MASTER

THESIS

Master Degree

Modelling and Simulation of Vehicle Kinematicsand Dynamics

Final Report

Balaji Kamalakkannan

Embedded and Intelligent Systems

Halmstad University, January 13, 2017– May 29, 2017

Balaji Kamalakkannan: Modelling and Simulation of Vehicle Kinematicsand Dynamics, Final Report ©

A B S T R A C T

With the rapid growth in the automotive industry, vehicles have be-come more complex and sophisticated. Vehicle development today,involves integration of both electrical and mechanical systems. Theirdesign and production are typically time and cost critical. To com-plement and support the process of vehicle development and design,majority of the automotive industry use modelling and simulationfor testing automotive applications, vehicle subsystems or the vehiclebehaviour in its entirety.

For the purpose of traffic simulations, where a large number ofvehicles and other elements of the road network are simulated, im-plementing a highly complex vehicle model would greatly affect theperformance of the simulation. The complexity of the vehicle modelwould entail a higher computation time of the system, making it un-suitable for any real time application. Therein lies the trade-off indesigning a model that is both fast and accurate. The majority of thevehicle models that have been designed are either domain specific,highly complex or generalized. Thus, in this thesis, two class specificvehicles’ kinematic models with good accuracy and low computationtime are presented.

Two different modelling paradigms have been adopted to designand test these models. The results, challenges and limitations thatpertain to these paradigms are also presented and discussed. Theresults show the feasibility of the proposed kinematic models.

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C O N T E N T S

List of Figures ivList of Tables viAcronyms vii1 introduction 1

2 related works 52.1 Detailed Modelling of Road Vehicles . . . . . . . . . . . 52.2 Modelling for Autonomous Vehicles . . . . . . . . . . . 7

3 the models 113.1 Vehicle models using Simulink . . . . . . . . . . . . . . 11

3.1.1 Model Components . . . . . . . . . . . . . . . . 113.1.2 Model I: Simple Rear Wheel Drive Model . . . . 133.1.3 Model II: Rear Wheel Drive Model with Custom

Transmission . . . . . . . . . . . . . . . . . . . . 163.2 Vehicle models using MATLAB . . . . . . . . . . . . . . 20

3.2.1 Modelling References . . . . . . . . . . . . . . . 213.2.2 Data Extraction . . . . . . . . . . . . . . . . . . . 243.2.3 Data Fitting . . . . . . . . . . . . . . . . . . . . . 253.2.4 Modelling . . . . . . . . . . . . . . . . . . . . . . 28

3.3 Validation Model . . . . . . . . . . . . . . . . . . . . . . 334 results 37

4.1 Computation Time . . . . . . . . . . . . . . . . . . . . . 374.2 Maximum Speed/Acceleration Profile . . . . . . . . . . 394.3 Ranged Speed Profile . . . . . . . . . . . . . . . . . . . . 424.4 Effects of simulation step and throttle . . . . . . . . . . 47

5 conclusion & future work 515.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . 51

a appendix 53

b appendix 61

bibliography 63

iii

L I S T O F F I G U R E S

Figure 1 The powertrain block representation[30] . . . . 2Figure 2 Speed profile using default LPF[13] . . . . . . . 8Figure 3 Speed profile from GCDC logged data[13] . . . 8Figure 4 Volvo S60 T6[9] . . . . . . . . . . . . . . . . . . 12Figure 5 Inputs to the models . . . . . . . . . . . . . . . 12Figure 6 Model I . . . . . . . . . . . . . . . . . . . . . . . 14Figure 7 Profiler Report for Model I . . . . . . . . . . . . 14Figure 8 Speed vs Time Response-Model I . . . . . . . . 15Figure 9 Power vs Time Response-Model I . . . . . . . . 15Figure 10 Model II . . . . . . . . . . . . . . . . . . . . . . 16Figure 11 Transmission Subsystem[8] . . . . . . . . . . . 17Figure 12 Clutch Schedule Subsystem[8] . . . . . . . . . . 17Figure 13 Shift Schedule Subsystem . . . . . . . . . . . . 18Figure 14 Profiler Report for Model II . . . . . . . . . . . 19Figure 15 Speed vs Time Response-Model II . . . . . . . 19Figure 16 Power vs Time Response-Model II . . . . . . . 20Figure 17 Performance Curve of Volvo S60-T6[1] . . . . . 22Figure 18 Volvo FH16[10] . . . . . . . . . . . . . . . . . . 23Figure 19 Performance Curve of Volvo FH16[10] . . . . . 24Figure 20 Data Fitting Trial . . . . . . . . . . . . . . . . . 26Figure 21 Flow Diagram . . . . . . . . . . . . . . . . . . . 29Figure 22 Profiler Report of Car Model . . . . . . . . . . 37Figure 23 Profiler Report of Truck Model . . . . . . . . . 38Figure 24 Maximum Speed Profile: Car . . . . . . . . . . 39Figure 25 Maximum Acceleration Profile: Car . . . . . . 40Figure 26 Maximum Speed Profile: Truck . . . . . . . . . 41Figure 27 Maximum Acceleration Profile: Truck . . . . . 41Figure 28 Ranged Speed Profile I: Car . . . . . . . . . . . 42Figure 29 Ranged Speed Profile II: Car . . . . . . . . . . . 43Figure 30 Ranged Speed Profile III: Car . . . . . . . . . . 43Figure 31 Ranged Speed Profile I: Truck . . . . . . . . . . 45Figure 32 Ranged Speed Profile II: Truck . . . . . . . . . 45Figure 33 Ranged Speed Profile III: Truck . . . . . . . . . 46Figure 34 Varying Simulation Steps: Speed Profile . . . . 47Figure 35 Varying Simulation Steps: Acceleration Profile 48Figure 36 Varying Throttle levels: Speed Profile . . . . . 49Figure 37 Varying Throttle levels: Acceleration Profile . . 49Figure 38 S-PS Converter . . . . . . . . . . . . . . . . . . . 53

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List of Figures v

Figure 39 PS-S Converter . . . . . . . . . . . . . . . . . . . 53Figure 40 Engine . . . . . . . . . . . . . . . . . . . . . . . 54Figure 41 Rigid Frame . . . . . . . . . . . . . . . . . . . . 55Figure 42 Inertia Module . . . . . . . . . . . . . . . . . . . 55Figure 43 Torque Converter . . . . . . . . . . . . . . . . . 56Figure 44 Gear Box . . . . . . . . . . . . . . . . . . . . . . 57Figure 45 Differential . . . . . . . . . . . . . . . . . . . . . 57Figure 46 Tire . . . . . . . . . . . . . . . . . . . . . . . . . 58Figure 47 Vehicle Body . . . . . . . . . . . . . . . . . . . . 59Figure 48 ODE Solver . . . . . . . . . . . . . . . . . . . . . 60

L I S T O F TA B L E S

Table 1 Vehicle Specific Parameters: Car & Truck . . . 31Table 2 Speed profiles of LPF, kinematic & other mod-

els: Car . . . . . . . . . . . . . . . . . . . . . . . 44Table 3 Speed profiles of LPF & kinematic models: Truck 46

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A C R O N Y M S

ABS Anti-Lock Braking System

CG Centre of Gravity

ECU Engine Control Unit

ESC Electronic Stability Control

GCDC Grand Cooperative Driving Challenge

LPF Low-Pass Filter

ODE Ordinary Differential Equation

SI Internation System of Units

SLR Static Loaded Radius

SUMO Simulation of Urban Mobility

SUV Suburban Utility Vehicle

TCU Transmission Control Unit

VeINS Vehicles in Network Simulation

VRML Virtual Reality Modelling Language

V2V Vehicle-to-Vehicle

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1I N T R O D U C T I O N

Vehicle system development is complicated and requires knowledgefrom various areas, such as mechanical design, electronics develop-ment and control systems. Such systems involve time and cost todevelop. Due to this reason, a general vehicle system simulation is acost-efficient and safe way to test automotive applications.

