This dissertation advances tools for robust control and analysis of complex nonlinear dynamical systems. Specifically, it leverages standard synthesis and robustness analysis techniques developed for linear systems and provides additional results to design robust controllers for nonlinear systems over the considered operating envelopes. To facilitate the application of these linear techniques, nonlinear systems are represented as uncertain linear models. A significant contribution of this dissertation is the development of data-driven approaches to generate these uncertain linear models, which capture the behavior of nonlinear systems reasonably well over the considered operating envelopes without being overly conservative. We propose two approaches where a nominal linear time-invariant (LTI) approximation of a nonlinear system is first obtained using traditional linearization techniques, and data-driven methods are then applied to model the discrepancies arising from this simplification. In the first approach, the discrepancies are modeled using polynomials, resulting in an improved linear parameter-varying (LPV) approximation that can be expressed as a linear fractional transformation (LFT) on uncertainties. The second approach utilizes coprime factorization and a data-driven lifting technique to approximate the nonlinear discrepancy model with an LTI state-space system in a higher-dimensional state space. Additionally, a purely data-driven modeling approach is proposed for nonlinear systems with uncertain initial conditions. In this approach, a deep learning framework is developed to approximate nonlinear dynamical systems with LPV state-space models in higher-dimensional spaces while simultaneously characterizing the uncertain initial states within the lifted state space. Another contribution is the development of a systematic method for identifying critical attack points in cyber-physical systems using integral quadratic constraints (IQCs). IQC analysis is also used in developing a framework focused on the design and analysis of robust path-following controllers for an autonomous underwater vehicle (AUV). In this framework, the AUV is modeled as an LFT on uncertainties and is affected by exogenous inputs such as measurement noise and ocean currents. A tuning routine is developed for robust control design, using the robust performance level derived from IQC analysis to guide the tuning process. This framework is applied to design \( H_\infty \), \( H_2 \), and LPV controllers for the AUV, with the results validated through extensive nonlinear simulations and underwater experiments. Finally, this dissertation presents novel controller synthesis and IQC analysis techniques for LPV systems with uncertain initial conditions. These methods, combined with the lifting-based LPV modeling approach, enable the design of static, nonstationary LPV controllers for nonlinear systems in a higher-dimensional space. When interpreted in the original state space, these controllers become nonlinear with explicit dependence on both the scheduling parameters and time. Through examples, it is demonstrated that these controllers outperform those designed using nominal linearized models. / Doctor of Philosophy / This dissertation focuses on robust control design and analysis for complex nonlinear dynamical systems using well-established methods developed for linear systems. These methods are relatively easier to implement than their counterparts for nonlinear systems and can provide both stability and performance guarantees. A major contribution of this dissertation is the development of data-driven approaches to generate linear approximations of nonlinear systems that are valid over larger operating envelopes compared to those obtained through traditional linearization techniques. Another contribution is the development of a systematic method for identifying critical attack points in cyber-physical systems using robust control tools. Robust control methods are also used in developing a framework focused on the design and analysis of robust path-following controllers for an autonomous underwater vehicle (AUV). In this framework, the AUV is modeled as an uncertain linear system and is affected by external inputs such as measurement noise and ocean currents. A tuning routine is developed to automate the control design process, and the framework is validated through extensive nonlinear simulations and underwater experiments. Finally, this dissertation presents novel controller synthesis and analysis techniques for linear systems with uncertain initial conditions. These methods, combined with a data-driven modeling approach, enable the design of nonlinear controllers that are demonstrated to outperform those designed using nominal linearized models.

