This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.

Introduction to the Finite Element Method

Analysis of cellular mechanotransduction, the mechanism by which cells convert mechanical signals into biochemical responses, has focused on identification of critical mechanosensitive molecules and cellular components. Stretch-activated ion channels, caveolae, integrins, cadherins, growth factor receptors, myosin motors, cytoskeletal filaments, nuclei, extracellular matrix, and numerous other structures and signaling molecules have all been shown to contribute to the mechanotransduction response. However, little is known about how these different molecules function within the structural context of living cells, tissues, and organs to produce the orchestrated cellular behaviors required for mechanosensation, embryogenesis, and physiological control. Recent work from a wide range of fields reveals that organ, tissue, and cell anatomy are as important for mechanotransduction as individual mechanosensitive proteins and that our bodies use structural hierarchies (systems within systems) composed of interconnected networks that span from the macroscale to the nanoscale in order to focus stresses on specific mechanotransducer molecules. The presence of isometric tension (prestress) at all levels of these multiscale networks ensures that various molecular scale mechanochemical transduction mechanisms proceed simultaneously and produce a concerted response. Future research in this area will therefore require analysis, understanding, and modeling of tensionally integrated (tensegrity) systems of mechanochemical control.

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Cellular mechanotransduction: putting all the pieces together again.

We consider distributed parameter systems where the underlying dynamics are spatially invariant, and where the controls and measurements are spatially distributed. These systems arise in many applications such as the control of vehicular platoons, flow control, microelectromechanical systems (MEMS), smart structures, and systems described by partial differential equations with constant coefficients and distributed controls and measurements. For fully actuated distributed control problems involving quadratic criteria such as linear quadratic regulator (LQR), H/sub 2/ and H/sub /spl infin//, optimal controllers can be obtained by solving a parameterized family of standard finite-dimensional problems. We show that optimal controllers have an inherent degree of decentralization, and this provides a practical distributed controller architecture. We also prove a general result that applies to partially distributed control and a variety of performance criteria, stating that optimal controllers inherit the spatial invariance structure of the plant. Connections of this work to that on systems over rings, and systems with dynamical symmetries are discussed.

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Distributed control of spatially invariant systems

The major challenge in biology today is biocomplexity: the need to explain how cell and tissue behaviors emerge from collective interactions within complex molecular networks. Part I of this two-part article, described a mechanical model of cell structure based on tensegrity architecture that explains how the mechanical behavior of the cell emerges from physical interactions among the different molecular filament systems that form the cytoskeleton. Recent work shows that the cytoskeleton also orients much of the cell's metabolic and signal transduction machinery and that mechanical distortion of cells and the cytoskeleton through cell surface integrin receptors can profoundly affect cell behavior. In particular, gradual variations in this single physical control parameter (cell shape distortion) can switch cells between distinct gene programs (e.g. growth, differentiation and apoptosis), and this process can be viewed as a biological phase transition. Part II of this article covers how combined use of tensegrity and solid-state mechanochemistry by cells may mediate mechanotransduction and facilitate integration of chemical and physical signals that are responsible for control of cell behavior. In addition, it examines how cell structural networks affect gene and protein signaling networks to produce characteristic phenotypes and cell fate transitions during tissue development.

Tensegrity II. How structural networks influence cellular information processing networks

https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1065&context=usafresearch

A review of space robotics technologies for on-orbit servicing

In-stream hydrokinetic electricity production, electricity generation from moving currents without the use of dams, has significant potential for increasing electric power production. This project evaluates a control system designed to regulate rotor rate (rpm) to improve power production from in-stream hydrokinetic turbines. The control algorithm is evaluated using both a numerical model of a rigidly mounted tidal turbine and a numerical model of a moored ocean current turbine system. These two system models are each coupled to an induction electric machine model. Based on the turbine torque-speed characteristic, as well as the asynchronous machine features, a Look-Up-Table (LUT) is used to generate the frequency of the sinusoidal voltages of the three phases to be supplied to the machine. However, to compensate for disturbances and perturbations of the power-plant a PI controller is generating a correction term for electrical frequency superimposed to the output of the LUT. A first round of simulations using the numerical models was performed in order to evaluate the developed algorithms.Copyright © 2014 by ASME

Power Take-Off Control of In-Stream Hydrokinetic Turbines

The design and tracking performance of model predictive controllers for complex, control oriented, physics based helicopter models is investigated. A nonlinear model of the helicopter, which also includes blade flexibility, is first linearized around specific flight conditions like level banked turns and helical turns. Model predictive controllers are then designed using the linearized helicopter models and their ability to track discontinuous maneuvering trajectories is evaluated. The performance metrics used herein are tracking quality, satisfaction of heterogeneous constraints, and computation time.

Model Predictive Control of Maneuvering Helicopters

Close tracking of equilibrium paths

The problem of finding the trajectory for an aerospace vehicle moving between two fixed points is investigated using Calculus of Variations (CV), which can provide necessary and sufficient conditions for trajectories that optimize a cost index. Within the framework of a systematic study aimed at tackling analytically the trajectory generation problem, this paper presents applications of the CV to find trajectories that optimize kinetic energy, energy consumption, and fuel consumption considering several environmental conditions.

http://faculty-staff.ou.edu/L/Andrea.LAfflitto-1/Documents/LAfflitto_Sultan_CDC_2009.pdf

Applications of Calculus of Variations to Aircraft and Spacecraft Path Planning

Linear Quadratic Gaussian (LQG) control is developed for a prestressed square membrane with bimorph actuators attached to it. The membrane is modeled using the finite element method and the membrane is assumed to be clamped on all edges. After obtaining the mass, damping, stiffness and input matrices in second order form using the weak form Finite Element Method (FEM), the problem is represented in first order form to develop the LQG controller. To study the robustness of the system, the control and observer gain matrices developed for the nominal system are applied to systems obtained from the nominal system by modifying material properties and prestress.Copyright © 2014 by ASME

Cornel Sultan

Papers

Power Take-Off Control of In-Stream Hydrokinetic Turbines

Model Predictive Control of Maneuvering Helicopters

Close tracking of equilibrium paths

Applications of Calculus of Variations to Aircraft and Spacecraft Path Planning

LQG Control and Robustness Study for a Prestressed Membrane With Bimorph Actuators