Accurate modelling of the kinematic and/or dynamics behavioursof 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, whichcould be from the human driver or automated functions. Besides,electric vehicles might have different characteristics. The goal is tohave accurate modelling of different types of vehicles, which couldbe executed in real-time in existing tools such as Simulation of UrbanMobility (SUMO)[6] or MATLAB/Simulink.

However, the idea of using and implementing near real world mod-els for the purpose of achieving realistic responses, is not new. Yet,there remains a trade-off. The prospect of having complex models orkeeping the system running at real time. The implementation of themodel discussed in the forthcoming chapters, involve not just realisticbehaviour, 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 usedto simulate and evaluate realistic road traffic conditions and hence,could sometimes be used for the purpose of traffic forecasting. SUMOis used to generate traffic formations and road conditions, and tostudy their mobility in the road network. While the Veins simula-tion framework is used for introducing vehicle-to-vehicle and vehicle-to-infrastructure (V2X) communication. However, all vehicles are notsame. Trucks are different from sedans, or hatchbacks or suburbanutility vehicles (SUVs). There are different parameters to be consid-ered, for not all vehicles alike, for near realistic performance even inthe simulation environment.

Yet another inhibiting factor to the realistic performance would bethe default dynamic responses for the vehicles in the aforementionedsoftware. A simple low-pass filter (LPF) has been used to exhibit theresponse of the vehicle. This is an elementary modelling of the pow-ertrain of the vehicle, and may not be accurate, and is most likely

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2 introduction

not applicable for all vehicles alike. To understand what exactly apowerplant is; in a motor vehicle, the term powertrain or powerplantdescribes the main components that generate power and deliver it tothe 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 controlare described. The vehicle level describes the flow of information andcontrol in a vehicle taking the entire powertrain as a module. Thepowertrain level describes the flow of information and control withina 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 reasonablecomputation time

Using MATLAB/Simulink, a more realistic model of a heavy dutytruck and a car, are to be created. These models would include thetorque output of a vehicle and use the data to compute a realisticvelocity-time response, instead of a simple LPF. The results from theclass specific vehicle models, are to be contrasted to the LPF modelresponses.

Although the default implementation of the LPF is a step closerto realism, it is not accurate enough. The variation of the kinematicresponse with time is a function of the different vehicle specific pa-rameters, typically those of the powertrain components. The response

introduction 3

depends on the torque output of the vehicle, and the possible sur-rounding forces like the air resistance, ascents, descents, and othergravitational forces. The idea is to be able to take into account theseforces, and reflect their impact on the kinematic response of the vehi-cle.

The vehicles’ kinematic models are intended for real time simula-tion purposes. Hence, computation time needs to be maintained aslow as possible. To do so, one needs to understand the level of ab-straction in the details of a model, that can be overlooked and thedetails of the model that need to be accurate [13].

To enumerate, the research questions that are answered from thework done in this thesis are:

1. Is the LPF model accurate enough to model the vehicles’ kinematicbehaviour?

2. What are the main differences between the LPF model and the kine-matic 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 chap-ters, in Chapter 2, the background work done in this field, alongsidetheir shortcomings, and how the proposed work aims at overcomingthe drawbacks or inheriting the established ideas are to be discussed.Further, in Chapter 3, the constructed models are discussed in de-tail alongside their limitations. The results obtained from the modelshave been compared and contrasted in Chapter 4, following whichthe conclusions and possible future work have been stated in Chap-ter 5. Information pertaining to the model setup have been describedin Appendix A and Appendix B.

2R E L AT E D W O R K S

Accurate and realistic modelling of vehicle kinematics has been madeeasy with several sophisticated simulation tools. In the following sec-tions the state of the art work in the field of modelling vehicle kine-matics have been described.

2.1 detailed modelling of road vehicles

Vehicle design is a multidisciplinary concept due to the complexity ofthe vehicles. Developing such models require the use of cutting edgetechnology. The trade-off as mentioned in ??, is the development ofa highly complex system or a system inclined for real time purposes.The level of abstraction of the vehicle model affects the inclination ofthe vehicle model to one of the above choices. For instance, in [36],a highly detailed and a near replica 3D model of the Mercedes BenzML270 model had been created. The model of the vehicle at this levelof detail had been designed using Autodesk 3ds Max. The model wasextracted in Virtual Reality Modelling Language (VRML)[16] formatand had been imported to MATLAB by using the inbuilt virtual real-ity toolbox. The model of the vehicle chosen to work on as a generalsimulation model for the vehicle system was a four wheel vehicledrive model. The scenario used to test the developed model was tohave the car park, in an empty parking space. The model, however,takes only the dimensional aspects of the Mercedes Benz ML270 intoaccount to model, such as the length, width, height and wheelbasemeasurements. The focus has been minimal on the powertrain or thetransmission characteristics of the model. This leaves the vehicle astandalone model in a non interactive environment. To be able to val-idate the true feasibility of any model, they need to be tested in arealistic environment, and the aim of this thesis, is just that. Unlikea highly detailed superficial modelling, more focus is to be on thefundamentals of what drives a vehicle and attempts to model themechanical subsystems.

Another approach to detailed vehicle modelling is to design all theavailable mechanical subsystems of a vehicle. For instance, in [21],a vehicle dynamics model had been developed with Modelica™as aprogramming language. The model was designed in the aim of test-

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6 related works

ing real time applications with the state of the art driving simulator atthe Swedish Road and Traffic Research Institute, also known as VTI.The model hence developed, features several components of the vehi-cle such as the chassis model, tire model, suspension system, steeringsystem, driveline, braking system and active safety systems such asthe Anti-Lock Braking System (ABS) and the Electronic Stability Con-trol (ESC). This particularly complex project was aimed at developingmodel for the VTI, SimIV simulator. This driving simulator providesa realistic driving experience not only with the 180°view-screen, butalso using sound systems and a motion mechanism for the simula-tion cabin, present in a revamped Volvo V60. This model features amodestly detailed drivetrain subsystem of the vehicle. The exact useof this model will be significantly different from the project at handsimply because of the domain of use. This driving simulator is stan-dalone as well. Unlike our project that features use of the SUMO andVeINS software, this used a more hardware oriented implementationof the model. Nevertheless, the detailed modelling of the several sub-systems for the VTI simulator set guidelines for other aspiring workin the field.

In the work recorded in [38], the vehicle’s kinematic model is repre-sented as a relationship of the forces acting on the vehicle, the acceler-ation input and the tire models. The simulation results of this modelare 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 re-sponse is plotted. The variable in the tests is the tire slip ratio. The slipratio provides a measure of difference in the surface contact speed ofthe vehicle and the actual angular velocity of the tires. This parameteraffects the model response and is highly dependent on the tire param-eters. The tires used are modelled using the Pacejka tire formula[15],which is also know as the Magic tire formula. This formula providesan empirical tire model. The effects of slip ratio at different speedshave been recorded and contrasted. Although, the tire parameters af-fect the vehicle model, it is assumed that, this effect is the only criticalfactor to modelling a vehicle. There however, are several other factorsaffecting the vehicle kinematic model, which are discussed in the fol-lowing section.

The complexity of the above models make it cumbersome and un-reliable for real time testing with the given hardware. For the purposeof reusing the model that is to be designed, a level of abstraction thatneglects a good amount of trivial details is required, as a really com-plex model could cost as computation time, especially if it is reused.The SUMO environment along with VeINS only support 2D move-

2.2 modelling for autonomous vehicles 7

ments, meaning, considering hill-climbs and gradients on the roadsare futile [6]. However, the modelling of the drivetrain of the vehicleis strongly advised as it defines the raw vehicle output in the absenceof all external forces.

2.2 modelling for autonomous vehicles

The following work involved designing of models characterizing kine-matic and dynamic for autonomous vehicles. Modelling is not impor-tant just for manned vehicles, but is also important in unmanned andautonomous vehicles as those are the vehicles which involve zeroon-road human interaction. For instance, in [33], an ideal kinematicmodel for, four wheeled car like vehicles have been created, based onthe Ackerman principle. The Ackerman principle entails the follow-ing 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 givenmodel. The kinematic properties given zero errors are contrasted withcertain familiar errors by modifying the kinematic relations. The con-trast is then plotted to show plausible real world performance. Froma simulation standpoint, the assumptions adopted in [33], are closelyrelated to the environment in SUMO, due to the completely 2D move-ment. However, external interferences like traction, air resistance andsome gravitational forces can be included in the given model to ap-proach realism.

