Modeling and Simulation of a Hybrid Electric Vehicle for the Challenge X Competition

Submitted to: The Engineering Honors Committee 119 Hitchcock Hall College of Engineering The Ohio State University Columbus, OH 43210

Michael Arnett 4091 Millsboro Rd W Mansfield, OH 44903

Dr. Giorgio Rizzoni, Advisor May 20, 2005 Abstract:

As the market shifts toward larger vehicles and growing concerns regarding petroleum consumption and emissions emerge, automakers have begun to explore new vehicle propulsion solutions. General Motors and The Department of Energy have joined together to create the Challenge X competition to explore hybrid-electric vehicles as one such solution. Seventeen teams across the United State will experience “real-world” HEV development over the three year competition. This process begins with vehicle architecture selection, modeling and simulation. A dynamic model of a hybrid-electric powertrain is developed here. This model is then implemented into two Simulink based simulators: the quasi-static cX-SIM, the dynamic cX-DYN. These simulators are used to validate the control strategy being developed for the Challenge X vehicle. Verification will include optimal performance in regards to fuel consumption, battery state-of-charge, and drivability. Techniques of validating the model and simulators using a rolling chassis are also being implemented. Preliminary data from the quasi-static simulator and the rolling chassis is presented herein.

Acknowledgements:

I would like to thank Dr. Giorgio Rizzoni, Joe Morbitzer, Osvaldo Barbarisi, Kerem Koprubasi, Jason Disalvo, John Neal and Christopher C. Mabry, for all of the help and support they have given me throughout the duration of this research.

ii Table Contents

CHAPTER 1: INTRODUCTION ...... 6 1.1 MOTIVATION ...... 6 1.2 VEHICLE ARCHITECTURE...... 8 1.2.1 Classifications of HEVs ...... 8 1.2.2 Vehicle Components...... 10 1.2.3 Modes of Operation...... 11 CHAPTER 2: MODELING...... 14 2.1 MODEL OF THE DRIVELINE ...... 14 2.1.1 Dynamic Equations of the Front Driveline...... 15 2.1.2 Dynamic Equations of Rear Driveline ...... 17 2.1.3 Dynamic Equation of the Vehicle...... 17 2.2 DYNAMIC SIMULINK MODEL OF THE FRONT DRIVELINE ...... 18 2.2.1 ICE Model ...... 19 2.2.2 Clutch Model...... 19 2.2.3 Front Gearbox Model ...... 20 2.2.4 Transmission ...... 21 2.2.5 Front Axle ...... 22 2.2.6 Front Brakes ...... 23 2.2.7 Front Wheels...... 24 2.3 DYNAMIC SIMULINK MODEL OF THE REAR DRIVELINE ...... 25 2.3.1 Electric Motor ...... 25 2.3.2 Rear Gearbox ...... 26 2.3.3 Rear Axle...... 27 2.3.4 Rear Brakes...... 28 2.3.5 Rear Wheels...... 29 CHAPTER 3: SIMULATION RESULTS...... 31 3.1 CX-SIM ...... 31 3.1.1 Driver...... 32 3.1.2 HEV Powertrain...... 33 3.1.3 Vehicle...... 34 3.2 CX-DYN ...... 34 3.3 CX GRAPHICS ...... 36 3.3.1 Set Layout for Plots Driver ...... 37 3.3.2 Set Layout for Plots Vehicle...... 38 3.3.3 Set Layouts for Plots Acceleration Test...... 39 3.3.4 Set Layout for Plots HEV Operation...... 40 3.3.5 Set Layout Plots for Conventional Operation ...... 41 3.3.6 Set Layout Plots for Electric Powertrain...... 42 CHAPTER 4: RESULTS & MODEL VERIFICATION...... 45 4.1 CX-SIM ...... 45 4.2 CX-DYN ...... 52 4.3 ROLLING CHASSIS...... 52 4.3.1 Launch Test...... 53 4.3.2 Model Verification & Mapping...... 57 4.3.3 cX Test ...... 60 CHAPTER 5: CONTROL STRATEGY DEVELOPMENT ...... 62 5.1 OVERVIEW...... 62 5.2 ECMS...... 63 5.3 BATTERY STATE-OF-CHARGE ...... 64

iii 5.4 DRIVABILITY ...... 65 REFERENCES ...... 67 APPENDIX ...... 68

List of Figures:

