Development of a Traction Control System for a Parallel-Series PHEV THESIS

Transcription

1 Development of a Traction Control System for a Parallel-Series PHEV THESIS Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University By Amanda Nicole Hyde Graduate Program in Mechanical Engineering The Ohio State University 2014 Master's Examination Committee: Professor Giorgio Rizzoni, Professor Shawn Midlam-Mohler

2 Copyright by Amanda Nicole Hyde 2014

3 Abstract The work presented in this thesis details the development of a traction control system for a parallel-series plug-in hybrid electric vehicle created by the Ohio State EcoCAR 2 team. The test vehicle is a rebuilt 2013 Chevrolet Malibu features a 1.8L ethanol engine, an 80 kw permanent magnet electric machine, and a 6-speed automated manual transmission to power the front axle while another 80 kw electric machine and a fixed speed gear box power the rear axle. A 340 V lithium ion battery pack acts as the energy storage system for the electric drivetrain components. The front and rear powertrains are not mechanically coupled and thus act independently of one another allowing the vehicle substantial flexibility of three major operating modes to achieve maximum efficiency without sacrificing vehicle range. While the slip detection and traction control algorithms developed in this work were intended specifically for the Ohio State EcoCAR 2 vehicle, they could be easily adapted to any vehicle with independent front and rear drivetrains. The existing quasi-static simulator of the test vehicle was expanded to account for the inertias and stiffnesses present in the powertrain and create a dynamic simulator. This was accomplished using the SimDriveline toolbox available in The Mathworks Simulink software. This model also incorporates longitudinal tire dynamics using the Pacejka Magic Formula and a longitudinal vehicle model. The resulting simulator is a suitable plant model ii

4 for traction control development, though further refinement is required for complete functionality in all modes. Using the dynamic plant model, a slip detection algorithm capable of detecting slip on either axle or both simultaneously is developed. The algorithm uses six wheel speed comparisons to determine the vehicle current slip scenario without requiring knowledge of the current vehicle speed. Next the traction control algorithm was developed to act independently on each axle if slip is detected. The system creates axle torque limits on the outputs of the operating strategy that reduce torque until wheel slip stops and then gradually reapplies the torque until the full driver torque request has been restored with no wheel slip. Software-in-the-Loop results for a large variety of tests show significant improvement in vehicle performance on low friction surfaces. Large decreases in peak wheel speed, peak slip ratio, and maximum slip interval were observed in all cases. In-vehicle validation was performed for a limited number of tests but adequately demonstrated real-world functionality of the slip detection and torque control algorithms on the vehicle. iii

5 Vita May Parkview High School B.S. Mechanical Engineering, University of Oklahoma M.S. Mechanical Engineering, Ohio State University Publications Hyde, A., Midlam-Mohler, S., and Rizzoni, G., "Development of a Dynamic Driveline Model for a Parallel-Series PHEV," SAE Int. J. Alt. Power. 3(2):2014 Fields of Study Major Field: Mechanical Engineering iv

6 Table of Contents ABSTRACT... II VITA... IV LIST OF TABLES... IX LIST OF FIGURES... X CHAPTER 1: MOTIVATION THESIS OVERVIEW... 3 CHAPTER 2: LITERATURE REVIEW ELECTRIC AND HYBRID VEHICLES Introduction Classifications EcoCAR THE TRACTION CONTROL PROBLEM Intro to Tire Physics CURRENT TRACTION CONTROL SOLUTIONS Torque Management Devices Four-Wheel and All-Wheel Drive Traction Control Systems The OSU EcoCAR 2 Traction Control Problem v

7 CHAPTER 3: SYSTEM AND COMPONENT MODELING TRACTION CONTROL PHILOSOPHY REQUIREMENTS ASSUMPTIONS POWERTRAIN MODELING Engine Front Electric Motor Transmission Rear Electric Machine and Gearbox Front and Rear Axles Wheel Dynamics Tire Model Vehicle Model CHAPTER 4: SIMULATION AND VEHICLE CONTROLS INTRODUCTION EXISTING SIMULATION TOOLS: ECOSIM VEHICLE CONTROL STRATEGY SIMULATION FOR TRACTION CONTROL: ECOSIM2 DYNAMIC ECOSIM2-DYNAMIC INITIAL VALIDATION ECOSIM2-DYNAMIC RESULTS CHAPTER 5: TRACTION CONTROL DEVELOPMENT VEHICLE CONFIGURATION ALGORITHM PLACEMENT ACTIVATING TRACTION CONTROL vi

8 5.3.1 Detecting Wheel Slip Determining Slip Scenario Handling for Non-Unique Slip Signatures Setting Slip Flags TRACTION CONTROL ALGORITHM IMPLEMENTATION Controls Hardware Required Signals and Sensors PARAMETER OPTIMIZATION SYSTEM PERFORMANCE METRICS SENSITIVITY TO ROAD FRICTION CHAPTER 6: TESTING AND RESULTS SOFTWARE-IN-THE-LOOP (SIL) TESTING CHARGE DEPLETING MODE - SOFTWARE-IN-THE-LOOP (SIL) RESULTS Results Summary Detailed Results All Wheels on Low Friction CHARGE DEPLETING MODE IN VEHICLE RESULTS Launch with All Wheels on Low Friction Launch with Left Wheels on Low Friction CHARGE SUSTAINING SERIES MODE SIL RESULTS Results Summary Detailed Results All Wheels on Low Friction CHAPTER 7: CONCLUSIONS AND FUTURE WORK CONCLUSIONS vii

9 7.2 FUTURE WORK BIBLIOGRAPHY viii

10 List of Tables Table 1: EcoCAR 2 Vehicle Technical Specifications Table 2: Gear and Drive Ratios of the Transmission Table 3: Friction Coefficient Variance Convention Table 4: Typical Friction Coefficients [11], [22] Table 5: Conditions for Slip Scenario Table 6: Conditions for Slip Scenario Table 7: Conditions for Slip Scenario Table 8: Conditions for Slip Scenario Table 9: Slip Flag Determination Table 10: Simulation Optimized Parameter Values Table 11: Friction Distributions Table 12: Results Summary for Charge Depleting Operation in SIL Table 13: Results Summary for Charge Sustaining Series Operation in SIL ix

11 List of Figures Figure 1: Oil Consumption in Select Regions [1]... 1 Figure 2: Sample Series Hybrid Architecture [3]... 7 Figure 3: Sample Parallel Hybrid Vehicle Architecture [3]... 8 Figure 4: Sample Power-Split Hybrid Architecture [3]... 9 Figure 5: OSU Powertrain Architecture Figure 6: Powertrain Configurations for Vehicle Operating Modes Figure 7: Tire Contact Mechanisms [2] Figure 8: Brush Model Representation of Tires [2] Figure 9: Characteristic Curve of Longitudinal Tire Force as a Function of Slip Ratio [8] Figure 10: Example Slip-Slope Curves [11] Figure 11: Free Body Diagram of Wheel During Acceleration [1] Figure 12: Clutch Type Limited Slip Differential [2], [15] Figure 13: Viscous Coupling Type Limited Slip Differential [2] Figure 14: Driveline Dynamic Model Figure 15: SAE Tire Axis System [14] Figure 16: Vehicle Model Block Diagram [22] Figure 17: Torque/Speed Structure of EcoSIM x

12 Figure 18: EcoSIM2 User Interface Figure 19: PHEV Powertrain Subsystem in EcoSIM Figure 20: EcoSIM2 Dynamic User Interface Figure 21: Initial Validation for EcoSIM2-Dynamic Figure 22: Actuator Torques and Speeds During US06 Cycle - μx = Figure 23: Wheel Speeds and Wheel Slip During Zero-to-Sixty Acceleration - μx = Figure 24: Actuator Torques and Speeds During US06 Cycle - μx = Figure 25: Wheel Speeds and Slips During US06 Cycle - μx = Figure 26: Control Strategy Flow Chart Figure 27: Slip Scenarios Figure 28: Torque Reduction Strategy Flow Chart Figure 29: Traction Control Illustration Figure 30: dspace MicroAutoBox II Figure 31: Friction Study Results Per Axle Figure 32: Overall Performance Metric Value for Friction Study Figure 33: Simulation for Friction Distribution A Overall Performance Metric = Figure 34: Simulation for Friction Distribution G Overall Performance Metric = Figure 35: Scenarios for SIL Testing Figure 36: Typical Accelerator Pedal Command Figure 37: Wheel Speeds and Slip All Wheels on Low Friction Traction Control Off Figure 38: Vehicle Speed and Pedal Profile xi

13 Figure 39: Wheel Speeds and Slip All Wheels on Low Friction Traction Control On Figure 40: Axle Torque Commands from Traction Control System Figure 41: Vehicle Acceleration Performance Figure 42: All Wheels on Ceramic Tiles Traction Control Off Figure 43: All Wheels on Ceramic Tiles Traction Control On Figure 44: Left Wheels on Low Friction Traction Control Off Figure 45: Left Wheels on Low Friction Traction Control On Figure 46: Wheel Speeds and Slip All Wheels on Low Friction Traction Control Off Figure 47: Wheel Speeds and Slip All Wheels on Low Friction Traction Control On Figure 48: Axle Torque Commands of Traction Control System Figure 49: Vehicle Acceleration Performance xii

14 Chapter 1: Motivation Petroleum is a non-renewable resource that is depleting with time. However the global population continues to be reliant on petroleum products and petroleum energy to power mobility around the world. Developing countries also contribute to a rapidly increasing demand for petroleum products. Global consumption of oil has nearly tripled since 1965 [1] as seen in Figure 1. Figure 1: Oil Consumption in Select Regions [1] 1

15 Because oil supplies are finite in nature, the peak and eventual decline of oil production rates are inevitable as adequate new supplies cannot be consistently found and brought to production at reasonable cost and in a timely manner. Over time, this has driven up the price of oil significantly. Much of the demand for oil in the United States is due to use as fuel in transportation and in automobiles in particular. As oil and fuel prices increase, the demand for fuel efficient vehicles, which can maximize the distance travelled per dollar, also increases. This demand is also pushed forward by ever increasing regulations limiting allowable emissions and mandating greater overall fuel economy. The response from automotive manufacturers has been to pursue various avenues for increasing fuel economy, decreasing emissions, and ensure sustainability into the future. One method pursued is advancements in efficiency for internal combustion engines. Another is the reduction of vehicle road loads with low rolling resistance tires, lightweight materials, low drag body designs, and active aerodynamics. A third avenue is the use of alternative fuels such as biodiesel, ethanol, natural gas, hydrogen, and electricity. A final common and promising solution that manufacturers are developing is hybrid electric vehicles. These are vehicles which use a minimum of two energy converters and minimum two energy sources which are stored on-board and used for vehicle propulsion [2]. Many types of hybrid vehicle are available on the market today including hybrid electric vehicles (HEV), plug-in hybrid electric vehicles (PHEV), and extended range electric vehicles (EREV). Hybrids provide a high level of flexibility in the powertrain 2

16 configuration which increases the capability of the vehicles over that of conventional vehicles to meet increasingly stringent fuel economy and emissions goals. It is not enough to assume that the existence of hybrids will make them attractive to consumers. In order to boost the sale of hybrids and encourage them to permeate both the market and the road, safety and consumer acceptability features must be comparable to or exceed those of modern conventional vehicles. Traction control is a feature important both to safety and consumer acceptability that is becoming standard on vehicles sold today. For this reason, the development of traction control for hybrid vehicles is a necessary endeavor. 1.1 Thesis Overview The work presented in this thesis discusses the development of a traction control system for Ohio State EcoCAR 2 competition vehicle. This includes the creation of a dynamic plant model of the vehicle powertrain, the development of a versatile slip detection algorithm, and finally the development of a traction control algorithm for the Ohio State EcoCAR 2 vehicle. The organization of this thesis is as follows: Chapter 2 provides background information on common types of hybrid vehicles, the EcoCAR 2 competition, and on the experimental vehicle architecture. It also explains the background information related to tire contact and traction control including explanations of current traction control solutions. 3

17 Chapter 3 details the development of a dynamic powertrain model necessary for use as the plant model in traction control development. Chapter 4 outlines the implementation of the model developed in Chapter 3 to create a simulator in Simulink Chapter 5 describes the simulation and control development of the slip detection strategy and the traction control algorithm Chapter 6 details the testing of the developed algorithm and the results obtained through simulation and in-vehicle testing Chapter 7 summarizes the work presented in the thesis and gives recommendations for future work on the topic 4