Another approach would be the combination of kinematic and dy-namic features of the vehicle. Taking a look in [38], the highlights ofthis given model are that, the computational efficiency is optimizedand the suggested model is applicable for all kinds of 4 wheeledvehicles. The entire model is built in MATLAB, as functions. Thesefunctions are run in Simulink environment to compute longitudinal,yaw and lateral accelerations. The model allows extraction of otherdynamic forces as well. This model sets a threshold for abstraction of

8 related works

unnecessary model details that could weigh down the computationstime due to the complexity.

In the work done in [13], the speed profiles generated by the soft-ware default LPF, is contrasted to the speed profile plotted fromthe GCDC logged data. The characteristics of the default LPF modelhas been exhibited using Plexe. The speed profiles shown below aregraphs 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]

2.2 modelling for autonomous vehicles 9

By plain observation alone it is convincing, however, the accuracyof this LPF implementation cannot be judged without deeper insight.The speed profile of a real world vehicle depends on aspects that gov-ern its performance such as the drive-train, engine, kerb/combinationweights, and other external forces.

To suffice, a lot of models are found in literature as both propri-etary software and publications. These models usually yield accurateresults. The accuracy is due to its highly complex specifications andtest 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 in-tended to replace the defaults in SUMO to evaluate realistic responses.The realistic response is achieved by replacing the LPF with the com-ponents governing the vehicle performance. These components aremechanical subsystems. Given the technological advancements, thesesubsystems are far too complicated and are vehicle specific. Each ve-hicle manufacturer has their own patented work. Yet, the models canbe created using generic components that are universal to all vehicles.

To have a realistic evaluation, the models need to replace existingdefaults, and at the same time, overcome the aforementioned disad-vantages. The trade-off between computational performance and ac-curacy of the results can be reasonable only by an appropriate levelof abstraction.

3T H E M O D E L S

In this section the models that have been created to study the vehicledynamics are described. The following models have different levelsof abstraction, hence, these models have different computation times.

All the simulations were run on the same machine, with the follow-ing specifications:-

• Operating System: Windows 10 Pro 64-bit

• System Manufacturer: Hewlett-Packard

• System Model: HP Pavilion 15 Notebook PC

• BIOS: InsydeH2O Version 03.72.38F.65

• Processor: Intel(R) Core(TM) i7-4500U CPU @ 1.80GHz (4 CPUs),2.4GHz

• Memory: 8192MB RAM

3.1 vehicle models using simulink

In the recent releases of Simulink by Mathworks™, the SimscapeDriveline[8] product line has been made available for rapid creationof models of physical systems in the Simulink environment. Simscapeprovides libraries of components for modelling and simulating me-chanical systems. It includes models of drivetrain components, tires,transmissions, engines and torque converters.

3.1.1 Model Components

The components provided by Simscape can be used to model thetransmission of mechanical power in helicopter drivetrains, industrialmachinery, automotive powertrains, and other applications[8]. Themodels are designed by closely shadowing the Volvo S60 T6.

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12 the models

Figure 4: Volvo S60 T6[9]

Since most of the newer vehicles have advanced and proprietarysystems, the following models were created using the available infor-mation from Volvo’s data-sheets and results from tests performed bythird party organizations. Furthermore, the engine models used areSimscape defaults, which uses a normalized third order polynomialto simulate the engine response.

Input Control: This module is created using the Signal Builder. Theinputs 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 thethrottle level. The wind speed and road incline are considered asexternal stimuli, although they are modelled in the same block, forconvenience. In order to focus on the mechanical subsystems of thevehicle, the inputs provided are set prior to running the simulationand are kept constant. The following are the settings:-

• Wind speed: 3 m/s

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 1being fully pressed down, and 0 being not pressed at all. The incline,wind speed and throttle input levels are displayed as red, pink andblue lines, respectively in Figure 5

Other components that have been implemented in the followingmodels and the parameters that have been set for experimentation,are described in Appendix A.

3.1.2 Model I: Simple Rear Wheel Drive Model

This Simscape model is designed to achieve the functionality of a asingle axle driven car. The components or the functional blocks usedto design these models are existent in all combustion engine vehicles.For the purpose of the simulation, the vehicle is driven by its rearwheels. This model, notably consists only of the components, thatare required to make the basic vehicle model work (or move). This isdone to develop a model with the highest level of abstraction achiev-able. Although this model constitutes only of the basic components,the component specific parameters such as the vehicle mass, enginepeak power, tire rolling radius, etc., have been set to the values corre-sponding to that of Volvo S60 T6.

The torque generated by the prime mover is sent to the torqueconverter which in turn transfers it to the gear box. The differentialconnected to the gear box splits the incoming torque equally into thetwo wheels. As mentioned earlier, the throttle is kept at wide open(fully pressed down), the wind speed is at constant 3 m/s, and theroad inclination is set to 0°.

14 the models

Figure 6: Model I

The simulation time recorded with Simulink Profiler feature, is asfollows:

Figure 7: Profiler Report for Model I

The recorded time is 1.77 s. Since, the data needs to be transferredto the SUMO environment, an additional delay will be added up in

3.1 vehicle models using simulink 15

the socket communication process. To speculate, the overall time toreceive the data in the SUMO environment, would be a little over 2s. This is not a very fast system, as we intend to achieve the overalltime consumed in computation and transfer to be at most 1 s, for realtime 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

16 the models

From the recorded graphs it is observable that, the maximum speedattainable in the model is 90 km/hr, at full throttle. The time takenfor the vehicle to attain its top speed is 10 sec. However, this model isrelatively less complex, as the gearbox implemented has a single gear.Furthermore, the recorded top speed achieved by Volvo S60 T6 is249.4 km/hr[14]. In addition, the power curve decreases exponentialywith time after its global maxima. This characteristic is not true forreal world vehicles. This model is moderately fast, but not realistic.

3.1.3 Model II: Rear Wheel Drive Model with Custom Transmission

This Simscape model is designed to achieve the functionality of a rearwheel driven car with a 4 Speed Transmission. Intuitively, it meansthat the vehicle has 4 gears, enabling it to move forward. The workingof this model is similar to that of Model I. Noticeably, the difference isthe transmission mechanism. In contrast to a single and continuousgearing, a more complex transmission mechanism is devised. Thegears are decided using the shift logic chart[8]. As mentioned earlier,the throttle is kept at wide open (fully pressed down), the wind speedis at constant 3 m/s, and the road inclination is set to 0°.

Figure 10: Model II

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 inFigure 12. The clutch schedule defines which clutch needs to be en-gaged. This subsystem is a part of an example provided by Math-works™, and has been implemented in this project. These ratios areset to default.

Figure 12: Clutch Schedule Subsystem[8]

The shift logic subsystem as seen in Figure 13 is a state machinethat governs the logic for gear change. There are 3 states correspond-ing to the selection_state and there are 4 states corresponding to the

18 the models

gear_state. The Simulink function computes the upshift and downshiftthresholds as a function of the currently engaged gear and throttle in-put level. For instance, assuming the car is initially engaged in 1stgear and has accelerated to its engine speed limit, then the shift logicachieves steady state. Depending on the throttle and the current gear,it decides if the car needs to shift gears, by comparing the thresholdsto the current vehicle speed. Since the current vehicle speed is com-pared with the shift thresholds, it prevents the model from shiftingup or shifting down by skipping a gear.

Figure 13: Shift Schedule Subsystem

In the real world model of the Volvo S60 T6, the transmission de-sign is a proprietary 8 Speed Geartronic Transmission[9]. The gearmechanism, clutch schedules and shift schedules are not for publicview, hence, the fidelity of this complex model is limited to a generic 4Speed Transmission. Furthermore, most newer vehicles are equippedwith advanced safety systems, an engine control unit (ECU) and atransmission control unit (TCU). Modelling these advanced featureswould definitely improve the model fidelity, however, the computa-tion time would be affected.

