MASTER THESIS. Modelling and Simulation of Vehicle Kinematics and Dynamics. Balaji Kamalakkannan. Final Report. Master Degree

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1 Master Degree MASTER THESIS Modelling and Simulation of Vehicle Kinematics and Dynamics Final Report Balaji Kamalakkannan Embedded and Intelligent Systems Halmstad University, January 13, 2017 May 29, 2017

2 Balaji Kamalakkannan: Modelling and Simulation of Vehicle Kinematics and Dynamics, Final Report

3 A B S T R A C T With the rapid growth in the automotive industry, vehicles have become more complex and sophisticated. Vehicle development today, involves integration of both electrical and mechanical systems. Their design and production are typically time and cost critical. To complement and support the process of vehicle development and design, majority of the automotive industry use modelling and simulation for testing automotive applications, vehicle subsystems or the vehicle behaviour in its entirety. For the purpose of traffic simulations, where a large number of vehicles and other elements of the road network are simulated, implementing a highly complex vehicle model would greatly affect the performance of the simulation. The complexity of the vehicle model would entail a higher computation time of the system, making it unsuitable for any real time application. Therein lies the trade-off in designing a model that is both fast and accurate. The majority of the vehicle models that have been designed are either domain specific, highly complex or generalized. Thus, in this thesis, two class specific vehicles kinematic models with good accuracy and low computation time are presented. Two different modelling paradigms have been adopted to design and test these models. The results, challenges and limitations that pertain to these paradigms are also presented and discussed. The results show the feasibility of the proposed kinematic models. i

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5 C O N T E N T S List of Figures List of Tables Acronyms 1 introduction 1 2 related works Detailed Modelling of Road Vehicles Modelling for Autonomous Vehicles the models Vehicle models using Simulink Model Components Model I: Simple Rear Wheel Drive Model Model II: Rear Wheel Drive Model with Custom Transmission Vehicle models using MATLAB Modelling References Data Extraction Data Fitting Modelling Validation Model results Computation Time Maximum Speed/Acceleration Profile Ranged Speed Profile Effects of simulation step and throttle conclusion & future work Future Work a appendix 53 b appendix 61 bibliography 63 iv vi vii iii

6 L I S T O F F I G U R E S Figure 1 The powertrain block representation[30] Figure 2 Speed profile using default LPF[13] Figure 3 Speed profile from GCDC logged data[13]... 8 Figure 4 Volvo S60 T6[9] Figure 5 Inputs to the models Figure 6 Model I Figure 7 Profiler Report for Model I Figure 8 Speed vs Time Response-Model I Figure 9 Power vs Time Response-Model I Figure 10 Model II Figure 11 Transmission Subsystem[8] Figure 12 Clutch Schedule Subsystem[8] Figure 13 Shift Schedule Subsystem Figure 14 Profiler Report for Model II Figure 15 Speed vs Time Response-Model II Figure 16 Power vs Time Response-Model II Figure 17 Performance Curve of Volvo S60-T6[1] Figure 18 Volvo FH16[10] Figure 19 Performance Curve of Volvo FH16[10] Figure 20 Data Fitting Trial Figure 21 Flow Diagram Figure 22 Profiler Report of Car Model Figure 23 Profiler Report of Truck Model Figure 24 Maximum Speed Profile: Car Figure 25 Maximum Acceleration Profile: Car Figure 26 Maximum Speed Profile: Truck Figure 27 Maximum Acceleration Profile: Truck Figure 28 Ranged Speed Profile I: Car Figure 29 Ranged Speed Profile II: Car Figure 30 Ranged Speed Profile III: Car Figure 31 Ranged Speed Profile I: Truck Figure 32 Ranged Speed Profile II: Truck Figure 33 Ranged Speed Profile III: Truck Figure 34 Varying Simulation Steps: Speed Profile Figure 35 Varying Simulation Steps: Acceleration Profile 48 Figure 36 Varying Throttle levels: Speed Profile Figure 37 Varying Throttle levels: Acceleration Profile.. 49 Figure 38 S-PS Converter iv

7 List of Figures v Figure 39 PS-S Converter Figure 40 Engine Figure 41 Rigid Frame Figure 42 Inertia Module Figure 43 Torque Converter Figure 44 Gear Box Figure 45 Differential Figure 46 Tire Figure 47 Vehicle Body Figure 48 ODE Solver

8 L I S T O F TA B L E S Table 1 Vehicle Specific Parameters: Car & Truck Table 2 Speed profiles of LPF, kinematic & other models: Car Table 3 Speed profiles of LPF & kinematic models: Truck 46 vi

9 A C R O N Y M S ABS CG ECU ESC Anti-Lock Braking System Centre of Gravity Engine Control Unit Electronic Stability Control GCDC Grand Cooperative Driving Challenge LPF Low-Pass Filter ODE Ordinary Differential Equation SI SLR Internation System of Units Static Loaded Radius SUMO Simulation of Urban Mobility SUV TCU Suburban Utility Vehicle Transmission Control Unit VeINS Vehicles in Network Simulation VRML Virtual Reality Modelling Language V2V Vehicle-to-Vehicle vii

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11 I N T R O D U C T I O N 1 Vehicle system development is complicated and requires knowledge from various areas, such as mechanical design, electronics development and control systems. Such systems involve time and cost to develop. Due to this reason, a general vehicle system simulation is a cost-efficient and safe way to test automotive applications. Accurate modelling of the kinematic and/or dynamics behaviours of a vehicle, are required to achieve reasonable simulation results. Heavy trucks and passenger cars have different engine characteristics. Thus, different vehicles react differently to the input signals, which could be from the human driver or automated functions. Besides, electric vehicles might have different characteristics. The goal is to have accurate modelling of different types of vehicles, which could be executed in real-time in existing tools such as Simulation of Urban Mobility (SUMO)[6] or MATLAB/Simulink. However, the idea of using and implementing near real world models for the purpose of achieving realistic responses, is not new. Yet, there remains a trade-off. The prospect of having complex models or keeping the system running at real time. The implementation of the model discussed in the forthcoming chapters, involve not just realistic behaviour, but also, quick response within a desirable time bound. Simulation tools such as Simulation of Urban Mobility (SUMO) and vehicles in network simulation (VeINS)[6][7], are together used to simulate and evaluate realistic road traffic conditions and hence, could sometimes be used for the purpose of traffic forecasting. SUMO is used to generate traffic formations and road conditions, and to study their mobility in the road network. While the Veins simulation framework is used for introducing vehicle-to-vehicle and vehicleto-infrastructure (V2X) communication. However, all vehicles are not same. Trucks are different from sedans, or hatchbacks or suburban utility vehicles (SUVs). There are different parameters to be considered, for not all vehicles alike, for near realistic performance even in the simulation environment. Yet another inhibiting factor to the realistic performance would be the default dynamic responses for the vehicles in the aforementioned software. A simple low-pass filter (LPF) has been used to exhibit the response of the vehicle. This is an elementary modelling of the powertrain of the vehicle, and may not be accurate, and is most likely 1

