Pontryagin's Minimum Principle based model predictive control of energy management for a plug-in hybrid electric bus

To improve computational efficiency of energy management strategies for plug-in hybrid electric vehicles (PHEVs), this paper proposes a stochastic model predictive controller (MPC) based on Pontryagin’s Minimum Principle (PMP), which differs from widely used dynamic programming (DP)-based predictive methods. First, short-time speed forecasting is achieved using a Markov chain model, based on real-world driving cycles. The PMP- and DP-based MPCs are compared under four preview horizons (5 s, 10 s, 15 s and 20 s), and the results show that the computational time of the DP-MPC is almost four times of that in the PMP-MPC. Moreover, the influence of predication horizon length on computational time and energy consumption is examined. Given a preview horizon of 5 s, the PMP-MPC holds a total energy consumption cost of 7.80 USD and computational time per second of 0.0130 s. When the preview horizon increases to 20 s, the total cost is 7.77 USD with the computational time per second increasing to 0.0502 s. Finally, DP, PMP, and rule-based strategies are contrasted to the PMP-MPC method, further demonstrating the promising performance and computational efficiency of the proposed methodology

Gear shift strategies for automotive transmissions

The development history of automotive engineering has shown the essential role of transmissions in road vehicles primarily powered by internal combustion engines. The engine with its physical constraints on the torque and speed requires a transmission to have its power converted to the drive power demand at the vehicle wheels. Under dynamic driving conditions, the transmission is required to shift in order to match the engine power with the changing drive power. Furthermore, a gear shift decision is expected to be consistent such that vehicle can remain in the next gear for a period of time without deteriorating the acceleration capability. Therefore, an optimal conversion of the engine power plays a key role in improving the fuel economy and driveability. Moreover, the consequences of the assumptions related to the discrete state variable-dependent losses, e.g. gear shifting, clutch slippage and engine starting, and their e¿ect on the gear shift control strategy are necessary to be analyzed to yield insights into the fuel usage. The ¿rst part of the thesis deals with the design of gear shift strategies for electronically controlled discrete ratio transmissions used in both conventional vehicles and Hybrid Electric Vehicles (HEVs). For conventional vehicles, together with the fuel economy, the driveability is systematically addressed in a Dynamic Programming (DP) based optimal gear shift strategy by three methods: i) the weighted inverse of the power re¬serve, ii) the constant power reserve, and iii) the variable power reserve. In addition, a Stochastic Dynamic Programming (SDP) algorithm is utilized to optimize the gear shift strategy, subject to a stochastic distribution of the power request, in order to minimize the expected fuel consumption over an in¿nite horizon. Hence, the SDP-based gear shift strategy intrinsically respects the driveability and is realtime implementable. By per¬forming a comparative analysis of all proposed gear shift methods, it is shown that the variable power reserve method achieves the highest fuel economy without deteriorating the driveability. Moreover, for HEVs, a novel fuel-optimal control algorithm, consist-ing of the continuous power split and discrete gear shift, engine on-o¿ problems, based on a combination of DP and Pontryagin’s Minimum Principle (PMP) is developed for the corresponding hybrid dynamical system. This so-called DP-PMP gear shift control approach benchmarks the development of an online implementable control strategy in terms of the optimal tradeo¿ between calculation accuracy and computational e¿ciency. Driven by an ultimate goal of realizing an online gear shift strategy, a gear shift map design methodology for discrete ratio transmissions is developed, which is applied for both conventional vehicles and HEVs. The design methodology uses an optimal gear shift algorithm as a basis to derive the optimal gear shift patterns. Accordingly, statis¬tical theory is applied to analyze the optimal gear shift pattern in order to extract the time-invariant shift rules. This alternative two-step design procedure makes the gear shift map: i) respect the fuel economy and driveability, ii) be consistent and robust with respect to shift busyness, and iii) be realtime implementation. The design process is ¿exible and time e¿cient such that an applicability to various powertrain systems con¿gured with discrete ratio transmissions is possible. Furthermore, the study in this thesis addresses the trend of utilizing the route information in the powertrain control system by proposing an integrated predictive gear shift strategy concept, consisting of a velocity algorithm and a predictive algorithm. The velocity algorithm improves the fuel economy in simulation considerably by proposing a fuel-optimal velocity trajectory over a certain driving horizon for the vehicle to follow. The predictive algorithm suc¬cessfully utilizes a prede¿ned velocity pro¿le over a certain horizon in order to realize a fuel economy improvement very close to that of the globally optimal algorithm (DP). In the second part of the thesis, the energetic losses, involved with the gear shift and engine start events in an automated manual transmission-based HEV, are modeled. The e¿ect of these losses on the control strategies and fuel consumption for (non-)powershift transmission technologies is investigated. Regarding the gear shift loss, the study ¿rstly ever discloses a perception of a fuel-e¿cient advantage of the powershift transmissions over the non-powershift ones applied for commercial vehicles. It is also shown that the engine start loss can not be ignored in seeking for a fair evaluation of the fuel economy. Moreover, the sensitivity study of the fuel consumption with respect to the prediction horizon reveals that a predictive energy management strategy can realize the highest achievable fuel economy with a horizon of a few seconds ahead. The last part of the thesis focuses on investigating the sensitivity of an optimal gear shift strategy to the relevant control design objectives, i.e. fuel economy, driveability and comfort. A singu¬lar value decomposition based method is introduced to analyze the possible correlations and interdependencies among the design objectives. This allows that some of the pos¬sible dependent design objective(s) can be removed from the objective function of the corresponding optimal control problem, hence thereby reducing the design complexity