3.1 vehicle models using simulink 19

The simulation time recorded with Simulink Profiler feature, is asfollows:

Figure 14: Profiler Report for Model II

The recorded time is 8.36 s, which is undoubtedly high for real timeapplications. 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

20 the models

Figure 16: Power vs Time Response-Model II

From the profiler result it can be observed that 100 more compo-nents had to be appended to Model I to achieve high fidelity. Fromthe recorded graphs it is observable that, the maximum speed attain-able in the model is 240 km/hr (accurately 240.32 km/hr), at fullthrottle. It is close to the real world model’s top speed, 249.4 km/hr.The time taken for this model to attain its top speed is 50 sec. It alsoreaches 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 recordedpeak power of Volvo S60 T6 is 223 kW[14]. This model closely resem-bles the real world car, however, it is far too complex as the gearboximplemented, involves a state machine and its corresponding logicalcomputations. This realism leaves us with a high computation time.

To summarise, Model I is moderately fast, but unrealistic. ModelII is very slow, but realistic. The following section describes anothermodelling approach that has been followed to create models usingMATLAB language.

3.2 vehicle models using matlab

Modelling with the functional blocks provided by Simscape in theSimulink environment, has proven to be rather unsuitable for the in-tended real time simulations. Hence, in this approach, mathematicalequations are used instead of blocks. Instead of using the Simulink

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 fol-lowed for designing the aforementioned models and the model de-scribed below. In the models in Section 3.1, functional blocks are com-bined together to design the powertrain of the vehicle. These functionblocks are subsystems or components, and are combined to form acomplex system. Hence, it is bottom-up approach to modelling. In themodelling approach discussed below, the powertrain of the vehicle isnot designed by integrating subsystems, but derived from the power-train performance graphs of real world cars. The powertrain perfor-mance graph is also known as a performance curve or a dyno plot.The performance graph is a document of the recorded performanceof the powertrain, in terms of producing power and torque, under agiven condition[3]. Using MATLAB curve fitting tools, equations per-taining to the model the vehicle’s powertrain have been derived. Incontrast to Model I and Model II, the entire system is modelled fromexisting powertrain curves instead of integrating individual blocks.Hence, the following is a top-down approach to modelling.

3.2.1 Modelling References

To compare the fidelity of the model designed by this approach, themodel of Volvo S60 response is intended to be compared to the re-sponses of Model I and Model II. Apart from the modelling of athe car’s powertrain, an attempt has been made to design the semi-trailer tractor’s powertrain, using the same approach. The actual caris shown in Figure 4, and the actual truck is shown in Figure 18. Thesemodels are described below.

3.2.1.1 VOLVO S60-T6

The following performance curve is implemented to create the pow-ertrain model. This curve has been recorded by BSR Svenska AB forthe Volvo S60-T6 model. This T6 engine model is currently being im-plemented in the Volvo S60 series[9].

The units adopted by BSR Svenska AB for the measurements are:-

• Power: HP

• Torque: Nm

• Engine Speed: RPM

22 the models

Figure 17: Performance Curve of Volvo S60-T6[1]

The performance curve depicts the performance of the stock pow-ertrain model as well as the optimized powertrain model. The stockperformance model is expressed as dashed lines and the optimizedperformance model is expressed as normal lines. In Figure 17, thepower vs engine speed responses and the torque vs engine speedresponses are indicated by red and blue lines, respectively. For thesimulation purpose, the optimized responses are used.

3.2.1.2 VOLVO FH16

Unlike the Volvo car, the Volvo truck performance graphs are avail-able in the Volvo database[10]. However, these graphs correspondonly to the kerb weight of the tractor and the weight of one human.

3.2 vehicle models using matlab 23

Figure 18: Volvo FH16[10]

The gross combination weight effects of the trailer attachment havenot been recorded. Thus, for the simulation purpose, only the tractoris taken into account. Hence, using the following performance graphof 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 theVolvo car, the following curve does not have optimizations. It hasbeen recorded using the truck’s stock components.

24 the models

Figure 19: Performance Curve of Volvo FH16[10]

In Figure 19, the power vs engine speed response and the torque vsengine speed response are indicated by blue and green lines, respec-tively.

3.2.2 Data Extraction

From the performance graphs in Figure 17 and Figure 19, the mathe-matical relationship between the torque and engine speed needs to de-rived. For this purpose, data needs to be extracted from these graphs.In order to extract the data, the image files of these graphs need tobe digitized. The WebPlotDigitizer application has been used for thispurpose. More information pertaining to this application is describedin Appendix B.

Unlike the Simulink environment, which assists in a heterogenousinput for the units of different variables, the MATLAB environmentrelies on the uniformity of the units, as the focus is laid on the equa-tions governing the model alone. For the purpose of the simulation,the International System of Units (SI) has been adopted. The units areas follows:-

• Power: W

• Torque: Nm

• Engine Speed: rad/s

• Physical Dimensions: m

3.2 vehicle models using matlab 25

The equations mentioned below were used to convert the non-standard 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] = 1.3558[Nm] (2)

3. To convert Revolutions per minute to Radians per second:

1[RPM] = 0.10472[rad/s] (3)

After converting the extracted data into SI units, they were im-ported to the MATLAB workspace.

3.2.3 Data Fitting

Data fitting is the process of fitting models to a set of data and manip-ulating the accuracy of the fitting models[2]. To relate the data points,an empirical form of the equation, or the fitting model would appearas:

torque = function(engine_speed) (4)

The concern with the data fitting model is the compensation be-tween the accuracy of the equation and the complexity of the fittingmodel. Since the performance curves are derived from a complexpowertrain model, it is unlikely that a lower order polynomial equa-tion would be an accurate fit. Simultaneously, since an ODE solverwould be implemented in the model for the computation of the speedvs time response, and a highly complex model would slow down thecomputations. By testing the accuracy of the fit, the equations derivedcan be seen in Figure 20.

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 5th and 10th order are red and greenlines, respectively. In the equations below, x denotes the engine speedand y denotes the torque output. The equation for the 5th order fittingmodel is of the form, where p1 to p6 are coefficients:

y = p1 ∗ x5 + p2 ∗ x4 + p3 ∗ x3 + p4 ∗ x2 + p5 ∗ x+ p6 (5)

The equation for the 10th order fitting model is of the form, where p1to p11 are coefficients:

y = p1 ∗ x10 + p2 ∗ x9 + p3 ∗ x8 + p4 ∗ x7 + p5 ∗ x6 + p6 ∗ x5 + p7 ∗ x4

+ p8 ∗ x3 + p9 ∗ x2 + p10 ∗ x+ p11(6)

From the graph, it can be observed that the 10th order model ismore accurate than the 5th order model. However, a 10th order modelwould add up to the time required to solve the ODE. To assess thegoodness of a fitting model, MATLAB provides a norm of residualsfunction. The lower the value of the residuals, the better the fit. Theresidual value is a measure of the outliers in the model. An outlier is

3.2 vehicle models using matlab 27

an observation that lies in an abnormal distance from other values ina sample of data. An acceptable residual value is considered to be inthe range of [0,10][2]. However, the residual value for the 5th ordermodel is 49.17 and the residual value for the 10th order model is 20.42(residual values are not shown). Clearly, both the residual values arehigher 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 apparentmaximas or peaks as delimiters, and the least complex fitting modelwith residual value below 10, is chosen. The equations that have beenderived for the powertrain performance graphs are listed below. Inthe equations in the subsections to follow:

• w denotes the engine speed [rad/s]

• T denotes the torque output [Nm]

3.2.3.1 Equations for VOLVO S60-T6 in Figure 17

if w >= 0 and w < 271.4357

T = −0.0045393 ∗w2 + 2.8486 ∗w+ 142.14; (7)

if w >= 271.4357 and w < 389.0008

T = −2.5006e− 07 ∗w4 + 0.00032699 ∗w3 − 0.15978 ∗w2

+ 34.681 ∗w− 2296.9(8)

if w >= 389.0008 and w 837.75

T = 0 (10)

If the engine speed exceeds 837.75 rad/s or goes below 0 rad/s,the torque produced is blended to 0 Nm. This is analogous to thestall speed and the maximum engine speed parameters used in theSimscape models.

