Speed profile optimization of an electrified train in Cat Linh-Ha Dong metro line based on pontryagin's maximum principle

An urban railway is a complex technical system that consumes large amounts of energy, but this means of transportation still has been obtained more and more popularity in densely populated cities because of its features of high-capacity transportation capability, high speed, security, punctuality, lower emission, reduction of traffic congestion. The improved energy consumption and environment are two of the main objectives for future transportation. Electrified trains can meet these objectives by the recuperation and reuse of regenerative braking energy and by the energy - efficient operation. Two methods are to enhance energy efficiency: one is to improve technology (e.g., using energy storage system, reversible or active substations to recuperate regenerative braking energy, replacing traction electric motors  by energy-efficient traction system as permanent magnet electrical motors; train's mass reduction by lightweight material mass...); the other is to improve operational procedures (e.g. energy efficient driving including: eco-driving; speed profile optimization; Driving Advice System (DAS); Automatic Train Operation (ATO); traffic management optimization...). Among a lot of above solutions for saving energy, which one is suitable for current conditions of metro lines in Vietnam. The paper proposes the optimization method based on Pontryagin's Maximum Principle (PMP) to find the optimal speed profile for electrified train of Cat Linh-Ha Dong metro line, Vietnam in an effort to minimize the train operation energy consumption

Optimal control of a flywheel-based automotive kinetic energy recovery system

This thesis addresses the control issues surrounding flywheel-based Kinetic Energy Recovery Systems (KERS) for use in automotive vehicle applications. Particular emphasis is placed on optimal control of a KERS using a Continuously Variable Transmission (CVT) for volume car production, and a wholly simulation-based approach is adopted. Following consideration of the general control issues surrounding KERS operation, a simplified system model is adopted, and the scope for use of optimal control theory is explored. Both Pontryagin’s Maximum Principle, and Dynamic Programming methods are examined, and the need for numerical implementation established. With Dynamic Programming seen as the most likely route to practical implementation for realistic nonlinear models, the thesis explores several new strategies for numerical implementation of Dynamic Programming, capable of being applied to KERS control of varying degrees of complexity. The best form of numerical implementation identified (in terms of accuracy and efficiency) is then used to establish via simulation, the benefits of optimal KERS control in comparison with a more conventional non-optimal strategy, showing clear benefits of using optimal control

Stochastic model predictive control for energy management of power-split plug-in hybrid electric vehicles based on reinforcement learning

In this paper, a stochastic model predictive control (MPC) method based on reinforcement learning is proposed for energy management of plug-in hybrid electric vehicles (PHEVs). Firstly, the power transfer of each component in a power-split PHEV is described in detail. Then an effective and convergent reinforcement learning controller is trained by the Q-learning algorithm according to the driving power distribution under multiple driving cycles. By constructing a multi-step Markov velocity prediction model, the reinforcement learning controller is embedded into the stochastic MPC controller to determine the optimal battery power in predicted time domain. Numerical simulation results verify that the proposed method achieves superior fuel economy that is close to that by stochastic dynamic programming method. In addition, the effective state of charge tracking in terms of different reference trajectories highlight that the proposed method is effective for online application requiring a fast calculation speed

Method and apparatus for creating time-optimal commands for linear systems

A system for and method of determining an input command profile for substantially any dynamic system that can be modeled as a linear system, the input command profile for transitioning an output of the dynamic system from one state to another state. The present invention involves identifying characteristics of the dynamic system, selecting a command profile which defines an input to the dynamic system based on the identified characteristics, wherein the command profile comprises one or more pulses which rise and fall at switch times, imposing a plurality of constraints on the dynamic system, at least one of the constraints being defined in terms of the switch times, and determining the switch times for the input to the dynamic system based on the command profile and the plurality of constraints. The characteristics may be related to poles and zeros of the dynamic system, and the plurality of constraints may include a dynamics cancellation constraint which specifies that the input moves the dynamic system from a first state to a second state such that the dynamic system remains substantially at the second state

