Adaptive Nonlinear Regulation Control of Thermoacoustic Oscillations in Rijke-Type Systems

Adaptive nonlinear control of self-excited oscillations in Rijke-type thermoacoustic systems is considered. To demonstrate the methodology, a well-accepted thermoacoustic dynamic model is introduced, which includes arrays of sensors and monopole-like actuators. To facilitate the derivation of the adaptive control law, the dynamic model is recast as a set of nonlinear ordinary differential equations, which are amenable to control design. The control-oriented nonlinear model includes unknown, unmeasurable, nonvanishing disturbances in addition to parametric uncertainty in both the thermoacoustic dynamic model and the actuator dynamic model. To compensate for the unmodeled disturbances in the dynamic model, a robust nonlinear feedback term is included in the control law. One of the primary challenges in the control design is the presence of input-multiplicative parametric uncertainty in the dynamic model for the control actuator. This challenge is mitigated through innovative algebraic manipulation in the regulation error system derivation along with a Lyapunov-based adaptive control law. To address practical implementation considerations, where sensor measurements of the complete state are not available for feedback, a detailed analysis is provided to demonstrate that system observability can be ensured through judicious placement of pressure (and/or velocity) sensors. Based on this observability condition, a sliding-mode observer design is presented, which is shown to estimate the unmeasurable states using only the available sensor measurements. A detailed Lyapunov-based stability analysis is provided to prove that the proposed closed-loop active thermoacoustic control system achieves asymptotic (zero steady-state error) regulation of multiple thermoacoustic modes in the presence of the aforementioned model uncertainty. Numerical Monte Carlo-type simulation results are also provided, which demonstrate the performance of the proposed closed-loop control system under various sets of operating conditions

Machine Learning and Its Application to Reacting Flows

This open access book introduces and explains machine learning (ML) algorithms and techniques developed for statistical inferences on a complex process or system and their applications to simulations of chemically reacting turbulent flows. These two fields, ML and turbulent combustion, have large body of work and knowledge on their own, and this book brings them together and explain the complexities and challenges involved in applying ML techniques to simulate and study reacting flows. This is important as to the world’s total primary energy supply (TPES), since more than 90% of this supply is through combustion technologies and the non-negligible effects of combustion on environment. Although alternative technologies based on renewable energies are coming up, their shares for the TPES is are less than 5% currently and one needs a complete paradigm shift to replace combustion sources. Whether this is practical or not is entirely a different question, and an answer to this question depends on the respondent. However, a pragmatic analysis suggests that the combustion share to TPES is likely to be more than 70% even by 2070. Hence, it will be prudent to take advantage of ML techniques to improve combustion sciences and technologies so that efficient and “greener” combustion systems that are friendlier to the environment can be designed. The book covers the current state of the art in these two topics and outlines the challenges involved, merits and drawbacks of using ML for turbulent combustion simulations including avenues which can be explored to overcome the challenges. The required mathematical equations and backgrounds are discussed with ample references for readers to find further detail if they wish. This book is unique since there is not any book with similar coverage of topics, ranging from big data analysis and machine learning algorithm to their applications for combustion science and system design for energy generation

