Model Order Reduction

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This three-volume handbook covers methods as well as applications. This third volume focuses on applications in engineering, biomedical engineering, computational physics and computer science

System- and Data-Driven Methods and Algorithms

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This first volume focuses on real-time control theory, data assimilation, real-time visualization, high-dimensional state spaces and interaction of different reduction techniques

Deep material networks for efficient scale-bridging in thermomechanical simulations of solids

We investigate deep material networks (DMN). We lay the mathematical foundation of DMNs and present a novel DMN formulation, which is characterized by a reduced number of degrees of freedom. We present a efficient solution technique for nonlinear DMNs to accelerate complex two-scale simulations with minimal computational effort. A new interpolation technique is presented enabling the consideration of fluctuating microstructure characteristics in macroscopic simulations

ℋ2 Guaranteed Cost Computation Of Discretized Uncertain Continuous-time Systems

This paper proposes a new discretization technique with constant sampling time for time-invariant systems with uncertain parameters belonging to a polytopic domain. The aim is to provide an equivalent discrete-time representation of the continuous-time system whose ℋ2 guaranteed cost is an upper bound for the ℋ2 worst case norm of the original system. The resulting discrete-time model is described in terms of homogeneous polynomial matrices obtained by Taylor series expansion of degree ℓ. The discretization residual error, associated to the chosen approximation degree, is represented by additive norm-bounded uncertain terms. As a second contribution, new linear matrix inequality (LMI) relaxations for the computation of ℋ2 guaranteed costs for discrete-time systems with polynomial dependence on the uncertain parameter and additive norm-bounded uncertainties are proposed. A numerical experiment shows that the ℋ2 costs of the discretized system become tighter to the continuous-time ones as the order in the Taylor series expansion, the degrees in the Lyapunov function and the Pólya's relaxation level increase. © 2014 American Automatic Control Council.50735078Boeing,et al.,GE Global Research,Honeywell,MathWorks,MitsubishiAckermann, J., (1993) Robust Control: Systems with Uncertain Physical Parameters, , London, UK: Springer VerlagShieh, L.S., Wang, W., Chen, G., Discretization of cascaded continuous-time controllers and uncertain systems (1998) Circ. Syst. Signal Process., 17 (5), pp. 591-611. , OctoberOliveira, R.C.L.F., Peres, P.L.D., A convex optimization procedure to compute H2 and H ∞ norms for uncertain linear systems in polytopic domains (2008) Optim. Control Appl. Meth., 29 (4), pp. 295-312. , July/AugustPalhares, R.M., Takahashi, R.H.C., Peres, P.L.D., H∞ and H2 guaranteed costs computation for uncertain linear systems (1997) Int. J. Syst. Sci., 28 (2), pp. 183-188. , FebruaryBoyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V., (1994) Linear Matrix Inequalities in System and Control Theory, , Philadelphia, PA: SIAM Studies in Applied MathematicsZhou, K., Doyle, J.C., Glover, K., (1996) Robust and Optimal Control, , Upper Saddle River, NJ, USA: Prentice HallDoyle, J.C., Glover, K., Khargonekar, P.P., Francis, B., State space solutions to the standard H2 and H ∞ control problems (1989) IEEE Trans. Autom. Control, 34 (8), pp. 831-847. , AugustOgata, K., (1995) Discrete-time Control Systems, , Upper Saddle River, NJ, USA: Prentice-Hall International, IncHetel, L., Daafouz, J., Iung, C., Analysis and control of LTI and switched systems in digital loops via an event-based modelling (2008) Int. J. Control, 81 (7), pp. 1125-1138. , JulyKothare, M.V., Balakrishnan, V., Morari, M., Robust constrained model predictive control using linear matrix inequalities (1996) Automatica, 32 (10), pp. 1361-1379. , OctoberLee, S., Won, S., Model Predictive Control for linear parameter varying systems using a new parameter dependent terminal weighting matrix (2006) IEICE Trans. on Fundamentals of Electronics, Communications and Computer Sciences, E89-A (8), pp. 2166-2172Wada, N., Saito, K., Saeki, M., Model predictive control for linear parameter varying systems using parameter dependent Lyapunov function (2006) IEEE Trans. Circuits & Syst. II: Exp. Briefs, 53 (12), pp. 1446-1450. , DecemberJungers, M., Oliveira, R.C.L.F., Peres, P.L.D., MPC for LPV systems with bounded parameter variations (2011) Int. J. Control, 84, pp. 24-36. , JanuaryBraga, M.F., Morais, C.F., Tognetti, E.S., Oliveira, R.C.L.F., Peres, P.L.D., A new procedure for discretization and state feedback control of uncertain linear systems (2013) Proc. 52nd IEEE Conf. Decision Control, pp. 6397-6402. , Florence, Italy, DecemberHara, S., Yamamoto, Y., Fujioka, H., Modern and classical analysis/synthesis methods in sampled-data control - A brief overview with numerical examples (1996) Proc. 35th IEEE Conf. Decision Control, pp. 1251-1256. , Kobe, Japan, DecemberChen, T., Francis, B.A., (1995) Optimal Sampled-data Control Systems, , London, UK: Springer-VerlagSouza, M., Deaecto, G.S., Geromel, J.C., Daafouz, J., Selftriggered linear quadratic networked control (2013) Optim. Control Appl. Meth., , http://dx.doi.org/10.1002/oca.2085Löfberg, J., YALMIP: A toolbox for modeling and optimization in MATLAB (2004) Proc. 2004 IEEE Int. Symp. on Comput. Aided Control Syst. Des., pp. 284-289. , Taipei, Taiwan, SeptemberSturm, J.F., Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones (1999) Optim. Method Softw., 11 (1-4), pp. 625-653. , http://sedumi.ie.lehigh.eduGonçalves, E.N., Palhares, R.M., Takahashi, R.H.C., Mesquita, R.C., New approach to robust D-stability analysis of linear timeinvariant systems with polytope-bounded uncertainty (2006) IEEE Trans. Autom. Control, 51 (10), pp. 1709-1714. , OctoberGonçalves, E.N., Palhares, R.M., Takahashi, R.H.C., Mesquita, R.C., H2 and H∞ ε-guaranteed cost computation of uncertain linear systems (2007) IET Control Theory & Appl., 1 (1), pp. 201-209. , Januar