Predictive Energy Management in Connected Vehicles: Utilizing Route Information Preview for Energy Saving

This dissertation formulates algorithms that use preview information of road terrain and traffic flow for reducing energy use and emissions of modern vehicles with conventional or hybrid powertrains. Energy crisis, long term energy deficit, and more restrictive environmental protection policies require developing more efficient and cleaner vehicle powertrain systems. An alternative to making advanced technology engines or electrifying the vehicle powertrain is utilizing ambient terrain and traffic information in the energy management of vehicles, a topic which has not been emphasized in the past. Today\u27s advances in vehicular telematics and advances in GIS (Geographic Information System), GPS (Global Positioning Systems), ITS (Intelligent Transportation Systems), V2V (Vehicle to Vehicle) communication, and VII (Vehicle Infrastructure Integration ) create more opportunities for predicting a vehicle\u27s trip information with details such as the future road grade, the distance to the destination, speed constraints imposed by the traffic flow, which all can be utilized for better vehicle energy management. Optimal or near optimal decision-making based on this available information requires optimal control methods, whose fundamental theories were well studied in the past but are not directly applicable due to the complexity of real problems and uncertainty in the available preview information. This dissertation proposes the use of optimal control theories and tools including Pontryagin minimum principle, Dynamic Programming (DP) which is a numerical realization of Bellman\u27s principle of optimality, and Model Predictive Control (MPC) in the optimization-based control of hybrid electric vehicles (HEVs), plug-in hybrid electric vehicles (PHEVs), and conventional vehicles based on preview of future route information. The dissertation includes three parts introduced as follows: First, the energy saving benefit in HEV energy management by previewing future terrain information and applying optimal control methods is explored. The potential gain in fuel economy is evaluated, if road grade information is integrated in energy management of hybrid vehicles. Real-world road geometry information is taken into account in power management decisions by using both Dynamic Programming (DP) and a standard Equivalent Consumption Minimization Strategy (ECMS), derived using Pontryagin minimum principle. Secondly, the contribution of different levels of preview to energy management of plug-in hybrid vehicles (PHEVs) is studied. The gains to fuel economy of plug-in hybrid vehicles with availability of velocity and terrain preview and knowledge of distance to the next charging station are investigated. Access to future driving information is classified into full, partial, or no future information and energy management strategies for real-time implementation with partial future preview are proposed. ECMS as well as Dynamic Programming (DP) is systematically utilized to handle the resulting optimal control problems with different levels of preview. We also study the benefit of future traffic flow information preview in improving the fuel economy of conventional vehicles by predictive control methods. According to the time-scale of the preview information and its importance to the driver, the energy optimization problem is decomposed into different levels. In the microscopic level, a model predictive controller as well as a car following model is employed for predictive adaptive cruise control by stochastically forecasting the driving behavior of the lead car. In the macroscopic level, we propose to incorporate the estimated macroscopic future traffic flow information and optimize the cost-to-go by utilizing a two-dimension Dynamic Programming (2D-DP). The algorithm yields the optimal trip velocity as the reference velocity for the driver or a low level controller to follow. Through the study, we show that energy use and emissions can be reduced considerably by using preview route information. The methodologies discussed in this dissertation provide an alternative mean for the automotive industry to develop more efficient and environmentally friendly vehicles by relying mostly on software and information and with minimal hardware investments