Figure 1. Ohio State Challenge X Vehicle Architecture [5]...... 10 Figure 2. Dynamic Model of the Driveline [8]...... 15 Figure 3. Simulink Diagram of ICE & ISA...... 19 Figure 4. Simulink Diagram of the Clutch...... 20 Figure 5. Simulink Diagram of the Front Gearbox...... 21 Figure 6. Simulink Diagram of the Automatic Transmission...... 22 Figure 7. Simulink Diagram of the Front Axle...... 23 Figure 8. Simulink Diagram of the Front Brakes...... 23 Figure 9. Simulink Model of the Front Wheels and Differential...... 24 Figure 10. Simulink Diagram of the Traction Motor...... 26 Figure 11. Simulink Block Diagram of the Rear Gearbox...... 27 Figure 12. Simulink Diagram of the Rear Axle...... 28 Figure 13. Simulink Diagram of the Rear Brakes...... 29 Figure 14. Simulink Diagram of the Rear Wheels...... 30 Figure 15. cX-SIM Top Layer...... 32 Figure 16. cX-SIM Powertrain Subsystem...... 33 Figure 17. cX-DYN Top Layer...... 35 Figure 18. cX-DYN Powertrain Subsystem...... 35 Figure 19. cX Graphics Top Layer...... 37 Figure 20. Driver Plot Options Screen...... 38 Figure 21. Vehicle Plot Options Screen...... 39 Figure 22. Acceleration Test Parameter Selection Screen...... 40 Figure 23. HEV Operation Plot Options Screen...... 41 Figure 24. Conventional Powertrain Plot Options Screen...... 42 Figure 25. Electric Powertrain Plot Options Screen...... 44 Figure 26. Actual & Desired Velocity from cX-SIM Preliminary Simulation...... 46 Figure 27. Deviation of Actual & Desired Vehicle Speed of cX-SIM Simulation...... 46 Figure 28. Total Output and Requested Torque during the cX-SIM Preliminary Simulation...... 47 Figure 29. Deviations Between Actual & Desired Torque of HEV Powertrain...... 48 Figure 30. ICE Operating Points during cX-SIM Preliminary Simulation...... 49 Figure 31. Operating Points of the EM during the cX-SIM Preliminary Simulation...... 50 Figure 32. ISA Power during the cX-SIM Preliminary Simulation...... 51 Figure 33. Battery SOC during cX-SIM Preliminary Simulation...... 52 Figure 34. Rolling Chassis Experimental Set-Up...... 55 Figure 35. Launch Test EM Motor Speed -40% Torque Limit...... 55 Figure 36. Launch Test Vehicle Speed- 40% Torque Limit...... 56 Figure 37. Launch Test EM Motor Speed--50% Torque Limit...... 56

iv Figure 38. Launch Test Vehicle Speed-- 50% Torque Limit...... 57 Figure 39. EM Torque Mapping Test: Vehicle Speed (B=30)...... 59 Figure 40. EM Torque Mapping Test: Acceleration (B=30)...... 60 Figure 41. cX Test Top Layer...... 61 Figure 42. cX -Test Graphics...... 61 Figure 43. Control Strategy Schematic...... 63

List of Tables: Table 1. Summary of Challenge X Vehicle Technical Specifications [9, 5]...... 7 Table 2. Vehicle Operating Modes [8]...... 12 Table 3. Nomenclature...... 68

Chapter 1

Introduction

The motivation for this research stems from the growing concern of energy consumption and environmental impacts of current automobiles. These issues have lead to the creation of Challenge X and Ohio State’s participation in this competition. Hybrid- electric vehicle architecture is developed using the general classifications of HEVs while considering the advantages and disadvantages of each solution. The components to drive this architecture and various modes of operation are also defined.