Application of non-linear system identification approaches to modelling, analysis, and control of fluid flows.

Flow control has become a topic of great importance for several applications, ranging from commercial aircraft, to intercontinental pipes and skyscrapers. In these applications, and many more, the interaction with a fluid flow can have a significant influence on the performance of the system. In many cases the fluids encountered are turbulent and detrimental to the latter. Several attempts have been made to solve this problem. However, due to the non-linearity and infinite dimensionality of fluid flows and their governing equations, a complete understanding of turbulent behaviour and a feasible control approach has not been obtained. In this thesis, model reduction approaches that exploit non-linear system identification are applied using data obtained from numerical simulations of turbulent three-dimensional channel flow, and two-dimensional flow over the backward facing step. A multiple-input multiple-output model, consisting of 27 sub-structures, is obtained for the fluctuations of the velocity components of the channel flow. A single-input single-output model for fluctuations of the pressure coefficient, and two multiple-input single-output models for fluctuations of the velocity magnitude are obtained in flow over the BFS. A non-linear model predictive control strategy is designed using identified one- and multi-step ahead predictors, with the inclusion of integral action for robustness. The proposed control approach incorporates a non-linear model without the need for expensive non-linear optimizations. Finally, a frequency domain analysis of unmanipulated turbulent flow is perfumed using five systems. Higher order generalized frequency response functions (GFRF) are computed to study the non-linear energy transfer phenomena. A more detailed investigation is performed using the output FRF (OFRF), which can elucidate the contribution of the n-th order frequency response to the output frequency response

Commande par mode glissant de paliers magnétiques actifs économes en énergie : une approche sans modèle