This thesis is concerned with investigations on two related issues of turbulent jet diffusion flame, namely (a) stabilization at liftoff and (b) autoignition in a turbulent jet diffusion flame. The approach of Conditional Moment Closure (CMC) has been taken. Fully elliptic first order CMC equations are solved with detailed chemistry to simulate lifted H2/N2 flame in vitiated coflow. The same approach is further used to simulate transient autoignition process in inhomogeneous mixing layers. In Chapter 1, difficulties involved in numerical simulation of turbulent combustion problems are explained. Different numerical tools used to simulate turbulent combustion are briefly discussed. Previous experimental, theoretical and numerical studies of lifted jet diffusion flames and autoignition are reviewed. Various research issues related to objectives of the thesis are discussed. In Chapter 2, the first order CMC transport equations for the reacting flows are presented. Various closure models that are required for solving the governing equations are given. Calculation of mean reaction rate term for detailed chemistry is given with special focus on the reaction rates for pressure dependent reactions. In Chapter 3, starting with the laminar flow code, further extension is carried to include kε turbulence model and PDF model. The code is validated at each stage of inclusion of different model. In this chapter, the code is first validated for the test problem of constant density, 2D, axisymmetric turbulent jet. Further, validation of PDF model is carried out by simulating the problem of nonreacting jet of cold air issuing into a vitiated coflow. The results are compared with the published data from experiments as well as numerical simulations. It is shown that the results compare well with the data. In Chapter 4, numerical results of lifted jet diffusion flame are presented. Detailed chemistry is modelled using Mueller mechanism for H2/O2 system with 9 species and 21 reversible reactions. Simulations are carried out for different jet velocities and coflow stream temperatures. The predicted liftoff generally agrees with experimental data, as well as joint PDF results. Profiles of mean scalar fluxes in the mixture fraction space, for different coflow temperatures reveal that (1) Inside the flamezone, the chemical term balances the molecular diffusion term, and hence the structure is of a diffusion flamelet for both cases. (2) In the preflame zone, the structure depends on the coflow temperature: for low coflow temperatures, the chemical term being small, the advective term balances the axial diffusion term. However, for the high coflow temperature case, the chemical term is large and balances the advective term, the axial diffusion term being small. It is concluded that, liftoff is controlled (a) by turbulent premixed flame propagation for low cofflow temperature while (b) by autoignition for high coflow temperature. In Chapter 5, the numerical results of autoignition in inhomogeneous mixing layer are presented. The configuration consists of a fuel jet issued into hot air for which transient simulations are performed. It is found that the constants assumed in various modelling terms can severely influence the results, particularly the flame temperature. Hence, modifications to these constants are suggested to obtain improved predictions. Preliminary work is carried out to predict autoignition lengths (which may be defined by Tign × Ujet incase of jet- and coflowvelocities being equal) by varying the coflow temperature. The autoignition lengths show a reasonable agreement with the experimental data and LES results. In Chapter 6, main conclusions of this thesis are summarized. Possible future studies on this problem are suggested.

This thesis describes the application of the first-order Conditional Moment Closure (CMC) to the autoignition of high-pressure fuel jets, and to piloted and lifted turbulent jet flames using classical and advanced CMC submodels. A Doubly-Conditional Moment Closure (DCMC) formulation is further proposed. In the first study, CMC is applied to investigate the impact of C₂H₆, H₂ and N₂ additives on the autoignition of high-pressure CH₄ jets injected into lower pressure heated air. A wide range of pre-combustion air temperatures is considered and detailed chemical kinetics are employed. It is demonstrated that the addition of C₂H₆ and H₂ does not change the main CH₄ oxidisation pathways. The decomposition of these additives provides additional ignition-promoting radicals, and therefore leads to shorter ignition delays. N₂ additives do not alter the CH₄ oxidisation pathways, however, they reduce the amount of CH₄ available for reaction, causing delayed ignition. It is further shown that ignition always occurs in lean mixtures and at low scalar dissipation rates. The second study is concerned with the modelling of a piloted CH₄/air turbulent jet flame. A detailed assessment of several Probability Density Function (PDF), Conditional Scalar Dissipation Rate (CSDR) and Conditional Velocity (CV) submodels is first performed. The results of two β-PDF-based implementations are then presented. The two realisations differ by the modelling of the CSDR. Homogeneous (inconsistent) and inhomogeneous (consistent) closures are considered. It is shown that the levels of all reactive scalars, including minor intermediates and radicals, are better predicted when the effects of inhomogeneity are included in the modelling of the CSDR. The two following studies are focused on the consistent modelling of a lifted H₂/N₂ turbulent jet flame issuing into a vitiated coflow. Two approaches are followed to model the PDF. In the first, a presumed β-distribution is assumed, whereas in the second, the Presumed Mapping Function (PMF) approach is employed. Fully consistent CV and CSDR closures based on the β-PDF and the PMF-PDF are employed. The homogeneous versions of the CSDR closures are also considered in order to assess the effect of the spurious sources which stem from the inconsistent modelling of mixing. The flame response is analysed over a narrow range of coflow temperatures (Tc). The stabilisation mechanism is determined from the analysis of the transport budgets in mixture fraction and physical spaces, and the history of radical build-up ahead of the stabilisation height. The β-PDF realisations indicate that the flame is stabilised by autoignition irrespective of the value of Tc. On the other hand, the PMF realisations reveal that the stabilisation mechanism is susceptible to Tc. Autoignition remains the controlling stabilisation mechanism for sufficiently high Tc. However, as Tc is decreased, stabilisation is achieved by means of premixed flame propagation. The analysis of the spurious sources reveals that their effect is small but non-negligible, most notably within the flame zone. Further, the assessment of several H₂ oxidation mechanisms show that the flame is very sensitive to chemical kinetics. In the last study, a DCMC method is proposed for the treatment of fluctuations in non-premixed and partially premixed turbulent combustion. The classical CMC theory is extended by introducing a normalised Progress Variable (PV) as a second conditioning variable beside the mixture fraction. The unburnt and burnt states involved in the normalisation of the PV are specified such that they are mixture fraction-dependent. A transport equation for the normalised PV is first obtained. The doubly-conditional species, enthalpy and temperature transport equations are then derived using the decomposition approach and the primary closure hypothesis is applied. Submodels for the doubly-conditioned unclosed terms which arise from the derivation of DCMC are proposed. As a preliminary analysis, the governing equations are simplified for homogeneous turbulence and a parametric assessment is performed by varying the strain rate levels in mixture fraction and PV spaces.