Near-Optimal Control of a Quadcopter Using Reinforcement Learning

This paper presents a novel control method for quadcopters that achieves near-optimal tracking control for input-affine nonlinear quadcopter dynamics. The method uses a reinforcement learning algorithm called Single Network Adaptive Critics (SNAC), which approximates a solution to the discrete-time Hamilton-Jacobi-Bellman (DT-HJB) equation using a single neural network trained offline. The control method involves two SNAC controllers, with the outer loop controlling the linear position and velocities (position control) and the inner loop controlling the angular position and velocities (attitude control). The resulting quadcopter controller provides optimal feedback control and tracks a trajectory for an infinite-horizon, and it is compared with commercial optimal control software. Furthermore, the closed-loop controller can control the system with any initial conditions within the domain of training. Overall, this research demonstrates the benefits of using SNAC for nonlinear control, showing its ability to achieve near-optimal tracking control while reducing computational complexity. This paper provides insights into a new approach for controlling quadcopters, with potential applications in various fields such as aerial surveillance, delivery, and search and rescue

Optimierung von Brennstoffzellen-Hybridfahrzeugen

The limited fossil fuel resources and the environmental concerns associated with burning those fossil fuels lie behind the increasing interest in hydrogen as a clean and sustainable alternative to fossil fuels, and in fuel cells as a clean converter of hydrogen into electrical energy especially in the transportation sector. Fuel cell hybrid vehicles (FCHVs) are characterized by the use of a fuel cell system (FCS) as the main power source and a battery, a supercapacitor or both as an energy storage system (ESS). Hybridizing the FCS with an ESS significantly improves the hydrogen economy, helps downsize the FCS, and resolves the issues related the long start-up time and slow dynamics of the FCS. The existence of multiple power sources in the powertrain gives rise to two important questions: How to coordinate the power contribution of the sources (i.e., power management strategy (PMS)), and how to size these sources in order to exploit the advantages of hybridization. The goal of this thesis is to develop a comprehensive framework for the optimization of PMS and size of FCHV powertrains. Depending on the type of ESS, three topologies are considered: fuel cell/ battery, fuel cell/ supercapacitor, and fuel cell/ battery/ supercapacitor. The PMS optimization is investigated on two levels; i.e., the vehicle level by simulation and the developed optimization algorithms are then validated on a small-scale test bench. When the driving cycle is known a priori, the off-line optimal PMS that globally minimizes the hydrogen consumption is calculated by two algorithms, namely, Dynamic Programming (DP) and Pontryagin’s Minimum Principle (PMP), and the two algorithms are compared. It has been found that PMP can be a superior approach for off-line optimization since it requires negligible computation resources without sacrificing the global optimality. The off-line optimal strategy is not real-time capable; hence, real-time strategies are designed and optimized while using the off-line optimal PMS as a benchmark. Special emphasize is put on the inclusion of multiple driving cycles, of different nature, in the optimization of the real-time PMS to increase its robustness. The sizing of the power sources of fuel cell/ battery and fuel cell/ supercapacitor hybrids considers hydrogen consumption and powertrain cost as two objectives and takes