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Extremum seeking control (ESC) is a classical adaptive control method aimed at locating and tracking optimal operating conditions in complex non-linear plants. Early results on ESC were restricted to plants that could bedescribed by Wiener or Hammerstein models. However, recent results haveshown that ESC will possess a stationary solution close to the optimum also for more general dynamical systems, provided the gradient estimation and feedback is sufficiently slow relative to the process dynamics. This thesis addresses the uniqueness of this solution and the achievable rate of convergence.The motivation for the work stems from the need to optimize a complex biofilm reactor, the CANON process, which if operated near a narrow optimum may significantly lower the cost of ammonium removal in wastewater treatment. Simulations of ESC applied to the CANON process reveal that, depending on initial conditions and tuning parameters, the ESC loop may converge to stationary solutions far removed from the optimum and that multiple stationary solutions may exist. Analysis of a general model for the ESC loop shows that the stationary solutions are characterized either by a gain condition or a phase lag condition on the locally linearized system, the latter indicating that the ESC loop can act as a phase-lock loop. The phase lag condition is shown to be satisfied close to the optimum, but can be fulfilled also at operating points with no relation to the optimality criterion whatsoever and this serves to explain the observed solution multiplicity. Bifurcation theory is employed to further analyze the stationary solutions of the ESC loop and conditions for existence of saddle-node bifurcations are derived. A saddle node bifurcation implies a hard loss of stability and the existence of multiple stationary solutions. It is also demonstrated, using examples, that the ESC loop may undergo other types of bifurcations, including period doubling bifurcations into chaos. For the considered example, the resulting chaotic solution is significantly closer to optimum than the underlying nominal limit cycle. Previous results on ESC applied to general dynamic systems have relied on the use of asymptotic methods, such as singular perturbations and averaging. This has resulted in a three time-scale separation of the problem, in which the gradient estimation and control have been forced to be significantly slower than the open-loop process dynamics. For most processes, including the CANON process studied in this thesis, this renders ESC of little practical use and we therefore consider relaxing some of the restrictive assumptions. Inparticular, we allow for any gradient estimation rate and significantly faster gradient feedback as compared to previous studies. Using a linear parameter varying (LPV) description of the plant, quantitative expressions for the convergence rate in terms of the ESC tuning parameters and plant properties are derived. / <p>QC 20141106</p>

Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2014-08-28T15:33:45Z No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertacao Marcos Antonio da Costa.pdf: 1237372 bytes, checksum: e4392b806f26f0293114e12b4ed829c9 (MD5) / Made available in DSpace on 2014-08-28T15:33:45Z (GMT). No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertacao Marcos Antonio da Costa.pdf: 1237372 bytes, checksum: e4392b806f26f0293114e12b4ed829c9 (MD5) Previous issue date: 2013-04-12 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / We deal with extremum values problems. Our focus is the high school students. We present simple ideas and techniques on solving classical optimization problems. Among other problems we cite the classical isoperimetric ploblem and the Heron0s problem. We are based on the book Stories About Maxima and Minima by Tikhomirov which lead with these classical problems using only elementary mathematical subjects. / Estudamos problemas envolvendo valores extremos, com foco nos estudantes do Ensino Médio. Apresentamos de forma simples e resumida, algumas ideias e teorias para a solução de tais problemas. Dentre os quais citamos o Problema de Dido e o de Heron. O principal referencial teórico para confecção deste trabalho foi o livro de Tikhomirov intitulado Stories About Maxima and Minima. Baseados em tal livro, aplicamos métodos e teorias elementares para solucionarmos problemas clássicos de máximos e mínimos.

Introduction. Couvertures des graphes par des cycles. Couverture par des circuits d'un matroïde régulier qui admet un Z.5- flot non nul. Flots de Fulkerson. Flots de Petersen. Constructions locales. Annexe. Bibliographie

<p>Data networks are an important part in an increasing number of applications with real-time and reliability requirements. To meet these demands a variety of approaches have been proposed. Forward error correction, which adds redundancy to the communicated data, is one of them. However, the redundancy occupies communication bandwidth, so it is desirable to control the amount of redundancy in order to achieve high reliability without adding excessive communication delay. The main contribution of the thesis is to formulate the problem of adjusting the redundancy in a control framework, which enables the dynamic properties of error correction control to be analyzed using control theory. The trade-off between application quality and resource usage is captured by introducing an optimal control problem. Its dependence on the knowledge of the network state at the transmission side is discussed. An error correction controller that optimizes the amount of redundancy without relying on network state information is presented. This is achieved by utilizing an extremum seeking control algorithm to optimize the cost function. Models with varying complexity of the resulting feedback system are presented and analyzed. Conditions for convergence are given. Multiple-input describing function analysis is used to examine periodic solutions. The results are illustrated through computer simulations and experiments on a wireless sensor network.</p>