3.2.3.2 Equations for VOLVO FH16 in Figure 19

if w >= 0 and w < 106.0779

T = 40 ∗w+ 1500 (11)

28 the models

if w >= 106.0779 and w < 137.615

T = 0.074577 ∗w+ 2760.1 (12)

if w >= 137.615 and w 179.139 and w 231.8

T = 0 (15)

If the engine speed exceeds 231.8 rad/s or goes below 0 rad/s,the torque produced is blended to 0 Nm. This is analogous to thestall speed and the maximum engine speed parameters used in theSimscape models.

3.2.4 Modelling

To model the equations presented in Section 3.2.3.1 and Section 3.2.3.2,MATLAB function files are used. The flow of data in MATLAB is rep-resented in Figure 22.

3.2 vehicle models using matlab 29

Figure 21: Flow Diagram

The following subsections explain in detail, the computation pro-cess and the parameters involved in achieving the kinematic responseof the vehicle’s model.

3.2.4.1 File 1: Powertrain

In this file, the powerplant characteristic equations as described inSection 3.2.3.1 and Section 3.2.3.2, are implemented using conditional

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 singlefile and are chosen depending upon the type of the ego vehicle. Theego vehicle is the vehicle whose characteristics are intended to beobserved. This file requires the most computation time as the ODEsolver calls it numerous times to compute the produced torque forthe vehicle to move forward. Thus, the complexity of the equationsgoverning the relationship between the engine speed and the pro-duced torque, need to be simple and accurate, simultaneously.

3.2.4.2 File 2: Acceleration

In this file, the acceleration of the vehicle is computed. The accel-eration is computed as a function of the vehicle’s velocity and theforces acting on it. The input and output parameters to this file are asfollows:-

• 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 thepowerplant characteristics, which are specified in File 1 as mentionedin Section 3.2.4.1. Some of the constant parameters for all the modelsare as follows:-

• Acceleration due to Gravity (g): 9.82165 m/s²

• Mass of Human: 70 kg

• Air Density (ρ): 1.225 kg/m³

The acceleration gained by an object because of gravitational forceis called its acceleration due to gravity. It is constant for all objects thatare in contact with the Earth’s surface. Also, it is considered that onlyone person is present in the vehicles. Since no mechanical system is100% efficient, the powertrain models are set to be 90% efficient.

The vehicle specific parameters for the Volvo S60-T6 and VolvoFH16 are [10][9][23]:-

3.2 vehicle models using matlab 31

Vehicle Specifics

Parameters Car Truck

Kerb Weight (mk) [kg] 1575 7415

Gross Weight (m) [kg] 1645 7485

Frontal Area (a) [m²] 3.111948 9

Tire Specification P235/40VR18 315/80R22.5

Final Drive Axle Ratio (if) 2.77 3.36

Rolling Resistance Coefficient (ur) 0.02 0.06

Friction Coefficient (uf) 0.8 0.8

Drag Coefficient (cd) 0.31 0.96

Gear Ratios (ig) 3.03/1.95/1.46/1.22/1 0.78

Table 1: Vehicle Specific Parameters: Car & Truck

In the equations, the following symbols are chosen to represent theparameters:-

• Powertrain Efficiency: η

• Static Rolling Radius: SLR

• Relative Velocity: v

• Torque: τ

• Road Incline: θ

• Number of driving wheels: nw

The following are the equations that implement the above parame-ters for the computation of the net force experienced by the vehicle.

1. Friction Force (Ff): This represents the force opposing the rela-tive motion of the vehicle. The coefficient of this force is charac-terized by the surface on which the vehicle is being driven[17].

Ff = uf ∗m ∗ g ∗ sinθ (16)

2. Rolling Resistance Force (Fr): This represents the force gener-ated in the tires. The non-elastic effects that are experienced dueto the hysterical losses in the compression and expansion of thetire region which is in contact with the road surface[23], accountfor this force. The coefficient of this force is characterized by thetype of the vehicle and the type of its tire.

Fr = ur ∗m ∗ g (17)

32 the models

3. Aerodynamic Drag Force (Fa): This represents a force actingopposite to the relative motion of any object moving with re-spect to the surrounding air. The drag force is proportionalto the frontal area of the vehicle and the square of its relativevelocity[27].

Fa = 0.5 ∗ ρ ∗ cd ∗ a ∗ v2 (18)

4. Gradient Force (Fg): This represents a force acting on a vehicleon an inclined plane. If the vehicle is on an ascending slope itacts against the vehicle, and if the vehicle is on a descendingslop it acts in favour of the vehicle[28].

Fg = m ∗ g ∗ sinθ (19)

This force can be used to demonstrate the vehicle behaviourwhile moving up a hill or down a hill.

5. Traction Force (Ft): This represents a force that is generated bythe engine, allowing the vehicle to move. This force is character-ized the powertrain components of the vehicle. This is the maindriving force of the vehicle. The throttle level lies in [0,1]. It de-fines the amount of throttle valve being opened. The value ofthrottle level is directly proportional to the traction force.

Ft = η ∗nw ∗ ig ∗ if ∗ throttle ∗ τ/SLR (20)

The Torque in Equation 23, is received from File 1 as mentionedin Section 3.2.4.1. The Static Loaded Radius or the rolling ra-dius (SLR) is the radius of the vehicle when there is a fixed loadapplied on it. Due to the compression of the tire, the actual ra-dius of the tire will be slightly higher than its SLR. The generalconvention 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 calcu-lated:

a)

depth = (aspectratio) ∗ (nominalwidth)/100 (22)

b)

rimouterradius = (rimdiameter[mm])/2 (23)

3.3 validation model 33

From Equation 25 and Equation 26, the SLR can be calculatedas[5]:

SLR = 0.96 ∗ (depth+ rimouterradius) (24)

Using Equation 27, the SLR of the vehicles have been calculatedto be:

• Volvo S60 T6: 0.30969 m

• Volvo FH16: 0.51624 m

From Equations 19-27, the net force acting on the vehicle isgiven as:

Fnet = Ft − (Ff + Fr + Fa + Fg) (25)

Using Newtons’s Second Law of motion which states that ’in aninertial reference frame, the vector sum of the forces F on an object isequal to the mass m of that object multiplied by the acceleration a ofthe object’, the acceleration of the vehicle can be computed.

Mathematically,

Fnet = mass ∗ acceleration (26)

3.2.4.3 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 pa-rameters 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 callsFile 2 to integrate the acceleration computed in the given time limitswith the set time step (0.01 s), to compute the velocity. File 2 calls File1 to compute the torque produced by the powertrain model. Further-more, the error tolerance of the ODE solver can be manipulated, fromthe default precision (1e-3). This may take longer to run as a result,but would be more accurate for a non-smooth powerplant character-istic.

3.3 validation model

To compare the models of the car and the truck as described in Sec-tion 3.2, the LPF model that has been implemented in SUMO, is mod-eled in this section, as described in ??.

34 the models

The usage of LPF in the SUMO environment is achieved using aspeed controller model[35]. The desired acceleration of the vehicleis considered to be the control parameter for longitudinal motion inthis environment. The controller is implemented based on certain fun-damental physics of controlling motion. The controller used for thepurpose is the classic Cruise Control[26]. This model has been com-mercially implemented in several vehicles as of today. This controllerallows the driver to select and maintain a desired speed, by takingover the throttle mechanism of the vehicle. The equation[35] govern-ing this controller is

ades = −k(v− vdes) + ζ (27)

where ades is the desired acceleration, v is the current speed, vdes isthe desired speed. k is the gain of the cruise controller, which is set to1 by default. ζ corresponds to random disturbances that might affectthe controller performance, which is set to 0 by default.