18 Chapter 2: Literature Review 2.1 Electric and Hybrid Vehicles Introduction The expanding prevalence of powertrain electrification demonstrates its popularity as a means to increase fuel economy and reduce emissions. An electrified powertrain can be either an electric vehicle (EV) or a hybrid electric vehicle (HEV). Electric vehicles do not contain an internal combustion engine and are propelled solely by one or more electric machines that are powered by a high voltage battery pack. Electric vehicles entirely eliminate the need for liquid fuel in the vehicle and as a result have zero tailpipe emissions. Electric vehicles also benefit from the high efficiency of electric machines in converting electrical energy to mechanical power and the ability to recapture some amount of mechanical energy and return it to the battery pack through the use of regenerative braking. The disadvantages of electric vehicles include a limited range between charges (<100 miles) and long charge times which make EVs impractical for use outside of cities where total daily commutes can be short. Other disadvantages to EVs include high purchase prices, lack of charging station infrastructure, and concerns over the life-span of a high voltage battery pack. 5

19 Hybrid electric vehicles combine the electric machines and battery pack of an EV with an internal combustion engine and liquid fuel to propel the vehicle. There are a variety of liquid fuels commonly used in hybrids including gasoline, E85, natural gas, and diesel. The combination of power sources allows the engine size to be reduced compared to that of conventional powertrains without sacrificing the vehicle s ability to meet driver power demands. The addition of liquid fuel also extends the range of the vehicle to be equivalent to the range of conventional vehicles. Hybrid vehicles are also able to recapture mechanical energy as electric energy through regenerative braking just as in EVs. The disadvantages of hybrid vehicles are similar to those of electric vehicles including high purchase price, charging infrastructure, and life of the battery pack Classifications Hybrids are divided further into three main classifications: series, parallel, and power split. These classifications are based upon the powertrain architecture used in the vehicle. Each type of hybrid has a unique configuration that comes with certain advantages and disadvantages Series Hybrid Series hybrids are among the simplest of hybrid architectures. In a series hybrid all of the propulsive power to the wheels is provided by an electric machine. Another electric machine is driven by an engine to provide power directly to the battery pack. The advantages of a series architecture include ease of packaging since the two motors need 6

20 not be near each other and a simple control strategy relative to other hybrid architectures since only one torque source is connected to the driven wheels. Engine efficiency and emissions can also be optimized since the engine is not mechanically coupled to the wheels and thus can remain at predetermined optimal operating points at all times. An example series architecture is given in Figure 2. Figure 2: Sample Series Hybrid Architecture [3] A disadvantage of the series architecture is the requirement for a large electric motor to be used for traction and the requirement of at least two electric motors. The powertrain also has inherent losses associated with the multiple energy conversions from mechanical to electrical and back to mechanical. 7

21 Parallel Hybrid Parallel hybrids have both an engine and electric machine coupled to the wheels through some mechanical coupling. A multi-gear transmission can also be used with the engine much like a conventional vehicle. The electric machine can be coupled before or after the transmission in the driveline. Also, the electric machine can be used to help propel the vehicle or act as a generator while the engine alone propels the vehicle. An advantage of the parallel architecture is that only one electric machine is required and both the engine and electric machine can be downsized since the sum of the power sources is used to drive the wheels. The parallel architecture also allows for compact packaging. The disadvantages of a parallel architecture include the inability to maintain the engine at optimal operating points and increased complexity of the control strategy since torque and speed must be balanced between multiple devices while also balancing the battery state of charge. An example of a parallel hybrid architecture is given in Figure 3. Figure 3: Sample Parallel Hybrid Vehicle Architecture [3] 8

22 Power-Split Hybrid Power-Split hybrids contain the functionality of both series and parallel configurations and are able to switch between the two. To obtain the ability to run in both modes, a powersplit hybrid typically contains two electric machines, one internal combustion engine, and a configuration of clutches and gear sets, typically planetary gear sets, that allow the vehicle to switch between modes. Power-split hybrids have the most complex controls problem of the three hybrid classifications due to the large number of actuators involved. Packaging can also be challenging due to the number of components involved. The main advantage of a power-split hybrid is the flexibility of the powertrain which increases the capability for improving fuel economy and emissions while maintaining vehicle performance [2]. An example of a power-split hybrid architecture is given in Figure 4. Figure 4: Sample Power-Split Hybrid Architecture [3] 9

23 2.1.3 EcoCAR 2 The rapidly advancing vehicle technology used in industry demands a particular skill set and experience for effective development. Many of the nation s top engineering universities do not focus on or teach students about these new technologies as a part of their degree programs, causing new engineering graduates to be inexperienced or ignorant of advanced vehicle technology prior to their first day on the job. To help fill this knowledge gap, the Advanced Vehicle Technology Competition (AVTC) series began and continues to the present where EcoCAR 2 is the currently active competition sequence. EcoCAR 2 and all AVTCs give students the opportunity to work first hand with the design and implementation of state of the art automotive technologies while still enrolled in school. EcoCAR 2 is an AVTC sponsored by General Motors and the US Department of Energy that challenges students to redesign a 2013 Chevrolet Malibu in order to obtain higher fuel economy and lower emissions without sacrificing performance, safety, or consumer acceptability. Fifteen teams across the US and Canada are participating in the competition with the task of designing, building, and optimizing a new powertrain for the Malibu culminating in a showroom ready vehicle by the end of the competition cycle. The vehicles are judged over a full range of criteria including fuel economy, emissions, drivability, acceleration, and braking performance, and consumer acceptability features. The competition runs for three years, each of which represent a distinct phase of the design process. Year 1 focuses on the design and computer simulation of the vehicles. 10

24 The year begins with an architecture selection phase which is followed by component selection, in depth packaging studies, development of the vehicle and component simulation plant models, and early development of the vehicle control strategy using Hardware-in-the-Loop testing equipment. Early in Year 2 teams receive the production vehicle from GM. Throughout the year each team tears down the stock Malibu and integrates the team designed powertrain and controls. The teams should have a functional mule vehicle capable of participating in dynamic driving events by the end of Year 2. Year 3 allows teams to refine and optimize the mechanical, electrical, and controls systems with the ultimate goal of a near production ready vehicle by the end of Year EcoCAR 2 Vehicle Technical Specifications The competition provides a set of vehicle technical specifications (VTS) that act as performance targets for the vehicle during development. Table 1 below gives a selection of relevant VTS for EcoCAR 2. The values for each metric for the stock 2013 Chevrolet Malibu are provided in the table as well as the competition target value and the 2014 predicted value for the Ohio State team vehicle. The values for the Ohio State proposed design are found using the simulation tools discussed later in Chapter 4. Table 1 clearly illustrates the competition goals of reducing emissions and improving fuel economy while maintaining performance and utility. This presents a significant design challenge for the competing teams. For example, the acceleration times of the vehicle must 11

25 remain comparable to the stock vehicle despite a significant increase in vehicle mass due to hybridization. Specification Table 1: EcoCAR 2 Vehicle Technical Specifications Production 2013 Malibu Competition Design Target OSU Proposed Design Acceleration 0-60 mph 8.2 sec 9.5 sec 10 sec Acceleration mph (Passing) 8.0 sec 8.0 sec 4.6 sec Braking 60-0 mph ft (43.7 m) ft (43.7 m) ft (43.7 m) Highway 20 min 10+% 3.5% mph Cargo Capacity 16.3 ft ft 3 10 ft 3 Passenger Capacity 5 >=4 5 Vehicle Mass 1589 kg <2250 kg 2075 kg Starting Time <2 sec <2 sec <10 sec Ground Clearance mm 155 mm >127 mm Vehicle Range 736 km 322 km >398 km Utility Factor (UF)-Weighted Fuel Energy Consumption* [457 mi] (CAFE) 8.83 (lge/100 km) [787 Wh/km] [200 mi]* 7.12 (lge/100 km) [634 Wh/km] [247 mi]* 1.36 (lge/100km) [121.1 Wh/km] UF-Weighted AC Electric Energy Consumption* N/A ** (Wh/km) UF-Weighted Total Energy Consumption* 787 (Wh/km) 634 (Wh/km) (Wh/km) UF-Weighted WTW Petroleum Energy (PE) Use* 774 (Wh PE/km) 624 (Wh PE/km) 43.1 (Wh PE/km) UF-Weighted WTW GHG Emissions* 253 (g GHG/km) 204 (g GHG/km) (g GHG/km) Criteria Emissions Tier 2 Bin 5 Tier 2 Bin 5 <Tier 2 Bin 5 The competition also evaluates qualitative consumer acceptability features such as interior noise, drive quality, ride, fit and finish, and stability. Though not listed in Table 1, these metrics are judged during the competition and thus were kept in mind throughout vehicle development process. 12

26 Ohio State Vehicle Architecture The OSU vehicle architecture is a Parallel-Series PHEV shown in Figure 5. The front axle is powered by a 1.8L Honda high compression ratio engine that can be coupled or decoupled from the transmission input with a clutch. An 80 kw permanent magnet electric machine is connected via belt drive to the transmission input shaft. The transmission itself is a 6-speed automated manual transmission. The rear axle is powered by another 80 kw electric machine connected to a fixed ratio gearbox which drives the rear wheels. The electric drivetrain components are powered by a 340 V, 18.9 kwh lithium-ion battery pack. This architecture has great versatility in its operation due to the independent front and rear drives and the transmission s ability to be used as an additional clutch when set to neutral or one of the six gear ratios. This allows the vehicle to operate in a charge depleting mode and a charge sustaining mode with both parallel and series configurations. Figure 5: OSU Powertrain Architecture 13

27 For charge depleting operation, the engine is decoupled from the transmission while both electric machines provide power to the wheels. For charge sustaining series operation, the transmission is shifted to neutral and the engine clutch is closed so that the engine charges the battery pack using the front electric machine as a generator and the rear electric machine drives the vehicle. For charge sustaining parallel operation, the clutch is closed and the transmission is in gear such that all three torque actuators are connected to the wheels. Diagrams showing the vehicle configuration for each mode are shown in Figure 6. Figure 6: Powertrain Configurations for Vehicle Operating Modes 14

28 An important intermediate operating mode is the engine start mode. During engine start, the powertrain configuration is the same as series configuration. All driver requested torque is sent to the rear electric machine and the front wheels are disconnected from the front actuators with the transmission in neutral. The engine clutch closes to couple it with the transmission input shaft and the secondary belt pulley. The front electric machine is then used to spin up the engine to the required starting speed as the engine begins firing. 2.2 The Traction Control Problem Active vehicle dynamics controls serve several important purposes. These include increasing the range of conditions under which a vehicle behaves predictably as well as enhancing vehicle comfort and response [4]. Traction control in particular maximizes longitudinal and lateral tractive forces between the vehicle s tires and the road for acceleration and cornering performance. This is accomplished using control inputs and available actuators to target an appropriate driven wheel slip. When thoroughly implemented, traction control allows inexperienced drivers to perform as well as or better than experienced drivers on slippery roads [4]. To understand traction control, it is necessary first to understand the fundamental physics of tire contact and traction. This chapter will give an introduction to traction physics that includes tire and vehicle forces, tire contact, and wheel slip. A survey of popular traction control methods currently used in conventional vehicles and novel traction control methods proposed for hybrid vehicles will also be given. The section will conclude with a detailed explanation of the unique traction control problem presented by the experimental vehicle. 15

29 2.2.1 Intro to Tire Physics Vehicle motion is primarily caused by forces generated at the contact patch between tires and the road. These forces are also produce the greatest non-linearity and uncertainty in the control of vehicle dynamics [4]. To address this problem, highly non-linear models are used to represent tire dynamics. However, only the underlying principles of tire contact will be presented here Contact Mechanisms A vehicle s ability to accelerate or decelerate is often limited by the frictional coupling between the tire and the road. The frictional coupling is a result mainly of two mechanisms: adhesion and hysteresis. Adhesion is the result of intermolecular bonds between rubber in the tire and aggregate in the road surface. Hysteresis represents energy loss as a result of deformation in the rubber as it slides over the road surface [5]. Both of these forces, as friction forces, rely upon some amount of slip occurring in the contact patch. Adhesion and hysteresis are illustrated in Figure 7. 16