This thesis describes the application of the first-order Conditional Moment Closure (CMC) to the autoignition of high-pressure fuel jets, and to piloted and lifted turbulent jet flames using classical and advanced CMC submodels. A Doubly-Conditional Moment Closure (DCMC) formulation is further proposed. In the first study, CMC is applied to investigate the impact of C₂H₆, H₂ and N₂ additives on the autoignition of high-pressure CH₄ jets injected into lower pressure heated air. A wide range of pre-combustion air temperatures is considered and detailed chemical kinetics are employed. It is demonstrated that the addition of C₂H₆ and H₂ does not change the main CH₄ oxidisation pathways. The decomposition of these additives provides additional ignition-promoting radicals, and therefore leads to shorter ignition delays. N₂ additives do not alter the CH₄ oxidisation pathways, however, they reduce the amount of CH₄ available for reaction, causing delayed ignition. It is further shown that ignition always occurs in lean mixtures and at low scalar dissipation rates. The second study is concerned with the modelling of a piloted CH₄/air turbulent jet flame. A detailed assessment of several Probability Density Function (PDF), Conditional Scalar Dissipation Rate (CSDR) and Conditional Velocity (CV) submodels is first performed. The results of two β-PDF-based implementations are then presented. The two realisations differ by the modelling of the CSDR. Homogeneous (inconsistent) and inhomogeneous (consistent) closures are considered. It is shown that the levels of all reactive scalars, including minor intermediates and radicals, are better predicted when the effects of inhomogeneity are included in the modelling of the CSDR. The two following studies are focused on the consistent modelling of a lifted H₂/N₂ turbulent jet flame issuing into a vitiated coflow. Two approaches are followed to model the PDF. In the first, a presumed β-distribution is assumed, whereas in the second, the Presumed Mapping Function (PMF) approach is employed. Fully consistent CV and CSDR closures based on the β-PDF and the PMF-PDF are employed. The homogeneous versions of the CSDR closures are also considered in order to assess the effect of the spurious sources which stem from the inconsistent modelling of mixing. The flame response is analysed over a narrow range of coflow temperatures (Tc). The stabilisation mechanism is determined from the analysis of the transport budgets in mixture fraction and physical spaces, and the history of radical build-up ahead of the stabilisation height. The β-PDF realisations indicate that the flame is stabilised by autoignition irrespective of the value of Tc. On the other hand, the PMF realisations reveal that the stabilisation mechanism is susceptible to Tc. Autoignition remains the controlling stabilisation mechanism for sufficiently high Tc. However, as Tc is decreased, stabilisation is achieved by means of premixed flame propagation. The analysis of the spurious sources reveals that their effect is small but non-negligible, most notably within the flame zone. Further, the assessment of several H₂ oxidation mechanisms show that the flame is very sensitive to chemical kinetics. In the last study, a DCMC method is proposed for the treatment of fluctuations in non-premixed and partially premixed turbulent combustion. The classical CMC theory is extended by introducing a normalised Progress Variable (PV) as a second conditioning variable beside the mixture fraction. The unburnt and burnt states involved in the normalisation of the PV are specified such that they are mixture fraction-dependent. A transport equation for the normalised PV is first obtained. The doubly-conditional species, enthalpy and temperature transport equations are then derived using the decomposition approach and the primary closure hypothesis is applied. Submodels for the doubly-conditioned unclosed terms which arise from the derivation of DCMC are proposed. As a preliminary analysis, the governing equations are simplified for homogeneous turbulence and a parametric assessment is performed by varying the strain rate levels in mixture fraction and PV spaces.