12 2 introduction not applicable for all vehicles alike. To understand what exactly a powerplant is; in a motor vehicle, the term powertrain or powerplant describes the main components that generate power and deliver it to the road surface, water, or air. This includes the engine, transmission, drive shafts, differentials, and the final drive [31]. Figure 1: The powertrain block representation[30] In the above, Figure 1, the two levels of the overall vehicle control are described. The vehicle level describes the flow of information and control in a vehicle taking the entire powertrain as a module. The powertrain level describes the flow of information and control within a powertrain by considering the major components as modules. My contribution and work intends to address the following ideas: Modelling two class specific vehicles; a semi-trailer and a sedan Achieving a more realistic vehicle behaviour, with reasonable computation time Using MATLAB/Simulink, a more realistic model of a heavy duty truck and a car, are to be created. These models would include the torque output of a vehicle and use the data to compute a realistic velocity-time response, instead of a simple LPF. The results from the class specific vehicle models, are to be contrasted to the LPF model responses. Although the default implementation of the LPF is a step closer to realism, it is not accurate enough. The variation of the kinematic response with time is a function of the different vehicle specific parameters, typically those of the powertrain components. The response

13 introduction 3 depends on the torque output of the vehicle, and the possible surrounding forces like the air resistance, ascents, descents, and other gravitational forces. The idea is to be able to take into account these forces, and reflect their impact on the kinematic response of the vehicle. The vehicles kinematic models are intended for real time simulation purposes. Hence, computation time needs to be maintained as low as possible. To do so, one needs to understand the level of abstraction in the details of a model, that can be overlooked and the details of the model that need to be accurate [13]. To enumerate, the research questions that are answered from the work done in this thesis are: 1. Is the LPF model accurate enough to model the vehicles kinematic behaviour? 2. What are the main differences between the LPF model and the kinematic models? 3. How to design accurate kinematic models for real time applications? To provide a general idea to the flow of text in the upcoming chapters, in Chapter 2, the background work done in this field, alongside their shortcomings, and how the proposed work aims at overcoming the drawbacks or inheriting the established ideas are to be discussed. Further, in Chapter 3, the constructed models are discussed in detail alongside their limitations. The results obtained from the models have been compared and contrasted in Chapter 4, following which the conclusions and possible future work have been stated in Chapter 5. Information pertaining to the model setup have been described in Appendix A and Appendix B.

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15 R E L AT E D W O R K S 2 Accurate and realistic modelling of vehicle kinematics has been made easy with several sophisticated simulation tools. In the following sections the state of the art work in the field of modelling vehicle kinematics have been described. 2.1 detailed modelling of road vehicles Vehicle design is a multidisciplinary concept due to the complexity of the vehicles. Developing such models require the use of cutting edge technology. The trade-off as mentioned in??, is the development of a highly complex system or a system inclined for real time purposes. The level of abstraction of the vehicle model affects the inclination of the vehicle model to one of the above choices. For instance, in [36], a highly detailed and a near replica 3D model of the Mercedes Benz ML270 model had been created. The model of the vehicle at this level of detail had been designed using Autodesk 3ds Max. The model was extracted in Virtual Reality Modelling Language (VRML)[16] format and had been imported to MATLAB by using the inbuilt virtual reality toolbox. The model of the vehicle chosen to work on as a general simulation model for the vehicle system was a four wheel vehicle drive model. The scenario used to test the developed model was to have the car park, in an empty parking space. The model, however, takes only the dimensional aspects of the Mercedes Benz ML270 into account to model, such as the length, width, height and wheelbase measurements. The focus has been minimal on the powertrain or the transmission characteristics of the model. This leaves the vehicle a standalone model in a non interactive environment. To be able to validate the true feasibility of any model, they need to be tested in a realistic environment, and the aim of this thesis, is just that. Unlike a highly detailed superficial modelling, more focus is to be on the fundamentals of what drives a vehicle and attempts to model the mechanical subsystems. Another approach to detailed vehicle modelling is to design all the available mechanical subsystems of a vehicle. For instance, in [21], a vehicle dynamics model had been developed with Modelica as a programming language. The model was designed in the aim of test- 5

16 6 related works ing real time applications with the state of the art driving simulator at the Swedish Road and Traffic Research Institute, also known as VTI. The model hence developed, features several components of the vehicle such as the chassis model, tire model, suspension system, steering system, driveline, braking system and active safety systems such as the Anti-Lock Braking System (ABS) and the Electronic Stability Control (ESC). This particularly complex project was aimed at developing model for the VTI, SimIV simulator. This driving simulator provides a realistic driving experience not only with the 180 view-screen, but also using sound systems and a motion mechanism for the simulation cabin, present in a revamped Volvo V60. This model features a modestly detailed drivetrain subsystem of the vehicle. The exact use of this model will be significantly different from the project at hand simply because of the domain of use. This driving simulator is standalone as well. Unlike our project that features use of the SUMO and VeINS software, this used a more hardware oriented implementation of the model. Nevertheless, the detailed modelling of the several subsystems for the VTI simulator set guidelines for other aspiring work in the field. In the work recorded in [38], the vehicle s kinematic model is represented as a relationship of the forces acting on the vehicle, the acceleration input and the tire models. The simulation results of this model are split based on two scenarios; high speed tests and low speed tests. The vehicle model is tested at high and low speeds, and the speed response is plotted. The variable in the tests is the tire slip ratio. The slip ratio provides a measure of difference in the surface contact speed of the vehicle and the actual angular velocity of the tires. This parameter affects the model response and is highly dependent on the tire parameters. The tires used are modelled using the Pacejka tire formula[15], which is also know as the Magic tire formula. This formula provides an empirical tire model. The effects of slip ratio at different speeds have been recorded and contrasted. Although, the tire parameters affect the vehicle model, it is assumed that, this effect is the only critical factor to modelling a vehicle. There however, are several other factors affecting the vehicle kinematic model, which are discussed in the following section. The complexity of the above models make it cumbersome and unreliable for real time testing with the given hardware. For the purpose of reusing the model that is to be designed, a level of abstraction that neglects a good amount of trivial details is required, as a really complex model could cost as computation time, especially if it is reused. The SUMO environment along with VeINS only support 2D move-