30 Figure 7: Tire Contact Mechanisms [2] Effective Rolling Radius An important concept that affects accurate tire modeling is the effective rolling radius. The effective rolling radius of the wheel relates the angular velocity and linear velocity of the wheel as it moves through the contact patch. The effective rolling radius differs from the nominal tire radius due to the linear deformation of the tire in the contact patch. It is important because typical vehicle operation occurs with a slip ratio of 10% or less for which the calculation is significantly impacted by small changes in tire radius [2]. The basic relationship between angular and linear velocity that defines effective rolling radius for a free rolling wheel is given by R eff = V x ω w ( 1) 17

31 where V x is the longitudinal speed of the wheel center and ω w is the angular velocity of the wheel [6]. In order to calculate the effective rolling radius without detecting wheel speed, alternative calculations exist. One such alternative is given by [2] sin {cos 1 ( r static r )} R eff = [ w cos 1 ( r ] r w ( 2) static r ) w where r w and r static represent the relaxed wheel radius and static wheel radius respectively. Static wheel radius is defined by [2] r static = r w F z k t ( 3) F z is the normal load on the tire and k t is the vertical tire stiffness. The vertical tire stiffness can be calculated using test data from the tire manufacturer Brush Model The brush model views the tire as a series of infinitesimal tread elements that reach laterally over the contact patch. These elements can be thought of as individual spring elements that can deform independently [2], [7]. The brush model also divides the contact patch into sliding and adhesion regions. In the adhesion region, the tread elements adhere to the road and the force generated is influenced by static friction. In the sliding region, the tread elements slide against the road surface and the forces developed are influenced by kinetic friction [7]. The sliding and adhesion forces cause the tread elements to bend as seen in Figure 8. 18

32 Figure 8: Brush Model Representation of Tires [2] Considering the longitudinal and angular velocities defined previously, the net velocity of the treads through the length of the contact patch, l cp, can be expressed as v tread = R eff ω w V x ( 4) For a driving wheel, R eff ω w is greater than V x implying that the net tread velocity is opposite the direction of the longitudinal velocity. If the net tread velocity is relatively small, the adhesion region exists which means that the tip of the element entering the adhesion region has zero velocity at the point of contact with the ground and a velocity of v tread at the other end of the tread element. This speed difference causes the tread elements 19

33 to bend in the direction of longitudinal vehicle motion as shown in Figure 8 [8]. At the point at which the tire deformation exceeds the capability of static friction between the tire and the road the tread element enters the sliding region of the contact patch. When the tread element exits the contact patch entirely it returns to a relaxed state [2]. For a braking wheel, r eff ω w is less than V x implying that the net tread velocity is in the same direction as the longitudinal speed. This causes the tread elements to bend in the same manner but opposite direction of that shown in Figure 8 [2], [8]. It also results in the positions of the sliding and adhesion regions being switched from that shown in Figure 8 with respect to the direction of vehicle motion. In the case of a freely rolling wheel, meaning that no driving or braking torque is applied, the tread elements remain vertical throughout the contact patch and thus develop no propulsive force [6] Wheel Slip From the net tread velocity and the understanding of the maximum bending capability of the tread elements explored above the slip ratio can be derived. The slip ratio is a unitless metric that defines how the maximum deflection of the tread element is proportional to the ratio of slip velocity in the contact patch to longitudinal velocity of the vehicle [5], [8]. Various expressions for wheel slip ratio exist, but for this work, the slip ratio is given by: κ = R effω w V x V x ( 5) 20

34 This expression yields positive slip ratios when the vehicle is accelerating and negative slip ratios when the vehicle is braking. Often a very small constant is added to the denominator of the expression to prevent the slip ratio from becoming undefined as the vehicle speed approaches 0. This yields a slip expression of: κ = R effω w V x V x + ε x ( 6) where ε x is the small constant Tire Friction Characteristics One of the most important features necessary for traction control is the ability to estimate friction between the tire and the road surface, or more specifically, the wheel-slip vs. adhesion-coefficient characteristics of the tire. The coefficient of friction depends on numerous variables and must be estimated in real time making it one of the greatest challenges in traction control development [9], [10]. Some of the involved factors include surface topography of the road, tread design, contaminants, tire speed, and the viscoelastic properties of the rubber compound which vary with temperature and pressure. Due to the complexity of the problem, tire friction characteristics are generally determined from experimental observations and an empirical formulation is created. One frequently used solution in current vehicles is the use of look-up tables based on experimental trials. While deemed adequate for many driving conditions, these are limited in their capability due to being a fixed control type. This means the tables are tuned to accommodate worst 21

35 case scenarios with poor road conditions which doesn t allow optimal performance in good conditions [9], [10]. Tire friction exhibits specific characteristics of peak and sliding friction. The peak coefficient, μ peak, denotes the maximum friction force that can be created between the tire and the road. Once the shear load between tire and road exceeds the force capability of the vertical load on the tire combined with static friction, the wheel begins to slip and sliding friction becomes the governing force [2]. This results in the total tractive force decreasing continuously until the wheel locks entirely for braking or pure sliding occurs for acceleration [10]. A typical characteristic curve of longitudinal tire force as a function of the slip ratio is shown in Figure 9. Figure 9: Characteristic Curve of Longitudinal Tire Force as a Function of Slip Ratio [8] 22

36 Considering only the longitudinal direction, the friction coefficient is given by μ = F x F z ( 7) Estimating Tire Friction Coefficient There are numerous methods in use or proposed for estimating tire friction coefficient in real-time. Some methods focus on detecting the many factors that affect friction and then analytically predicting the peak friction coefficient. These methods frequently utilize specialized sensors such as lubricant sensors or optical sensors which look at road reflections [11]. Other methods look at the effects created by tire friction and then backcalculate to determine the friction coefficient. The effects typically utilized are acoustic characteristics, tread deformation, and wheel slip. The first two again use specialized sensors, an acoustic sensor for acoustic characteristics and a sensor affixed to the inner surface of the tire to detect tread deformation, and rely on an understanding of very complex characteristics that make it difficult to obtain an accurate estimation [8], [11]. Friction estimation based on wheel slip utilizes wheel speed and input force data to observe the correlation between the tire slip at a given force to determine the friction coefficient. Finally, there are methods of friction estimation that utilize longitudinal vehicle dynamics to estimate tire friction coefficient. The most well-known of these methods is the slipslope method. The slip-slope method uses predetermined maps of slip-slope and friction data to estimate μ in real-time based on the slip-slope calculated from sensor data [8]. A generic example of the type of maps used with the slip-slope method is shown in Figure 23

37 10. This method does have several drawbacks. First, it is only valid for low slip ratios. Second, driven wheel speed is usually used to determine vehicle speed which leaves allwheel drive vehicles such as the Ohio State EcoCAR 2 vehicle without an accurate source of absolute vehicle speed. This has been solved in some vehicles by adding a 5th nondriven wheel to the vehicle or utilizing GPS speedometers [8], [11]. This method also requires experimental data for the particular type of vehicle and tires in order to obtain accurate slip-slope curves since the factors affecting the peak and shape of the curves is different for each vehicle. Figure 10: Example Slip-Slope Curves [11] Longitudinal Tractive Force At low slip ratios, the longitudinal tractive force of the tire can be given by [2]: 24

38 F x = K T κ ( 8) where K T represents the longitudinal stiffness of the tire. This linear slip-slope region can be seen easily in Figure 9. The linear region ends at the inflection point μ peak. Beyond this point at high slip ratios the relationship becomes highly non-linear as traction is lost [2], [8]. Also, once the peak friction point has been passed, the tire force response is saturated causing the longitudinal force to decrease continuously until the wheels either lock or reach a complete spin [10] Tire Rolling Resistance Due to internal damping of the tire material, not all of the energy used to deform the tire as it rolls is recovered when the tread elements exit the contact patch and return to their original shape. Also, the distribution of the normal load on the tire becomes asymmetric when the tire is rotating. This is because the spring elements are not purely elastic but instead have viscous dissipation which prevents the force used to compress the springs from being recovered in the rear half of the contact patch [8]. This shifts the normal load distribution towards the forward portion of the contact patch. The loss of energy can be represented as a force on the tires which opposes the motion of the vehicle. This force, called the tire rolling resistance, can be represented by [12]: F RR = Mg cos(α) C r ( 9) For this equation, M, g, and α represent the vehicle mass, acceleration of gravity, and grade angle of the road respectively. C r is a rolling resistance coefficient that is a function of 25

39 vehicle speed. It is also dependent on the type of tire, inflation pressure, temperature, vehicle mass, and road surface characteristics [12]. C r is typically approximated as a constant with values in a range of for smooth pavement. For a passenger vehicle with radial tires on a normal road surface, the value is assumed at A lower limit that can be reached with special low rolling resistance tires is C r =0.008 [8], [12] Wheel Dynamics The free body diagram given in Figure 11 shows the primary forces acting on a wheel during acceleration. T ax is the torque transmitted to the wheels by the half-shafts, T RR is the torque from rolling resistance, J w is the combined inertia of a wheel and tire, and ω w is the angular acceleration of the wheel. Figure 11: Free Body Diagram of Wheel During Acceleration [1] 26

40 x represents the direction of motion and F x is the longitudinal tractive force. From this diagram, Newton s second law can be applied to derive the basic dynamic expression for the wheels: ω w = ( 1 J w ) T ax T RR F x R eff ( 10) 2.3 Current Traction Control Solutions Various systems are currently in use to address the traction control problem. Many of these systems use active and passive devices to manage the torque transmitted to the wheels. Some systems employ the use of additional, specialized control strategies to detect and reduce wheel spin. The following sections address the most common methods of traction control currently in use and some proposed traction control strategies for the unique traction control problem presented by hybrid vehicles Torque Management Devices Torque management devices (TMD) are the primary hardware used for traction control. These devices can be passive or actively controlled. Passive TMDs engage automatically when certain conditions are met based on their mechanical design. They can activate based on speed or torque. Active TMDs use a hydraulic or electronic actuator to engage a clutch pack or similar mechanism. When one or more wheels lose traction, these devices help to redirect torque in the powertrain towards the wheels with traction. The following are several of the common torque management devices used in vehicles and traction control systems [13]. 27

41 Open Differential Differentials allow the inside and outside wheels on an axle to spin at different speeds as the vehicle turns around a corner while continuing to deliver torque. Open differentials send an equal amount of torque to each of the two wheels. The wheel with the least traction limits the amount of torque that can be delivered by the wheels to the road. This means that if one of the wheels comes off the ground or is on a very low-µ surface, both wheels lose their ability to transmit torque to the road [2]. This is the major drawback of open differentials in a traction control application Limited-Slip Differential To address the drawbacks of an open differential, a limited slip differential can be used. The limited slip differential adds a semi-rigid coupling between the gears of an open differential. This is a passive torque management device. The semi-rigid coupling causes the gears to resist spinning at different speeds. The result is that when one wheel loses traction, the other is still able to transmit some torque to the road [2]. While the amount of torque transmitted is small, it is still an improvement upon the open differential as it allows the vehicle to continue forward motion. Two common types of limited slip differential are a clutch type and a viscous coupling type. A clutch-type limited slip differential uses a spring pack to push the gears against the clutches which provides the resistance against rotation at different speeds [2]. A cutaway view of a clutch type limited slip differential can be seen in Figure 12. A viscous coupling 28

42 type uses two sets of plates inside of a thick fluid. Each set of plates is connected to one of the output shafts. When one output shaft spins faster than the other, the viscous friction of the fluid causes some torque to continue being transferred to the other shaft [2]. A cross sectional view of a viscous coupling type limited slip differential can be seen in Figure 13. Clutch Spring Figure 12: Clutch Type Limited Slip Differential [2] 29

43 Figure 13: Viscous Coupling Type Limited Slip Differential [2] Actively controlled limited slip differentials are also available. Electronically actuated differentials use an electric motor to engage the clutch pack when necessary. Advantages of actively controlled electronic differentials include that they weigh less, can transmit higher torques, and require smaller speed differences to activate [13] Locking Differential Active control allows for the creation of a locking differential. Typically used in serious off-road vehicles, a locking differential uses an electric, pneumatic, or hydraulic mechanism to lock the differential such that it behaves like a solid axle. This means that both wheels receive the same amount of torque and rotate at the same speed regardless of the road surface. Locking differentials are generally manually activated with a switch by the driver [2]. 30