into account the drivability constraints such as top speed, gradeablity and acceleration time. The interesting designs (i.e., FCS size and ESS size), which represent the most efficient trade-off between the objectives, are then extracted and analyzed. The effect of battery aging on the optimal powertrain size is investigated by an Ampere-hour throughput model. It has been found that the battery aging leads to less efficient powertrain designs and the supercapacitor can become a more efficient option in comparison to batteries of poor lifetime.Die begrenzten fossilen Ressourcen und die Umweltsorgen, die mit der Verbrennung dieser fossilen Brennstoffe verbunden sind, stecken hinter dem steigenden Interesse am Wasserstoff als sauberer und nachhaltiger Alternative, und an Brennstoffzellen als sauberen Wandlern des Wasserstoffs in elektrische Energie, vor allem im Verkehrssektor. Ein Brennstoffzellen-Hybridfahrzeug (FCHV) verwendet ein Brennstoffzellensystem (FCS) als eine Hauptenergiequelle und eine Batterie, einen Superkondensator oder beide als Energiespeichersystem (ESS). Hybridisierung des FCS mit einem ESS verringert erheblich den Wasserstoffverbrauch, hilft das FCS zu verkleinern, und behebt das Problem der langen Anlaufzeit und der langsamen Dynamik des FCS. Die Existenz von mehreren Stromquellen im Antriebsstrang wirft zwei wichtige Fragen auf: Wie ist die Leistungsanforderung des Fahrzeugs zwischen den Quellen zu verteilen (d.h. Power-Management-Strategie (PMS)) und wie sind diese Quellen zu dimensionieren, um die Hybridisierung auszunutzen. Das Ziel dieser Arbeit ist es, einen umfassenden Rahmen für die Optimierung der PMS und Dimensionierung der Brennstoffzellen-basierten hybriden Antriebsstränge zu entwickeln. Abhängig von der Art des ESS werden drei Topologien berücksichtigt: Brennstoffzelle/ Batterie, Brennstoffzelle/ Superkondensator und Brennstoffzelle/ Batterie/ Superkondensator. Die PMS-Optimierung wird auf zwei Ebenen untersucht, und zwar die Fahrzeugebene durch Simulation und die Prüfstandsebene, worauf die entwickelten Optimierungsalgorithmen experimentell validiert werden. Wenn der Lastzyklus im Voraus bekannt ist, kann die offline optimale PMS, die den Wasserstoffverbrauch global minimiert, berechnet werden. Dazu werden die zwei Algorithmen, Dynamische Programmierung (DP) und Pontryagins Minimumprinzip (PMP), verglichen. Es wurde herausgefunden, dass das PMP ein überlegener Ansatz für die offline-Optimierung sein kann, da es viel weniger Rechenressourcen braucht, ohne die globale Optimalität zu opfern. Die offline optimale Strategie ist nicht echtzeitfähig, und deshalb werden Echtzeit-Strategien entworfen und optimiert, indem die offline optimale PMS als Maßstab verwendet wird. Beim Designen der echtzeitfähigen Strategien werden mehrere Fahrzyklen unterschiedlicher Natur beachtet, um die Robustheit der Strategien zu erhöhen. Die Dimensionierung der Stromquellen der Brennstoffzelle/ Batterie und Brennstoffzelle/ Superkondensator Hybriden betrachtet den Wasserstoffverbrauch und die Kosten des Antriebsstrangs als zwei Ziele. Es wird dabei die Fahrbarkeit, d.h. Höchstgeschwindigkeit, Steigfähigkeit und Beschleunigungszeit, berücksichtigt. Die interessanten Konfigurationen (FCS-Größe und ESS-Größe), die den effizientesten Kompromiss zwischen den Zielen darstellen, werden dann herausgefunden und analysiert. Die Wirkung der Batteriealterung auf die optimale Antriebsstrang-Größe wird durch ein Ampere-Stunden-Durchsatzmodell untersucht. Es wurde herausgefunden, dass die Batterie-Alterung weniger effiziente Antriebsstrang-Konfigurationen ergibt, und dass der Superkondensator eine effizientere Alternative zur Batterie sein kann, wenn er mit Batterien von schlechter Lebensdauer verglichen wird

