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Optimal Control for Automotive Powertrain Applications

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Optimal Control for Automotive Powertrain Applications Universitat Politecnica` de Valencia` Departamento de Maquinas´ y Motores Termicos´ Optimal Control for Automotive Powertrain Applications PhD Dissertation Presented by Alberto Reig Advised by Dr. Benjam´ınPla Valencia, September 2017 PhD Dissertation Optimal Control for Automotive Powertrain Applications Presented by Alberto Reig Advised by Dr. Benjam´ınPla Examining committee President: Dr. Jos´eGalindo Lucas Secretary: Dr. Octavio Armas Vergel Vocal: Dr. Marcello Canova Valencia, September 2017 To the geniuses of the past, who built our future; to those names in the shades, bringing our knowledge. They not only supported this work but also the world we live in. If you can solve it, it is an exercise; otherwise it's a research problem. | Richard Bellman e Resumen El Control Optimo´ (CO) es esencialmente un problema matem´aticode b´us- queda de extremos, consistente en la definici´onde un criterio a minimizar (o maximizar), restricciones que deben satisfacerse y condiciones de contorno que afectan al sistema. La teor´ıade CO ofrece m´etodos para derivar una trayectoria de control que minimiza (o maximiza) ese criterio. Esta Tesis trata la aplicaci´ondel CO en automoci´on,y especialmente en el motor de combusti´oninterna. Las herramientas necesarias son un m´etodo de optimizaci´ony una representaci´onmatem´aticade la planta motriz. Para ello, se realiza un an´alisiscuantitativo de las ventajas e inconvenientes de los tres m´etodos de optimizaci´onexistentes en la literatura: programaci´ondin´amica, principio m´ınimode Pontryagin y m´etodos directos. Se desarrollan y describen los algoritmos para implementar estos m´etodos as´ıcomo un modelo de planta motriz, validado experimentalmente, que incluye la din´amicalongitudinal del veh´ıculo,modelos para el motor el´ectricoy las bater´ıas,y un modelo de motor de combusti´onde valores medios. El CO puede utilizarse para tres objetivos distintos: 1. Control aplicado, en caso de que las condiciones de contorno est´en definidas. Puede aplicarse al control del motor de combusti´onpara un ciclo de conducci´ondado, traduci´endoseen un problema matem´aticode grandes dimensiones. Se estudian dos casos particulares: la gesti´onde un sistema de EGR de doble lazo, y el control completo del motor, en particular de las consignas de inyecci´on,SOI, EGR y VGT. 2. Obtenci´onde reglas de control cuasi-´optimas,aplicables en casos en los que no todas las perturbaciones se conocen. A este respecto, se analizan el c´alculode calibraciones de motor espec´ıficas para un ciclo, y la gesti´on energ´eticade un veh´ıculoh´ıbridomediante un control estoc´asticoen bucle cerrado. 3. Empleo de trayectorias de CO como comparativa o referencia para tareas de dise~noy mejora, ofreciendo un criterio objetivo. La ley de combusti´on as´ıcomo el dimensionado de una planta motriz h´ıbridase optimizan mediante el uso de CO. Las estrategias de CO han sido aplicadas experimentalmente en los traba- jos referentes al motor de combusti´on,poniendo de manifiesto sus ventajas sustanciales, pero tambi´enanalizando dificultades y l´ıneas de actuaci´onpara superarlas. Los m´etodos desarrollados en esta Tesis Doctoral son generales y aplicables a otros criterios si se dispone de los modelos adecuados. f Resum El Control Optim` (CO) ´esessencialment un problema matem`aticde cerca d'extrems, que consisteix en la definici´od'un criteri a minimitzar (o maxim- itzar), restriccions que es deuen satisfer i condicions de contorn que afecten el sistema. La teoria de CO ofereix m`etodes per a derivar una traject`oriade control que minimitza (o maximitza) aquest criteri. Aquesta Tesi tracta l’aplicaci´odel CO en automoci´oi especialment al motor de combusti´ointerna. Les ferramentes necess`ariess´onun m`etode d’optimitzaci´oi una representaci´omatem`aticade la planta motriu. Per a aix`o,es realitza una an`alisiquantitatiu dels avantatges i inconvenients dels tres m`etodes d’optimitzaci´oexistents a la literatura: programaci´odin`amica, principi m´ınimde Pontryagin i m`etodes directes. Es desenvolupen i descriuen els algoritmes per a implementar aquests m`etodes aix´ıcom un model de planta motriu, validat experimentalment, que inclou la din`amicalongitudinal del vehicle, models per al motor el`ectrici les bateries, i un model de motor de combusti´ode valors mitjans. El CO es pot utilitzar per a tres objectius diferents: 1. Control aplicat, en cas que les condicions de contorn estiguen definides. Es pot aplicar al control del motor de combusti´oper a un cicle de conducci´oparticular, traduint-se en un problema matem`aticde grans dimensions. S'estudien dos casos particulars: la gesti´od'un sistema d'EGR de doble lla¸c,i el control complet del motor, particularment de les consignes d’injecci´o,SOI, EGR i VGT. 2. Obtenci´ode regles de control quasi-`optimes, aplicables als casos on no totes les pertorbacions s´onconegudes. A aquest respecte, s'analitzen el c`alculde calibratges espec´ıficsde motor per a un cicle, i la gesti´o energ`etica d'un vehicle h´ıbridmitjan¸cant un control estoc`asticen bucle tancat. 