44 Torque Sensing Differential A torque sensing differential uses a set of gears designed to bind together when a torque differential develops across the two output shafts. When equal torque is being delivered to each wheel, the torque sensing differential behaves as an open differential. When a torque differential develops, the gears multiply the torque of the slipping wheel and transmits it to the other wheel. The factor by which the torque is multiplied is called the torque bias ratio and is determined by the design of the gears [2]. This unique type of differential transmits a relatively large amount of torque to the non-slipping wheel without needing an active mechanism Four-Wheel and All-Wheel Drive The most widely used and known passive systems for traction control are four-wheel drive and all-wheel drive. Four wheel drive typically refers to a part time system that can be engaged or disengaged by the driver using some type of switch. When disengaged, the vehicle has only two driven wheels. All-wheel drive systems are full time systems such that the vehicle has four driven wheels at all times. These systems cannot typically be switched off. Four and all-wheel drive systems are very similar in composition. One of the key components is a transfer case which divides power between the front and rear axles. Transfer cases in four-wheel drive systems are able to decouple one of the axles from the power input when the system is disengaged. Transfer cases for all-wheel drive systems 31

45 contain a viscous coupling or similar type of differential to allow a speed difference between the two axles allowing the system to function properly on any surface since it cannot be turned off [2], [13]. Four and all-wheel drive systems also must contain a differential on each axle. Four-wheel drive systems often contain locking differentials that allow for multiple four-wheel drive modes [2], [13]. Typical modes include 4HI in which the transfer case is engaged to activate four-wheel drive and the differentials are left open, 4LO in which the transfer case and differentials are locked, and auto-4wd in which the transfer case is used as a limitedslip differential. 4HI is useful when four-wheel drive is needed but it is not likely that several wheels will encounter a low coefficient of friction all at once. With the front and rear differentials open, such conditions would result in insufficient torque transfer to the road. 4LO directs an identical amount of torque to each wheel regardless of the road conditions. This is useful for serious off-road driving, however turning becomes difficult since there can be no speed difference between any of the wheels [2]. All-wheel drive systems take further advantage of the limited slip capabilities of the transfer case. An on-demand all-wheel drive system primarily uses one axle to drive the vehicle but transfers torque to whichever axle has traction if the wheels of one axle being to slip [13]. A full-time all-wheel drive system utilizes torque sensing differentials rather viscous couplings is the transfer case to transfer torque to all wheels at all times based on the torque bias ratios of the differentials [2]. 32

46 2.3.3 Traction Control Systems Passive, mechanical systems such as the ones discussed in the previous sections can be highly beneficial for certain conditions, however their utility is very limited due to being primarily or entirely passive systems. To enhance the response and capability of traction control, actively controlled systems have been developed. The objective of an actively controlled system is to control wheel slip by estimating the friction between the tire and road surface and using a control system to regulate the wheel slip. The result is improved vehicle stability and traction Anti-lock Braking System (ABS) The first active traction control system was the anti-lock braking system (ABS) [4]. ABS was designed to eliminate high slip during braking that results from the wheels locking. By preventing wheel-lock, ABS is very effective at improving driver control, steerability, and stopping distance during heavy braking. Work on ABS led to the development of traction control systems as the acceleration analog of ABS [4]. Traction control (TC) systems work to control vehicle acceleration by targeting a certain driven wheel slip. The target slip value is based on the driver steering input and accelerator pedal position. At high pedal input and low steering input, a higher driven slip will be targeted to achieve maximum longitudinal force for acceleration. When a higher steering input is detected, the target slip will decrease because lateral traction peaks at lower slip levels than longitudinal slip [4]. 33

47 Traction Control in Conventional Vehicles Modern traction control in conventional vehicles relies on reducing engine torque, applying brakes to the spinning wheel, or some combination of the two [13]. In some cases, such as driving on a surface of uniform friction, reducing the torque output from the powertrain is sufficient for traction control. Changes in spark advance and air/fuel ratio are widely used methods for engine torque control, however cylinder cutting, shifting the transmission, and electronic throttle control are also used. Careful control must be used when combining these methods since each has its own operational bandwidth and engine emissions can be affected [4]. If the driving surface friction is not uniform such that the driven wheels encounter different coefficients of friction, the use of brakes in the traction control system is necessary [4]. Traction control systems utilizing the brakes are generally used in conjunction with an open differential. The application of brakes to the spinning wheel allows a higher torque output from the wheel with traction thus allowing the vehicle to accelerate [13]. The same applies to four or all-wheel drive vehicles whose transfer case is an open differential. When one axle loses traction, brakes are applied to both wheels of the axle to allow torque to be transmitted to the axle with traction. However braking the spinning wheel or wheels wastes a significant portion of the engine torque being produced so the resulting acceleration is still far from optimal and excessive system noise can also result [4], [13]. Brake based systems also have the disadvantage of being very difficult to tune, particularly tuning the brake and powertrain controls so they function smoothly in tandem [4]. 34

48 Modern Advances in Traction Control Advancement in vehicle control and the introduction of electronic and hybrid drivetrains has led to vast improvements in the control capabilities of traction control systems. There have also been adaptations of existing traction control strategies to apply them to new hybrid and electric drivetrains. There has also been development of a new kind of traction control system that works to monitor and control wheel slip at all times. This works to prevent wheel slip from occurring in the first place, rather than activating only to fix the problem once it has occurred. These systems can provide the added benefit of maximizing traction at all times because they are able to continuously target the optimum wheel slip in all conditions. Systems have also been developed to address the problem of detecting vehicle speed and wheel slip on four-wheel drive vehicles where there are no non-driven wheels from which to determine an accurate vehicle speed. This section will discuss several advancements in these areas. In [14], a continuously functional system was developed for an EV with two hub motors. The maximum tractive force of the wheels under current conditions is calculated and used to limit the torque requests to the motors. This creates a half closed loop system when the wheels are not slipping because the feedback Tmax has no effect on the system and thus it functions as an open loop system. The loop automatically closes when the wheels begin slipping causing the maximum effective torque to dip below the reference torque and limit the torque request. This system has the advantage of being simple to implement, however it depends on the two driven wheels being independent of each other and it depends upon 35

49 non-driven wheels to obtain vehicle speed and thus its usefulness in all-wheel drive vehicles is limited. [15] proposed a general traction control law that makes use of a simplified vehicle model and detected wheel slip. The test vehicle was primarily a front wheel drive vehicle with a rear powertrain that was activated only when additional power was needed for acceleration or when wheel slip was detected. The proposed traction control strategy minimizes an objective function, which represents the combined wheel slip of front and rear wheels, with respect to the motor torque. The resulting motor torque is then applied to the rear electric drive of the powertrain to assist in controlling the vehicle and regaining traction with the front wheels. The performance of the system was limited, however, by lack of coordination with the engine for reduction of torque on the front wheels. A simple bang-bang type controller was employed by [9] on an electric drivetrain. The control strategy transmitted the requested torque to the wheels until wheel slip above a set threshold was detected. At that point the torque request was set to zero until the detected slip dropped back into the stable region and the driver requested torque was again transmitted to the wheels. This controller is effectively an acceleration version of ABS and depends on the inertia of the wheels and vehicle to smooth the torque modulation. A state-observer was used with knowledge of current slip to estimate the road load on the drivetrain and determine the allowable slip threshold value. 36

50 The traction control system proposed by [16] goes beyond correcting for loss of traction and works to maximize the vehicle s longitudinal force and acceleration at all times by actively optimizing wheel slip at all time. The goal of the system is to maintain the slip ratio at the point of peak friction at all times. This is accomplished by slightly varying the slip target and noting any resulting change in longitudinal force and vehicle acceleration. Positive changes in acceleration indicate the slip target is below the current optimal value and the slip target is incrementally increased. When the change in acceleration becomes negative it indicates that the peak point has been passed and the slip target will be decreased. The amount of increase or decrease is determined by a PID controller. This continuous testing ensures that the optimum slip point is always tracked without a need for large stored look-up tables, prior knowledge of the road or tire characteristics, large equations, or complicated logic. The strategy is computationally light and can be implemented on a standard embedded platform, but requires the ability to accurately determine and control slip. Fuzzy logic control techniques have been developed by several researchers in recent years for use in various electronic control systems including transmission control, engine control, and ABS [9]. They have generally found them to have better performance than traditional control algorithms [17]. Fuzzy logic has the advantage of being able to efficiently model highly complex and non-linear systems. It can also handle uncertainty and noise in data effectively [9]. 37

51 2.3.4 The OSU EcoCAR 2 Traction Control Problem The traction control problem presented by the Ohio State EcoCAR 2 vehicle is unique in many ways. Because the vehicle is a prototype built for the specific purpose of competing in the EcoCAR 2 competition, its powertrain configuration and the components therein are not seen in any other vehicle. The competition rules and team goals also introduced a set of specific constraints to the traction control problem. First, the final traction control algorithm needs to be largely self-contained. This means that all functions directly pertaining to traction control should exist in a single area of the vehicle s supervisory control and have no interaction with the low level controls. Second, the traction control algorithm must be designed such that it can be easily and directly integrated with the existing controls architecture created during the first two years of the competition without major modifications to any other portion of the code. The competition rules specifically prohibit any controls action which interferes with or modifies the operation of ABS and normal braking action in any way. The end result of this rule places two constraints on the traction control development. One is that the traction control can only function during acceleration and the vehicle will rely upon the stock ABS system as the means of traction control during heavy braking. The second is that the traction control system cannot actuate the brakes in order to slow a spinning wheel that has lost traction or to transfer torque across the open differentials. Another constraint was placed in order to prevent the vehicle from exceeding the competition maximum weight requirement, no additional torque splitting components could be added to the vehicle. This 38

52 means that the open differentials included in the gearboxes on the vehicle are the only available means for the vehicle to divide torque between the left and right wheels on an axle. Open differentials are not controllable so the traction control algorithm must be designed with an uncontrolled left-to-right torque split in mind. Finally, to avoid additional weight on the vehicle and to avoid unnecessary complication of the vehicle wiring and controls, the addition of sensors to the vehicle was to be minimized or avoided altogether. 39

53 Chapter 3: System and Component Modeling 3.1 Traction Control Philosophy Because the plant model is intended for traction control development, the intended traction control strategy is an important factor to consider in model development. The intended traction control strategy, which will be discussed in detail in a later chapter, takes advantage of the electric motors to control the torque to the wheels during a traction control event. The control strategy of the vehicle utilizes a charge depleting mode for heavy acceleration in which the electric motors accelerate the vehicle while the engine is off and disconnected from the rest of the powertrain. This is when an acceleration traction control event is most likely to occur. If a traction control event occurs while the vehicle is using the charge depleting mode traction control will be applied directly. If the battery state-ofcharge is too low to allow the vehicle to function in charge depleting mode, the vehicle will enter the charge sustaining series mode for traction control. The series mode leaves the front axle with no propulsive torque input from the powertrain and the rear electric motor to control the torque transmitted to the rear wheels in order to maintain traction. 3.2 Requirements Based on the background given in the previous sections, the requirements for the plant model can be described: 40

54 High fidelity of the model to capture high frequency vibrations is not required as only lower frequency dynamics will be important for traction control The model must be capable of modeling slip on all four wheels and demonstrating differential action between the two wheels on a given axle The model must be available for SIL work prior to mechanical realization of the vehicle 3.3 Assumptions The following assumptions were used in the development of the dynamic model, driven by the requirements listed above. Only longitudinal vehicle dynamics are considered The torsional stiffness of shafts and gears except half shafts are assumed to be infinitely large Environmental factors such as temperature, pressure, and humidity are not taken into consideration Drivetrain losses are represented by lumped efficiency and friction models The supervisory control strategy developed for the test vehicle converts a percentage-based torque request from the pedals into actual torque requests for each of the three torque generating components based on the optimization of fuel economy and emissions. The dynamic model presented here focuses on translating the torque requests into the torque 41

55 realized by the engine and motors and how it propagates through the powertrain to the wheels. The following sections will describe each of the model components in detail. 3.4 Powertrain Modeling It is necessary to derive dynamic equations to describe the components of the powertrain. Figure 14 shows the model of the driveline upon which the derived equations are based. The component models are designed to translate engine and motor torque requests into the torque realized by the actuators and to trace how the torque produced and its effects on component speeds propagate through the system. The following sections will describe each of the model components in detail. Figure 14: Driveline Dynamic Model 42