Optimization of Energy-Efficient Speed Profile for Electrified Vehicles

This work presents a study of the energy-efficient operation of all-electric vehicles leveraging route information, such as road grade, to adjust the velocity trajectory Minimization of energy consumption is one of the main targets of research for both passenger vehicles in terms of economic benefit, and army vehicles in terms of mission success and decision making. The optimization of a speed profile is one of the tools used to achieve energy minimization and it can also help in the useful utilization of autonomy in vehicles. The optimization of speed profile is typically addressed as an Optimal Control Problem (OCP). The obstacle that disrupts the implementation of optimization is the heavy computational load that results from the number of state variables, control inputs, and discretization, i.e., the curse of dimensionality. In this work, Pontryagin's Maximum Principle (PMP) is applied to derive necessary conditions and to determine the possible discrete operating modes. The analysis shows that only five modes are required to achieve minimum energy consumption; full propulsion, cruising, coasting, full regeneration, and full braking. Then, the problem is reformulated and solved in the distance domain using Dynamic Programming to find the optimal speed profiles. Various simulation results are shown for a lightweight autonomous military vehicle. Army Programs use various drive cycles including time, speed, and grade, for testing and validating new vehicle systems and models. Among those cycles, two different drive conditions are studied: relatively flat, Convoy, and hilly terrain, Churchville B. For the Convoy cycle, the optimal speed cycle uses 21% less energy for the same trip duration or reduces the time by 14% with the same energy consumption while for the Churchville B cycle, it uses 24% less energy or provides 24% reduction in time. Furthermore, the sensitivity of energy consumption to regenerative-braking power limits and trip time is investigated. These studies provide important information that can be used in designing component size and scheduling operation to achieve the desired vehicle range. Lastly, the work provides parametric studies about the influence of the efficiency of an electric motor on performance including energy consumption and control modes.Master of Science in EngineeringAutomotive Systems Engineering, College of Engineering & Computer ScienceUniversity of Michigan-Dearbornhttps://deepblue.lib.umich.edu/bitstream/2027.42/146793/1/Hadi_Abbas_Thesis (1).pdfDescription of Hadi_Abbas_Thesis (1).pdf : Thesi

