We consider the problem of controlling a thermal convection flow by feedback. The system is governed by the Boussinesq approximation of the coupled set of Navier-Stokes and heat equations. The control is applied through Dirichlet boundary conditions. We concentrate on a two-dimensional mode and use a semidiscrete Galerkin scheme for numerical computations. We construct both a linear control and a non-linear quadratic control and apply them to the full non-linear model. First, we test these controllers on a one-mode approximation. The convergence of the numerical scheme is analyzed. We also consider LQR control for a two-dimensional heat equation. / Ph. D.

This dissertation examines the effects of instantaneous constant-power loads (CPLs) on power converters. These CPLs are prevalent in distributed power architectures and are also present in certain motor-drive applications. CPLs introduce a destabilizing nonlinear effect on power converters through an inverse voltage term that leads to significant oscillations in the main bus voltage or to its collapse. Boundary control is studied in order to stabilize dc-dc converters with instantaneous CPLs. The three basic topologies are studied: buck, boost, and buck-boost. Converter dynamics are analyzed in both switching states and the various operating regions of switch interaction with a first-order switching surface are identified. The analysis reveals important characteristics of CPLs. For non-minimum phase converters, in order to avoid issues related with the fact that the closed-loop state-dependent switching function is undefined on the switching surface, reflective mode solutions to both converter systems are defined in the sense of Filippov. Sufficient conditions for large-signal stability of the closed loop converter operating points are established. It is shown that first-order switching surfaces with negative slopes achieve large-signal stability, while positive slopes lead to instability. In particular, for the boost converter it is illustrated via simulations and experiments that positive slopes may lead to another closed-loop limit cycle. It is also shown that instability as well as system-stalling, which is termed the invariant-set problem, may still occur in reflective mode. However, a hysteresis band that contains the designed boundary may be used to prevent system-stalling, and also allow for a practical implementation of the controller by avoiding chattering. Regulation is also achieved. The dynamic behavior of single-phase full-wave uncontrolled rectifiers with instantaneous CPLs is also explored. Stable operation is shown to be dependent on initial condition and circuit parameters, which must fall within reasonable ranges that validate a CPL model. A necessary condition for stable operation of the rectifier system is thus derived. Furthermore, input and output characteristics of the rectifier with a CPL are investigated, and comparisons are made with the resistive case. A more complete model for the rectifier system that incorporates line-voltage distortion is also utilized to study the rectifier system. Simulations and experimental results are included for verification. / text

With a nation-wide aim toward reducing operational energy costs in buildings, it is important to understand the dynamics of controlled heating, cooling, and air circulation of an individual room, the "One-Room Model Problem." By understanding how one most efficiently regulates a room's climate, one can use this knowledge to help develop overall best-practice power reduction strategies. A key toward effectively analyzing the "One-Room Model Problem" is to understand the capabilities and limitations of existing commercial tools designed for similar problems. In this thesis we develop methodology to link commercial Computational Fluid Dynamics (CFD) software COMSOL with standard computational mathematics software MATLAB, and design controllers that apply inlet airflow and heating or cooling to a room and investigate their effects. First, an appropriate continuum model, the Boussinesq System, is described within the framework of this problem. Next, abstract and weak formulations of the problem are described and tied to a Finite Element Method (FEM) approximation as implemented in the interface between COMSOL and MATLAB. A methodology is developed to design Linear Quadratic Regulator (LQR) controllers and associated functional gains in MATLAB which can be implemented in COMSOL. These "closed-loop" methods are then tested numerically in COMSOL and compared against "open-loop" and average state closed-loop controllers. / Ph. D.

This work focuses on a comparison of numerical methods for linear quadratic regulator (LQR) problems defined by parabolic partial differential equations. In particular, we study various methods for computing functional gains to boundary control problems for the heat equation. These methods require us to solve various equations including the algebraic Riccati equation, the Riccati partial differential equation and the Chandrasekhar partial differential equations. Numerical results are presented for control of a one-dimensional and a two-dimensional heat equation with Dirichlet or Robin boundary control. / Ph. D.