17 2.2 modelling for autonomous vehicles 7 ments, meaning, considering hill-climbs and gradients on the roads are futile [6]. However, the modelling of the drivetrain of the vehicle is strongly advised as it defines the raw vehicle output in the absence of all external forces. 2.2 modelling for autonomous vehicles The following work involved designing of models characterizing kinematic and dynamic for autonomous vehicles. Modelling is not important just for manned vehicles, but is also important in unmanned and autonomous vehicles as those are the vehicles which involve zero on-road human interaction. For instance, in [33], an ideal kinematic model for, four wheeled car like vehicles have been created, based on the Ackerman principle. The Ackerman principle entails the following assumptions [32]: 1. All wheels are not flexible 2. The wheels joined by axes are parallel to the surface 3. All wheels are perpendicular to the surface without deflections 4. Vehicle moves in a planar surface 5. Contact between wheel and surface is a point 6. The wheels rotate in pure motion without slip, brake and slide These assumptions define the amount of abstraction for the given model. The kinematic properties given zero errors are contrasted with certain familiar errors by modifying the kinematic relations. The contrast is then plotted to show plausible real world performance. From a simulation standpoint, the assumptions adopted in [33], are closely related to the environment in SUMO, due to the completely 2D movement. However, external interferences like traction, air resistance and some gravitational forces can be included in the given model to approach realism. Another approach would be the combination of kinematic and dynamic features of the vehicle. Taking a look in [38], the highlights of this given model are that, the computational efficiency is optimized and the suggested model is applicable for all kinds of 4 wheeled vehicles. The entire model is built in MATLAB, as functions. These functions are run in Simulink environment to compute longitudinal, yaw and lateral accelerations. The model allows extraction of other dynamic forces as well. This model sets a threshold for abstraction of

18 8 related works unnecessary model details that could weigh down the computations time due to the complexity. In the work done in [13], the speed profiles generated by the software default LPF, is contrasted to the speed profile plotted from the GCDC logged data. The characteristics of the default LPF model has been exhibited using Plexe. The speed profiles shown below are graphs of speed vs time response of the respective models. Figure 2: Speed profile using default LPF[13] Figure 3: Speed profile from GCDC logged data[13]

19 2.2 modelling for autonomous vehicles 9 By plain observation alone it is convincing, however, the accuracy of this LPF implementation cannot be judged without deeper insight. The speed profile of a real world vehicle depends on aspects that govern its performance such as the drive-train, engine, kerb/combination weights, and other external forces. To suffice, a lot of models are found in literature as both proprietary software and publications. These models usually yield accurate results. The accuracy is due to its highly complex specifications and test domain. However still, these are disadvantageous because: Higher the complexity, lower the computational performance [12][37] Lower the complexity, poorer the accuracy of the results [39][19] Highly specific application bounds and restraints [40][11] The kinematic/dynamic models from the project at hand are intended to replace the defaults in SUMO to evaluate realistic responses. The realistic response is achieved by replacing the LPF with the components governing the vehicle performance. These components are mechanical subsystems. Given the technological advancements, these subsystems are far too complicated and are vehicle specific. Each vehicle manufacturer has their own patented work. Yet, the models can be created using generic components that are universal to all vehicles. To have a realistic evaluation, the models need to replace existing defaults, and at the same time, overcome the aforementioned disadvantages. The trade-off between computational performance and accuracy of the results can be reasonable only by an appropriate level of abstraction.

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21 T H E M O D E L S 3 In this section the models that have been created to study the vehicle dynamics are described. The following models have different levels of abstraction, hence, these models have different computation times. All the simulations were run on the same machine, with the following specifications:- Operating System: Windows 10 Pro 64-bit System Manufacturer: Hewlett-Packard System Model: HP Pavilion 15 Notebook PC BIOS: InsydeH2O Version F.65 Processor: Intel(R) Core(TM) i7-4500u 1.80GHz (4 CPUs), 2.4GHz Memory: 8192MB RAM 3.1 vehicle models using simulink In the recent releases of Simulink by Mathworks, the Simscape Driveline[8] product line has been made available for rapid creation of models of physical systems in the Simulink environment. Simscape provides libraries of components for modelling and simulating mechanical systems. It includes models of drivetrain components, tires, transmissions, engines and torque converters Model Components The components provided by Simscape can be used to model the transmission of mechanical power in helicopter drivetrains, industrial machinery, automotive powertrains, and other applications[8]. The models are designed by closely shadowing the Volvo S60 T6. 11

22 12 the models Figure 4: Volvo S60 T6[9] Since most of the newer vehicles have advanced and proprietary systems, the following models were created using the available information from Volvo s data-sheets and results from tests performed by third party organizations. Furthermore, the engine models used are Simscape defaults, which uses a normalized third order polynomial to simulate the engine response. Input Control: This module is created using the Signal Builder. The inputs to be set are wind speed [m/s], inclination of the road [deg] and the throttle [dimensionless]. Figure 5: Inputs to the models From the driver s perspective, the only input to be provided is the throttle level. The wind speed and road incline are considered as external stimuli, although they are modelled in the same block, for convenience. In order to focus on the mechanical subsystems of the vehicle, the inputs provided are set prior to running the simulation and are kept constant. The following are the settings:- Wind speed: 3 m/s