1.1 Motivation As the global economy begins to strain under the pressure of raising petroleum prices and environmental concerns, automobile manufacturers constantly strive to produce more fuel efficient and environmentally friendly vehicles. The primary objective of manufacturing automobiles subject to such constraints is to ensure consumer mobility. Given the current resources and technologies, the most feasible solution is hybrid electric vehicles. In order to accelerate the research involved with creating these vehicles, the General Motors Corporation and The Department of Energy have created the Challenge X Competition. This is a three year long competition that requires 17 universities across the United States to design, develop, and build a hybrid-electric Chevrolet Equinox sport- utility vehicle. The goal of this competition is to secure consumer sustainable mobility. The first, and current, year involves the preliminary design of the vehicle, component selection, control strategy development, and vehicle modeling and simulation. General Motors and The Department of Energy have created a list of goals each team is

6 to achieve with the development of their hybrid electric vehicle. These “Vehicle Technical Specifications” can be seen in Table 1. The idea behind such specifications is to maintain stock Chevrolet Equinox performance and capacity while decreasing fuel consumption and emissions. Throughout the first year each team must develop and simulate a hybrid electric vehicle architecture that meets, or surpasses, these goals.

Table 1. Summary of Challenge X Vehicle Technical Specifications [9, 5].

COMPETITION OHIO STATE DESCRIPTION GOAL VTS IVM – 60 MPH < 9.0 S < 10.0 S 50 – 70 MPH < 6.8 S < 7.0 S VEHICLE MASS < 4400 LBS < 4275 LBS

COMBINED FUEL > 32.0 > 35.0 MPGGE ECONOMY MPGGE

HIGHWAY RANGE > 200 MI > 275 MI

5 PASSENGER CAP. 5 PASSENGERS PASSENGERS

EMISSIONS LEVEL TIER 2, BIN 5 TIER 2, BIN 5 TRAILERING CAP. 2500 LBS 2500 LBS STARTING TIME < 5.0 S < 2.0 S

During the second and third year, each team then integrates their HEV configuration onto the actual vehicle to compete. Upon receiving their Equinox during the second year, each team must implement their hybrid electric architecture onto the vehicle. Confirming the developed architecture meets competition specifications is the objective for the second year. The actual competition involving a “show room” Equinox hybrid is be held during the third year. Here each team competes against one another in the hopes that their hybrid electric vehicle best achieves the aforementioned specifications.

7 1.2 Vehicle Architecture The most critical task to achieve the goals listed in Table 1 is selecting and developing an effective HEV architecture. Performance of the vehicle automatically increases with a hybrid electric configuration due to increased fuel savings, reduced energy losses with regenerative braking, and emissions control. Hybrid electric vehicle architectures are organized into three classes: parallel, series and power-split hybrids.

1.2.1 Classifications of HEVs The parallel configuration allows for the electric machine(s) and the internal combustion engine to provide mechanical power to the driveline. Parallel hybrids can be further classified in two ways: electrical assist parallel hybrids and ICE assist parallel hybrids. In the electrical assist architecture, the ICE operates only within the optimal region to reduce emissions and fuel consumption. The EM assists whenever necessary in order to uphold this constraint. The ICE assist architecture involves the ICE only being turned on for hard accelerations, hill climbing, and high speeds. This also reduces emissions and fuel consumption as the EM acts as the primary actuator for vehicle motion [1]. The other configuration is a series hybrid. In a series HEV, the vehicle is propelled solely by the EM. The EM obtains the required energy from either a battery, or a motor-generator set. The MG set supplies power to the EM and an energy storage device (i.e. a battery or super capacitor). The purpose of the energy storage device is to allow more power to be drawn by the EM during more demanding driving conditions (hill climbing, hard accelerations, etc.) [6]. Both configurations have their own distinct advantages. The parallel configuration allows for the ICE and EM to be reduced in size since their propelling power can be summed to meet driver demand. Moreover, efficiency increases with this configuration since fewer energy conversions take place. However, a parallel configuration is far more complex than the series architecture. The series architecture allows for easier packaging since the EM and MG set do not need to be close together. The control problem for this type of HEV is also far less complex [1, 6]. Moreover, the series configuration allows for