Supervisory Control Optimization for a Series Hybrid Electric Vehicle with Consideration of Battery Thermal Management and Aging

This dissertation integrates battery thermal management and aging into the supervisory control optimization for a heavy-duty series hybrid electric vehicle (HEV). The framework for multi-objective optimization relies on novel implementation of the Dynamic Programing algorithm, and predictive models of critical phenomena. Electrochemistry based battery aging model is integrated into the framework to assesses the battery aging rate by considering instantaneous lithium ion (Li+) surface concentration rather than average concentration. This creates a large state-action space. Therefore, the computational effort required to solve a Deterministic or Stochastic Dynamic Programming becomes prohibitively intense, and a neuro-dynamic programming approach is proposed to remove the ‘curse of dimensionality’ in classical dynamic programming. First, unified simulation framework is developed for in-depth studies of series HEV system. The integration of a refrigerant system model enables prediction of energy use for cooling the battery pack. Side reaction, electrolyte decomposition, is considered as the main aging mechanism of LiFePO4/Graphite battery, and an electrochemical model is integrated to predict side reaction rate and the resulting fading of capacity and power. An approximate analytical solution is used to solve the partial difference equations (PDEs) for Li+ diffusion. Comparing with finite difference method, it largely reduces the number of states with only a slight penalty on prediction accuracy. This improves computational efficiency, and enables inclusion of the electrochemistry based aging model in the power management optimization framework. Next, a stochastic dynamic programming (SDP) approach is applied to the optimization of supervisory control. Auxiliary cooling power is included in addition to vehicle propulsion. Two objectives, fuel economy and battery life, are optimized by weighted sum method. To reduce the computation load, a simplified battery aging model coupled with equivalent circuit model is used in SDP optimization; Li+ diffusion dynamics are disregarded, and surface concentration is represented by the average concentration. This reduces the system state number to four with two control inputs. A real-time implementable strategy is generated and embedded into the supervisory controller. The result shows that SDP strategy can improve fuel economy and battery life simultaneously, comparing with Thermostatic SOC strategy. Further, the tradeoff between fuel consumption and active Li+ loss is studied under different battery temperature. Finally, the accuracy of battery aging model for optimization is improved by adding Li+ diffusion dynamics. This increases the number of states and brings challenges to classical dynamic programming algorithms. Hence, a neuro-dynamic programming (NDP) approach is proposed for the problem with large state-action space. It combines the idea of functional approximation and temporal difference learning with dynamic programming; in that case the computation load increases linearly with the number of parameters in the approximate function, rather than exponentially with state space. The result shows that ability of NDP to solve the complex control optimization problem reliably and efficiently. The battery-aging conscientious strategy generated by NDP optimization framework further improves battery life by 3.8% without penalty on fuel economy, compared to SDP strategy. Improvements of battery life compared to the heuristic strategy are much larger, on the order of 65%. This leads to progressively larger fuel economy gains over time

