Journal of Advanced Transportation

Volume 2018, Article ID 3614025, 20 pages

https://doi.org/10.1155/2018/3614025

## Model-Based Optimization of Velocity Strategy for Lightweight Electric Racing Cars

Silesian University of Technology, Institute of Fundamentals of Machinery Design, 18A Konarskiego Street, 44-100 Gliwice, Poland

Correspondence should be addressed to Wojciech Skarka; lp.lslop@akrakS.hceicjoW

Received 17 December 2017; Revised 24 April 2018; Accepted 10 May 2018; Published 7 June 2018

Academic Editor: Sara Moridpour

Copyright © 2018 Mirosław Targosz et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The article presents a method for optimizing driving strategies aimed at minimizing energy consumption while driving. The method was developed for the needs of an electric powered racing vehicle built for the purposes of the Shell Eco-marathon (SEM), the most famous and largest race of energy efficient vehicles. Model-based optimization was used to determine the driving strategy. The numerical model was elaborated in* Simulink *environment, which includes both the electric vehicle model and the environment, i.e., the race track as well as the vehicle environment and the atmospheric conditions. The vehicle model itself includes vehicle dynamic model, numerical model describing issues concerning resistance of rolling tire, resistance of the propulsion system, aerodynamic phenomena, model of the electric motor, and control system. For the purpose of identifying design and functional features of individual subassemblies and components, numerical and stand tests were carried out. The model itself was tested on the research tracks to tune the model and determine the calculation parameters. The evolutionary algorithms, which are available in the* MATLAB Global Optimization Toolbox*, were used for optimization. In the race conditions, the model was verified during SEM races in Rotterdam where the race vehicle scored the result consistent with the results of simulation calculations. In the following years, the experience gathered by the team gave us the vice Championship in the SEM 2016 in London.

#### 1. Introduction

The issue of energy saving in road transport is getting more and more important. It is especially significant in the context of electric drives in vehicles becoming widespread. Reduction of energy consumption together with the development of new energy sources of greater capacity is seen as a method of overcoming the main limitation of electric vehicles which is range.* Shell Eco-marathon* car race is the testing ground for new solutions in designing energy saving vehicles. A team of scientists and students from the Silesian University of Technology has been taking part in it since 2012, in energy saving vehicles with electric drives, which are designed and built by them in the following categories: Prototype, UrbanConcept with Battery Electric, and UrbanConcept with Hydrogen Fuel Cell Stack. Significant reduction in energy consumption is achieved by the usage of two methods [1]. The first one includes design changes which result in lower energy consumption whereas the latter one introduces new strategies of driving and drive steering, which allows minimalizing the energy consumption on a given route. By means of this method, it is possible to reduce considerably the energy consumption in vehicles and in particular in electric vehicles. Currently, electric vehicles (city cars: segment B) can reach the result of about 5km/kWh of energy, whereas respective vehicles of UrbanConcept Battery Electric category reach up to 200 km/kWh in simulated conditions of driving in a city. However, prototype battery electric vehicles which are different type as far as their structure is concerned reach the result of 1000 km/kWh. It shows the potential of the design solutions and the strategy of driving. In both categories numerical simulation vehicle models are used, which allow determining the direction of designing changes as well as planning the proper strategy of driving. These models are also used for optimization based on Model-Based Optimization methodology (MBO). This proprietary methodology used for vehicles development and planning the driving strategy has been described in this paper. Vehicles modelling and in particular electric vehicles modelling are widely known and become of an increased interest to research, in particular with hybrid drive or power source. The necessity to model phenomena and objects is commonly known and creates substantial branch of science and engineering activities. The research and analysis of mechanical systems, technological processes, and other phenomena in real world are possible thanks to the use of proper mathematical apparatus which is based on previously assumed mathematical models of these processes [2]. According to this, by means of mathematical model, one should understand mathematical description of an object, process, or phenomenon which it represents.