23 3.1 vehicle models using simulink 13 Inclination: 0 Throttle Level: 1 The value of the throttle can be set in the range of [0,1], with 1 being fully pressed down, and 0 being not pressed at all. The incline, wind speed and throttle input levels are displayed as red, pink and blue lines, respectively in Figure 5 Other components that have been implemented in the following models and the parameters that have been set for experimentation, are described in Appendix A Model I: Simple Rear Wheel Drive Model This Simscape model is designed to achieve the functionality of a a single axle driven car. The components or the functional blocks used to design these models are existent in all combustion engine vehicles. For the purpose of the simulation, the vehicle is driven by its rear wheels. This model, notably consists only of the components, that are required to make the basic vehicle model work (or move). This is done to develop a model with the highest level of abstraction achievable. Although this model constitutes only of the basic components, the component specific parameters such as the vehicle mass, engine peak power, tire rolling radius, etc., have been set to the values corresponding to that of Volvo S60 T6. The torque generated by the prime mover is sent to the torque converter which in turn transfers it to the gear box. The differential connected to the gear box splits the incoming torque equally into the two wheels. As mentioned earlier, the throttle is kept at wide open (fully pressed down), the wind speed is at constant 3 m/s, and the road inclination is set to 0.

24 14 the models Figure 6: Model I The simulation time recorded with Simulink Profiler feature, is as follows: Figure 7: Profiler Report for Model I The recorded time is 1.77 s. Since, the data needs to be transferred to the SUMO environment, an additional delay will be added up in

25 3.1 vehicle models using simulink 15 the socket communication process. To speculate, the overall time to receive the data in the SUMO environment, would be a little over 2 s. This is not a very fast system, as we intend to achieve the overall time consumed in computation and transfer to be at most 1 s, for real time application purposes. The responses derived from the simulations are as follows. Figure 8: Speed vs Time Response-Model I Figure 9: Power vs Time Response-Model I

26 16 the models From the recorded graphs it is observable that, the maximum speed attainable in the model is 90 km/hr, at full throttle. The time taken for the vehicle to attain its top speed is 10 sec. However, this model is relatively less complex, as the gearbox implemented has a single gear. Furthermore, the recorded top speed achieved by Volvo S60 T6 is km/hr[14]. In addition, the power curve decreases exponentialy with time after its global maxima. This characteristic is not true for real world vehicles. This model is moderately fast, but not realistic Model II: Rear Wheel Drive Model with Custom Transmission This Simscape model is designed to achieve the functionality of a rear wheel driven car with a 4 Speed Transmission. Intuitively, it means that the vehicle has 4 gears, enabling it to move forward. The working of this model is similar to that of Model I. Noticeably, the difference is the transmission mechanism. In contrast to a single and continuous gearing, a more complex transmission mechanism is devised. The gears are decided using the shift logic chart[8]. As mentioned earlier, the throttle is kept at wide open (fully pressed down), the wind speed is at constant 3 m/s, and the road inclination is set to 0. Figure 10: Model II

27 3.1 vehicle models using simulink 17 The transmission block consists of five (one for reverse motion) clutches bound to the two planetary gears as shown in Figure 11. Figure 11: Transmission Subsystem[8] The ratios of these gears decide the clutch schedule as shown in Figure 12. The clutch schedule defines which clutch needs to be engaged. This subsystem is a part of an example provided by Mathworks, and has been implemented in this project. These ratios are set to default. Figure 12: Clutch Schedule Subsystem[8] The shift logic subsystem as seen in Figure 13 is a state machine that governs the logic for gear change. There are 3 states corresponding to the selection_state and there are 4 states corresponding to the

28 18 the models gear_state. The Simulink function computes the upshift and downshift thresholds as a function of the currently engaged gear and throttle input level. For instance, assuming the car is initially engaged in 1st gear and has accelerated to its engine speed limit, then the shift logic achieves steady state. Depending on the throttle and the current gear, it decides if the car needs to shift gears, by comparing the thresholds to the current vehicle speed. Since the current vehicle speed is compared with the shift thresholds, it prevents the model from shifting up or shifting down by skipping a gear. Figure 13: Shift Schedule Subsystem In the real world model of the Volvo S60 T6, the transmission design is a proprietary 8 Speed Geartronic Transmission[9]. The gear mechanism, clutch schedules and shift schedules are not for public view, hence, the fidelity of this complex model is limited to a generic 4 Speed Transmission. Furthermore, most newer vehicles are equipped with advanced safety systems, an engine control unit (ECU) and a transmission control unit (TCU). Modelling these advanced features would definitely improve the model fidelity, however, the computation time would be affected.

29 3.1 vehicle models using simulink 19 The simulation time recorded with Simulink Profiler feature, is as follows: Figure 14: Profiler Report for Model II The recorded time is 8.36 s, which is undoubtedly high for real time applications. This is due to the relatively complex powertrain model. The responses derived from the simulations are as follows. Figure 15: Speed vs Time Response-Model II

30 20 the models Figure 16: Power vs Time Response-Model II From the profiler result it can be observed that 100 more components had to be appended to Model I to achieve high fidelity. From the recorded graphs it is observable that, the maximum speed attainable in the model is 240 km/hr (accurately km/hr), at full throttle. It is close to the real world model s top speed, km/hr. The time taken for this model to attain its top speed is 50 sec. It also reaches the top speed of Model I, 90 km/hr, in 5.4 s. Furthermore, the power generated in the engine peaks at 216 kw, and the recorded peak power of Volvo S60 T6 is 223 kw[14]. This model closely resembles the real world car, however, it is far too complex as the gearbox implemented, involves a state machine and its corresponding logical computations. This realism leaves us with a high computation time. To summarise, Model I is moderately fast, but unrealistic. Model II is very slow, but realistic. The following section describes another modelling approach that has been followed to create models using MATLAB language. 3.2 vehicle models using matlab Modelling with the functional blocks provided by Simscape in the Simulink environment, has proven to be rather unsuitable for the intended real time simulations. Hence, in this approach, mathematical equations are used instead of blocks. Instead of using the Simulink