56 3.4.1 Engine A detailed thermodynamic model describing engine dynamics does not provide substantial additional information for the validation of a traction control oriented dynamic vehicle model, particularly because the engine will not be used to transmit torque to the wheels in the intended traction control strategy as described previously. Such detailed models are often used for the design of engine control systems, however for this work a simplified representation of the engine model is used to reflect the dynamics between torque request and resulting engine speed. The engine is modeled as an ideal torque actuator with a constant inertia connected through the crankshaft to the rest of the powertrain. The resulting crankshaft dynamics are given by: 1 ω e = ( ) T J e + J e T e,fr T C ( 11) C1 Where ω e T e T e,fr T C J e J C1 = engine angular acceleration = engine indicated torque = engine friction torque = torque transmitted by the clutch = lumped engine inertia = inertia of the clutch flywheel attached to the engine The engine friction is modeled by a lookup table constructed from experimental data. A delay between torque request and torque generation is included in the model to account for the induction-to-power stroke transport delay. 43

57 3.4.2 Front Electric Motor Because the pulleys on which the belt is mounted are coupled directly to the electric machine and transmission, they are modeled as lumped inertias with those components. The primary pulley, denoted by the subscript s1, is coupled to the output shaft of the electric machine. Belt dynamics are ignored. Taking into account these assumptions, the dynamics of the front electric machine are given by: 1 ω FM = ( ) T J FM + J FM T FM,fr T belt ( 12) s1 Where ω FM T FM T FM,fr T belt J FM J s1 = Front electric machine angular acceleration = Front electric machine torque = Front electric machine internal friction torque = Torque transmitted by the belt = Front electric machine inertia = Inertia of primary belt pulley The front electric machine friction term is modeled as the combined friction of all components at the node of the front electric machine, the belt and pulleys, and the transmission primary shaft when the engine clutch is open. 44

58 3.4.3 Transmission The clutch disk and secondary belt pulley are coupled directly to the input shaft of the transmission so they are modeled as a lumped inertia. A highly detailed dynamic model of the transmission would not provide significant useful information for the development of traction control because the vehicle will be kept in a fixed gear during a traction control event so a simplified model was chosen to prevent unnecessary model complexity and maintain an efficient model based design. The simplified model represents the torque on the input and output shafts of the transmission by a static multiplication by the gear ratio as shown in ( 13). The dynamics of the transmission input are given by 1 ω GB1 = ( ) T J C2 + J s2 + J C + B T belt T GB1 ( 13) GB1 Where ω GB1 B T C T GB1 J C2 J s2 J GB1 = Transmission input angular acceleration = Belt ratio = Torque transmitted by the clutch = Torque transmitted to transmission primary shaft = Clutch disk inertia = Inertia of belt pulley attached to transmission input = Equivalent transmission primary shaft inertia The dynamics of the transmission output are given by 45

59 ω GB2 = ( 1 J GB2 ) R T GB1 T ax,f ( 14) Where ω GB2 T ax,f J GB2 R = Transmission output angular acceleration = Torque transmitted to the front wheels = Equivalent transmission secondary shaft inertia = Transmission gear ratio Table 2 contains the gear ratios for the transmission and final drive. Table 2: Gear and Drive Ratios of the Transmission Gear Ratio 1 st nd rd th th th Differential Efficiency Rear Electric Machine and Gearbox Similar to the engine and front electric machine, the rear electric machine is modeled as a lumped inertia, ideal torque actuator. The rear powertrain dynamics can be described with a lumped model that reflects all inertias to the rear electric machine output shaft. 46

60 ω RM = ( 1 J RM + J g1 + J g2 r 2 ) T RM T RM,fr T ax,r r ( 15) Where ω RM T RM T RM,fr T ax,r J RM J g1 J g2 r = Rear electric machine angular acceleration = Rear electric machine torque = Rear electric machine friction torque = Torque transmitted to the rear wheels = Rear electric machine inertia = Gearbox primary shaft inertia = Gearbox secondary shaft inertia = Gearbox gear ratio The rear electric machine friction term is modeled as the combined friction of the rear electric motor and gearbox. Electric machines experience a small lag between torque request and torque output which can be represented with a pure delay with a time constant τ EM of 0.01s. A delay of 0.01s represents the typical lag exhibited by electric machines [2], [18]. This delay precedes ( 12) and ( 15) in the implementation of the model and can be represented as [18] T EM = 1 τ EM (T EM,req T EM ) ( 16) 47

61 T EM,req and T EM represent the torque request and actual torque output of the electric machine. This is represented generically here but applies to both the front and rear electric machine individually Front and Rear Axles The torsional stiffness and damping of the axle shafts are taken into account for this work. Keeping this in mind, the torque transmitted to the wheels by the front and rear half shafts can be given by the following relationship T ax,i = k ax,i (θ ax,i) + b ax,i ( ω ax,i ) ( 17) The subscript i = {f, r} is used to indicate the front and rear axles, k ax,i is the stiffness of a single half-shaft on axle i, and b ax,i is the damping coefficient of a single half-shaft on axle i. The torsional displacement on a half-shaft and the relative angular speed are given as θ ax,i = ω ax,i = { ω GB2 ω w,f, ω g2 ω w,r i = f i = r ( 18) where ω w,i is the wheel speed Wheel Dynamics The free body diagram given in Figure 11 shows the simple forces acting on a wheel during acceleration. From this diagram, Newton s second law can be applied to derive the basic dynamic expression for the wheels 48

62 ω w,i = ( 1 J w ) T ax,i T RR F x,i R eff ( 19) Rolling resistance is given by [1, 4] F RR = Mg cos(α) C r ( 20) The mass of the vehicle, acceleration due to gravity, and grade angle of the road are given by M, g, and α respectively. C r the rolling resistance coefficient assumed for this work to have a value of about as explained in Chapter 2 [12]. The torque due to rolling resistance can be determined by multiplying the rolling resistance force from ( 20) by the tire s effective rolling radius. Due to the weight distribution in the vehicle, each wheel has a slightly different effective rolling radius Tire Model In the development of traction control, modeling of the tire-road interaction and forces is very important. Due to the non-linear behavior of tires and the great variance in vehicle handling caused by the tires, it is important that a realistic non-linear tire model is used. Existing tire models are predominantly semi-empirical in nature which use experimental data to determine the model parameters [19]. One of the most prevalent tire models in use is the Pacejka Magic Formula model. This work uses the Pacejka Magic Formula model in a form considering only longitudinal forces to model tire behavior. This model was chosen in part due to its prevalence which allowed the necessary empirical coefficients to be directly obtained from the tire manufacturer. It was chosen over popular theoretical 49

63 models because theoretical models generally must be based on simplifying assumptions which limits their practical use and makes them undesirable for use in traction control development [7]. The following sign conventions were used: Angles, forces, and moments use sign conventions consistent with SAE definitions as shown in Figure 15. Longitudinal sip κ is positive during acceleration and negative during braking as given by ( 6) which is repeated here for clarity κ = R effω w V x V x + ε x ( 6) Figure 15: SAE Tire Axis System [14] 50

64 The magic formula is given by F x0 = D x sin(c x arctan[{b x κ x E x [B x κ x arctan(b x κ x )]}]) + S Vx ( 21) The coefficients B, C, D, and E are dimensionless coefficients that are functions of the tire load. They are the stiffness factor, shape factor, peak value, and curvature factor respectively. The load dependent coefficients are defined by D x = μ x F z ( 22) μ x = D x1 + D x2 df z ( 23) B x = F z (K x1 + K x2 df z )e K x3 df z C x D x + ε x ( 24) E x = (E x1 + E x2 df z + E x3 df z 2 )(1 E x4 sign(κ x )) ( 25) Where df z = (F z F z0 ) F z ( 26) κ x = κ + S Hx ( 27) S Hx = H x1 + H x2 df z ( 28) S Vx = F z (V x1 + V x2 df z ) ( 29) S Vx and S Hx represent an offset to the slip and longitudinal force. μ x is the load-dependent friction coefficient in the longitudinal direction. ε x is a small constant intended to avoid division by zero as the vertical load approaches zero [20]. The tires for the test vehicle are being custom developed for this team for light weight and low rolling resistance. The rolling resistance will be approximately half that of a normal tire. As the tire development 51

65 is completed, the empirical coefficients for the tire model will be obtained by the tire manufacturer through testing and provided for use in this work Vehicle Model The motion of the vehicle results from the sum of all forces acting on the vehicle body. These forces are shown in Figure 16. Figure 16: Vehicle Model Block Diagram [20] In this diagram, a, b V x F d F xf, F xr = Distance of front and rear axles, respectively, from the plane of the vehicle center of gravity (CG) = Longitudinal velocity of vehicle = Force of aerodynamic drag = Longitudinal force generated between the road and the front and rear wheels, respectively 52

66 F zf, F zr h m = Normal forces on the front and rear wheels, respectively = Height of vehicle CG above ground = Vehicle mass g = Acceleration of gravity (9.81 m/s 2 ) β = Angle of incline of the road The vehicle model is based upon the following properties and assumptions: Two axles with two equally sized wheels on each axle The vehicle axles are parallel Only longitudinal motion is considered Longitudinal motion occurs perpendicular to the axles The normal z direction is always perpendicular to the axle plane Vehicle weight and aerodynamic drag act through the center of gravity Pitch and vertical motion are not considered Newton s second law as applied to the vehicle model is given as: mv x = F x F d mg sin β ( 30) The longitudinal force is determined by F x = 2(F xf + F xr ) ( 31) The aerodynamic drag force is given by F d = 1 2 C dρa(v x V w ) 2 sign(v x V w ) ( 32) 53

67 where V w represents the headwind speed. The normal forces on the wheels are found by F zf = h(f d + mg sin β + mv x) + bmg cos β n(a + b) F zr = h(f d + mg sin β + mv x) + bmg cos β n(a + b) ( 33) ( 34) and must satisfy the condition F zf + F zr = mg cos β/n ( 35) Equations ( 30) through ( 35) comprise the vehicle model [20]. 54

68 Chapter 4: Simulation and Vehicle Controls 4.1 Introduction The model described in Chapter 3 is designed for implementation as a simulator. The Ohio State EcoCAR 2 team utilizes Simulink from The MathWorks in order to create simulators for use in control development during the three years of the competition. This chapter contains a discussion of the primary simulator used by the team to illustrate why an additional, unique simulator was necessary for the development of traction control. The development of the new simulator is also discussed as well as a brief description of the primary control algorithms used in the vehicle around which the traction control development was focused. 4.2 Existing Simulation Tools: EcoSIM2 The primary simulator utilized by the Ohio State team is an energy based quasi-static model called EcoSIM2. The simulator is based on the concept of feed-forward torque which is delivered from the actuators and through the powertrain gearing to the wheels where a longitudinal force is generated which acts on the vehicle mass to propel the vehicle forward. The forward acceleration is determined by dividing the force by the vehicle mass. It is then integrated to determine the vehicle velocity. Vehicle velocity is then converted to a wheel rotational velocity once divided by the wheel radius. The rotational velocity is then 55

69 fed back through the powertrain and the gearing to determine the actuator rotational speeds. This concept is illustrated in Figure 17. Figure 17: Torque/Speed Structure of EcoSIM2 EcoSIM2 is used to evaluate fuel economy and to develop control strategies and perform basic tuning of controls for the vehicle. The simulator is quasi-static meaning that the time constants of components in the system are considered negligible when compared to the greatest inertia which is the vehicle itself [21]. With this assumption, the components in EcoSIM2 are modeled based on static maps, simple transfer functions, and simplified soft ECUs [22]. This allows the model to be computationally inexpensive and run quickly for rapid controls iterations. The simulator is comprised four primary segments as seen in the user interface shown in Figure

70 The Driver subsystem is a PID controller that uses the difference between a vehicle speed trace and the current vehicle speed to generate accelerator and brake pedal commands. Typical speed traces include the Federal Urban Driving (FUDS) cycle, Federal Highway Driving (FHDS) cycle, US06 cycle, and team created cycles designed for fault or performance testing. Figure 18: EcoSIM2 User Interface The PHEV Powertrain subsystem contains the aforementioned maps, transfer functions, and soft ECUs that model the components of the drivetrain. The PHEV Powertrain subsystem can be seen in Figure 19. The EcoCAR2 Vehicle subsystem contains a version 57