Abstract : Over the past three decades, various fields have witnessed a successful application of active magnetic bearing (AMB) systems. Their favorable features include supporting high-speed rotation, low power consumption, and rotor dynamics control. Although their losses are much lower than roller bearings, these losses could limit the operation in some applications such as flywheel energy storage systems and vacuum applications. Many researchers focused their efforts on boosting magnetic bearings energy efficiency via minimizing currents supplied to electromagnetic coils either by a software solution or a hardware solution. According to a previous study, we adopt the hardware solution in this thesis. More specifically, we investigate developing an efficient and yet simple control scheme for regulating a permanent magnet-biased active magnetic bearing system. The control objective here is to suppress the rotor vibrations and reduce the corresponding control currents as possible throughout a wide operating range. Although adopting the hardware approach could achieve an energy-efficient AMB, employing an advanced control scheme could achieve a further reduction in power consumption. Many advanced control techniques have been proposed in the literature to achieve a satisfactory performance. However, the complexity of the majority of control schemes and the potential requirement of powerful platform could discourage their application in practice. The motivation behind this work is to improve the closed-loop performance without the need to do model identification and following the conventional procedure for developing a model-based controller. Here, we propose applying the hybridization concept to exploit the classical PID control and some nonlinear control tools such as first- and second-order sliding mode control, high gain observer, backstepping, and adaptive techniques to develop efficient and practical control schemes. All developed control schemes in this thesis are digitally implemented and validated on the eZdsp F2812 control board. Therefore, the applicability of the proposed model-free techniques for practical application is demonstrated. Furthermore, some of the proposed control schemes successfully achieve a good compromise between the objectives of rotor vibration attenuation and control currents minimization over a wide operating range.Résumé: Au cours des trois dernières décennies, divers domaines ont connu une application réussie des systèmes de paliers magnétiques actifs (PMA). Leurs caractéristiques favorables comprennent une capacité de rotation à grande vitesse, une faible consommation d'énergie, et le contrôle de la dynamique du rotor. Bien que leurs pertes soient beaucoup plus basses que les roulements à rouleaux, ces pertes pourraient limiter l'opération dans certaines applications telles que les systèmes de stockage d'énergie à volant d'inertie et les applications sous vide. De nombreux chercheurs ont concentré leurs efforts sur le renforcement de l'efficacité énergétique des paliers magnétiques par la minimisation des courants fournis aux bobines électromagnétiques soit par une solution logicielle, soit par une solution matérielle. Selon une étude précédente, nous adoptons la solution matérielle dans cette thèse. Plus précisément, nous étudions le développement d'un système de contrôle efficace et simple pour réguler un système de palier magnétique actif à aimant permanent polarisé. L'objectif de contrôle ici est de supprimer les vibrations du rotor et de réduire les courants de commande correspondants autant que possible tout au long d'une large plage de fonctionnement. Bien que l'adoption de l'approche matérielle pourrait atteindre un PMA économe en énergie, un système de contrôle avancé pourrait parvenir à une réduction supplémentaire de la consommation d'énergie. De nombreuses techniques de contrôle avancées ont été proposées dans la littérature pour obtenir une performance satisfaisante. Cependant, la complexité de la majorité des systèmes de contrôle et l'exigence potentielle d’une plate-forme puissante pourrait décourager leur application dans la pratique. La motivation derrière ce travail est d'améliorer les performances en boucle fermée, sans la nécessité de procéder à l'identification du modèle et en suivant la procédure classique pour développer un contrôleur basé sur un modèle. Ici, nous proposons l'application du concept d'hybridation pour exploiter le contrôle PID classique et certains outils de contrôle non linéaires tels que contrôle par mode glissement du premier et du second ordre, observateur à grand gain, backstepping et techniques adaptatives pour développer des systèmes de contrôle efficaces et pratiques. Tous les systèmes de contrôle développés dans cette thèse sont numériquement mis en oeuvre et évaluées sur la carte de contrôle eZdsp F2812. Par conséquent, l'applicabilité des techniques de modèle libre proposé pour l'application pratique est démontrée. En outre, certains des régimes de contrôle proposés ont réalisé avec succès un bon compromis entre les objectifs au rotor d’atténuation des vibrations et la minimisation des courants de commande sur une grande plage de fonctionnement