The thesis consists of two parts. The first part discusses the initial value problem of a fifth-order Korteweg-de Vries type of equation w_t + w_xxx - w_xxxxx - ⁿ&#8721;_j=1 a_jw^jw_x = 0, w(x, 0) = w₀(x) posed on a periodic domain x &#8712; [0, 2&#960;] with boundary conditions w_ix(0, t) = w_ix(2&#960;, t), i = 0, 2, 3, 4 and an L²-stabilizing feedback control law w_x(2&#960;, t) = &#945;w_x(0, t) + (1 - &#945;)w_xxx(0; t) where n is a fixed positive integer, a_j, j = 1, 2, ... n, &#945; are real constants, and |&#945;| < 1. It is shown that for w₀(x) &#8712; H¹_&#945;(0, 2&#960;) with the boundary conditions described above, the problem is locally well-posed for w &#8712; C([0, T]; H¹_&#945;(0, 2&#960;)) with a conserved volume of w, [w] = &#8747;^2&#960;₀ w(x, t)dx. Moreover, the solution with small initial condition exists globally and approaches to [w₀(x)]/(2&#960;) as t &#8594; + &#8734;. The second part concerns wave motions on water in a rectangular basin with a wave generator mounted on a side wall. The linear governing equations are used and it is assumed that the surface tension on the free surface is not zero. Two types of generators are considered, flexible and rigid. For the flexible case, it is shown that the system is exactly controllable. For the rigid case, the system is not exactly controllable in a finite-time interval. However, it is approximately controllable. The stability problem of the system with the rigid generator controlled by a static feedback is also studied and it is proved that the system is strongly stable for this case. / Ph. D.

The dissertation focuses on the nonlinear Schrodinger equation iu_t+u_{xx}+kappa|u|^2u =0, for the complex-valued function u=u(x,t) with domain t>=0, 0<=x<= L, where the parameter kappa is any non-zero real number. It is shown that the problem is locally and globally well-posed for appropriate initial data and the solution exponentially decays to zero as t goes to infinity under the boundary conditions u(0,t) = beta u(L,t) and beta u_x(0,t)-u_x(L,t) = ialpha u(0,t), where L>0, and alpha and beta are any real numbers satisfying alpha*beta<0 and beta does not equal 1 or -1. Moreover, the numerical study of controllability problem for the nonlinear Schrodinger equations is given. It is proved that the finite-difference scheme for the linear Schrodinger equation is uniformly boundary controllable and the boundary controls converge as the step sizes approach to zero. It is then shown that the discrete version of the nonlinear case is boundary null-controllable by applying the fixed point method. From the new results, some open questions are presented. / Ph. D. / The dissertation concerns the solutions of nonlinear Schrodinger (NLS) equation, which arises in many applications of physics and applied mathematics and models the propagation of light waves in fiber optics cables, surface water-waves, Langmuir waves in a hot plasma, oceanic and optical rogue waves, etc. Under certain dissipative boundary conditions, it is shown that for given initial data, the solutions of NLS equation always exist for a finite time, and for small initial data, the solutions exist for all the time and decay exponentially to zero as time goes to infinity. Moreover, by applying a boundary control at one end of the boundary, it is shown using a finite-difference approximation scheme that the linear Schrodinger equation is uniformly controllable. It is proved using fixed point method that the discrete version of the NLS equation is also boundary controllable. The results obtained may be applicable to design boundary controls to eliminate unwanted waves generated by noises as well as create the wave propagation that is important in applications.

The primary goal of this thesis is to study finite element based a priori and a posteriori error estimates of optimal control problems of various kinds governed by linear elliptic PDEs (partial differential equations) of second and fourth orders. This thesis studies interior and boundary control (Neumann and Dirichlet) problems. The initial chapter is introductory in nature. Some preliminary and fundamental results of finite element methods and optimal control problems which play key roles for the subsequent analysis are reviewed in this chapter. This is followed by a brief literature survey of the finite element based numerical analysis of PDE constrained optimal control problems. We conclude the chapter with a discussion on the outline of the thesis. An abstract framework for the error analysis of discontinuous Galerkin methods for control constrained optimal control problems is developed in the second chapter. The analysis establishes the best approximation result from a priori analysis point of view and delivers a reliable and efficient a posteriori error estimator. The results are applicable to a variety of problems just under the minimal regularity possessed by the well-posedness of the problem. Subsequently, the applications of p p - interior penalty methods for a boundary control problem as well as a distributed control problem governed by the bi-harmonic equation subject to simply supported boundary conditions are discussed through the abstract analysis. In the third chapter, an alternative energy space based approach is proposed for the Dirichlet boundary control problem and then a finite element based numerical method is designed and analyzed for its numerical approximation. A priori error estimates of optimal order in the energy norm and the m norm are derived. Moreover, a reliable and efficient a posteriori error estimator is derived with the help an auxiliary problem. An energy space based Dirichlet boundary control problem governed by bi-harmonic equation is investigated and subsequently a l y - interior penalty method is proposed and analyzed for it in the fourth chapter. An optimal order a priori error estimate is derived under the minimal regularity conditions. The abstract error estimate guarantees optimal order of convergence whenever the solution has minimum regularity. Further an optimal order l l norm error estimate is derived. The fifth chapter studies a super convergence result for the optimal control of an interior control problem with Dirichlet cost functional and governed by second order linear elliptic PDE. An optimal order a priori error estimate is derived and subsequently a super convergence result for the optimal control is derived. A residual based reliable and efficient error estimators are derived in a posteriori error control for the optimal control. Numerical experiments illustrate the theoretical results at the end of every chapter. We conclude the thesis stating the possible extensions which can be made of the results presented in the thesis with some more problems of future interest in this direction.