3. Utilitzaci´ode traject`oriesde CO com comparativa o refer`enciaper a tasques de disseny i millora, oferint un criteri objectiu. La llei de combusti´oaix´ıcom el dimensionament d'una planta motriu h´ıbrida s'optimitzen mitjan¸cant l'´usde CO. Les estrat`egiesde CO han sigut aplicades experimentalment als treballs referents al motor de combusti´o,manifestant els seus substancials avantatges, per`otamb´eanalitzant dificultats i l´ıniesd’actuaci´oper superar-les. Els m`etodes desenvolupats a aquesta Tesi Doctoral s´ongenerals i aplicables a uns altres criteris si es disposen dels models adequats. g Abstract Optimal Control (OC) is essentially a mathematical extremal problem. The procedure consists on the definition of a criterion to minimize (or maximize), some constraints that must be fulfilled and boundary conditions or disturbances affecting to the system behavior. The OC theory supplies methods to derive a control trajectory that minimizes (or maximizes) that criterion. This dissertation addresses the application of OC to automotive control problems at the powertrain level, with emphasis on the internal combustion engine. The necessary tools are an optimization method and a mathematical representation of the powertrain. Thus, the OC theory is reviewed with a quantitative analysis of the advantages and drawbacks of the three optimization methods available in literature: dynamic programming, Pontryagin minimum principle and direct methods. Implementation algorithms for these three methods are developed and described in detail. In addition to that, an experimentally validated dynamic powertrain model is developed, comprising longitudinal vehicle dynamics, electrical motor and battery models, and a mean value engine model. OC can be utilized for three different purposes: 1. Applied control, when all boundaries can be accurately defined. The engine control is addressed with this approach assuming that a the driving cycle is known in advance, translating into a large mathematical problem. Two specific cases are studied: the management of a dual-loop EGR system, and the full control of engine actuators, namely fueling rate, SOI, EGR and VGT settings. 2. Derivation of near-optimal control rules, to be used if some disturbances are unknown. In this context, cycle-specific engine calibrations calcula- tion, and a stochastic feedback control for power-split management in hybrid vehicles are analyzed. 3. Use of OC trajectories as a benchmark or base line to improve the system design and efficiency with an objective criterion. OC is used to optimize the heat release law of a diesel engine and to size a hybrid powertrain with a further cost analysis. OC strategies have been applied experimentally in the works related to the internal combustion engine, showing significant improvements but non-negligible difficulties, which are analyzed and discussed. The methods developed in this dissertation are general and can be extended to other criteria if appropriate models are available. h i Agradecimientos El director de tesis es como una buj´ıa:lo necesitas en tiempos de compresi´on, debes darle la mezcla adecuada y su chispa hace que todo funcione. De estar bien dirigido depende que una tesis doctoral sufra o evite el knock. Y creo que he sido enormemente afortunado de haber contado con Benjam´ınPla durante este largo camino. No solo me ha transmitido su pasi´onpor todo lo que hace, desde la primera idea, hasta el ´ultimo experimento, pasando por todas y cada una de las l´ıneas de c´odigo,sino que m´asque un director ha sido un compa~nero y amigo que ha soportado todas mis dudas y errores, que no han sido pocos. Ya hace tiempo convirti´olo que pretend´ıaser un simple proyecto acad´emicoen todo un reto cient´ıfico, descubri´endomelo que era el mundo de la investigaci´on, algo que por aquel entonces me era totalmente ajeno. De ´elhe aprendido a apreciar la belleza que reside en los problemas: son una elegante excusa para recorrer el camino hasta la soluci´on.Sin su contagiosa pasi´onjam´asme habr´ıa embarcado en este viaje y no habr´ıaconseguido algo de lo que hoy me siento realmente satisfecho. Es por ello que todo lo que he aprendido, todo lo que hay en esta tesis y toda mi experiencia, se la debo a ´el. Otro pilar fundamental ha sido Carlos Guardiola que, sin perder ese aire informal, cercano y desenfadado que le caracteriza, siempre ha estado dispuesto a ofrecer una visi´oncr´ıticae incluso disruptiva de mis ideas. Su capacidad de asimilar en pocos minutos un problema completamente desconocido para ´ely ofrecer otro punto de vista ha sido, a parte de envidiable, fundamental para darme cuenta que muchas veces los ´arboles no me dejaban ver el bosque. Por supuesto, merece una menci´onespecial mi querido compa~nerode doctorado, Pau Bares. Aunque me hagas rabiar y me queje constantemente de ti, lo cierto es que ha sido muy divertido tenerte al lado todo este tiempo.
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