Control of systems modeled by hyperbolic partial diferential equations

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia de Automação e Sistemas, Florianópolis, 2017.Sistemas com parâmetros distribuídos representam uma vasta gama de processos da engenharia. Neste caso, as variáveis do sistema irão conter termos dependentes do tempo assim como gradientes espaciais e, portanto, é natural representa-los por equações diferenciais parciais. Exemplos podem ser encontrados em diversas áreas: desde processos químicos e térmicos, sistemas de produção e distribuição de energia, e problemas relacionados ao transporte de fluidos e ciência médica. Esta tese trata dois tipos de problemas: estabilização de equações diferenciais parciais lineares hiperbólicas com variável de controle na condição de contorno e controle regulatório de sistemas descritos por equações diferenciais parciais quasi-lineares hiperbólicas com variável de controle no domínio. Com relação ao primeiro, estudaram-se duas metodologias de controle: (i) uma lei de controle estática que garante convergência do sistema para o ponto de equilíbrio desejado. A metodologia de controle utiliza uma função de Lyapunov para encontrar os valores dos parâmetros do controlador que garantem estabilidade exponencial em malha fechada. Resultados de simulação para o problema de supressão de golfadas em sistemas de produção de petróleo são apresentados para ilustrar a eficiência do método; (ii) uma lei de controle baseada nas ferramentas clássicas do domínio da frequência. Neste caso, aplicamos a transformada de Laplace na equação diferencial parcial para obter uma função de transferência irracional e então, ferramentas clássicas do domínio da frequência são usadas para projetar o controlador, de maneira similar aos sistemas de dimensão finita com função de transferência racional. Estes resultados foram aplicados experimentalmente no problema de controle de oscilações termoacústicas do tubo de Rijke, mostrando a efetividade do método. Para o segundo problema, utiliza-se o método das características combinado com a técnica de controle por modos deslizantes. O método das características é usado para transformar o sistema de equações diferenciais parciais em um conjunto de equações diferenciais ordinárias que descrevem o sistema original. O projeto de controle é então realizado a partir deste conjunto de equações diferenciais ordinárias através de resultados bem conhecidos da teoria de equações diferenciais ordinárias. Os resultados obtidos foram testados experimentalmente em dois sistemas de escala industrial: uma planta solar e um fotobiorreator tubular.Abstract : Distributed parameter systems represent a wide range of engineeringprocesses. In this case, the system variables will contain temporally dependentterms as well spatial gradients and, therefore, it is natural to representthem by partial dierential equations. Examples can be found in manyelds: chemical and thermal processes, production and distribution energysystems, and problems related to uid transport and medical science.This thesis deals with two dierent problems: stabilization of linear hyperbolicpartial dierential equations with boundary control and regulatorycontrol of systems described by quasilinear hyperbolic partial dierentialequations with in domain control. Concerning the boundary control problem,we studied two control methodologies: (i) a static control law thatguarantees convergence of the system to the desired equilibrium point. Thiscontrol methodology uses a Lyapunov function to nd the values of thecontrol parameters that guarantee closed-loop exponential stability. Simulationresults for the slugging control problem in oil production facilities arepresented to illustrate the eciency of the methodology; (ii) a control lawbased on the frequency domain tools. In this case, we applied the Laplacetransform on the partial dierential equation to obtain an irrational transferfunction and then classical frequency domain tools are used to designthe control law. These results were applied experimentally to the controlproblem of thermoacoustic oscillations in the Rijke tube, showing the effectivenessof the method. Regarding the regulatory control problem, weuse the method of characteristics together with the sliding mode controlmethodology. The method of characteristics is used to transform the partialdierential equations into a system of ordinary dierential equations thatdescribes the original system without any kind of approximation. Then,the control design is performed on the ordinary dierential equations withwell-known results of the theory of lumped parameter systems. The resultswere validated experimentally in two industrial scale systems: a solar powerplant and a tubular photobioreactor

Machine Learning and Its Application to Reacting Flows

This open access book introduces and explains machine learning (ML) algorithms and techniques developed for statistical inferences on a complex process or system and their applications to simulations of chemically reacting turbulent flows. These two fields, ML and turbulent combustion, have large body of work and knowledge on their own, and this book brings them together and explain the complexities and challenges involved in applying ML techniques to simulate and study reacting flows. This is important as to the world’s total primary energy supply (TPES), since more than 90% of this supply is through combustion technologies and the non-negligible effects of combustion on environment. Although alternative technologies based on renewable energies are coming up, their shares for the TPES is are less than 5% currently and one needs a complete paradigm shift to replace combustion sources. Whether this is practical or not is entirely a different question, and an answer to this question depends on the respondent. However, a pragmatic analysis suggests that the combustion share to TPES is likely to be more than 70% even by 2070. Hence, it will be prudent to take advantage of ML techniques to improve combustion sciences and technologies so that efficient and “greener” combustion systems that are friendlier to the environment can be designed. The book covers the current state of the art in these two topics and outlines the challenges involved, merits and drawbacks of using ML for turbulent combustion simulations including avenues which can be explored to overcome the challenges. The required mathematical equations and backgrounds are discussed with ample references for readers to find further detail if they wish. This book is unique since there is not any book with similar coverage of topics, ranging from big data analysis and machine learning algorithm to their applications for combustion science and system design for energy generation