La chaîne d'air du moteur est devenue un élément essentiel dans le développement des moteurs modernes. Le contrôle du système d'air a un impact direct sur les performances du moteur ainsi que sur son niveau d'émission de polluants. En effet, les stratégies qui agissent sur le système d'air permettent de contrôler les composants introduits dans le cylindre, ce qui est un moyen efficace et rentable de réduire les émissions polluantes. En conséquence, les chaînes d'air des moteurs modernes sont devenues de plus en plus complexes afin d'atteindre les stratégies de réduction de pollution et de permettre des réductions de consommation de carburant. Dans ce contexte, cette thèse se focalise sur la modélisation et le contrôle de la chaîne d'air des moteurs Diesel. / The engine air-path has become a crucial part in the development of modern engines. The control of the air-path has a direct impact on the engine performance as well as on its pollutant emission level. Indeed, air system strategies allow controlling the species that are introduced in the cylinder, which is a cost-effective way to reduce pollutant emissions. As a consequence, the automotive air systems have become increasingly complex in order to achieve pollutant reduction strategies and to allow fuel consumption reductions. In this context, this thesis focuses on the modeling and control of the air-path of Diesel engines. We divide this work into short-term developments and medium-long term developments.

The way people work today is shaped by the constant changes in society. The development within informative and communication technology is rapidly evolving, which can be seen as a contributory factor to the way society is shaping. Smartphones and computers lessens the need for physical availability at work, which increases the demands on workers to create an accessibility through their technical devices instead. The changed ways of working can be challenging due to the fact that people, as a result, get bigger influence to arrange their own workday. That leads us to a boundless kind of labor, which comes with both opportunities and risks. This thesis attempts to examine the experience of female managers of two age groups, connected to the boundless conditions that has relevance for their working environment. The purpose of this essay is to look at the female managers own experiences of boundless work conditions and what kind of meaning it has for their wellbeing. In order to provide with knowledge that goes in line with our purpose, theories revolving flexibility, accessibility, the job demand-control model and separation of the two spheres work and leisure have been used in combination with previous research. Previous research within the field has shown that clear boundaries between work and leisure is of importance for one's wellbeing and overall satisfaction with life. The satisfaction can be forsaken when for example working from home. Our conclusions demonstrate that a high workload often results in difficulties within boundary control. The respondents appreciate work flexibility since it enables them to achieve a higher level of concentration. No differences between the age groups were found. / Dagens samhälle präglas av arbetssätt som är under ständig förändring. Utveckling av informations- och kommunikationstekniska medel går framåt med rasande fart vilket bidrar till förändringen. Mobiler och datorer minskar behovet att befinna sig på arbetsplatsen i fysisk bemärkelse, vilket kan kompenseras med att vara nåbar på andra vis både på jobbet och utanför. De förändrade arbetssätten skapar utmaningar för människor där individen har fått ökat inflytande att styra över arbetsdagen. Att ett gränslöst arbete har skapats bär med sig både möjligheter och risker. Den här uppsatsen har författats i ett försök att belysa kvinnliga chefers upplevelse av det gränslösa arbetet som präglar deras arbetsplats samt om detta skiljer sig ur en åldersaspekt. Syftet med uppsatsen är att bidra med kunskap om chefernas egna upplevelse av gränslöst arbete och vad det har för betydelse för deras välmående. För att kunna bidra med denna kunskap har teorier om tillgänglighet och flexibilitet, krav- och kontrollmodellen och teori om de två sfärerna arbete och fritid använts i kombination med tidigare forskning och empiri. Tidigare forskning inom området tyder på att en tydlig gränsdragning mellan arbete och fritid är av vikt för ett fungerande liv präglat av balans mellan sfärerna, vilket lätt försakas till följd av arbete i hemmet. Uppsatsen har resulterat i slutsatser som pekar på att arbetet följer med hem vid hög arbetsbelastning vilket försvårar gränsdragningen. Cheferna uppskattar flexibiliteten i deras arbete då det ger möjlighet till koncentrerad arbetstid. Vi har inte observerat några skillnader ur en åldersaspekt.

We present a linear-quadratic regulator (LQR) design for a heat transfer model describing the cooling process of steel profiles in a rolling mill. Primarily we consider a feedback control approach for a linearization of the nonlinear model given there, but we will also present first ideas how to use local (in time) linearizations to treat the nonlinear equation with a regulator approach. Numerical results based on a spatial finite element discretization and a numerical algorithm for solving large-scale algebraic Riccati equations are presented both for the linear and nonlinear models.