Using the above equation, the acceleration at the nth time step iscomputed as

a[n] = β · ades[n] + (1−β) · a[n− 1] (28)

where

β = ∆t/(γ+∆t) (29)

Acceleration at the nth time step is computed based on ades, whichis computed by the controller, and the acceleration at n− 1th timestep. In the above equation, ∆t is the increment value of every timestep and γ represents the time constant. The default values assignedby 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 nis computed as

v[n] = v[n− 1] + a[n] ∗∆t (30)

A ceiling value and a floor value for acceleration are applied toall vehicles in SUMO[6], and hence, the acceleration of the vehicle atany point is limited as a ∈ [amin,amax]. These values that are set bySUMO, depend on the type of the vehicle.

The default amin and amax values for a passenger car are -7.5m/s²and 2.9 m/s², respectively. The default amin and amax values

3.3 validation model 35

for a truck are -4 m/s²and 1.3 m/s², respectively[6]. These limits areused to model an average human-comfort behaviour. Nonetheless,these values are not the actual physical limits to the vehicles. To com-pare, the same limits have been incorporated in the models describedin Section 3.2, as well.

In Chapter 4, the speed vs time and acceleration vs time responsesof the models presented in Section 3.2 have been compared and con-trasted to the LPF model described above. It is important to note thatthe 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

4R E S U LT S

In this section, results recorded by comparing and contrasting themodels in Section 3.2 and Section 3.3 have been described. The differ-ent comparison aspects have been elaborated below.

4.1 computation time

The computation time plays an important factor in the feasibility ofthe model, because, as seen in Section 3.1, a complex model coststhe system as computation time. Hence, these kinds of models areunsuitable for real time application purposes. However, the recordedcomputation time of the models in Section 3.2 are shown in Figure 22and Figure 23.

Figure 22: Profiler Report of Car Model

37

38 results

Figure 23: Profiler Report of Truck Model

The total time taken for the models to compute is the sum of timetaken by all the child processes and functions that have been called.The total time of the car model is recorded to be 0.619 s and the totaltime of the truck model is recorded to be 0.605 s. The major contrib-utor for the computation time is the ODE45 solver. This solver callsthe function handle that computes acceleration. It can be observedthat the function handle is called 3998 times and 2996 times, for thecar and the truck models respectively. The velocity computed is bynumerically solving the ODE, where acceleration is represented asdv/dt. In contrast to the Figure 7 and Figure 10, it can be observed inFigure 22 and Figure 23 that this modelling paradigm has taken lessertime to compute, and is in the order of milliseconds. These models,are hence, suitable for being used for real time simulation purpose.

4.2 maximum speed/acceleration profile 39

4.2 maximum speed/acceleration profile

Maximum Speed/Acceleration Profile displays the maximum speedvs time and the maximum acceleration vs time responses of the vehi-cle. This aspect of comparison highlights the accuracy of the modelsto the real world vehicle. The LPF model was also set to exhibit be-haviour for the same speed range. The responses corresponding tothe car model are as shown below.

Figure 24: Maximum Speed Profile: Car

40 results

Figure 25: Maximum Acceleration Profile: Car

The red dashed line represents the LPF model response while thekinematic model response is represented by the blue dot-dashed line.The recorded maximum speed of the car model is 198.8 km/h, whilethe real world model tops at 249.4 km/h[14]. This difference can beattributed to the rather simple 4 speed transmission that has beenimplemented in the kinematic model as opposed to the proprietaryGeartronic 8 speed transmission[9] used by Volvo in the real worldmodel. However, it can be observed that the LPF model reaches thetarget speed faster than the kinematic model in Figure 24. It is im-portant to note that the ceiling and floor limits for acceleration havebeen applied to the vehicles, as mentioned in Section 3.3. In Figure 25,it can be observed that the acceleration reaches the ceiling limit forthe LPF model instantaneously, as opposed to the smooth curve inthe kinematic model. Also, the decrease in acceleration is gradual asopposed to the LPF model. This is because, the acceleration of thecar model, depends on the forces acting on it, causing this non lineareffect. In contrast, the LPF model uses a cruise controller to computethe acceleration. It is important to note that, while the real world cartakes 8 s to go from 0-100 km/h[14], the LPF model takes 7.6 s andthe kinematic model takes 8.8 s.

The responses corresponding to the truck model are as shown be-low.

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 implementedwith ceiling and floor limits to the acceleration. It can be observedthat the LPF reaches the target speed much faster than the truckmodel. The real world FH16 truck takes 40 s to reach its top speed of135.2 km/h[4], while the kinematic model takes 45.24 s and the LPFmodel takes 24.08 s, to reach 134.4 km/h. The LPF model responseis rather unrealistic in the case of a truck. The mass of the truck and

42 results

the increased effective external forces play an important role in thekinematic response of the truck. The LPF fails to emulate this realis-tic behaviour because it does not consider the mass or the externalforces acting on the vehicle. The acceleration responses have the nonlinear effect due to the gear ratios, similar occurrence as observed inthe car model.

4.3 ranged speed profile

Ranged Speed Profile displays the speed vs time response for rel-atively small transitions in speed. This aspect of comparison shedsmore focus on the effect of gear ratios in speed transitions. For all thetransitions below, the throttle position is set to 80%. The following arethe 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 shiftsgear at 45 km/h and the gear ratio is changed from 1.46 to 1.22. Itcan be observed that the LPF model leads the kinematic model by asmall margin.

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 shiftsgear at 75 km/h and the gear ratio is changed from 1.22 to 0.81. Itcan 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 shiftsgear at 75 km/h and the gear ratio is changed from 1.22 to 0.81. It canbe observed that the kinematic model leads the LPF model.

44 results

Speed Ranges

ModelTime [s]

0-Max[km/h]

30-50[km/h]

50-80[km/h]

70-120[km/h]

LPF 16.32 2.72 3.44 4.96

Kinematic 22.23 2.32 4.66 8.6

Simscape II 21.75 1.82 3.94 6.95

Real World 24.3* 3.2 4.5 n/a

Table 2: Speed profiles of LPF, kinematic & other models: Car

From Table 2 we can observe that, while comparing the real worldmodel of the Volvo S60 T6, the kinematic model has a more realis-tic response than the LPF model, while transitioning from 0 to topspeed[14]. It can also be observed that, with higher initial speed themodels tend to perform alike. The data pertaining to the real worldmodel of the vehicle is available on third party performance testingindustries[25]. Furthermore, the Simscape model described in Sec-tion 3.1.3 has also been used to contrast the speed profiles of theLPF and the kinematic models. (*)- In the third party tests performed,the real world model was fitted with a speed governor, limiting itstop speed to 200 km/h.

Unlike profiles pertaining to the car above, the truck modelling hasbeen implemented with a fixed intermediate gear ratio of 0.78, asdescribed in Section 3.2.4.2. The following are the responses of thetruck model.

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. Itcan 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.

46 results

Figure 33: Ranged Speed Profile III: Truck

Figure 33 represents speed transition from 50 km/h to 80 km/h. Itcan be observed that the kinematic model leads the LPF model.

Speed Ranges

ModelTime [s]

0-Max[km/h]

0-20[km/h]

50-80[km/h]

80-125[km/h]

LPF 24.08 4.56 6.16 8.8

Kinematic 45.24 5.05 6.42 13.75

Table 3: Speed profiles of LPF & kinematic models: Truck

From Table 3 it can be observed that the LPF model has a highlyunrealistic response for the transition from 0 to top speed, as thereal world model takes 40 s to reach the top speed of 135.2 km/h. Incontrast, the kinematic model has a more realistic response to the realworld truck[4]. The speed profiles for the other speed ranges do notexhibit any significant discrepancies.