Active Stabilization of Thermoacoustic Oscillation

Combustion processes serve as important sources of energy for both power generation and for transport, ranging from large scale power stations to micro turbines and aeroplane engines. Lean premixed combustion offers a potential to reduce the emission levels, but suffers from instability problems which can be overcome by the use of active control. This thesis addresses the problem of actively controlling thermoacoustic instabilities in a laboratory test com- bustion chamber. Different strategies for actuation are discussed and evaluated experimentally. Relations to industrial relevance are taken into consideration, and a fuel actuator is developed and implemented. Experiments confirm the general view within the combustion control community that actuator design is a significant challenge and limitation for the success of active combustion control. The dynamics of the different configurations of the combustion chambers is modeled using both analytical methods and system identification methods. System identification shows the best potential to be transfered to more sophisticated combustion chambers. Successful damping of the combustion oscillations is shown with different control design methods. The most convincing results are obtained with a Kalman filter based LQR control design

Modelling and control of combustion instabilities with anchored laminar ducted flames

This thesis deals with the derivation of new semi-analytical methods for the modelling of combustion instabilities in anchored laminar flame combustors. In a first part, through an analysis of the motion of the acoustic discontinuity in a ducted flame model, it shows that the movement of the flame induced discontinuity can lead to stability changes. For unstable combustors, it can also affect the amplitude of limit cycle oscillations. In a second part, the problems that are encountered when attempting to obtain the transfer functions for linearly unstable systems from within limit cycle are demonstrated. Indeed, under these circumstances, both the phase and amplitude of the unstable mode need to be corrected. Whilst the correction to the phase can easily be determined, the correction to the gain cannot, supporting the need for robust model based controllers or adaptive control methods which do not require system identification. Lastly, this thesis presents the derivation and implementation of the first asymptotic-based mathematical models which account for the flame motion, hydrodynamic field and acoustic field in an anchored ducted flame setup. This modelling exploits the difference in length scales associated with the flame, hydrodynamic field and acoustic waves. Unlike ducted flame models which omit the hydrodynamic field, this allows us to capture instability mechanisms such as Rayleigh-Taylor, or Darrieus-Landau instabilities, in the context of anchored laminar flames. This is done for two simplified configurations: a weakly conical flame shape, and a conical flame shape case with small mean heat release.Open Acces

Critical transition and spatial organization in climate and engineering systems

Diese Arbeit zielt darauf ab, die raumzeitlichen Regelmäßigkeiten an Übergängen aufzudecken, die in saisonalen Klima- und Ingenieursystemen beobachtet werden, indem moderne Methoden der komplexen Systemwissenschaft verwendet werden. Das erste System ist der indische Sommermonsun - eine Regenzeit, deren jährliche Schwankungen das Leben und den Wohlstand von mehr als einer Milliarde Menschen auf dem indischen Subkontinent beeinflussen und die Wirtschaft des von der Landwirtschaft abhängigen Landes stark beeinträchtigen. Insbesondere die Kenntnis des zeitlichen Ablaufs des Übergangs vom Vormonsun zum Monsun ist für die Planung landwirtschaftlicher Aktivitäten dringend erforderlich. Die Vorhersage des Monsunzeitpunkts über dem indischen Kontinent bleibt jedoch eine große wissenschaftliche Herausforderung. Das zweite ist ein Verbrennungssystem, das anfällig für ein katastrophales Phänomen namens thermoakustische Instabilität ist, das verhindert, dass das Verbrennungssystem unter klimafreundlichen Bedingungen betrieben wird. Eine solche Brennkammer ist typisch für Energie- und Antriebssysteme wie Gasturbinentriebwerke, Boiler und Raketen. Zu verstehen, wann der Übergang zur thermoakustischen Instabilität auftritt und wie dieser Übergang unterdrückt werden kann, sind Schlüsselfragen für die Entwicklung klimafreundlicher Motoren. Diese Dissertation liefert ein neues Verständnis des indischen Sommermonsuns und der thermoakustischen Instabilität durch auf statistischer Physik basierende Ansätze, die verborgene Merkmale in diesen Systemen nahe ihren jeweiligen Übergängen aufdecken.This thesis aims to reveal the spatiotemporal regularities at transitions observed in seasonal climate and engineering systems by utilizing modern methods of complex systems science. The first system is the Indian Summer Monsoon - a rainy season whose yearly variability affects the life and prosperity of more than a billion people in the Indian subcontinent and strongly impacts the economy of the agriculture-dependent country. In particular, knowledge of the timing of the transition from pre-monsoon to monsoon is greatly needed for the planning of agriculture activities. However, the prediction of monsoon timing over the Indian continent remains a significant scientific challenge. The second is a combustion system prone to a catastrophic phenomenon called thermoacoustic instability, which prevents the combustion system from being operated in climate-friendly conditions. Such a combustor is typical in power and propulsion systems such as gas turbine engines, boilers, and rockets. Understanding when the transition to thermoacoustic instability occurs and how to suppress this transition are key questions for developing climate-friendly engines. This thesis provides a new understanding of the Indian Summer Monsoon and thermoacoustic instability through statistical physics-based approaches that reveal hidden features in these systems near their respective transitions