31 3.2 vehicle models using matlab 21 environment to design the model, programming is done in the MAT- LAB environment. There however exists, one main difference in the paradigms followed for designing the aforementioned models and the model described below. In the models in Section 3.1, functional blocks are combined together to design the powertrain of the vehicle. These function blocks are subsystems or components, and are combined to form a complex system. Hence, it is bottom-up approach to modelling. In the modelling approach discussed below, the powertrain of the vehicle is not designed by integrating subsystems, but derived from the powertrain performance graphs of real world cars. The powertrain performance graph is also known as a performance curve or a dyno plot. The performance graph is a document of the recorded performance of the powertrain, in terms of producing power and torque, under a given condition[3]. Using MATLAB curve fitting tools, equations pertaining to the model the vehicle s powertrain have been derived. In contrast to Model I and Model II, the entire system is modelled from existing powertrain curves instead of integrating individual blocks. Hence, the following is a top-down approach to modelling Modelling References To compare the fidelity of the model designed by this approach, the model of Volvo S60 response is intended to be compared to the responses of Model I and Model II. Apart from the modelling of a the car s powertrain, an attempt has been made to design the semitrailer tractor s powertrain, using the same approach. The actual car is shown in Figure 4, and the actual truck is shown in Figure 18. These models are described below VOLVO S60-T6 The following performance curve is implemented to create the powertrain model. This curve has been recorded by BSR Svenska AB for the Volvo S60-T6 model. This T6 engine model is currently being implemented in the Volvo S60 series[9]. The units adopted by BSR Svenska AB for the measurements are:- Power: HP Torque: Nm Engine Speed: RPM

32 22 the models Figure 17: Performance Curve of Volvo S60-T6[1] The performance curve depicts the performance of the stock powertrain model as well as the optimized powertrain model. The stock performance model is expressed as dashed lines and the optimized performance model is expressed as normal lines. In Figure 17, the power vs engine speed responses and the torque vs engine speed responses are indicated by red and blue lines, respectively. For the simulation purpose, the optimized responses are used VOLVO FH16 Unlike the Volvo car, the Volvo truck performance graphs are available in the Volvo database[10]. However, these graphs correspond only to the kerb weight of the tractor and the weight of one human.

33 3.2 vehicle models using matlab 23 Figure 18: Volvo FH16[10] The gross combination weight effects of the trailer attachment have not been recorded. Thus, for the simulation purpose, only the tractor is taken into account. Hence, using the following performance graph of the tractor s powertrain, a model is designed. The units adopted by Volvo Trucks for the measurements are:- Power: HP Torque: lb-ft Engine Speed: RPM In contrast to the third party powertrain curve obtained for the Volvo car, the following curve does not have optimizations. It has been recorded using the truck s stock components.

34 24 the models Figure 19: Performance Curve of Volvo FH16[10] In Figure 19, the power vs engine speed response and the torque vs engine speed response are indicated by blue and green lines, respectively Data Extraction From the performance graphs in Figure 17 and Figure 19, the mathematical relationship between the torque and engine speed needs to derived. For this purpose, data needs to be extracted from these graphs. In order to extract the data, the image files of these graphs need to be digitized. The WebPlotDigitizer application has been used for this purpose. More information pertaining to this application is described in Appendix B. Unlike the Simulink environment, which assists in a heterogenous input for the units of different variables, the MATLAB environment relies on the uniformity of the units, as the focus is laid on the equations governing the model alone. For the purpose of the simulation, the International System of Units (SI) has been adopted. The units are as follows:- Power: W Torque: Nm Engine Speed: rad/s Physical Dimensions: m

35 3.2 vehicle models using matlab 25 The equations mentioned below were used to convert the nonstandard units to SI units. 1. To convert Horsepower to Watts: 1[HP] = 745.7[W] (1) 2. To convert Foot-Pound to Newton-Metre: 1[lb ft] = [Nm] (2) 3. To convert Revolutions per minute to Radians per second: 1[RPM] = [rad/s] (3) After converting the extracted data into SI units, they were imported to the MATLAB workspace Data Fitting Data fitting is the process of fitting models to a set of data and manipulating the accuracy of the fitting models[2]. To relate the data points, an empirical form of the equation, or the fitting model would appear as: torque = function(engine_speed) (4) The concern with the data fitting model is the compensation between the accuracy of the equation and the complexity of the fitting model. Since the performance curves are derived from a complex powertrain model, it is unlikely that a lower order polynomial equation would be an accurate fit. Simultaneously, since an ODE solver would be implemented in the model for the computation of the speed vs time response, and a highly complex model would slow down the computations. By testing the accuracy of the fit, the equations derived can be seen in Figure 20.

36 26 the models Figure 20: Data Fitting Trial The actual plotted data points are represented by the blue line, while the fitting models of the 5 th and 10 th order are red and green lines, respectively. In the equations below, x denotes the engine speed and y denotes the torque output. The equation for the 5 th order fitting model is of the form, where p1 to p6 are coefficients: y = p1 x 5 + p2 x 4 + p3 x 3 + p4 x 2 + p5 x + p6 (5) The equation for the 10 th order fitting model is of the form, where p1 to p11 are coefficients: y = p1 x 10 + p2 x 9 + p3 x 8 + p4 x 7 + p5 x 6 + p6 x 5 + p7 x 4 + p8 x 3 + p9 x 2 + p10 x + p11 From the graph, it can be observed that the 10 th order model is more accurate than the 5 th order model. However, a 10 th order model would add up to the time required to solve the ODE. To assess the goodness of a fitting model, MATLAB provides a norm of residuals function. The lower the value of the residuals, the better the fit. The residual value is a measure of the outliers in the model. An outlier is (6)