Optimal Control for Automotive Powertrain Applications

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 calculation, 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.El Control Óptimo (CO) es esencialmente un problema matemático de búsqueda de extremos, consistente en la definición de un criterio a minimizar (o maximizar), restricciones que deben satisfacerse y condiciones de contorno que afectan al sistema. La teoría de CO ofrece métodos para derivar una trayectoria de control que minimiza (o maximiza) ese criterio. Esta Tesis trata la aplicación del CO en automoción, y especialmente en el motor de combustión interna. Las herramientas necesarias son un método de optimización y una representación matemática de la planta motriz. Para ello, se realiza un análisis cuantitativo de las ventajas e inconvenientes de los tres métodos de optimización existentes en la literatura: programación dinámica, principio mínimo de Pontryagin y métodos directos. Se desarrollan y describen los algoritmos para implementar estos métodos así como un modelo de planta motriz, validado experimentalmente, que incluye la dinámica longitudinal del vehículo, modelos para el motor eléctrico y las baterías, y un modelo de motor de combustión de valores medios. El CO puede utilizarse para tres objetivos distintos: 1. Control aplicado, en caso de que las condiciones de contorno estén definidas. Puede aplicarse al control del motor de combustión para un ciclo de conducción dado, traduciéndose en un problema matemático de grandes dimensiones. Se estudian dos casos particulares: la gestión de un sistema de EGR de doble lazo, y el control completo del motor, en particular de las consignas de inyección, SOI, EGR y VGT. 2. Obtención de reglas de control cuasi-óptimas, aplicables en casos en los que no todas las perturbaciones se conocen. A este respecto, se analizan el cálculo de calibraciones de motor específicas para un ciclo, y la gestión energética de un vehículo híbrido mediante un control estocástico en bucle cerrado. 3. Empleo de trayectorias de CO como comparativa o referencia para tareas de diseño y mejora, ofreciendo un criterio objetivo. La ley de combustión así como el dimensionado de una planta motriz híbrida se optimizan mediante el uso de CO. Las estrategias de CO han sido aplicadas experimentalmente en los trabajos referentes al motor de combustión, poniendo de manifiesto sus ventajas sustanciales, pero también analizando dificultades y líneas de actuación para superarlas. Los métodos desarrollados en esta Tesis Doctoral son generales y aplicables a otros criterios si se dispone de los modelos adecuados.El Control Òptim (CO) és essencialment un problema matemàtic de cerca d'extrems, que consisteix en la definició d'un criteri a minimitzar (o maximitzar), restriccions que es deuen satisfer i condicions de contorn que afecten el sistema. La teoria de CO ofereix mètodes per a derivar una trajectòria de control que minimitza (o maximitza) aquest criteri. Aquesta Tesi tracta l'aplicació del CO en automoció i especialment al motor de combustió interna. Les ferramentes necessàries són un mètode d'optimització i una representació matemàtica de la planta motriu. Per a això, es realitza una anàlisi quantitatiu dels avantatges i inconvenients dels tres mètodes d'optimització existents a la literatura: programació dinàmica, principi mínim de Pontryagin i mètodes directes. Es desenvolupen i descriuen els algoritmes per a implementar aquests mètodes així com un model de planta motriu, validat experimentalment, que inclou la dinàmica longitudinal del vehicle, models per al motor elèctric i les bateries, i un model de motor de combustió de 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 combustió per a un cicle de conducció particular, traduint-se en un problema matemàtic de grans dimensions. S'estudien dos casos particulars: la gestió d'un sistema d'EGR de doble llaç, i el control complet del motor, particularment de les consignes d'injecció, SOI, EGR i VGT. 2. Obtenció de regles de control quasi-òptimes, aplicables als casos on no totes les pertorbacions són conegudes. A aquest respecte, s'analitzen el càlcul de calibratges específics de motor per a un cicle, i la gestió energètica d'un vehicle híbrid mitjançant un control estocàstic en bucle tancat. 3. Utilització de trajectòries de CO com comparativa o referència per a tasques de disseny i millora, oferint un criteri objectiu. La llei de combustió així com el dimensionament d'una planta motriu híbrida s'optimitzen mitjançant l'ús de CO. Les estratègies de CO han sigut aplicades experimentalment als treballs referents al motor de combustió, manifestant els seus substancials avantatges, però també analitzant dificultats i línies d'actuació per superar-les. Els mètodes desenvolupats a aquesta Tesi Doctoral són generals i aplicables a uns altres criteris si es disposen dels models adequats.Reig Bernad, A. (2017). Optimal Control for Automotive Powertrain Applications [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/90624TESI