La problématique de la stabilisation des flammes non-prémélangées reste primordiale. Il faut pour la résoudre déterminer l’importance relative des phénomènes aérodynamiques, thermiques et chimiques intervenant dans les mécanismes de stabilisation. La démarche expérimentale utilisée pour cela au cours de cette thèse porte une attention particulière sur l’influence des conditions aux limites thermiques, et comporte deux volets à travers lesquels le rôle des transferts thermiques est mis en exergue. D’abord, la zone d’attachement d’une flamme stabilisée derrière la lèvre du brûleur est examinée, en considérant les couplages entre le positionnement du bout de flamme à proximité du brûleur et la température de la lèvre. Différentes régions ont ainsi pu être identifiées selon le comportement du bout de flamme, qui évolue depuis une nature diffusive vers une nature propagative à l’approche des limites aérodynamiques de stabilité. Par ailleurs, une modification des propriétés thermiques du brûleur a permis de mettre en évidence une évolution, avec la température de la lèvre, du rôle relatif des modes de coincement thermique et chimique de la flamme par la paroi du brûleur. Ensuite, l’étude concerne non plus un état stabilisé de la flamme, mais les transitions entre les différents régimes de combustion, et plus particulièrement le décrochage d’une flamme attachée. L’examen des conditions conduisant à la déstabilisation de la flamme est un moyen d’apporter des éléments-clefs de compréhension quant aux couplages et aux équilibres aérothermochimiques prévalant préalablement au décrochage. Une évolution du processus de décrochage a ainsi été mise en avant avec l’augmentation de la température initiale des réactants, en lien avec l’évolution de phénomènes transitoires d’extinction locale de la zone de réaction. / Non-premixed flame stabilization is still an important issue in combustion. Addressing this issue requires to evaluate the relative importance of aerodynamic, thermal and chemical phenomena involved in the stabilization mechanisms. This thesis develops to this end an experimental approach, with a particular focus on the influence of thermal boundary conditions, examining the role of heat transfer in a twofold analysis. At first, the attachment zone of a rim-stabilized jet-flame is investigated, by careful consideration of the coupling existing between the burner lip temperature and the flame attachment location relative to the burner. Several regions have been identified according to the flame leading edge behavior, which evolves from diffusive to propagative closer to the aerodynamic stability limits. Besides, by modifying the burner thermal properties, a change has been shown in the relative roles of thermal and chemical quenching of the flame by the burner wall, depending on the burner lip temperature. Secondly, the attention is directed to transitions between different combustion regimes, namely attached and lifted flames. In particular, beyond the stable state of an attached flame, its lifting process is investigated. Examining in which conditions destabilization of the flame occurs indeed appears to be an ideal opportunity to gain insight into the aerothermochemical coupling and equilibriums existing prior to lift-off. Thus, the lifting process has been shown to be modified by the reactant initial temperature, in close relationship with the change in occurrence of localized transitory extinction events of the reaction zone.

Ce travail s'intéresse à la compréhension du comportement des flammes non-prémélangées issues d'un jet de méthane assisté par un coflow d'air dilué avec du CO2, ou d'autres gaz chimiquement inertes pour discriminer les différents phénomènes impliqués dans la dilution. Les phénomènes transitionnels, décrochage et extinction, quantifiés par des limites de stabilité, sont analysés à l'aide de grandeurs physiques représentatives. Le domaine de stabilité de flamme est limité par des surfaces 3D dans le domaine physique ( Qdiluant/Qair (taux de dilution), Uair (vitesse d'air), UCH4 (vitesse de méthane)), révélant un effet compétitif entre l'aérodynamique et la dilution. Des cartographies génériques de décrochage et d'extinction communes à tous ces diluants sont proposées. Des grandeurs liées à la stabilisation sont toutes soumises à des lois d'évolution auto-simlilaires. Il en ressort que la vitesse de propagation de flamme est l'élément clé du mécanisme de stabilisation lors de la dilution. / This work focuses on the understanding of the behaviours of non-premixed methane flame inside an air coflow diluted by carbon dyoxide (CO2) or by other chemically inert diluents in order to discriminate different phenomena involved in dilution. Transitional phenomena (liftoff and extinction) quantified trough the stability limits, are analyzed trough representative physical quantities. The flame stability domain is limited by 3D-surfaces (liftoff and extinction) in the physical domain (Qdiluant/Qair (dilution level), Uair (air velocity), UCH4 (methane velocity)) revealing a competitive effect between aerodynamics and dilution. Generic diagrams of flame liftoff and extinction are proposed for all the diluents. Physical quantities related to flame stabilization process are all submitted to, regardless of diluent, self-similar laws. This is explained by flame burning velocity which is considered as the key element in the flame stabilization mechanism with air-side dilution.