Compared to cars with internal combustion engines, electric cars have a relatively simpler drive system; however, in order to achieve a significant reduction in energy consumption in the electric car's drive system, additional systems such as the energy recovery system, additional mechatronic subsystems, and advanced control systems are integrated, resulting in a continuous increase in the complexity of the electric drive systems currently used. The complexity of the technical means influences the complexity of the mathematical model of the vehicle. Among the models describing the dynamics of vehicles, which are used in the analysis and optimization of energy consumption, two approaches are generally observed due to the type of model used and the following models are distinguished:(i)Analytical ones in which the model response to the signal is recorded as a motion equation(ii)Models in the black box concept where the model is based on experimental data

The created vehicle simulation model can be a combination of two model types. To some extent, the mathematical description of a given phenomenon is based on known dependencies, while another fragment of the model is created in the concept of a black box. Taking into account the direction of information processing in the model, the following models [3] are distinguished:(i)Simple: where the calculations made by the model start with the engine, energy is transferred to the wheels of the vehicle, and vehicle behaviour can be analyzed(ii)Reverse: in which the behaviour of the body of the vehicle is modelled, e.g., the speed, and on this basis the required torque and the speed of rotation of the motor shaft are determined.

The choice of model type is mainly determined by the need for which the model is to be used. For modelling of dynamics of electric vehicles, many computer programs are used; among them noteworthy is the* ADVISOR* (*Advanced Vehicle Simulator*) platform [4–6] written as a program in the* MATLAB*-*Simulink* package. The program in its libraries gives you the opportunity to analyze many of the solutions of the power system, drive system, or vehicle body. Another platform running in the* MATLAB*-*Simulink* environment is* PSAT* (*The Powertrain System Analysis Toolkit*), which simulates many predefined solutions for conventional, electric, and other vehicles [7]. The evolution of* PSAT* is* Autonomy* [8] available on* LMS Imagine.Lab*. In addition to these simulation environments, where models are abstract and which take into account the mechatronic nature of the electric vehicle's propulsion system, there are many specialized dynamic analysis programs utilizing the multibody formalism, such as the* LS-Dyna*,* Adams*, or* MotionSolve* software. Simulation models designed to analyze and optimize energy consumption should allow for less time consuming calculations. This is especially important in optimization tasks, where simulation is performed many times (often over several tens of thousands of times). You can say that the faster the model is, the more abstract it is. In paper [9], this is demonstrated by the synchronous motor, written in* MATLAB* and* Simplorer*. In order to reduce the computational time, the model should be written in a low-level language, e.g.,* C*, as given in [10] and the simulation time can be reduced by up to 20 times compared to a program written in* MATLAB's* own language.

#### 2. Research Methodology

In order to optimize the control strategy for a light, electric racing vehicle, the general methodology described below is presented, which explains the basic ideas and above all the definitions of the key concepts from energy consumption domain. The general functional structure of the drive system with particular attention to drive control and the optimization scheme are also presented below.

*Energy Consumption E of the Movement*. Movement of the vehicle is a consequence of the longitudinal force, which overcoming the force of inertia and resistance against the movement performs work on a particular road section [12]. The energy that is associated with this work is called energy intensity and, in the case of wheeled vehicles, it can be expressed as where* F*_{N}* is *driving force and* D*_{C} is travelled distance.

Energy consumption of the movement determines the amount of energy supplied to the drive wheels and** does not depend on the nature of the drive unit and the transmission**.

*Total Energy Consumption E*_{c}. It determines total energy expenditure. In the case of an internal combustion engine unit expressed as the product of the fuel and its calorific value, or in the case of an electrical unit, the energy is taken from an electric source.* Total energy consumption E*_{c} is the sum of the energy consumption* E* and the power losses in the motor* ΔE*_{m} and in the transmission system* ΔE*_{TS} [12]:The losses from (2) are usually taken into account in* efficiency η:*

The overall efficiency of the drive system is the product of the motor efficiency *η*_{m} and the efficiency of the transmission *η*_{TS}:

The total energy consumption* E*_{c}, of the process, which is defined as driving of the given distance* D*_{C}, is influenced by many factors, the vehicle's structural parameters, the energy losses generated when generating and transmitting the driving torque, and the control method. A function describing the speed of a vehicle along a certain route is the so-called speed profile [12, 13]. The speed profile is usually determined by the driver of the vehicle, by means of appropriate accelerator pedal control and shift gear selection or by electronic control. A cruise control system controls the power delivered to the drive wheels in order to maintain a certain speed.

If the vehicle is equipped with one drive system, it can be presented in the functional diagram as shown in Figure 1.