71 of the vehicle body model that uses dynamometer coefficients to calculate the road loads on the vehicle. The MABX Primary Controller subsystem contains the control algorithms used to govern vehicle mode, gear, and transitions between modes. This subsystem is where vehicle control development occurs. Figure 19: PHEV Powertrain Subsystem in EcoSIM2 Additional blocks in the primary user interface include an Inputs subsystem to load variables from the workspace into the model, an Outputs subsystem to save variables from the model into the workspace, and the Economy subsystem to display selected vehicle status indicators and performance metrics during simulation. 4.3 Vehicle Control Strategy The vehicle control strategy determines operating mode based on the battery state of charge (SOC) and vehicle speed. On a full charge, the vehicle starts in charge depleting mode 58

72 using the electric machines to propel the vehicle. When the SOC drops below 18%, the vehicle transitions to charge sustaining mode. Once charge sustaining mode is activated, the vehicle selects between charge sustaining series and charge sustaining parallel based on the vehicle speed. When vehicle speed is less than 50 kph, charge sustaining series is selected. Above 50 kph, the vehicle transitions to charge sustaining parallel. Within each mode, efficiency is maximized to produce maximum fuel economy and vehicle range. The energy management in the control strategy is performed by an algorithm called the Equivalent Consumption Minimization Strategy (ECMS) to determine the optimal power split between the torque actuators in the powertrain during charge sustaining modes. A modified version is used during charge depleting mode to determine the most efficient split between the two electric machines. ECMS reduces a global optimization problem to an instantaneous, local optimization method [23]. ECMS assigns both electricity and liquid fuel a cost function designed to balance energy use and power output. The control strategy minimizes the energy cost function while maintaining the power output necessary to meet the requested torque and then assigns torque commands to the torque actuators accordingly. More detailed information on ECMS can be found in [24]. Another important aspect of the vehicle control strategy is the gear shifting process. When a shift is requested, the transmission first shifts to neutral. While in neutral, the front electric machine is used to control the speed of the transmission input and match it to the speed of 59

73 the transmission output for the new gear prior to engaging the gear. This minimizes any grinding of the synchronizers and allows for a smooth feel to shifting in the vehicle. 4.4 Simulation for Traction Control: EcoSIM2 Dynamic EcoSIM2 is very useful for its primary purpose of control development for improved fuel economy and basic performance. However, the model does not account for powertrain dynamics such as inertias and shaft stiffnesses. The model also assumes the wheels behave as rigid discs and that perfect contact exists between the wheels and the road with no slip. For these reasons, the model is insufficient for traction control development. Figure 20: EcoSIM2 Dynamic User Interface 60

74 To accommodate the desired development, a new model was developed which expanded upon EcoSIM2 to take the powertrain dynamics into account and incorporate the Pacejka Magic Formula tire model. EcoSIM2 Dynamic is a model derived from EcoSIM2 that uses Simulink s SimDriveline toolbox to implement the dynamic model described in Chapter 3. The user interface of EcoSIM2 Dynamic is shown in Figure 20. The structure of the model was kept almost identical. All changes were made within the plant models for each component subsystem shown in Figure 19. Implementing the dynamics and the use of the SimDriveline toolbox required an important modification to the original simulator. SimDriveline systems are best used with a variable step solver. However the MABX controller simulator must be run at a fixed time step to most accurately model the functionality of the controller hardware which is a digital system. To accomplish this, the MABX Primary Controller subsystem was isolated as an atomic subsystem and all continuous functions within it were discretized with a time step of 0.01 sec to match the time step of the controller hardware. Another change was the addition of a feedback loop directly from the vehicle subsystem to the powertrain subsystem which brings the calculated normal forces to the tire model. A limitation of the simulator using SimDriveline is the inability to accurately simulate speed control for the motors. The electric motors can be controlled in a torque control mode or a speed control mode. When in torque control mode, the inverter controls the motor by sending it a torque set point based on the torque commands from the MABX and allowing 61

75 the speed to vary naturally based upon the torque. In speed control mode, the inverter commands a specific motor speed and continuously varies the torque in order to meet the speed command. Because the torque variance in speed control mode is performed by the inverter and not in the supervisory controller, it is not captured in the simulator. Furthermore, speed control mode is only used during gear shifting to match the transmission input and output speeds while in neutral during a shift. EcoSIM2 is able to mimic the speed control functionality by directly commanding the front electric machine speed rather than back propagating as shown in Figure 17. However, the structure of the SimDriveline model requires torque control to be used at all times. Therefore, speed matching does not properly occur. Another limitation of the model is that the coefficient of friction for each wheel must remain constant throughout the simulation. This makes it impossible to accurately model a wheel transitioning from low friction to high friction or from high friction to low friction. For example, if a simulation begins with the front wheels on a low friction surface and the rear wheels on a high friction surface, the rear wheels will never enter the low friction zone during the simulation even if the vehicle displacement is large. 4.5 EcoSIM2-Dynamic Initial Validation To validate the updates to the EREV powertrain subsystem from the creation of EcoSIM2- Dynamic, data collected from the vehicle during a zero-to-sixty acceleration is compared to data generated from the model. The actuator torque commands recorded from the vehicle 62

76 were used as inputs to the model and the resulting vehicle speed in the model is compared to the actual vehicle speed recorded in the data. The simulator behavior mimics that of the vehicle quite well with slight inaccuracy in the speed. The simulator speed slightly lags the actual speed for about 10 seconds and reaches a peak speed approximately 2 kph greater than the actual vehicle speed. Based upon these results, further refinement of the EcoSIM2- Dynamic plant model is not necessary for the development of traction control. 120 Vehicle Speed [kph] Vehicle Data Simulation Data time [s] Figure 21: Initial Validation for EcoSIM2-Dynamic 4.6 EcoSIM2-Dynamic Results To demonstrate the simulator s ability to model friction between the tires and the road, several simulations were run. Sample results are given below. Realistically, driving surfaces are imperfect and non-uniform causing each wheel to experience a slightly different friction coefficient. To simulate this, the friction coefficient for each wheel can be varied slightly in the simulation. Throughout this work, the following convention will 63

77 be used for variance in friction coefficient unless otherwise specified. In Table 3, μ x represents the nominal friction coefficient. Table 3: Friction Coefficient Variance Convention Left Wheel Right Wheel Front Axle μ x 0.01 μ x 0.03 Rear Axle μ x 0.03 μ x Typical nominal friction coefficients for various road surfaces are given in Table 4. Table 4: Typical Friction Coefficients [11], [20] Surface Nominal Friction Coefficient Dry Pavement Wet Pavement Snow Ice The initial simulation was performed with a longitudinal load-dependent friction coefficient (μ x in equation ( 23) ) of 1. This is the value of the coefficient provided for the Magic Formula model to represent dry pavement [20], [25]. Figure 22 shows the torque and rotational speed of the torque actuators as well as a plot of vehicle speed compared to the speed trace defined by the drive cycle. The wheel speeds and wheel slip values as defined by ( 6) are shown in Figure 23. For clarity, only the first 60 seconds are shown. 64

78 Torque [Nm] FEM REM ICE Speed [rpm] Speed [kph] FEM 4000 REM ICE Vehicle velocity Cycle Velocity time [s] Figure 22: Actuator Torques and Speeds During US06 Cycle - μ x = 1.0 Wheel Speed [rpm] Wheel Speed [rpm] FR FL RR RL time [s] Wheel Slip Wheel Slip FR FL RR RL time [s] Figure 23: Wheel Speeds and Wheel Slip During Zero-to-Sixty Acceleration - μ x =

79 The wheel speeds and slip clearly illustrate the oscillations in the powertrain captured by EcoSIM2-Dynamic that are absent from the quasi-static simulations in EcoSIM2. Traction was maintained throughout the simulation as evinced by slip values that stay very low. The maximum slip seen by the wheels is Next, the same simulation was run with a nominal friction coefficient of 0.26 which represents a low friction driving surface such as a snow covered road. Plots of the actuator torques and speeds and of the wheel speeds and slip are given in Figure 24 and Figure Torque [Nm] Speed [rpm] Speed [kph] 0 FEM REM -200 ICE 0 2 x FEM REM 1 ICE Vehicle velocity Cycle Velocity time [s] Figure 24: Actuator Torques and Speeds During US06 Cycle - μ x =

80 Wheel Speed [rpm] Wheel Speed [rpm] FR FL RR RL time [s] Wheel Slip Wheel Slip FR FL RR RL time [s] Figure 25: Wheel Speeds and Slips During US06 Cycle - μ x = 0.26 A comparison shows much higher wheel speeds and slip values for Figure 25 where the friction between the tires and the road is low than for Figure 23 where friction is optimal. For the low friction simulation the slip on the front axle peaks at a value of 10. Figure 25 also illustrates the effect of a non-uniform surface on wheel slip. For example, the rear left wheel accelerates to a speed several times that of the rear right wheel due to the open differential and the lower friction experienced by the rear left wheel. Because the friction experienced by the left wheel is lower, it is the first of the two to lose traction. Once the left wheel breaks loose, the differential transfers all of the torque to the left wheel and none to the right. The right wheel maintains traction due to lack of input torque and continues spinning at a rate directly proportional to vehicle speed since the vehicle is the force driving the right wheel. This phenomenon is also seen on the front axle. 67

81 An examination of Figure 24 shows a sharp increase in the speed of the electric machines disproportionate to the increase in input torque during the times that the wheels lose traction. The sudden loss of load, because it is uncontrolled and because the torque input is sustained as if the load were still present, causes the electric machines to far exceed the rated operating speeds of the electric machines. Accordingly, the wheels are accelerated to excessive speeds as well. On a vehicle rather than in simulation, these kinds of effects would cause significant damage to the vehicle and danger to the driver, further emphasizing the need for effective traction control. 68

82 Chapter 5: Traction Control Development 5.1 Vehicle Configuration When determining the approach for traction control on the Ohio State EcoCAR 2 vehicle, the constraints described in Chapter 2 must be taken into consideration. The constraint prohibiting the use of the brakes dictates that the traction control approach will use the reduction of input torque to the powertrain as the sole mechanism to reduce and eliminate wheel slip. It is desirable to use the electric machines for torque reduction on the EcoCAR 2 as they provide the most direct and best controlled avenue for torque reduction as well as offering the ability to reduce to zero or negative torque if necessary. The engine is only able to reduce to idle speed and torque without stalling or potentially damaging the engine. When the vehicle is in the charge depleting configuration, the electric machines are the only sources of torque so their use for torque reduction can be easily implemented. When in the charge sustaining series configuration, the rear wheels are the only driven wheels so the rear electric machine is the natural avenue for torque reduction. In the charge sustaining parallel configuration, however, the engine is connected to both the wheels and front electric machine. If torque reduction occurs on the front axle in this configuration, it is necessarily limited by the engine in order to prevent the engine from stalling. Energy management also becomes a concern if traction control is applied in the charge sustaining 69

83 parallel configuration. Thus, the traction control strategy needs to transition the vehicle from the parallel configuration to the series configuration if wheel slip is detected while the vehicle is in charge sustaining configuration. 5.2 Algorithm Placement As discussed in Chapter 2, there are many methods by which wheel slip and traction can be managed. It was necessary to determine which of these methods would be utilized for the Ohio State vehicle. First a determination of whether an active system, passive system, or both would be used. Because the vehicle contains open differentials and it is impractical to replace them with limited slip or torque sensing differentials, no passive approach is possible. As such, the Ohio State vehicle must rely entirely upon an active traction control strategy implemented in the vehicle controls. There are two primary methods of implementing traction control within the vehicle control strategy. First, traction control can be implemented as an operating mode that is entirely separate from the normal operating modes and is activated upon detection of wheel slip as seen in [2]. The other option is to implement traction control as a modification to the torque request within the existing operating modes. Examples of this option presented in Chapter 2 include the on-off torque request of the bang-bang controller presented in [9], the half closed loop system in [14], and several others. The creation of additional modes for traction control in multiple powertrain configurations would add considerable complexity to the mode selection and mode transition logic of the controller. To prevent this, it was decided 70

84 that traction control would be implemented as a modification to the torque request within the existing operating mode algorithms, almost entirely eliminating the need for modification to mode selection and transition algorithms. One transition condition must still be added to ensure the vehicle moves to the charge sustaining series configuration when wheel slip is detected during charge sustaining operation. To illustrate the final structure of the vehicle control strategy, a diagram of the control strategy is shown in Figure 26. Figure 26: Control Strategy Flow Chart The logic to determine the reduced torque request can be self-contained in a subsystem independent from the rest of the operating mode logic. The only necessary point of 71