37 3.2 vehicle models using matlab 27 an observation that lies in an abnormal distance from other values in a sample of data. An acceptable residual value is considered to be in the range of [0,10][2]. However, the residual value for the 5 th order model is and the residual value for the 10 th order model is (residual values are not shown). Clearly, both the residual values are higher than the limits for a quality model. In order to surpass this issue and have an reasonable complexity, the performance curve has been split into parts, with the apparent maximas or peaks as delimiters, and the least complex fitting model with residual value below 10, is chosen. The equations that have been derived for the powertrain performance graphs are listed below. In the equations in the subsections to follow: w denotes the engine speed [rad/s] T denotes the torque output [Nm] Equations for VOLVO S60-T6 in Figure 17 if w >= 0 and w < T = w w ; (7) if w >= and w < T = e 07 w w w w (8) if w >= and w <= T = e 08 w w w w (9) if w < 0 and w > T = 0 (10) If the engine speed exceeds rad/s or goes below 0 rad/s, the torque produced is blended to 0 Nm. This is analogous to the stall speed and the maximum engine speed parameters used in the Simscape models Equations for VOLVO FH16 in Figure 19 if w >= 0 and w < T = 40 w (11)

38 28 the models if w >= and w < T = w (12) if w >= and w <= T = w w w (13) if w > and w <= T = w (14) if w > T = 0 (15) If the engine speed exceeds rad/s or goes below 0 rad/s, the torque produced is blended to 0 Nm. This is analogous to the stall speed and the maximum engine speed parameters used in the Simscape models Modelling To model the equations presented in Section and Section , MATLAB function files are used. The flow of data in MATLAB is represented in Figure 22.

39 3.2 vehicle models using matlab 29 Figure 21: Flow Diagram The following subsections explain in detail, the computation process and the parameters involved in achieving the kinematic response of the vehicle s model File 1: Powertrain In this file, the powerplant characteristic equations as described in Section and Section , are implemented using conditional

40 30 the models statements. The input and output parameters to this file are as follows:- Input: Engine Speed [rad/s] Output: Torque [Nm] The engine models described earlier are integrated into a single file and are chosen depending upon the type of the ego vehicle. The ego vehicle is the vehicle whose characteristics are intended to be observed. This file requires the most computation time as the ODE solver calls it numerous times to compute the produced torque for the vehicle to move forward. Thus, the complexity of the equations governing the relationship between the engine speed and the produced torque, need to be simple and accurate, simultaneously File 2: Acceleration In this file, the acceleration of the vehicle is computed. The acceleration is computed as a function of the vehicle s velocity and the forces acting on it. The input and output parameters to this file are as follows:- Input: Current time [s], Velocity at current time [m/s] & Torque [Nm] Output: Acceleration [m/s²] All the vehicle characteristics are specified in this file, except for the powerplant characteristics, which are specified in File 1 as mentioned in Section Some of the constant parameters for all the models are as follows:- Acceleration due to Gravity (g): m/s² Mass of Human: 70 kg Air Density (ρ): kg/m³ The acceleration gained by an object because of gravitational force is called its acceleration due to gravity. It is constant for all objects that are in contact with the Earth s surface. Also, it is considered that only one person is present in the vehicles. Since no mechanical system is 100% efficient, the powertrain models are set to be 90% efficient. The vehicle specific parameters for the Volvo S60-T6 and Volvo FH16 are [10][9][23]:-

41 3.2 vehicle models using matlab 31 Vehicle Specifics Parameters Car Truck Kerb Weight (m k ) [kg] Gross Weight (m) [kg] Frontal Area (a) [m²] Tire Specification P235/40VR18 315/80R22.5 Final Drive Axle Ratio (i f ) Rolling Resistance Coefficient (u r ) Friction Coefficient (u f ) Drag Coefficient (c d ) Gear Ratios (i g ) 3.03/1.95/1.46/1.22/ Table 1: Vehicle Specific Parameters: Car & Truck In the equations, the following symbols are chosen to represent the parameters:- Powertrain Efficiency: η Static Rolling Radius: SLR Relative Velocity: v Torque: τ Road Incline: θ Number of driving wheels: n w The following are the equations that implement the above parameters for the computation of the net force experienced by the vehicle. 1. Friction Force (F f ): This represents the force opposing the relative motion of the vehicle. The coefficient of this force is characterized by the surface on which the vehicle is being driven[17]. F f = u f m g sinθ (16) 2. Rolling Resistance Force (F r ): This represents the force generated in the tires. The non-elastic effects that are experienced due to the hysterical losses in the compression and expansion of the tire region which is in contact with the road surface[23], account for this force. The coefficient of this force is characterized by the type of the vehicle and the type of its tire. F r = u r m g (17)

42 32 the models 3. Aerodynamic Drag Force (F a ): This represents a force acting opposite to the relative motion of any object moving with respect to the surrounding air. The drag force is proportional to the frontal area of the vehicle and the square of its relative velocity[27]. F a = 0.5 ρ c d a v 2 (18) 4. Gradient Force (F g ): This represents a force acting on a vehicle on an inclined plane. If the vehicle is on an ascending slope it acts against the vehicle, and if the vehicle is on a descending slop it acts in favour of the vehicle[28]. F g = m g sinθ (19) This force can be used to demonstrate the vehicle behaviour while moving up a hill or down a hill. 5. Traction Force (F t ): This represents a force that is generated by the engine, allowing the vehicle to move. This force is characterized the powertrain components of the vehicle. This is the main driving force of the vehicle. The throttle level lies in [0,1]. It defines the amount of throttle valve being opened. The value of throttle level is directly proportional to the traction force. F t = η n w i g i f throttle τ/slr (20) The Torque in Equation 23, is received from File 1 as mentioned in Section The Static Loaded Radius or the rolling radius (SLR) is the radius of the vehicle when there is a fixed load applied on it. Due to the compression of the tire, the actual radius of the tire will be slightly higher than its SLR. The general convention for tire specification is of the following format: P(nominalwidth[mm])/(aspectratio)R(rimdiameter[in]) (21) To compute the SLR, the following parameters must be calculated: a) b) depth = (aspectratio) (nominalwidth)/100 (22) rimouterradius = (rimdiameter[mm])/2 (23)