Membrane Distillation (MD) is an emerging sustainable desalination technique. While MD has many advantages and can be powered by solar thermal energy, its main drawback is the low water production rate. However, the MD process has not been fully optimized in terms of its manipulated and controlled variables. This is largely due to the lack of adequate dynamic models to study and simulate the process. In addition, MD is prone to membrane fouling, which is a fault that degrades the performance of the MD process. This work has three contributions to address these challenges. First, we derive a mathematical model of Direct Contact Membrane Distillation (DCMD), which is the building block for the next parts. Then, the proposed model is extended to account for membrane fouling and an observer-based fouling detection method is developed. Finally, various control strategies are implemented to optimize the performance of the DCMD solar-powered process. In part one, a reduced-order dynamic model of DCMD is developed based on lumped capacitance method and electrical analogy to thermal systems. The result is an electrical equivalent thermal network to the DCMD process, which is modeled by a system of nonlinear differential algebraic equations (DAEs). This model predicts the water-vapor flux and the temperature distribution along the module length. Experimental data is collected to validate the steady-state and dynamic responses of the proposed model, with great agreement demonstrated in both. The second part proposes an extension of the model to account for membrane fouling. An adaptive observer for DAE systems is developed and convergence proof is presented. A method for membrane fouling detection is then proposed based on adaptive observers. Simulation results demonstrate the performance of the membrane fouling detection method. Finally, an optimization problem is formulated to maximize the process efficiency of a solar-powered DCMD. The adapted method is known as Extremum Seeking (ES). A Newton-based ES is designed and the proposed model is used to accurately forecast the distilled water flux. Although good results are obtained with this method, a practical modification to the ES scheme is proposed to enhance the practical stability.

Indiana University-Purdue University Indianapolis (IUPUI) / With the increasing demand of economy and environmental pollutions, more and more renewable energy systems with clean sources appear and have attracted attention of systems involving solar power, wind power and hybrid new energy powers[1]. However, there are some difficulties associated with combined utilization of solar and wind, such as their intermittent behavior and their peak hours mismatch in generation and consumption[1]. For this purpose, advanced network of a variety of renewable energy systems along with controllable load and storage units have been introduced[1-3]. This thesis proposes some configurations of hybrid energy harvesting systems, including wind-wind-storage DC power system with BOOST converters, solar-solar-storage DC power system with cascade BOOST converters, wind-solar-storage DC power system with BOOST converter and cascade BOOST converter, and wind-solar DC power system with SEPIC converter and BOOST converter. The models of all kinds of systems are built in Matlab/Simulink and the mathematical state-space models of combined renewable energy systems are also established. Several MPPT control strategies are introduced and designed to maximize the simultaneous power capturing from wind and solar, such as Perturb & Observe (P&O) algorithm for solar and wind, Tip Speed Ratio (TSR) control and Power Signal Feedback (PSF) control for wind, and Sliding Mode Extremum Seeking Control (SM-ESC) for wind and solar systems[4]. The control effects of some of these MPPT methods are also compared and analyzed. The supervisory control strategies corresponding to each configurations are also discussed and implemented to maximize the simultaneous energy harvesting from both renewable sources and balance the energy between the sources, battery and the load[2]. Different contingencies are considered and categorized according to the power generation available at each renewable source and the state of charge in the battery[2]. Applying the system architectures and control methods in the proposed hybrid new energy systems is a novel and significant attempt, which can be more general in the practical applications. Simulation results demonstrate accurate operation of the supervisory controller and functionality of the maximum power point tracking algorithm in each operating condition both for solar and for wind power[3]

Data networks are an important part in an increasing number of applications with real-time and reliability requirements. To meet these demands a variety of approaches have been proposed. Forward error correction, which adds redundancy to the communicated data, is one of them. However, the redundancy occupies communication bandwidth, so it is desirable to control the amount of redundancy in order to achieve high reliability without adding excessive communication delay. The main contribution of the thesis is to formulate the problem of adjusting the redundancy in a control framework, which enables the dynamic properties of error correction control to be analyzed using control theory. The trade-off between application quality and resource usage is captured by introducing an optimal control problem. Its dependence on the knowledge of the network state at the transmission side is discussed. An error correction controller that optimizes the amount of redundancy without relying on network state information is presented. This is achieved by utilizing an extremum seeking control algorithm to optimize the cost function. Models with varying complexity of the resulting feedback system are presented and analyzed. Conditions for convergence are given. Multiple-input describing function analysis is used to examine periodic solutions. The results are illustrated through computer simulations and experiments on a wireless sensor network. / QC 20101105

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