Online Control of Automotive systems for improved Real-World Performance

[ES] La necesidad de mejorar el consumo de combustible y las emisiones de los sistemas propulsivos de automoción en condiciones reales de conducción es la base de esta tesis. Para ello, se exploran dos ejes: En primer lugar, el control de los sistemas de propulsión. El estado del arte de control en los sistemas propulsivos de automoción se basa en gran medida en el uso de técnicas de optimización que buscan las leyes de control que minimizan una función de coste en un conjunto de condiciones de operación denidas a priori. Estas leyes se almacenan en las ECUs de producción en forma de mapas de calibración de los diferentes actuadores del motor. Las incertidumbres asociadas al conjunto limitado de condiciones en el proceso de calibración dan lugar a un funcionamiento subóptimo del sistema de propulsión en condiciones de conducción real. Por lo tanto, en este trabajo se proponen métodos de control adaptativo que optimicen la gestión de la planta propulsiva a las condiciones esperadas de funcionamiento para un usuario y un caso determinado en lugar de a un conjunto genérico de condiciones. El segundo eje se reere a optimizar, en lugar de los parámetros de control del sistema propulsivo, la demanda de potencia de este, introduciendo al propio conductor en el bucle de control, sugiriéndole las acciones a tomar. En particular, este segundo eje se reere al control de la velocidad del vehículo (conocido popularmente como Eco-Driving en la literatura) en condiciones reales de conducción. Se proponen sistemas de aviso en tiempo real al conductor acerca de la velocidad óptima para minimizar el consumo del vehículo. Los métodos de control desarrollados para cada aplicación se describen en detalle en la tesis y se muestran ensayos experimentales de validación en los casos de estudio diseñados. Ambos ejes representan un problema de control óptimo, denido por un sistema dinámico, unas restricciones a cumplir y un coste a minimizar, en este sentido las herramientas desarrolladas en la tesis son comunes a los dos ejes: Un modelo de vehículo, una herramienta de predicción del ciclo de conducción y métodos de control óptimo (Programación Dinámica, Principio Mínimo de Pontryagin y Estrategia de Consumo Equivalente Mínimo). Dependiendo de la aplicación, los métodos desarrollados se implementaron en varios entornos experimentales: un motor térmico en sala de ensayos simulando el resto del vehículo, incluyendo el resto del sistema de propulsión híbrido y en un vehículo real. Los resultados muestran mejoras signicativas en el rendimiento del sistema de propulsión en términos de ahorro de combustible y emisiones en comparación con los métodos empleados en el estado del arte actual.[CA] La necessitat de millorar el consum de combustible i les emissions dels sistemes propulsius d'automoció en condicions reals de conducció és la base d'aquesta tesi. Per a això, s'exploren dos eixos: En primer lloc, el control dels sistemes de propulsió. L'estat de l'art de control en els sistemes propulsius d'automoció es basa en gran manera en l'ús de tècniques d'optimització que busquen les lleis de control que minimitzen una funció de cost en un conjunt de condicions d'operació denides a priori. Aquestes lleis s'emmagatzemen en les Ecus de producció en forma de mapes de calibratge dels diferents actuadors del motor. Les incerteses associades al conjunt limitat de condicions en el procés de calibratge donen lloc a un funcionament subòptim del sistema de propulsió en condicions de conducció real. Per tant, en aquest treball es proposen mètodes de control adaptatiu que optimitzen la gestió de la planta propulsiva a les condicions esperades de funcionament per a un usuari i un cas determinat en lloc d'un conjunt genèric de condicions. El segon eix es refereix a optimitzar, en lloc dels paràmetres de control del sistema propulsiu, la demanda de potència d'aquest, introduint al propi conductor en el bucle de control, suggerint-li les accions a prendre. En particular, aquest segon eix es refereix al control de la velocitat del vehicle (conegut popularment com Eco-*Driving en la literatura) en condicions reals de conducció. Es proposen sistemes d'avís en temps real al conductor sobre la velocitat òptima per a minimitzar el consum del vehicle. Els mètodes de control desenvolupats per a cada aplicació es descriuen detalladament en la tesi i es mostren assajos experimentals de validació en els casos d'estudi dissenyats. Tots dos eixos representen un problema de control òptim, denit per un sistema dinàmic, unes restriccions a complir i un cost a minimitzar, en aquest sentit les eines desenvolupades en la tesi són comunes als dos eixos: Un model de vehicle, una eina de predicció del cicle de conducció i mètodes de control òptim (Programació Dinàmica, Principi Mínim de *Pontryagin i Estratègia de Consum Equivalent Mínim). Depenent de l'aplicació, els mètodes desenvolupats es van implementar en diversos entorns experimentals: un motor tèrmic en sala d'assajos simulant la resta del vehicle, incloent la resta del sistema de propulsió híbrid i en un vehicle real. Els resultats mostren millores signicatives en el rendiment del sistema de propulsió en termes d'estalvi de combustible i emissions en comparació amb els mètodes emprats en l'estat de l'art actual.[EN] The need of improving the real-world fuel consumption and emission of automotive applications is the basis of this thesis. To this end, two verticals are explored: First is the online control of the powertrain systems. In state-of-the-art Optimal Control techniques (such as Dyanmic Programming, Pontryagins Minimum Principle, etc...) are extensively used to formulate the optimal control laws. These laws are stored in the production ECUs in the form of feedforward calibration maps. The unaccounted uncertainities related to the real-world during the powertrain calibration result in suboptimal operations of the powertrain in actual driving. Therefore, adaptive control methods are proposed in this work which, optimise the energy management of the conventional and the HEV powertrain control on real driving mission. The second vertical is regarding the vehicle speed control (popularly known as Eco-Driving in the literature) methods in real driving condition. In particular, speed advisory systems are proposed for real time application on a vehicle. The control methods developed for each application are described in details with their verication and validation on the designed case studies. Apart from the developed control methods, there are three tools that were developed and used at various stages of this thesis: A vehicle model, A driving cycle prediction tool and optimal control methods (dynamic programming, PMP and ECMS). Depending on the application, the developed methods were implemented on the Hardware-In-Loop Internal Combustion Engine testing setup or on a real vehicle. The results show signicant improvements in the performance of the powertrain in terms of fuel economy and emissions in comparison to the state-of-the-art methods.Pandey, V. (2021). Online Control of Automotive systems for improved Real-World Performance [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/173716TESI