43 3.3 validation model 33 From Equation 25 and Equation 26, the SLR can be calculated as[5]: SLR = 0.96 (depth + rimouterradius) (24) Using Equation 27, the SLR of the vehicles have been calculated to be: Volvo S60 T6: m Volvo FH16: m From Equations 19-27, the net force acting on the vehicle is given as: F net = F t (F f + F r + F a + F g ) (25) Using Newtons s Second Law of motion which states that in an inertial reference frame, the vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration a of the object, the acceleration of the vehicle can be computed. Mathematically, F net = mass acceleration (26) File 3: Speed vs Time Response In this file, the speed and the position of the vehicle are computed. They are computed as a function of time. The input and output parameters to this file are as follows:- Input: Initial Velocity[m/s] & Run-Time[s] Output: Final Velocity[m/s] & Distance[m] In essence, this file calls ode45(), an ODE solver. This solver calls File 2 to integrate the acceleration computed in the given time limits with the set time step (0.01 s), to compute the velocity. File 2 calls File 1 to compute the torque produced by the powertrain model. Furthermore, the error tolerance of the ODE solver can be manipulated, from the default precision (1e-3). This may take longer to run as a result, but would be more accurate for a non-smooth powerplant characteristic. 3.3 validation model To compare the models of the car and the truck as described in Section 3.2, the LPF model that has been implemented in SUMO, is modeled in this section, as described in??.

44 34 the models The usage of LPF in the SUMO environment is achieved using a speed controller model[35]. The desired acceleration of the vehicle is considered to be the control parameter for longitudinal motion in this environment. The controller is implemented based on certain fundamental physics of controlling motion. The controller used for the purpose is the classic Cruise Control[26]. This model has been commercially implemented in several vehicles as of today. This controller allows the driver to select and maintain a desired speed, by taking over the throttle mechanism of the vehicle. The equation[35] governing this controller is a des = k(v v des ) + ζ (27) where a des is the desired acceleration, v is the current speed, v des is the desired speed. k is the gain of the cruise controller, which is set to 1 by default. ζ corresponds to random disturbances that might affect the controller performance, which is set to 0 by default. Using the above equation, the acceleration at the n th time step is computed as where a[n] = β a des [n] + (1 β) a[n 1] (28) β = t/(γ + t) (29) Acceleration at the n th time step is computed based on a des, which is computed by the controller, and the acceleration at n 1 th time step. In the above equation, t is the increment value of every time step and γ represents the time constant. The default values assigned by SUMO for these temporal parameters are: Simulation time-step ( t) : 0.01 s Time constant (γ) : 0.5 s Incorporating the above equations, velocity at a given time step n is computed as v[n] = v[n 1] + a[n] t (30) A ceiling value and a floor value for acceleration are applied to all vehicles in SUMO[6], and hence, the acceleration of the vehicle at any point is limited as a [a min, a max ]. These values that are set by SUMO, depend on the type of the vehicle. The default a min and a max values for a passenger car are -7.5 m/s²and 2.9 m/s², respectively. The default a min and a max values

45 3.3 validation model 35 for a truck are -4 m/s²and 1.3 m/s², respectively[6]. These limits are used to model an average human-comfort behaviour. Nonetheless, these values are not the actual physical limits to the vehicles. To compare, the same limits have been incorporated in the models described in Section 3.2, as well. In Chapter 4, the speed vs time and acceleration vs time responses of the models presented in Section 3.2 have been compared and contrasted to the LPF model described above. It is important to note that the default temporal parameter values, as mentioned in Section 3.3, have been overridden as: Simulation time-step ( t) : 0.1 s Time constant (γ) : 0.3 s

46

47 R E S U LT S 4 In this section, results recorded by comparing and contrasting the models in Section 3.2 and Section 3.3 have been described. The different comparison aspects have been elaborated below. 4.1 computation time The computation time plays an important factor in the feasibility of the model, because, as seen in Section 3.1, a complex model costs the system as computation time. Hence, these kinds of models are unsuitable for real time application purposes. However, the recorded computation time of the models in Section 3.2 are shown in Figure 22 and Figure 23. Figure 22: Profiler Report of Car Model 37

48 38 results Figure 23: Profiler Report of Truck Model The total time taken for the models to compute is the sum of time taken by all the child processes and functions that have been called. The total time of the car model is recorded to be s and the total time of the truck model is recorded to be s. The major contributor for the computation time is the ODE45 solver. This solver calls the function handle that computes acceleration. It can be observed that the function handle is called 3998 times and 2996 times, for the car and the truck models respectively. The velocity computed is by numerically solving the ODE, where acceleration is represented as dv/dt. In contrast to the Figure 7 and Figure 10, it can be observed in Figure 22 and Figure 23 that this modelling paradigm has taken lesser time to compute, and is in the order of milliseconds. These models, are hence, suitable for being used for real time simulation purpose.

49 4.2 maximum speed/acceleration profile maximum speed/acceleration profile Maximum Speed/Acceleration Profile displays the maximum speed vs time and the maximum acceleration vs time responses of the vehicle. This aspect of comparison highlights the accuracy of the models to the real world vehicle. The LPF model was also set to exhibit behaviour for the same speed range. The responses corresponding to the car model are as shown below. Figure 24: Maximum Speed Profile: Car

50 40 results Figure 25: Maximum Acceleration Profile: Car The red dashed line represents the LPF model response while the kinematic model response is represented by the blue dot-dashed line. The recorded maximum speed of the car model is km/h, while the real world model tops at km/h[14]. This difference can be attributed to the rather simple 4 speed transmission that has been implemented in the kinematic model as opposed to the proprietary Geartronic 8 speed transmission[9] used by Volvo in the real world model. However, it can be observed that the LPF model reaches the target speed faster than the kinematic model in Figure 24. It is important to note that the ceiling and floor limits for acceleration have been applied to the vehicles, as mentioned in Section 3.3. In Figure 25, it can be observed that the acceleration reaches the ceiling limit for the LPF model instantaneously, as opposed to the smooth curve in the kinematic model. Also, the decrease in acceleration is gradual as opposed to the LPF model. This is because, the acceleration of the car model, depends on the forces acting on it, causing this non linear effect. In contrast, the LPF model uses a cruise controller to compute the acceleration. It is important to note that, while the real world car takes 8 s to go from km/h[14], the LPF model takes 7.6 s and the kinematic model takes 8.8 s. The responses corresponding to the truck model are as shown below.

