interactions. Empirical basis functions are obtained both using Fourier modes in the streamwise and spanwise directions, with POD modes in the wall-normal direction, and using 3D (non-Fourier) POD modes that can translate in the streamwise direction (traveling modes). Traveling modes capture more energy than standard Fourier-POD for the same number of modes. In addition, models of a channel flow linearized about a laminar profile are constructed using both POD and balanced POD, an approximation to balanced truncation that is tractable for very large systems. Balanced POD models significantly outperform standard POD, especially at including the effects of actuation

Mass-Producible 2D-MoS2‑Impregnated Screen-Printed Electrodes

This document is the Accepted Manuscript version of a Published Work that appeared in final form in ACS Applied Materials and Interfaces, copyright © American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see https://pubs.acs.org/doi/10.1021/acsami.7b05104Two-dimensional molybdenum disulfide (2D-MoS2) screen-printed electrodes (2D-MoS2-SPEs) have been designed, fabricated, and evaluated toward the electrochemical oxygen reduction reaction (ORR) within acidic aqueous media. A screen-printable ink has been developed that allows for the tailoring of the 2D-MoS2 content/mass used in the fabrication of the 2D-MoS2-SPEs, which critically affects the observed ORR performance. In comparison to the graphite SPEs (G-SPEs), the 2D-MoS2-SPEs are shown to exhibit an electrocatalytic behavior toward the ORR which is found, critically, to be reliant upon the percentage mass incorporation of 2D-MoS2 in the 2D-MoS2-SPEs; a greater percentage mass of 2D-MoS2 incorporated into the 2D-MoS2-SPEs results in a significantly less electronegative ORR onset potential and a greater signal output (current density). Using optimally fabricated 2D-MoS2-SPEs, an ORR onset and a peak current of approximately +0.16 V [vs saturated calomel electrode (SCE)] and −1.62 mA cm–2, respectively, are observed, which exceeds the −0.53 V (vs SCE) and −635 μA cm–2 performance of unmodified G-SPEs, indicating an electrocatalytic response toward the ORR utilizing the 2D-MoS2-SPEs. An investigation of the underlying electrochemical reaction mechanism of the ORR within acidic aqueous solutions reveals that the reaction proceeds via a direct four-electron process for all of the 2D-MoS2-SPE variants studied herein, where oxygen is electrochemically favorably reduced to water. The fabricated 2D-MoS2-SPEs are found to exhibit no degradation in the observed achievable current over the course of 1000 repeat scans. The production of such inks and the resultant mass-producible 2D-MoS2-SPEs mitigates the need to modify post hoc an electrode via the drop-casting technique that has been previously shown to result in a loss of achievable current over the course of 1000 repeat scans. The 2D-MoS2-SPEs designed, fabricated, and tested herein could have commercial viability as electrocatalytic fuel cell electrodes because of being economical as a result of their scales of economy and inherent tailorability. The technique utilized herein to produce the 2D-MoS2-SPEs could be adapted for the incorporation of different 2D nanomaterials, resulting in SPEs with the inherent advantages identified above