하이브리드 차량의 주행 정보 기반 에너지 관리 전략에 대한 연구

학위논문(석사)--서울대학교 대학원 :공과대학 기계항공공학부,2019. 8. 차석원.In this thesis, an energy management strategy (EMS) using prediction model based on driving information is proposed to improve the fuel efficiency of hybrid electric vehicle (HEV). HEV uses both an engine and a motor, and is a representative eco-friendly vehicle with high fuel efficiency. To improve the efficiency of a HEV, the EMS of the supervisory controller that controls various powertrain components is very important. An equivalent consumption minimization strategy (ECMS) used in this study is a real-time optimization-based strategy that considers equivalent energy consumption of fuel and battery. A ECMS is easy to develop and have good real-time applicability, but a performance is largely dependent on the equivalent factor that equalize between the two energies. As with most optimization-based control strategies, the optimal equivalent factor can be obtained only when the entire future driving profile is known. In this thesis, a method of changing the equivalent factor at every specific time period is used, and a prediction model that predicts the factor of the next time window through the current driving information is proposed. The prediction model receives the time series data of the current time window driving information and several feature values extracted from it, and predicts an optimized equivalent factor for the next time window. The model was developed based on recurrent neural network (RNN) using long short-term memory (LSTM) and multi-layer perceptron (MLP). In order to prepare the data for the training of the prediction model, the cumulative driving information is divided into specific time windows, and the optimal equivalent factors for each time window are obtained based on the simulation. After training the prediction model using the collected data and testing it on separate data, it is confirmed that there is a high correlation between the predicted factor and the optimal factor. For the verification of vehicle simulation, the prediction model is combined with the EMS model using the ECMS to construct predictive-ECMS, and the forward simulation is performed using the vehicle and the driver model. Simulation results for test cycle showed less energy use compared to existing rule-based strategy and were more similar to the global optimized factor case. The control strategy proposed in this thesis is an optimization-based control strategy that can improve the energy efficiency by using prediction model based on driving information. It is expected that the optimization -based control strategy will be realized through continuous research.본 논문에서는 하이브리드 차량의 연비 향상을 위해 주행 정보 기반 예측 모델을 활용한 에너지 관리 전략을 제안하였다. 하이브리드 차량은 엔진과 모터를 동시에 사용하는 차량으로, 기존의 내연기관 차량에 비해 연비와 효율이 높은 대표적인 친환경 차량이다. 이러한 하이브리드 차량의 효율 향상을 위해서는 엔진과 모터를 포함한 다양한 파워트레인 구성요소를 제어하는 상위제어기의 에너지 관리 전략이 매우 중요하다. 본 연구에 사용된 등가 소모 최소화 전략은 연료의 소모량과 배터리의 전기에너지 소모량을 등가화한 등가 에너지를 고려한 실시간 최적화 기반 제어 전략이다. 등가 소모 최소화 전략은 개발이 용이하고 실시간 적용성이 좋은 편이지만, 두 에너지간의 등가화를 조정하는 등가 계수에 의해 성능이 크게 좌우된다. 특히 대부분의 최적화 기반 제어 전략과 마찬가지로, 미래의 전체 주행속도 프로파일을 알고 있을 때만이 전역 최적화된 등가계수를 알 수 있다. 본 논문에서는 특정 시간주기별로 등가계수를 변화시키는 방법을 사용하였으며, 현재시점의 주행 정보를 통해 다음 시간주기의 등가계수를 예측하는 예측 모델을 제안하였다. 예측 모델은 현재시점 주행 정보의 시계열 데이터와 이로부터 추출된 몇 개의 특성 값들을 입력받아, 다음 시간주기에 대해 최적화된 등가계수를 예측한다. 모델은 장단기 기억 순환 신경망과 다층 신경망을 기반으로 개발되었다. 예측 모델의 학습을 위한 데이터 준비를 위해, 누적된 대량의 주행 정보를 특정 시간주기별로 나누어 각 시간주기에 대한 최적 등가계수를 시뮬레이션 기반으로 수집하였다. 수집된 데이터를 사용하여 예측모델을 학습한 후 별도의 데이터에 대하여 시험해본 결과, 예측된 계수와 최적 계수 간에 높은 상관관계가 있음을 확인하였다. 차량 시뮬레이션 검증을 위하여 학습된 예측 모델을 등가 소모 최소화 전략을 이용한 에너지 관리 전략 제어 모델과 결합하고, 차량 모델과 운전자 모델을 사용하여 전방향 시뮬레이션을 수행하였다. 연비 시험 사이클에 대한 시뮬레이션 결과 기존의 규칙기반 제어전략 대비 감소된 에너지 사용량을 보였으며, 전역 최적화된 등가계수를 사용한 경우에 보다 가까운 결과를 나타내었다. 본 논문에서 연구된 제어 전략은 주행 정보 기반의 예측모델을 활용하여 에너지 효율을 향상 시킬 수 있는 최적화 기반 제어 전략이다. 지속적인 연구를 통해 최적화 기반 제어 전략의 상용화가 가능할 것으로 기대된다.Chapter 1. Introduction 1 1.1 Motivation 1 1.2 Background Studies 4 1.3 Contributions 7 1.4 Thesis Outlines 8 Chapter 2. Vehicle Model Development 9 2.1 Target Vehicle 9 2.2 Vehicle Modeling 11 2.2.1 Engine Model 11 2.2.2 Motor Model 12 2.2.3 Battery Model 13 2.2.4 Vehicle Model 15 2.3 Energy Management Strategy 17 2.3.1 Rule-Based Strategy 17 2.3.2 Equivalent Consumption Minimization Strategy 18 2.3.3 Implementation of ECMS 19 2.4 Forward Simulation Environment 22 Chapter 3. Prediction Model Development 23 3.1 Problem Definition 23 3.1.1 Optimal Equivalent Factor 23 3.1.2 Periodic Application of Optimal Equivalent Factor 26 3.1.3 Training Data Preprocessing 31 3.2 Prediction Model based on Driving Information 33 3.2.1 LSTM Model using Time Series Data 33 3.2.2 MLP Model using Feature Data 35 3.2.3 LSTM-MLP Model using Multiple Data 36 Chapter 4. Simulation Analysis 38 4.1 Prediction Model Training 38 4.1.1 LSTM Model using Time Series Data 38 4.1.2 MLP Model using Feature Data 39 4.1.3 LSTM-MLP Model using Multiple Data 41 4.2 Vehicle Simulation using Energy Management Strategy based on Predictive ECMS 43 Chapter 5. Conclusion 53 5.1 Conclusion 53 5.2 Future Work 55Maste