51 4.2 maximum speed/acceleration profile 41 Figure 26: Maximum Speed Profile: Truck Figure 27: Maximum Acceleration Profile: Truck Similar to the car model, the truck model had been implemented with ceiling and floor limits to the acceleration. It can be observed that the LPF reaches the target speed much faster than the truck model. The real world FH16 truck takes 40 s to reach its top speed of km/h[4], while the kinematic model takes s and the LPF model takes s, to reach km/h. The LPF model response is rather unrealistic in the case of a truck. The mass of the truck and

52 42 results the increased effective external forces play an important role in the kinematic response of the truck. The LPF fails to emulate this realistic behaviour because it does not consider the mass or the external forces acting on the vehicle. The acceleration responses have the non linear effect due to the gear ratios, similar occurrence as observed in the car model. 4.3 ranged speed profile Ranged Speed Profile displays the speed vs time response for relatively small transitions in speed. This aspect of comparison sheds more focus on the effect of gear ratios in speed transitions. For all the transitions below, the throttle position is set to 80%. The following are the responses of the car model. Figure 28: Ranged Speed Profile I: Car In Figure 28, the car goes from 30 km/h to 50 km/h. The car shifts gear at 45 km/h and the gear ratio is changed from 1.46 to It can be observed that the LPF model leads the kinematic model by a small margin.

53 4.3 ranged speed profile 43 Figure 29: Ranged Speed Profile II: Car In Figure 29, the car goes from 50 km/h to 80 km/h. The car shifts gear at 75 km/h and the gear ratio is changed from 1.22 to It can be observed that the kinematic model leads the LPF model. Figure 30: Ranged Speed Profile III: Car In Figure 30, the car goes from 70 km/h to 120 km/h. The car shifts gear at 75 km/h and the gear ratio is changed from 1.22 to It can be observed that the kinematic model leads the LPF model.

54 44 results Model Time [s] 0-Max [km/h] Speed Ranges [km/h] [km/h] [km/h] LPF Kinematic Simscape II Real World 24.3* n/a Table 2: Speed profiles of LPF, kinematic & other models: Car From Table 2 we can observe that, while comparing the real world model of the Volvo S60 T6, the kinematic model has a more realistic response than the LPF model, while transitioning from 0 to top speed[14]. It can also be observed that, with higher initial speed the models tend to perform alike. The data pertaining to the real world model of the vehicle is available on third party performance testing industries[25]. Furthermore, the Simscape model described in Section has also been used to contrast the speed profiles of the LPF and the kinematic models. (*)- In the third party tests performed, the real world model was fitted with a speed governor, limiting its top speed to 200 km/h. Unlike profiles pertaining to the car above, the truck modelling has been implemented with a fixed intermediate gear ratio of 0.78, as described in Section The following are the responses of the truck model.

55 4.3 ranged speed profile 45 Figure 31: Ranged Speed Profile I: Truck Figure 31 represents speed transition from 0 km/h to 20 km/h. It can be observed that the kinematic model leads the LPF model. Figure 32: Ranged Speed Profile II: Truck Figure 32 represents speed transition from 80 km/h to 125 km/h. It can be observed that the kinematic model leads the LPF model.

56 46 results Figure 33: Ranged Speed Profile III: Truck Figure 33 represents speed transition from 50 km/h to 80 km/h. It can be observed that the kinematic model leads the LPF model. Model Time [s] 0-Max [km/h] Speed Ranges 0-20 [km/h] [km/h] LPF [km/h] Kinematic Table 3: Speed profiles of LPF & kinematic models: Truck From Table 3 it can be observed that the LPF model has a highly unrealistic response for the transition from 0 to top speed, as the real world model takes 40 s to reach the top speed of km/h. In contrast, the kinematic model has a more realistic response to the real world truck[4]. The speed profiles for the other speed ranges do not exhibit any significant discrepancies. From Figures 39-44, it can be observed that the speed vs time responses of the car and the truck are similar to that of the LPF model, except for certain speed ranges. This is attributed to the fact that, in the kinematic model, the acceleration is computed as a function of the net force acting on the vehicle. In turn, the net force acts as a function of the torque produced. The torque curves for the car and truck are shown in Figure 17 and Figure 19, respectively. Due to this

57 4.4 effects of simulation step and throttle 47 dependency on the vehicles powertrain characteristics, they model the real world vehicle better than the LPF model. 4.4 effects of simulation step and throttle In the LPF model configuration, the choice of simulation step alters the slope of the speed vs time, and the acceleration vs time responses. This effect is exhibited in the figures below. Figure 34: Varying Simulation Steps: Speed Profile

58 48 results Figure 35: Varying Simulation Steps: Acceleration Profile Figure 34 and Figure 35 exhibit the effect of different simulation step values in the speed and acceleration profiles. In both the figures, blue dashed line corresponds to a simulation step of 0.1 s, red dashed line corresponds to a simulation step of 0.2 s and yellow dashed line corresponds to a simulation step of 0.05 s. It can be observed that as the choice of simulation step value decreases, the slope of the speed vs time response increases. In the acceleration profile it can be observed that, with the decrease in the value of the simulation step, the time taken to reach the acceleration ceiling increases, and hence, the general decrease in the slope of the acceleration profile. The default choice of simulation step in SUMO is 0.01 s. Analogously, the simulation step can be related to the cutoff frequency of the LPF; simulation step of 0.01 s is analogous to a cutoff frequency of 100 Hz. This implies that, for every simulation step, 0.01 sec of real time is simulated. For the purpose of simulation, all responses shown in Section 4.2 and Section 4.3 have been used with a time step of 0.1 s or cutoff frequency of 10 Hz. For the purpose of demonstrating the effect of different throttle levels, the kinematic model of the car has been used, and the observations recorded are as shown below.

59 4.4 effects of simulation step and throttle 49 Figure 36: Varying Throttle levels: Speed Profile Figure 37: Varying Throttle levels: Acceleration Profile Analogous to the simulation step in the LPF model the kinematic model has a parameter that can be varied. This parameter is the throttle level. In a simple throttle, the throttle level acts as a gain to the torque generated by the engine[20]. This value is thus set in the range as, throttle level [0,1]. In Figure 36 and Figure 37, blue line corresponds to 0.50, red line corresponds to 0.60, yellow line corresponds

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