Stochastic optimal control of Lithium-Ion battery operations

El control òptim en bateries de ions de liti maximitza la vida útil de la bateria alhora que garanteix la càrrega ràpida i un ús segur. Les propietats de les bateries fabricades poden diferir del valor de disseny i canviar amb el temps en degradar-se. La limitació d'anteriors simulacions de bateries és que utilitzen valors deterministes per aquests paràmetres que no es coneixen amb precisió. L'anàlisi estocàstic inclou aquestes incerteses d'aplicacions reals en simulacions. Després d'integrar les incerteses, l'objectiu és quantificar-ne la propagació per veure com afecta als estats finals. Aquesta investigació integra incerteses estocàstiques en el control de bateries òptim definint amb distribucions de probabilitat alguns paràmetres, com la temperatura ambient. La propagació de la incertesa es fa utilitzant anàlisi de sensibilitat lineal. S'ha dissenyat una metodologia per quantificar aquesta propagació d'incertesa a les bateries de ions de liti per a qualsevol conjunt de paràmetres incerts i qualsevol model de càrrega òptim. Aquesta metodologia pot calcular sensibilitats lineals en qualsevol sistema d'equacions discretes i algebraiques. En simulació de bateries, permet calcular sensibilitats en sistemes de càrrega híbrids (continus-discrets) resolent els inconvenients típics d'implementar salts discontinus o controlar estats no observables. La metodologia dissenyada és una eina versàtil per a simulacions estocàstiques de bateries. Pot redefinir rutes de càrrega òptimes i precises per futures aplicacions en temps real o per determinar noves especificacions de fabricació més segures. Per demostrar la precisió d'aquest mètode, els resultats presenten múltiples casos d'estudi, incloent la cinètica de reacció i els models de càrrega òptims. Els exemples consideren els efectes de definir una temperatura ambient incerta en estats de la bateria com el voltatge, la temperatura o l'estat de salut per protocols rellevants de càrrega òptima.El control óptimo de baterías de iones de litio maximiza la vida útil de la batería garantizando también la carga rápida y un uso seguro. Las propiedades de las baterías fabricadas pueden diferir de los valores de diseño o cambiar con el tiempo por degradación. La limitación de anteriores simulaciones de baterías es que utilizan valores deterministas para parámetros que no se conocen con precisión. El análisis estocástico incluye estas incertidumbres reales en las simulaciones. Después de integrar las incertidumbres, el objetivo es cuantificar su propagación para saber cómo afectan a los estados finales. Esta investigación integra incertidumbres en el control óptimo de baterías definiendo como distribuciones de probabilidad algunos parámetros del modelo, como la temperatura ambiente. La propagación de la incertidumbre se implementa utilizando análisis de sensibilidad lineal. Se ha diseñado una metodología para cuantificar esta propagación de incertidumbre en baterías de iones de litio para cualquier conjunto de parámetros inciertos y modelo de carga óptima. Esta metodología permite calcular sensibilidades lineales en cualquier sistema de ecuaciones discretas y algebraicas. Para simulaciones de baterías, puede calcular sensibilidades en sistemas de carga híbridos (continuos-discretos) resolviendo limitaciones comunes en saltos discontinuos y controlar estados no observables. La metodología utilizada es una herramienta versátil para simular baterías estocásticas. Puede redefinir rutas de carga óptimas y precisas para futuras aplicaciones en tiempo real o para determinar nuevas especificaciones de fabricación más seguras. Para demostrar la precisión de este método, los resultados presentan múltiples casos de estudio, incluida la cinética de reacción y modelos de carga óptimos. Los ejemplos consideran la implicación de definir una temperatura ambiente incierta en estados de la batería como el voltaje o el estado de salud en protocolos relevantes de carga óptima.Optimal charging of lithium-ion batteries maximizes battery life while ensuring fast charging and safe usage. The properties of manufactured batteries can differ from design values and change over time due to degradation. The limitation of past battery simulations is that they use fixed deterministic values for these parameters that may not be accurately known. Stochastic analysis includes real-world uncertainties in simulations to represent this manufacturing variation. This study aims to propagate the uncertainty of model parameters onto output states, such as voltage or cell temperature. This research integrates stochastic uncertainties in optimal battery control by using probabilistic distributions to define model parameters such as the ambient temperature. The uncertainty propagation is then performed using linear sensitivity analysis. The linearized sensitivity is validated using Monte Carlo with several hundreds of replicates, proving that sensitivity analysis is significantly less computationally expensive. A methodology is designed to quantify uncertainty propagation in lithium-ion batteries for any set of probabilistic parameters and optimal charging paths. This methodology computes linear sensitivities on any system of differential-algebraic equations. For battery modeling, it can accurately compute sensitivities on mixed continuous-discrete simulations, solving typical issues found with discrete stages and the control of non-measurable states. The methodology given is a powerful tool for stochastic battery simulations. It can help redefine accurate optimal charging paths for future onboard applications and determine safer manufacturing specifications. Multiple case studies are presented to validate this methodology, including reaction kinetics and optimal charging paths. The examples analyzed consider how an uncertain ambient temperature affects battery's voltage, temperature, and state of health for relevant optimal charging protocols.Outgoin