From Figures 39-44, it can be observed that the speed vs time re-sponses 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, inthe kinematic model, the acceleration is computed as a function ofthe net force acting on the vehicle. In turn, the net force acts as afunction of the torque produced. The torque curves for the car andtruck are shown in Figure 17 and Figure 19, respectively. Due to this

4.4 effects of simulation step and throttle 47

dependency on the vehicles’ powertrain characteristics, they modelthe 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 altersthe 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

48 results

Figure 35: Varying Simulation Steps: Acceleration Profile

Figure 34 and Figure 35 exhibit the effect of different simulationstep values in the speed and acceleration profiles. In both the figures,blue dashed line corresponds to a simulation step of 0.1 s, red dashedline corresponds to a simulation step of 0.2 s and yellow dashed linecorresponds to a simulation step of 0.05 s. It can be observed that asthe choice of simulation step value decreases, the slope of the speedvs time response increases. In the acceleration profile it can be ob-served that, with the decrease in the value of the simulation step, thetime taken to reach the acceleration ceiling increases, and hence, thegeneral decrease in the slope of the acceleration profile.

The default choice of simulation step in SUMO is 0.01 s. Analo-gously, the simulation step can be related to the cutoff frequency ofthe LPF; simulation step of 0.01 s is analogous to a cutoff frequencyof 100 Hz. This implies that, for every simulation step, 0.01 sec of realtime is simulated. For the purpose of simulation, all responses shownin Section 4.2 and Section 4.3 have been used with a time step of 0.1s or cutoff frequency of 10 Hz.

For the purpose of demonstrating the effect of different throttlelevels, the kinematic model of the car has been used, and the obser-vations recorded are as shown below.

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 kinematicmodel has a parameter that can be varied. This parameter is the throt-tle level. In a simple throttle, the throttle level acts as a gain to thetorque generated by the engine[20]. This value is thus set in the rangeas, throttle level ∈ [0,1]. In Figure 36 and Figure 37, blue line corre-sponds to 0.50, red line corresponds to 0.60, yellow line corresponds

50 results

to 0.70 and violet line corresponds to 0.80 levels of throttle, respec-tively. It can be observed that, as the throttle value increases, the timetaken to achieve the desired speed reduces. In essence, this level in-duces an effect similar to that of the LPF simulation step on the re-spective models. From the acceleration profile shown in Figure 37, itcan be observed that with lower levels of throttle, the car does notreach the ceiling limit of acceleration, which is the realistic behaviour,unlike the response recorded from the LPF as shown in Figure 35.

In Chapter 5, the conclusions from the speed vs time responses arestated, following which, possible future work to enhance this modelhave been suggested.

5C O N C L U S I O N & F U T U R E W O R K

The speed and acceleration profiles recorded from the LPF modelhave been compared to the kinematic models created in the MATLABenvironment. The factors highlighting the kinematic models’ feasibil-ity and fidelity for real time applications were discussed. From theprofiles presented in Chapter 4, the major drawback of the LPF modelthat has been observed is that, since there is no consideration of massor external forces, the time taken to reach the desired speed in cer-tain speed ranges is unrealistic as seen in Table 2 and Table 3. Thekinematic model overcomes this unrealistic behaviour, as it takes intoaccount the external forces and powertrain characteristics of the vehi-cle. The transition time from the initial speed to the desired speed iscomputed by the amount of torque that the engine produces at thegiven time. This torque vs engine relationship is derived from thepowertrain performance curves as shown in Figure 17 and Figure 19.The models created using the Simscape Toolbox in the Simulink envi-ronment, as described in Section 3.1, were either inaccurate and rela-tively slow, or accurate and very slow, and thus, were not consideredfor comparison.

To summarize:

1. Kinematic models for two different class specific vehicles, carand truck, were created and compared against the LPF model.

2. The kinematic models have a computation time that is accept-able for real time purposes.

3. The LPF model exhibits unrealistic behaviour in certain speedranges, which is eliminated in the kinematic models.

To conclude, the kinematic models are more realistic than the LPFmodel, as they reflect the real world vehicles closely and the executiontime for these models are suitable for real time applications, hence,they can be implemented to replace the LPF model in SUMO.

5.1 future work

The kinematic models do not use a controller. In essence, they areopen loop systems. The effect of this can be seen as a lack of a steady

51

52 conclusion & future work

state in the speed profiles, as the speed approaches the desired value.This can be attributed to the heterogeneous input to the models. TheLPF model takes initial speed, desired speed and acceleration limitsas inputs, while the kinematic models takes initial speed, time andthrottle level as inputs. Work could be done to achieve the cruisecontrol behaviour in the kinematic models by incorporating desiredspeed as an input to the model.

The Simscape model described in Section 3.1.3 is accurate andclosely represents the real world vehicle behaviour. However, thismodel has a high computation time. Work could be done to furthersimplify the model without compromising the fidelity, to achieve acomputation time suitable for real time applications.

The feasibility and accuracy of the vehicles’ kinematic models werecompared against the LPF model that was implemented in MATLAB.Work could be done to integrate these kinematic models in SUMOitself.

AA P P E N D I X

This section contains information of the simulation model setup asdescribed in Section 3.1.

1. Simulink to PS converter: This block converts the dimensionlessinput signal to a Physical Signal that can be used by a block thattakes physical signals as inputs.

Figure 38: S-PS Converter

The unit expression in ’Input signal unit’ parameter is associ-ated with the dimensionless input signal. The desired unit canbe assigned to the Physical Signal[8].

2. PS to Simulink converter: This block converts the input PhysicalSignal to a dimensionless output signal.

Figure 39: PS-S Converter

The unit expression in ’Output signal unit’ parameter mustmatch with the unit of the Physical Signal and determines theconversion from the Physical Signal to the dimensionless outputsignal[8].

3. Engine: Figure 40 represents a system-level model of a spark-ignition engine. A spark-ignition engine generally refers to apetrol engine. In this type of engines the air-fuel mixture inthe combustion chamber is ignited by a spark generated by thespark plug. The Volvo S60 T6 uses petrol as fuel. The engine isthe prime mover, as the fuel is converted to mechanical energyis this component[29]. The throttle input signal T lies between

53

54 appendix

zero and one and specifies the torque demanded from the en-gine as a fraction of the maximum possible torque[8].

Figure 40: Engine

Connections F and B are mechanical rotational conserving portsassociated with the engine crankshaft and engine block, respec-tively. The crankshaft is an engine component that converts thelinear motion of the piston into rotary motion. Connections Pand FC are physical signal output ports through which enginepower and fuel consumption rate are reported. A scope is con-nected to the connection P to record the engine power generated.The following are the settings[9]:-

• Maximum Power: 302 HP

• Engine Speed at Maximum Power: 5300 RPM

• Maximum Engine Speed: 8500 RPM

• Inertia: 0.2 kg*m²

• Initial Engine Speed: 1500 RPM

• Stall Speed: 500 RPM

• Speed Threshold: 100 RPM

The Maximum Power signifies the maximum possible powerthat can be generated by the engine prior to the transmissionof torque across the driveline. The Engine Speed at MaximumPower signifies the rotary speed of the engine crankshaft at theMaximum Power. The simulation fails if the engine speed ex-ceeds the Maximum Engine Speed setting. Since the engine hasrotating components, there exists resistance to changes in ro-tational speeds. As the engine speed varies, an inertia is ex-perienced. The Initial Engine Speed signifies the speed of theengine at the start of the simulation. The Stall Speed signifiesthat, when the engine speed generated by the model falls belowits value, the torque produced is blended to 0 Nm. The SpeedThreshold signifies the minimum step change needed in the en-gine speed, in order to generate torque. Both the Stall Speed

appendix 55

and Speed Threshold settings, yield 0 Nm of torque if violated,however, it helps distinguish between possible discrepancies inthe simulation.

4. Mechanical Rotational Reference: Figure 41 represents a me-chanical rotational reference point.

Figure 41: Rigid Frame

It is used to connect mechanical rotational ports that are rigidlyaffixed to the frame. In this case, the mechanical rotational portfrom the engine connection port B, is rigidly attached to theframe, which is the vehicle body[8].

5. Inertia: Figure 42 represents an ideal mechanical rotational iner-tia. All rotating components have inertia. Some blocks are pro-vided with an option to set the inertia. Additional inertia blocksare used where there is no option.

Figure 42: Inertia Module

The block has one mechanical rotational conserving port. Theblock positive direction is from its port to the reference point.This means that the inertia torque is positive if the inertia isaccelerated in the positive direction[8].