85 interaction with existing control is an override of the torque request with the final reduced torque request at an appropriate place within the algorithm. This structure satisfies the necessity to minimize impact on the existing controls architecture. 5.3 Activating Traction Control First, the conditions under which traction control will be activated must be determined. Because the front and rear powertrains operate independently with no rigid connection between the axles, traction control can act on each axle separately. To accomplish this, two slip flag variables were introduced: Reduce_Front and Reduce_Rear. Both variables are Boolean indicators where a value of 1 indicates that slip has been detected on the front or rear axle, respectively. If either of these variables is set to 1 while the vehicle is in charge depleting mode or charge sustaining series mode, traction control strategy within those modes will be activated and no changes to the vehicle configuration will occur. If either variable is set to 1 while in charge sustaining parallel, the transmission will be moved to neutral to activate charge sustaining series mode and the traction control strategy within series mode will be activated as well. If either variable is set to 1 while the vehicle is in engine start mode, traction control can be activated within engine start mode since the mode occurs in the series powertrain configuration which is desirable for traction control. Once the engine has started, the controls can pass into charge sustaining series mode and activate traction control within series mode without any changes to the powertrain configuration that could interfere with wheel traction. 72

86 Another case to be considered is when the vehicle is in charge depleting mode with traction control active and the battery SOC drops below 18%. To prevent draining the battery pack beyond a safe limit, the vehicle will still be passed to engine start mode by shifting the transmission to neutral and then to charge sustaining series, all with traction control still active Detecting Wheel Slip Next, an algorithm to detect slip and set the Reduce_Front and Reduce_Rear flags to 1 must be developed. The slip flags will be triggered dependent upon what slip scenario the vehicle is experiencing. A wide range of slip scenarios are possible in the vehicle and should be considered for detection. These scenarios include: 1. Launch under low mu conditions on all four wheels 2. Launch with low mu on one axle (front or rear) 3. Launch with low mu on one side of vehicle (left or right) 4. Launch with low mu on any one of the four wheels 5. Left-right split mu encountered while driving 6. Temporary front-rear split mu while driving if a patch of low mu is entered or exited while driving An example of these scenarios is illustrated in Figure

87 Figure 27: Slip Scenarios Wheel slip in vehicles is typically determined by comparing the speeds of driven wheels to the vehicle speed and determining if the current wheel speeds properly correspond to the vehicle speed. The vehicle speed is determined from non-driven wheels on the vehicle since they are driven by the vehicle inertia and thus do not slip during acceleration. The challenge presented by the Ohio State vehicle is that all four wheels are driven and thus there is not guaranteed to be a reliable source of vehicle speed at all times, particularly when all four wheels are on a low friction surface. To combat this problem, the slip detection algorithm was designed in such a way that knowledge of the vehicle speed is not necessary. This was accomplished by using several different comparisons of the wheel speeds on the vehicle to determine which scenario the car has encountered and thus which slip flag should be activated. This method of slip detection is predicated on the assumption that the only time that all four wheels will be at approximately the same speed is when all four wheels have traction. 74

88 This is true for the Ohio State vehicle even if slip occurs on all four wheels simultaneously on an ideal surface with uniform friction because the front and rear axles will never have an equal axle torque input under normal operation. The differing total gear ratios for the front and rear powertrains, different normal forces on each wheel, and the torque split determined by the operating strategy ensure that there will always be a meaningful difference between the front axle and rear axle torque. If the torque at the axle is different for each axle, one axle will spin its wheels faster than the other and this difference in speeds can be captured by one of the wheel speed comparisons elaborated in this section. The following naming convention is used throughout this work to designate each wheel: ω FR ω FL ω RR ω RL = Front Right wheel speed = Front Left wheel speed = Rear Right wheel speed = Rear Left wheel speed Three speed differentials are calculated to help determine the slip scenario. The first two differentials are right versus left wheel speed across the front axle and right versus left wheel speed across the rear axle. The differentials are calculated and four resulting intermediate indicators (D 1, D 2, D 3, D 4 ) are designated as shown: D 1 = 1 if ω FR ω FL ε s ( 36) D 2 = 1 if ω FL ω FR ε s ( 37) D 3 = 1 if ω RR ω RL ε s ( 38) D 4 = 1 if ω RL ω RR ε s ( 39) 75

89 The indicators D 1, D 2, D 3, and D 4 are Booleans that default to false unless the conditions in ( 36) - ( 39) are met. The threshold value ε s that the speed differentials must exceed in order to become true is a variable threshold that takes into account normal variances in wheel speeds that occur during driving as well as signal noise in the wheel speed sensors. An additional buffer is included to ensure significant wheel slip is occurring. The threshold is calculated as: ε s = ε n + ε b + ε θ ( 40) Where ε n ε θ ε b = Allowable speed differential due to signal noise and normal variance between wheels = Allowable speed differential due to steering angle = Buffer for speed differential The value of ε n was determined from analyzing wheel speed data from several driving tests combined with an analysis of the typical noise in the signal remaining after filtering the wheel speed signals. To avoid high latency, a simple filter was used which contained noise within approximately a 6 rpm band around the actual wheel speed. Normal variance between the wheel speeds during straight line driving peaked around 20 rpm between the wheels on the front axle and 15 rpm between the wheels on the rear axle. The normal variance seen between the front and rear axle speeds peaked at about 20 rpm as well. The value of ε b was determined through data analysis and calibration which set it at a final value of 10 rpm. The value of ε θ was determined from analyzing vehicle data from constant 76

90 radius tests and autocross tests and was implemented as a gain placed upon the steering angle, θ, as shown: ε θ = 0.08 θ ( 41) An important feature of the D 1 -D 4 indicators is that no more than two of them can be true at any one time since only one wheel from each axle can be faster than the other. This means that at any time either D 1 or D 2 can be true but not both. Similarly, either D 3 or D 4 can be true but not both. This is an inherent property of the indicators since they represent opposite ends of a single comparison. The third differential is a comparison between the front and rear axle speeds. The axle speed is defined as the average of the speeds of the two wheels on the axle. The third differential and its two intermediate indicators are given as D 5 = 1 if ( ω FR + ω FL 2 D 6 = 1 if ( ω RR + ω RL 2 ) ( ω RR + ω RL ) ε 2 s ( 42) ) ( ω FR + ω FL ) ε 2 s ( 43) This differential exhibits the same property as the left-right differential. Either D 5 or D 6 can be true at any point in time but not both. The ε θ term was excluded in the calculation of ε s for the D 5 and D 6 differentials because steering angle was seen to have a negligible effect on the difference between average axle speeds. Because both axles contain open differentials, the differences between left and right wheels on each axle is approximately 77

91 the same and thus the average speed of the axle is changed the same for front and rear leaving the variances between them the same as when the vehicle is traveling straight Determining Slip Scenario The combination of these six indicators is enough to isolate the slip scenario being experienced by the vehicle with a significant degree of accuracy. Simulations were run with several variations of friction distribution across the wheels in order to confirm the necessary combinations of indicators. This includes an ideal scenario of uniform friction distribution so that each tire experiences exactly the same friction coefficient. While this is not realistic, it is important to include this case to develop a robust slip detection algorithm. Each possible configuration of slipping wheels is enumerated below with the corresponding conditions. First, the conditions for slip scenario 1 from Figure 27 are shown in Table 5. Slip scenario 1 is characterized by the presence of a D 1 -D 4 indicator from each axle as well as the presence of D 5 or D 6. Either D 5 or D 6 can be true for this configuration depending upon which gear the transmission is in and the current torque input to each axle. All permutations of indicators meeting these conditions can indicate slip scenario 1. The permutations in the first two columns which are highlighted in the lighter gray in Table 5 contain D 1 -D 4 indicators that correspond to wheels on opposite corners of the vehicle spinning, either front right and rear left or front left and rear right. These permutations are 78

92 wholly unique to slip scenario 1. The permutations highlighted in darker gray correspond to wheels on the same side of the vehicle spinning. The far right column corresponds to the case of ideal uniform friction distribution so both wheels on each axle slip at the same speed and none of the left-right comparisons are set true. Neither of these are unique as will be explained later in this section. Table 5: Conditions for Slip Scenario 1 Case Indicator All Wheels on Low Mu Values D 1 (FR Slip) D 2 (FL Slip) D 3 (RR Slip) D 4 (RL Slip) D 5 (Faxle Slip) D 6 (Raxle Slip) The conditions for slip scenario 2 are given in Table 6. The two possible configurations within slip scenario 2 are front wheels on low friction or rear wheels on low friction. In either configuration, the axle that is on low friction will trigger the corresponding D 5 or D 6 indicator and one of the D 1 -D 4 indicators will be set true corresponding to one of the wheels on the appropriate axle. In the rare case of uniform friction distribution, both wheels on the slipping axle will slip at the same speed and none of the D 1 -D 4 indicators will be set true. These conditions are also not unique. Handling for these will be discussed in section

93 Table 6: Conditions for Slip Scenario 2 Case Front on Rear on Indicator Low Mu Low Mu Values D 1 (ω FR > ω FL ) D 2 (ω FL > ω FR ) D 3 (ω RR > ω RL ) D 4 (ω RL > ω RR ) D 5 (ω Faxle > ω Raxle ) 1 0 D 6 (ω Raxle > ω Faxle ) 0 1 The conditions for slip scenario 3 are given in Table 7. Slip scenario 3 represents a splitmu configuration for which there are two possible cases: left wheels on low friction or right wheels on low friction. These configurations are primarily characterized by the appearance of D 1 and D 3 together or D 2 and D 4 together. Either D 5 or D 6 can be true for either splitmu configuration depending upon which gear the transmission is in and the current torque input to each axle. The permutations in Table 7 are identical to permutations highlighted in darker gray from slip scenario 1 rendering them non-unique to either scenario. Handling for these will be discussed in section Indicator Values Table 7: Conditions for Slip Scenario 3 Case 80 Left on Low Mu Right on Low Mu D 1 (ω FR > ω FL ) 0 1 D 2 (ω FL > ω FR ) 1 0 D 3 (ω RR > ω RL ) 0 1 D 4 (ω RL > ω RR ) 1 0 D 5 (ω Faxle > ω Raxle ) D 6 (ω Raxle > ω Faxle )

94 There are four possible configurations for slip scenario 4, shown in Table 8, representing each individual wheel on a low friction surface. Each case is characterized by the D 1 -D 4 indicator corresponding to the specific wheel that is slipping being set true while the other three remain false. The D 5 or D 6 indicator corresponding to the axle containing the spinning wheel will also be true. The permutations for slip scenario 4 are identical to those for slip scenario 2 rendering them non-unique to either scenario. Handling for these is discussed in section Indicator Values Table 8: Conditions for Slip Scenario 4 Case FR on Low Mu FL on Low Mu RR on Low Mu RL on Low Mu D 1 (ω FR > ω FL ) D 2 (ω FL > ω FR ) D 3 (ω RR > ω RL ) D 4 (ω RL > ω RR ) D 5 (ω Faxle > ω Raxle ) D 6 (ω Raxle > ω Faxle ) For detection purposes, slip scenario 5 will appear the same to the slip detection algorithm as scenario 4 when one axle has entered the low friction surface and will appear the same as scenario 3 when both axles have entered the low friction surface. Similarly, scenario 6 will appear the same as scenario 2 or scenario 1. This means that scenario 5 and 6 are already covered by the analysis above and further analysis specific to these scenarios is not necessary. 81

95 5.3.3 Handling for Non-Unique Slip Signatures There are identical permutations of slip indicators for slip scenarios 1 and 3 as well as for slip scenarios 2 and 4. This makes it impossible to determine the exact combination of wheels that are slipping. Fortunately, the indicators give enough information for the purposes of traction control that it is not necessary to obtain additional information. For example, cases that are indistinguishable include a single wheel on low friction or both wheels of an axle on low friction. A traction control system can react to a spinning wheel in one of two ways: reducing the input torque to the wheel or braking the spinning wheel. In either scenario, one wheel or both wheels of an axle on low friction, the traction control system would react by either reducing the input torque to the axle or braking the wheel that is spinning faster to control the wheel speed and aid in transferring torque to the other wheel of the axle. Thus it is not necessary to distinguish further which scenario the vehicle is experiencing Setting Slip Flags As demonstrated in section and section 5.3.3, the proposed slip detection algorithm determines the slip scenario with enough accuracy to determine which slip flag, Reduce_Front or Reduce_Rear, should be set to true. The appropriate slip flag or flags to be set true based on detected slip scenario is shown in Table 9. This logic is implemented as a truth table in the vehicle controller. 82

