Aerospace Engineering Research Works

Permanent URI for this collectionhttp://hdl.handle.net/1903/1655

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Author: search.filters.author.Shapiro, Benjamin

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Now showing 1 - 9 of 9
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    High-Frequency Nonlinear Vibrational Control
    (IEEE, 1997-01) Shapiro, Benjamin; Zinn, B. T.
    This paper discusses the feasibility of high-frequency nonlinear vibrational control. Such control has the advantage that it does not require state measurement and processing capabilities that are required in conventional feedback control. Bellman et al. [1] investigated nonlinear systems controlled by linear vibrational controllers and proved that vibrational control is not feasible if the Jacobian matrix has a positive trace. This paper extends previous work to include nonlinear vibrational controllers. A stability criteria is derived for nonlinear systems with nonlinear controllers, and it is shown that a nonlinear vibrational controller can stabilize a system even if the Jacobian matrix has a positive trace.
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    Workshop on Control of Micro- and Nano-Scale Systems
    (2005-04) Shapiro, Benjamin
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    Arbitrary Steering of Multiple Particles Independently in an Electro-Osmotically Driven Microfluidic System
    (IEEE, 2006-07) Shapiro, Benjamin; Chaudhary, Satej
    We demonstrate how to use feedback control of microflows to steer multiple particles independently in planar microfluidic systems driven by electro-osmotic actuation. This technique enables the handling of biological materials, such as cells, bacteria, DNA, and drug packets, in a hand-held format using simple and easy-to-fabricate actuators. The feedback loop consists of a vision system which identifies the positions of the particles in real-time, a control algorithm that computes the actuator (electrode) inputs based on information received from the vision system, and a set of electrodes (actuators) that create the required flow through electro-osmotic forces to steer all the particles along their desired trajectories and correct for particle position errors and thermal noise. Here, we focus on the development of control algorithms to achieve the steering of particles: vision system implementation, fabrication of devices, and experimental validation is addressed in other publications. In particular, steering of a single (yeast cell) particle has been demonstrated experimentally in our prior research and we have recently demonstrated experimental steering of three particles independently. In this paper, we develop the control algorithms for steering multiple particles independently and we validate our control techniques using simulations with realistic sources of initial position errors and thermal noise. In this study, we assume perfect measurement and actuation.
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    Using Feedback Control of Microflows to Independently Steer Multiple Particles
    (IEEE, 2006-08) Shapiro, Benjamin; Armani, Michael D.; Chaudhary, Satej; Probst, Roland
    In this paper, we show how to combine microfluidics and feedback control to independently steer multiple particles with micrometer accuracy in two spatial dimensions. The particles are steered by creating a fluid flow that carries all the particles from where they are to where they should be at each time step. Our control loop comprises sensing, computation, and actuation to steer particles along user-input trajectories. Particle locations are identified in real-time by an optical system and transferred to a control algorithm that then determines the electrode voltages necessary to create a flow field to carry all the particles to their next desired locations. The process repeats at the next time instant. Our method achieves inexpensive steering of particles by using conventional electroosmotic actuation in microfluidic channels. This type of particle steering does not require optical traps and can noninvasively steer neutral or charged particles and objects that cannot be captured by laser tweezers. (Laser tweezers cannot steer reflective particles, or particles where the index of refraction is lower than (or for more sophisticated optical vortex holographic tweezers does not differ substantially from) that of the surrounding medium.)We show proof-of-concept PDMS devices, having four and eightelectrodes, with control algorithms that can steer one and three particles, respectively. In particular, we demonstrate experimentally that it is possible to use electroosmotic flow to accurately steer and trap multiple particles at once.
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    Modeling the Fluid Dynamics of Electrowetting on Dielectric (EWOD)
    (IEEE, 2006-08) Shapiro, Benjamin; Walker, Shawn
    This paper discusses the modeling and simulation of a parallel-plate Electrowetting On Dielectric (EWOD) device that moves fluid droplets through surface tension effects.We model the fluid dynamics by using Hele–Shaw type equations with a focus on including the relevant boundary phenomena. Specifically, we show that contact angle saturation and hysteresis are needed to predict the correct shape and time scale of droplet motion.We demonstrate this by comparing our simulation to experimental data for a splitting droplet.Without these boundary effects, the simulation shows the droplet splitting into three pieces instead of two and the motion is over 15 times faster than the experiment. We then show how including the saturation characteristics of the device, and a simple model of contact angle hysteresis, allows the simulation to better predict the splitting experiment. The match is not perfect and suffers mainly because contact line pinning is not included. This is followed by a comparison between our simulation, whose parameters are now frozen, and a new experiment involving bulk droplet motion. Our numerical implementation uses the level set method, is fast, and is being used to design algorithms for the precise control of microdroplet motion, mixing, and splitting.