Flame Transfer Function: description, interpretation and use for prediction and control of thermoacoustic instabilities in premixed methane and biogas flames

Las inestabilidades termoacústicas han cobrado gran importancia en el campo de las turbinas de gas desde que la combustión de premezcla pobre se convirtió en la tecnología de combustión predominante en este tipo de plantas. Esta estrategia de combustión permite reducir considerablemente las emisiones de gases contaminantes; sin embargo, el empobrecimiento de las llamas aumenta la probabilidad de generar inestabilidades dinámicas provocadas por el acoplamiento constructivo entre la fluctuación de calor desprendido por la llama y el campo acústico del quemador.La función de transferencia de la llama (Flame Transfer Function, FTF) representa la respuesta de la llama, en el rango lineal, a excitaciones acústicas, y constituye un elemento fundamental para analizar los fenómenos termoacústicos. Este trabajo investiga diversas facetas de la FTF, desde su descripción e interpretación hasta su uso para la predicción y el control de inestabilidades de llama.La primera parte presenta un método novedoso para procesar imágenes de llama filtradas en bandas de quimioluminiscencia, que se ha denominado “Cross-Correlation Mapping Method” (CCM). Este método permite describir la contribución local de cada parte de la llama a la formación de la FTF global. Este procesado de imágenes ha sido desarrollado teóricamente y posteriormente validado mediante ensayos específicos. La investigación ha revelado un alto potencial del CCM para la interpretación, tanto cuantitativa como cualitativa, de los fenómenos que generan la dinámica de las llamas analizadas.En la segunda parte, la FTF ha sido utilizada como datos de entrada para un modelo termoacústico simplificado de un quemador, también conocido con el nombre de “ecuación de dispersión”. El objetivo era analizar la validez de la respuesta lineal de la llama para la predicción de los modos inestables del sistema, condiciones en las cuales la respuesta de la llama resulta extremadamente no lineal. Para este análisis se ha llevado a cabo un amplio estudio experimental, variando sistemáticamente ciertos parámetros de operación, con el objetivo de estudiar condiciones de fuerte inestabilidad auto-inducida (ciclo límite). Los modos identificados por el modelo presentan una buena correspondencia con los registrados experimentalmente, demostrando que la FTF puede utilizarse para predecir los modos inestables de un quemador. Dado que la FTF está descrita por una única curva, esto representa una notable simplificación en términos de coste computacional y experimentalrespecto al uso de la FDF (Flame Describing Function), que requiere la generación y utilización de una familia de curvas.La tercera y última parte de este estudio se centra en el desarrollo de un novedoso sistema de control, llamado pseudo-active instability control (PAIC). Su funcionamiento se basa en los principios de sistemas de control activos (inyección fluctuante de combustible secundario modulada por un elemento activo), con la diferencia de que el PAIC está formado únicamente por elementos puramente pasivos; de esta manera, este nuevo concepto podría combinar las ventajas de ambos sistemas de control. En este trabajo se ha desarrollado una primera evaluación del funcionamiento del PAIC, siendo la mayor dificultad encontrada en el estudio la definición de la FTF de la llama piloto utilizada para controlar las inestabilidades. Aunque la definición de la FTF de la llama piloto resulte de fundamental importancia para el diseño de un sistema PAIC, el análisis muestra un alto potencial del concepto propuesto para amortiguar las inestabilidades generadas en quemadores de premezcla pobre.Un valor añadido de este trabajo reside en el análisis de la respuesta dinámica de llamas de metano y biogás. Mientras que las primeras han sido analizadas en un gran número de estudios, la información disponible sobre llamas de biogás es muy escasa. En particular, no se ha encontrado en literatura ningún estudio que analice la FTF asociada a la respuesta dinámica de una llama de biogás. Este trabajo recoge un análisis detallado de la dinámica de llamas de biogás, comparándola con la de llamas de metano para una amplia variedad de condiciones de operación.La mayor parte de la información presentada en esta tesis se ha publicado en cinco artículos científicos firmados por el autor (y por varios coautores) en revistas y congresos internacionales.<br /