96 Table 9: Slip Flag Determination Slip Flag Slip Scenario Reduce_Front Reduce_Rear Normal Traction 0 0 All Wheels on Low Mu (Scenario 1) 1 1 Front on Low Mu (Scenario 2) 1 0 Rear on Low Mu (Scenario 2) 0 1 Left Side on Low Mu (Scenario 3) 1 1 Right Side on Low Mu (Scenario 3) 1 1 FR on Low Mu (Scenario 4) 1 0 FL on Low Mu (Scenario 4) 1 0 RR on Low Mu (Scenario 4) 0 1 RL on Low Mu (Scenario 4) 0 1 After the truth table logic, hysteresis is added to the slip flags to prevent them from rapidly switching on and off. It also prevents a slip flag from signaling true if the speed difference goes out of range for a very short amount of time. The hysteresis holds the final slip flags at false until the truth table output of the flag remains true for longer than t delay_on seconds. More importantly, the hysteresis holds the slip flags on and prevents them from becoming false until the truth table output of the flag is false for longer than t delay_off seconds. This allows for a continuous torque reduction action in the traction control strategy when the wheels are struggling to gain traction and experience speed oscillations around the slip threshold. The fact that this method of slip detection does not require any measure of vehicle speed to determine slip as is required by the traditional slip calculation given in ( 5) gives it a distinct advantage over traditional slip detection methods. It also has an advantage over 83

97 previously used methods of slip detection on all wheel drive vehicles which considered only the differential between front and rear axle speeds to detect slip. The addition of the left to right comparisons on each axle grants the ability to detect when both axles are slipping simultaneously. 5.4 Traction Control Algorithm The approach taken for traction control in the Ohio State EcoCAR 2 vehicle is to reduce the input torque to the axle experiencing wheel slip. The torque reduction is implemented as a maximum axle torque limit imposed upon the torque requests output from the control strategy for the current operating mode. This limit acts as a maximum allowable torque for the axle meaning that the driver requested torque will be overridden by the traction control limit if it is greater than the limit, however the driver torque request will be followed if it is below the traction control limit. A flow chart of the torque reduction and reapplication process is illustrated using the front axle as an example in Figure 28. In Figure 28, t indicates the amount of time that the current state has been active. When no wheel slip is detected, the torque limit is set well above the driver torque request to ensure that torque does not become unnecessarily limited. When slip is detected, the axle torque limit for the appropriate axle is instantly reduced by a value of T drop Nm below the current front or rear, respectively, axle torque request. The limit is then reduced linearly from that value at a rate of T redu Nm/time step until slip is no longer detected. 84

98 Figure 28: Torque Reduction Strategy Flow Chart To avoid unwanted regenerative braking, a safety mechanism in the traction control algorithm saturates the traction control torque limit at 0 Nm and so will not allow the algorithm to request a negative torque. A negative torque request is never necessary for traction control as a torque request of zero will always allow the wheels to regain traction as they will be driven by the inertia of the vehicle through road contact. A negative torque request also risks the introduction of negative slip. However, if the driver requested torque becomes negative, that torque request would still be passed out of the control system to the actuators. 85

99 Once the slip flag has been set to 0 again, the torque limit will continue to reduce at the same rate for a short period of time, t redu, to add a small safety factor and will then be held at the reduced value for a predetermined amount of time, t hold, after which it will be linearly increased at a rate of T inc Nm/time step until the torque limit again exceeds the driver commanded torque. During the torque reduction, hold, and torque increase stages, if the slip flag is set to 1 again at any time the torque begins reducing again even if the full process has not completed. Figure 29 illustrates this process on an exaggerated time scale for clarity. Figure 29: Traction Control Illustration 5.5 Implementation With the traction control algorithm determined on paper, implementation in EcoSIM2- Dynamic follows as well as final implementation on the Ohio State vehicle. The algorithm 86

100 is first implemented into code and tested within the dynamic simulator. Once development in software is complete, the algorithm can be implemented in the vehicle and tested on the ceramic tile surfaces at the Transportation Research Center in East Liberty, Ohio Controls Hardware The traction control algorithm is located within the vehicle s supervisory controller. The highly complex architecture chosen by the Ohio State team demands an extensive supervisory control strategy capable of optimizing a complex system in real time. To accommodate the control strategy, the controller hardware must meet several requirements including: 3 ADC inputs and DAC outputs 3 CAN busses Ability to execute complex controls in real time Allows for rapid-prototyping and tuning Robust hardware that can withstand vibration and temperatures experienced in vehicle cabin The Ohio State team chose a dspace MicroAutoBox II (MABX II) for the EcoCAR 2 vehicle because it suitably met these criteria with a large amount of computing power, the ability to compile and flash code quickly, and a record of reliability with the Ohio State team during several past AVTCs. Full manufacturer specifications for the MABX II are given in [26]. A view of the MABX II controller can be seen in Figure

101 Figure 30: dspace MicroAutoBox II Required Signals and Sensors Necessary signals for proper function of the traction control algorithm are: Front Right wheel speed Front Left wheel speed Rear Right wheel speed Rear Left wheel speed Current electric machine torque outputs Current gear command Current electric machine torque commands The wheel speeds are obtained from the stock hall-effect wheel speed sensors and transmitted to the MABX by CAN from the stock brake controller. The wheel speed sensors have a resolution of 48 ticks/rev. The current electric machine torques are obtained via CAN from the inverters and the current gear is obtained via CAN from the transmission controller. Current actuator torque and gear commands are calculated within the MABX at 88

102 its operating time step of 0.01 sec and the values are routed directly into the traction control algorithm. The incoming signals are appropriately mapped or converted from their original signals prior to use in the traction control algorithm. 5.6 Parameter Optimization The final slip detection and traction control algorithm contain a total of 7 tunable parameters for each axle. These parameters are t delay_on, t delay_off, T drop, T redu, t redu, t hold, and T inc. To optimize these parameters, a genetic algorithm optimization was used with the results of the algorithm implemented in EcoSIM2-Dynamic. The objective function to be minimized considered the difference between the appropriate wheel speeds for the current vehicle speed and the actual wheel speeds. This could be accomplished in simulation because the vehicle speed during wheel slip can be found in simulation through the magic formula and vehicle body models. An acceleration performance term was also included in the objective function that considers the vehicle s ability to continue accelerating during traction control operation by comparing the target vehicle speed to the actual speed achieved during simulation. The objective function to optimize the parameters using the genetic algorithm is given as Err = ( v veh r eff,fr ω FR ) + ( v veh r eff,fl ω FL ) + ( v veh ω r RR ) + ( v veh ω eff,rr r RL ) eff,rl + 6 v target v final ( 44) 89

103 Where v target v final = Target speed for acceleration test in mph = Final vehicle speed achieved during simulation in mph The objective function acts as an overall performance metric for the traction control system. It will be used throughout the remainder of this work and referred to as the overall performance metric. While a term to consider vehicle performance is included in the optimization, its relative weight as compared to the other terms is much less. Typical differences between target and final speed seen during these simulations are less than 8 mph. Typical values for the terms considering wheel speeds are on the order of This means that even when multiplied by two in the objective function, the performance term carries considerably less weight than the other terms. Performance considerations were given such a small weight because the safety concerns surrounding the control of wheel speeds are of much higher importance than acceleration performance during that time. The simulation for use with the genetic algorithm optimization considered a 0-30 mph acceleration with all wheels on low friction and a perfectly uniform low friction surface with a nominal coefficient of friction of This scenario was used because it represents a worst case scenario. The final values for the parameters generated by the optimization are given in Table

104 Table 10: Simulation Optimized Parameter Values Parameter Front Axle Value Rear Axle Value t delay_on sec sec t delay_off sec sec t redu sec sec t hold sec sec T redu 11.0 Nm 23.7 Nm T inc 7.0 Nm 5.86 Nm T drop Nm 500 Nm 5.7 System Performance Metrics Before presenting any simulation results, it is important to outline some metrics to help measure the performance improvement granted by the traction control. The following metrics will be looked at for each axle in all test scenarios: Maximum wheel speed (ω max ) Maximum slip ratio value (κ max ) Maximum interval of slip (t slip,max ) Overall Performance Metric (OPM) Slip ratios are defined in ( 6). The maximum interval of slip is defined as the longest interval for which a slip flag is active. The overall performance metric is defined as the objective function value as given by ( 44). For all metrics, lower values are more desirable. 91

105 5.8 Sensitivity to Road Friction To ensure that the system is effective across a wide range of conditions, the worst case scenario of all wheels on low friction was repeated using a variety of friction distributions across the tires and the resulting performance was compared. Table 11 shows the friction distributions that were considered. Table 11: Friction Distributions Distribution Front Left Front Right Rear Left Rear Right A μ x μ x μ x μ x B μ x μ x 0.01 μ x 0.02 μ x C μ x μ x 0.02 μ x 0.01 μ x D μ x 0.03 μ x μ x μ x 0.04 E μ x 0.01 μ x 0.03 μ x 0.02 μ x F μ x 0.01 μ x 0.03 μ x 0.03 μ x G μ x μ x μ x 0.01 μ x The 0-30 mph simulation was run with traction control active for each friction scenario. The results for each of these scenarios is summarized in Figure 31. The effect on each axle is shown separately in the plot. The results show clear trends in the behavior of each performance metric as the friction difference increases between the right and left wheels on an axle. 92

106 Wheel Speed [rpm] Front Rear Slip Interval [s] Slip Ratio Front 0.8 Rear Figure 31: Friction Study Results Per Axle Front Rear Difference in Mu The following trends can be seen: For both axles, ω max peaks when there is a slight difference in friction between the wheels, but then rapidly declines as the friction differential grows. The maximum slip ratio, κ max, for the rear axle stays somewhat constant as it oscillates within a small band of values, however the front axle maximum slip ratio increases steadily as the friction differential increases. The slip interval increases slightly for the front wheels and decreases slightly for the rear wheels. 93

107 While these trends display that there is some change in the performance of the system, the scale of the change is relatively small. A better illustration of this is seen in Figure 32 where the change in the overall performance metric is seen as a function of the maximum deviance from the nominal coefficient of friction seen by one of the wheels. This is particularly useful as an overall measure of the performance of the system that takes both axles into account rather than only one axle at a time. There is a clear trend of improved performance with a diminishing return as the maximum friction differential increases. It is important to note, however, that the system is still effective and capable of adequately controlling slip, even in the worst case scenario of a uniform low friction surface. Overall Performance Metric Maximum Difference in Mu Figure 32: Overall Performance Metric Value for Friction Study Overall performance metric values less than 1000 indicate that traction control is functional and at least moderately effective whereas overall performance metric values for simulations with no traction control active is typically on the order of Examples of this can be seen in Table 12 and Table 13 in Chapter 0. Figure 33 and Figure 34 show the results 94

108 of the simulation with overall performance metric of 559 and 302, respectively, to illustrate the difference in vehicle performance associated with each overall performance metric value. Wheel Speed [rpm] Wheel Speed [rpm] FR FL RR RL time [s] RR 6 RL Figure 33: Simulation for Friction Distribution A Overall Performance Metric = 559 Wheel Slip Wheel Slip FR FL time [s] 95

109 Wheel Speed [rpm] Wheel Speed [rpm] FR FL RR RL time [s] Figure 34: Simulation for Friction Distribution G Overall Performance Metric = 302 Wheel Slip Wheel Slip FR FL RR RL time [s] 96

110 Chapter 6: Testing and Results 6.1 Software-in-the-Loop (SIL) Testing The traction control algorithm was first tested in EcoSIM 2 Dynamic. Several slip scenarios were tested in the software configuration. Due to the limitations discussed in Chapter 4, the most accurate slip scenarios for simulation are launch under low mu conditions for all four wheels and launch with a left-right split-mu scenario. To test the slip detection and flexibility of the traction control algorithm, front-rear split mu scenarios and a single wheel on low-mu were tested as well. Figure 35 shows the subset of scenarios from Figure 27 that were chosen for SIL testing. Figure 35: Scenarios for SIL Testing 97