6. Torque Converter: Figure 43 represents a three-part torque con-verter consisting of impeller, turbine, and stator. The impelleris mechanically moved by the engine. The turbine drives theload produced. The stator is positioned in between the turbineand the impeller to alter the level of oil flow from then tur-bine to the impeller. For this purpose, the stator remains in afixed position. The torque converter is responsible for separat-ing the torque from the power source (engine) and multiplying

56 appendix

it to be sent through the driveline[24] by a fluid coupling mech-anism. Connections I (impeller) and T (turbine) are mechani-cal rotational conserving ports associated with the impeller andturbine, respectively[8]. The impeller takes the input from theengine crankshaft.

Figure 43: Torque Converter

The following are the settings:-

• Torque Transmission Time Constant: 0.02 s

• Speed Ratio Vector: [0.0, 0.5, 0.6, 0.7, 0.8, 0.87, 0.92, 0.94,0.96, 0.97]

• Torque Ratio Vector: [2.232, 1.5462, 1.4058, 1.2746, 1.1528,1.0732, 1.0192, 0.9983, 0.9983, 0.9983]

The Torque Transmission Time Constant signifies the fixed timeperiod taken to convert the input power to the impeller as out-put torque from the turbine. For forward movement or accelera-tion, the torque needs to be positive; it flows from port I (input)to port T (output). The torque ratio is (Output torque)/(Inputtorque). The speed ratio is (Output angular speed)/(Input an-gular speed). The speed and torque ratio vectors are functionblock defaults.

7. Gear Box: Figure 44 represents an ideal, non-planetary, fixedgear ratio gear box. The gear box is characterized by its onlyparameter, Gear ratio, which can be positive or negative. Con-nections S and O are mechanical rotational conserving ports as-sociated with the box input and output shaft, respectively. Thegear ratio is determined as the ratio of the input shaft angu-lar velocity to that of the output shaft. The input shaft angularvelocity is a characteristic of the driving gear, whilst the outputshaft angular velocity is a characteristic of the driven gear. Sincethe gears are of different sizes with different number of teeth,the gear ratio provides a measure of the combined efficiency[8].The gearbox takes the input from the torque converter turbine.

appendix 57

Figure 44: Gear Box

The following is the setting[9]:-

• Gear Ratio: 2.77

The block generates torque in positive direction if a positivetorque is applied to the input shaft and the gear ratio is assigneda positive value.

8. Differential: Figure 45 represents the differential which is ar-ranged as a planetary bevel gear train equipped with an addi-tional bevel gear transmission between the driveshaft and thecarrier. The pinion gear of this transmission is attached to thedriveshaft while the large bevel crown gear is affixed to the car-rier. The differential allows the outer wheel to rotate faster thanthe inner wheel in a turn. This is important in turns as the outerwheel rolls farther and faster than the inner wheel. The averageof the rotational speeds of the two wheels being driven equalsthe input rotational speed of the drive shaft. An increase in thespeed of one wheel is balanced by a decrease in the speed ofthe other, by splitting the angular rotational velocities depend-ing on the direction of the turn[22].

Figure 45: Differential

The following are the settings:-

• Crown wheel location: Right

• Carrier (C) to driveshaft (D) teeth ratio (NC/ND): 4

• Carrier inertia: 0 kg*m²

• Planet gear inertia: 0 kg*m²

Connections D, S1, and S2 are mechanical rotational conservingports associated with the driveshaft and the two output shafts,

58 appendix

respectively. S1 and S2 are the shafts belonging to the two sungears. When there is no relative slippage across the differential,and if the crown wheel is located to the right of the centre line,then S1 and S2 rotate forward, if D rotates forward[8]. The dif-ferential takes the input from the gearbox output shaft.

9. Tire: Figure 46 represents the tire model used in the vehicle.

Figure 46: Tire

Connection A is the mechanical rotational conserving port forthe wheel axle. Connection H is the mechanical translationalconserving port for the wheel hub through which the thrustdeveloped by the tire is applied to the vehicle. Connection N isa physical signal input port that applies the normal force actingon the tire. The force is considered positive if it acts downwards.Connection S is a physical signal output port that reports thetire slip[8]. The models discussed below use four tires, howeveronly the two driving tires are modelled. The input to the tireat the wheel axle, is provided from the differential shafts. Thefollowing are the settings[9]:-

• Rolling Radius: 0.3097 m

• Rolling Resistance Constant: 0.02

The rolling resistance in tires is caused due to the non-elasticeffects that are experienced due to the hysterical losses in thecompression and expansion of the tire region which is in con-tact with the road surface[18]. The rolling radius signifies theradius of the tire with a fixed load. The rolling resistance con-stant value corresponds to cars on concrete or asphalt roads[23].

10. Vehicle Body: Figure 47 represents a two-axle vehicle body inlongitudinal motion. The block accounts for body mass, aerody-namic drag, road incline, and weight distribution between axlesdue to acceleration and road profile. The vehicle does not pitchor move vertically relative to the ground.

appendix 59

Figure 47: Vehicle Body

Connection H is the mechanical translational conserving portassociated with the horizontal motion of the vehicle body. Theresulting traction motion developed by tires is connected tothis port. Connections V, NF, and NR are physical signal out-put ports for vehicle velocity and front and rear normal wheelforces, respectively. Since the models used are rear wheel driven,the NF physical signal output port is ignored. Wheel forces areconsidered positive if acting downwards. Connections W andbeta are physical signal input ports corresponding to headwindspeed and road inclination angle, respectively[8]. The connec-tions to W and beta are provided from the input control block.The following are the settings[9]:-

• Mass: 1645 kg

• Number of wheels per axle: 2

• Horizontal distance from CG to front axle: 1.4 m

• Horizontal distance from CG to rear axle: 1.6 m

• CG height above ground: 0.5 m

• Frontal area: 3.111948 m²

• Drag coefficient: 0.31

• Initial velocity: 0 km/hr

The drag coefficient corresponds to vehicles shaped like theVolvo S60 T6. Mass represents the sum of kerb weight and theload present in the vehicle. For simulation purposes, one person(70 kg) is considered to be present in the vehicle. The centre ofgravity (CG) parameters calculate the effect of weight distribu-tion. The frontal area and the drag coefficient account for theaerodynamic force experienced by the vehicle.

11. Solver: Figure 48 represents the ordinary differential equation(ODE) solver. The default solver is used, ode23t[8].

60 appendix

Figure 48: ODE Solver

This block solves for acceleration at every time step in order tocompute the speed vs time response graph.

BA P P E N D I X

The WebPlotDigitizer application designed by Ankit Rohatgi[34] hasbeen used to extract the data from the images of the performancegraphs. Some features of the WebPlotDigitizer are as follows[34]:-

1. Web based. No installation needed.

2. Supports XY charts (even skewed and non-orthogonal), polarplots, ternary diagrams and maps.

3. Automatic curve extraction algorithms aid rapid extraction of alarge number of data points.

4. Distance and angle measurement tools for measuring maps.

5. Generates data in .CSV format which can for data analysis.

6. User scriptable in Javascript.

7. Freeware and is distributed under the GNU General Public Li-cense Version 3.

61

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IEEE Transactions on Control Systems Technology, 19(3):664–672,2011.

AbstractContentsList of FiguresList of Figures

List of TablesList of Tables

AcronymsAcronyms

1 Introduction2 Related Works2.1 Detailed Modelling of Road Vehicles2.2 Modelling for Autonomous Vehicles

3 The Models3.1 Vehicle models using Simulink3.1.1 Model Components3.1.2 Model I: Simple Rear Wheel Drive Model3.1.3 Model II: Rear Wheel Drive Model with Custom Transmission

3.2 Vehicle models using MATLAB3.2.1 Modelling References3.2.2 Data Extraction3.2.3 Data Fitting3.2.4 Modelling

3.3 Validation Model

4 Results4.1 Computation Time4.2 Maximum Speed/Acceleration Profile4.3 Ranged Speed Profile4.4 Effects of simulation step and throttle

5 Conclusion & Future Work5.1 Future Work

A AppendixB AppendixBibliography