On Optimal Mission Planning for Vehicles over Long-distance Trips

This thesis proposes a mission planner for vehicles over long-distance trips, for finding the optimal trade-off between trip time, energy efficiency, anddriver comfort, subject to road information, traffic situations, and weather conditions. The mission planner consists of three components, i.e. logisticsplanner, eco-driving supervisor, and thermal and charging supervisor. The logistics planner aims at optimising the mission start and/or finish time byminimising energy consumption and trip time. The eco-driving supervisor computes the velocity profile of the driving vehicle, by optimising the energyconsumption and penalising driver discomfort. To do so, an online-capable algorithm has been formulated in a model predictive control framework, subject to road and traffic information, and the pre-optimised mission start and/or finish time. This algorithm is computationally efficient and enables the driving vehicle to adapt and optimally respond to predicted disturbances within a short amount of time. Eco-driving has also been achieved for a vehicleconfronted with wind, by applying stochastic dynamic programming method. The thermal and charging supervisor regulates battery temperature and state of charge by coordinating the energy use of different thermal components. Within the thermal and charging supervisor design, a heat pump has been included for waste heat recovery purposes. Also, the charging stops have been optimally planned, in favour of energy efficiency and trip time. The performance of the proposed algorithms over a road with a hilly terrain is assessed using simulations. According to the simulation results, it is observed that total travel time is reduced up to 5.5 % by optimising the mission start time, when keeping an average cruising speed of about 75 km/h. Also, compared to standard cruise control, the energy savings of using this algorithm is up to 11.6 %. Furthermore, total charging time and energy consumption are reduced by up to 19.4 % and 30.6 %, respectively by developing the thermal and charging supervisor, compared to a case without the heat pump activated and without charge point optimisation

An Optimal Energy Management Strategy for Hybrid Electric Vehicles

Hybrid Electric Vehicles (HEVs) are used to overcome the short-range and long charging time problems of purely electric vehicles. HEVs have at least two power sources. Therefore, the Energy Management (EM) strategy for dividing the driver requested power between the available power sources plays an important role in achieving good HEV performance. This work, proposes a novel real-time EM strategy for HEVs which is named ECMS-CESO. ECMS-CESO is based on the Equivalent Consumption Minimization Strategy (ECMS) and is designed to Catch Energy Saving Opportunities (CESO) while operating the vehicle. ECMS-CESO is an instantaneous optimal controller, i. e., it does not require prediction of the future demanded power by the driver. Therefore, ECMS-CESO is tractable for real-time operation. Under certain conditions ECMS achieves the maximum fuel economy. The main challenge in employing ECMS is the estimation of the optimal equivalence factor L*. Unfortunately, L* is drive-cycle dependent, i. e., it changes from driver to driver and/or route to route. The lack of knowledge about L* has been a motivation for studying a new class of EM strategies known as Adaptive ECMS (A-ECMS). A-ECMS yields a causal controller that calculates L(t) at each moment t as an estimate of L*. Existing A-ECMS algorithms estimate L*, by heuristic approaches. Here, instead of direct estimation of L*, analytic bounds on L* are determined which are independent of the drive-cycle. Knowledge about the range of L*, can be used to adaptively set L(t) as performed by the ECMS-CESO algorithm. ECMS-CESO also defines soft constraints on the battery state of charge (SOC) and a penalty for exceeding the soft constraints. ECMS-CESO is allowed to exceed a SOC soft constraint when an energy saving opportunity is available. ECMS-CESO is efficient since there is no need for prediction and the intensive calculations for finding the optimal control over the predicted horizon are not required. Simulation results for 3 different HEVs are used to confirm the expected performance of ECMS-CESO. This work also investigates the performance of the model predictive control with respect to the predicated horizon length