Non-constructive interval simulation of dynamic systems

Publisher PD

Automatic solver for non-linear partial differential equations with implicit local laws: Application to unilateral contact

International audienceIn general, non-linear continuum mechanics combine global balance equations and local constitutive laws. In this work, frictionless contact between a rigid tool and a thin elastic shell is considered. This class of boundary value problems involves two non-linear algebraic laws: the first one gives explicitly the stress field as a function of the strain throughout the continuum part, whereas the second one is a non-linear equation relating the contact forces and the displacement at the boundary.Given the fact that classical computational approaches sometimes require significant effort in implementation of complex non-linear problems, a computation technique based on automatic differentiation of constitutive laws is presented in this paper. The procedure enables to compute automatically the higher-order derivatives of these constitutive laws and thereafter to define the Taylor series that are the basis of the continuation technique called asymptotic numerical method. The algorithm is about the same with an explicit or implicit constitutive relation. In the modelling of forming processes, many tool shapes can be encountered. The presented computational technique permits an easy implementation of these complex surfaces, for instance in a finite element code : the user is only required to define the tool geometry and the computer is able to obtain the higher-order derivatives

An Analysis of the Implementation of Acquisition Reform Initiatives and Contract Cost Variance

This thesis examines the impact of acquisition reform initiatives implemented since 1993 on contract cost performance. Many initiatives implemented during the 1990s focused on saving the government money in procuring weapon systems. For decades, cost overruns have plagued Department of Defense weapons systems development and procurement costing the government money. The passage of the Federal Acquisition Streamlining Act (FASA) of 1994 and the Clinger-Cohen Act of 1996, marked significant congressional action on aiding the Department of Defense develop and procure systems cheaper. Conclusions drawn in this thesis may aid leadership in supporting current initiatives and drafting new changes

EOOLT 2007 – Proceedings of the 1st International Workshop on Equation-Based Object-Oriented Languages and Tools

Computer aided modeling and simulation of complex systems, using components from multiple application domains, such as electrical, mechanical, hydraulic, control, etc., have in recent years witness0065d a significant growth of interest. In the last decade, novel equation-based object-oriented (EOO) modeling languages, (e.g. Mode- lica, gPROMS, and VHDL-AMS) based on acausal modeling using equations have appeared. Using such languages, it has become possible to model complex systems covering multiple application domains at a high level of abstraction through reusable model components. The interest in EOO languages and tools is rapidly growing in the industry because of their increasing importance in modeling, simulation, and specification of complex systems. There exist several different EOO language communities today that grew out of different application areas (multi-body system dynamics, electronic circuit simula- tion, chemical process engineering). The members of these disparate communities rarely talk to each other in spite of the similarities of their modeling and simulation needs. The EOOLT workshop series aims at bringing these different communities together to discuss their common needs and goals as well as the algorithms and tools that best support them. Despite the short deadlines and the fact that this is a new not very established workshop series, there was a good response to the call-for-papers. Thirteen papers and one presentation were accepted to the workshop program. All papers were subject to reviews by the program committee, and are present in these electronic proceedings. The workshop program started with a welcome and introduction to the area of equa- tion-based object-oriented languages, followed by paper presentations and discussion sessions after presentations of each set of related papers. On behalf of the program committee, the Program Chairmen would like to thank all those who submitted papers to EOOLT'2007. Special thanks go to David Broman who created the web page and helped with organization of the workshop. Many thanks to the program committee for reviewing the papers. EOOLT'2007 was hosted by the Technical University of Berlin, in conjunction with the ECOOP'2007 conference

An Updating Method for Finite Element Models of Flexible-Link Mechanisms Based on an Equivalent Rigid-Link System

This paper proposes a comprehensive methodology to update dynamic models of flexible-link mechanisms (FLMs) modeled through ordinary differential equations. The aim is to correct mass, stiffness, and damping matrices of dynamic models, usually based on nominal and uncertain parameters, to accurately represent the main vibrational modes within the bandwidth of interest. Indeed, the availability of accurate models is a fundamental step for the synthesis of effective controllers, state observers, and optimized motion profiles, as those employed in modern control schemes. The method takes advantage of the system dynamic model formulated through finite elements and through the representation of the total motion as the sum of a large rigid-body motion and the elastic deformation. Model updating is not straightforward since the resulting model is nonlinear and its coordinates cannot be directly measured. Hence, the nonlinear model is linearized about an equilibrium point to compute the eigenstructure and to compare it with the results of experimental modal analysis. Once consistency between the model coordinates and the experimental data is obtained through a suitable transformation, model updating has been performed solving a constrained convex optimization problem. Constraints also include results from static tests. Some tools to improve the problem conditioning are also proposed in the formulation adopted, to handle large dimensional models and achieve reliable results. The method has been experimentally applied to a challenging system: a planar six-bar linkage manipulator. The results prove their capability to improve the model accuracy in terms of eigenfrequencies and mode shapes