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    Interconnection of Subsystem Reduced-Order Models in the Electro-Thermal Analysis of Large Systems
    (IEEE, 2007-06) Shapiro, Benjamin; Mathai, Pramod
    Heat conduction in an electronic device is commonly modeled as a discretized thermal system (eg, finite element or finite difference models) that typically uses large matrices for solving complex problems. The large size of electronic-system heat transfer models can be reduced using model reduction methods and the resulting reduced-order models can yield accurate results with far less computational costs. Electronic devices are typically composed of components, like chips, printed circuit boards, and heat sinks that are coupled together. There are two ways of creating reduced-order models for devices that have many coupled components. The first way is to create a single reduced-order model of the entire device. The second way is to interconnect reduced-order models of the components that constitute the device. The second choice (which we call the “reduce then interconnect” approach) allows the heat transfer specialist to perform quick simulations of different architectures of the device by using a library of reduced-order models of the different components that make up the device. However, interconnecting reduced-order models in a straightforward manner can result in unstable behavior. The purpose of this paper is two-fold: creating reduced-order models of the components using a Krylov subspace algorithm and interconnecting the reducedorder models in a stable manner using concepts from control theory. In this paper we explain the logic behind the “reduce then interconnect” approach, formulate a control-theoretic method for it, and finally exhibit the whole process numerically, by applying it to an example heat conduction problem.
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    Symmetry Approach to Extension of Flutter Boundaries via Mistuning
    (American Institute of Aeronautics and Astronautics, 1998-05) Shapiro, Benjamin
    A general framework is presented for analyzing and optimizing stability increases resulting from mistuning. The framework given is model independent and is based primarily on symmetry arguments. Difficult practical issues are transformed to tractable mathematical questions. It is shown that mistuning analysis reduces to a block circular matrix eigenvalue/vector problem that can be solved efficiently even for large problems. Similarly, the optimization becomes a standard linear constraint quadratic programming problem and can be solved numerically. Because the methods given are model-independent, they can be applied to various models and allow the researcher to easily conclude which models accurately capture mistuning and which do not. A simple quasisteady model for flutter in a cascade is used to illustrate and validate results in this paper.
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    Solving for Mistuned Forced Response by Symmetry
    (American Institute of Aeronautics and Astronautics, 1999-03) Shapiro, Benjamin
    The introduction of mistuning in jet-engine bladed disks can lead to large changes in stability and forced response. Even small random mistuning (within the bounds of manufacturing tolerance) can lead to unacceptable response and high-cycle fatigue. Meanwhile, intentional mistuning may improve stability and forced response under manufacturing uncertainty. This paper presents a general framework for predicting forced response as a function of mistuning. Because the forced response problem is an almost singular linear problem, its solution is highly nonlinear in the mistuning parameters. Our methods exploit symmetry arguments and eigenstructure perturbation to provide a method valid for any model. It is shown that, by perturbing eigenvectors in the numerator and the inverse of eigenvalues in the denominator (exploiting symmetry in both computations), we can accurately approximate the forced response as a function of mistuning. Results are demonstrated for a simple lightly damped model, and the consequent sharp nonlinear behavior is captured almost perfectly. We also show that intentional mistuning may guarantee improved stability and forced response under fixed manufacturing tolerances. Thus, intentional mistuning should be considered as a practical means of increasing safety and enhancing engine performance.
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    Analyzing Mistuning of Bladed Disks by Symmetry and Reduced-Order Areodynamic Modeling
    (American Institute of Aeronautics and Astronautics, 2003-03) Shapiro, Benjamin; Willcox, Karen
    The mistuned behavior of bladed disks is analyzed and optimized using an unsteady, transonic, computational fluid dynamic model (CFD). This result is enabled by the integration of two frameworks: the first is based on symmetry arguments and an eigenvalue/vector perturbation scheme, while the second is a reduction technique based on the proper orthogonal decomposition (POD). The first framework reduces the complexity of the problem, reveals engineering trade offs and suggests the existence of an intentional robust mistuning which improves both stability and forced response with respect to random variations in blade parameters. The second framework permits the reduction of state-of-the-art computational fluid dynamic codes to reduced-order models, which capture the accuracy of the original simulation but fit within the mistuning analysis framework. Together, these methodologies allow the analysis of a transonic, bladed disk with stiffness mistuning (see Fig. 1).Moreover, because of the low order of the aeroelasticmodel, a robust control¹ uncertainty analysis can be used to prove that the intentional mistuning suggested by the symmetry analysis framework is indeed robust. Hence this paper contains the first rigorous demonstration that intentional mistuning can robustly improve both the stability and forced response for a model that includes sophisticated aerodynamic effects.