Reduced Order Models and Large Eddy Simulation for Combustion Instabilities in aeronautical Gas Turbines

Increasingly stringent regulations as well as environmental concerns have lead gas turbine powered engine manufacturers to develop the current generation of combustors, which feature lower than ever fuel consumption and pollutant emissions. However, modern combustor designs have been shown to be prone to combustion instabilities, where the coupling between acoustics of the combustor and the flame results in large pressure oscillations and vibrations within the combustion chamber. These instabilities can cause structural damages to the engine or even lead to its destruction. At the same time, considerable developments have been achieved in the numerical simulation domain, and Computational Fluid Dynamics (CFD) has proven capable of capturing unsteady flame dynamics and combustion instabilities for aforementioned engines. Still, even with the current large and fast increasing computing capabilities, time remains the key constraint for these high fidelity yet computationally intensive calculations. Typically, covering the entire range of operating conditions for an industrial engine is still out of reach. In that respect, low order models exist and can be efficient at predicting the occurrence of combustion instabilities, provided an adequate modeling of the flame/acoustics interaction as appearing in the system is available. This essential piece of information is usually recast as the so called Flame Transfer Function (FTF) relating heat release rate fluctuations to velocity fluctuations at a given point. One way to obtain this transfer function is to rely on analytical models, but few exist for turbulent swirling flames. Another way consists in performing costly experiments or numerical simulations, negating the requested fast prediction capabilities. This thesis therefore aims at providing fast, yet reliable methods to allow for low order combustion instabilities modeling. In that context, understanding the underlying mechanisms of swirling flame acoustic response is also targeted. To address this issue, a novel hybrid approach is first proposed based on a reduced set of high fidelity simulations that can be used to determine input parameters of an analytical model used to express the FTF of premixed swirling flames. The analytical model builds on previous works starting with a level-set description of the flame front dynamics while also accounting for the acoustic-vorticity conversion through a swirler. For such a model, validation is obtained using reacting stationary and pulsed numerical simulations of a laboratory scale premixed swirl stabilized flame. The model is also shown to be able to handle various perturbation amplitudes. At last, 3D high fidelity simulations of an industrial gas turbine powered by a swirled spray flame are performed to determine whether a combustion instability observed in experiments can be predicted using numerical analysis. To do so, a series of forced simulations is carried out in en effort to highlight the importance of the two-phase flow flame response evaluation. In that case, sensitivity to reference velocity perturbation probing positions as well as the amplitude and location of the acoustic perturbation source are investigated. The analytical FTF model derived in the context of a laboratory premixed swirled burner is furthermore gauged in this complex case. Results show that the unstable mode is predicted by the acoustic analysis, but that the flame model proposed needs further improvements to extend its applicability range and thus provide data relevant to actual aero-engine