8 direct battery charging and electric power supply which is essential for effective hybrid travel. There are two additional types of HEVs when not speaking of the vehicle architecture: charge-sustaining and grid dependent. If the HEV can sustain the charge of the battery in every driving condition without the assistance of an outside electrical power grid, the HEV is considered charge-sustaining. If the vehicle needs to be integrated with an outside electrical power grid from time-to-time to recharge the battery, the vehicle is referred to as grid-dependent [6]. Charge-sustaining HEVs, although more complex, are more appealing to the consumer. This is due to the longer range of the HEV over a conventional vehicle without sacrificing performance [6]. Ohio State has chosen to develop a charge-sustaining HEV. In order to obtain the benefits from both HEV architecture configurations, the Ohio State Challenge X team has chosen to develop the third class of HEV: power-split. [5]. This configuration combines both parallel and series architectures. To accomplish this, the powertrain is divided into two independent sections. The first is the conventional powertrain. This consists of an ICE coupled with an integrated starter/alternator (ISA) that powers the front axle of the Equinox. An electric powertrain drives the rear wheels of the HEV. To do this, an electric machine, with a gearbox appropriately sized for vehicle propulsion, is used [7]. This vehicle architecture is represented in Figure 1.

9 Integrated Starter Alternator (ISA) Traction Motor & Gearbox (EM)

(ICE)

(AT)

Front Back

Figure 1. Ohio State Challenge X Vehicle Architecture [5].

1.2.2 Vehicle Components With the architecture defined, the individual components that make up the vehicle are chosen. The main actuator of the conventional powertrain is a diesel engine. Specifically, a Fiat 1.9L diesel engine is used. This is one of the engines provided by the Challenge X organizers as being acceptable for use during the competition. Diesel engines are more efficient than gasoline powered internal combustion engines due to higher compression ratios and lack of engine pumping loses. To reduce emissions, Biodiesel B20 is the selected fuel [7]. As shown in Figure 1, an ISA rigidly connects to the diesel engine via the crankshaft. The ISA is simply an electric machine that is capable of being used to start the diesel engine, or be used by the diesel engine as an alternator to provide electrical energy. This is one of the components that make this HEV charge-sustaining. The ISA can also supply a minimal amount of torque to the front wheels for propulsion assistance [5].

10 The EM, referred to as the “Traction Motor” the Figure 1, is the electrical propulsion unit used to the power the EV1 electric car by General Motors. This 103 kW electric motor and gearbox is now used to drive the rear wheels of the Equinox HEV. Not only can this unit provide power to the wheels, but it can also absorb power from the wheels and be used as a generator. This process occurs when the driver requests stopping torque. At this point, the EM absorbs torque from the rear axle slowing the vehicle, and will use this torque to generate energy for the replenishment of the battery [5]. This is another feature that classifies this HEV as charge-sustaining. Initially, the Ohio State Challenge X team agreed to use an automated manual transmission [7]. However, these types of transmissions are hard to acquire, so the automatic transmission that accompanies the Fiat diesel engine is used. Automatic transmissions are not as efficient as automated manual or manual transmissions, but they are the most acceptable to the consumer [5]. Only one nickel-metal hydride battery pack powers both electric machines and the vehicle accessories. As shown above, there are two separate inverters for the EM and the ISA, as well as, a DC-to-DC converter to power 12 volt vehicle accessories (interior lamps, radio, head lights, etc.). A switch box routes high-voltage flow [5]. One of the main reasons for selecting a charge-sustaining HEV configuration involves current battery technology. The market is filled with low efficiency, low energy storage capacity, and long charge time solutions [1]. As previously stated, to cater to the desires of the consumer, a charge-sustaining strategy eliminates these undesirable issues. 1.2.3 Modes of Operation With the architecture depicted in Figure 1, various operating modes for the vehicle can be achieved. These operating modes have been summarized in Table 2. During a typical driving mission, the HEV operates in both hybrid, and conventional modes [1]. This can be seen in the table below.

Table 2. Vehicle Operating Modes [8].

MODE ICE ISA EM TRAN.

Idle Off Off Off Neutral

ICE, EM, AND ISA ARE SHUTOFF. ELECTRICAL ACCESSORIES.

ELECTRIC LAUNCH OFF MOT. OFF NEUTRAL

VEHICLE STARTED FROM REST WITH EM.

ENGINE START START MOT. MOT. NEUTRAL

AT A CERTAIN VEHICLE SPEED, ICE QUICKLY STARTED BY ISA.

MOT. OR MOT. OR NORMAL ON DRIVE GEN. GEN. TORQUE REQUESTS DETERMINED BY PRIMARY CONTROL STRATEGY.

ON OR DRIVE OR DECELERATION GEN. GEN. OFF NEUTRAL REGENERATIVE BRAKING BY EM AND ISA AS BATTERY ALLOWS.

GEN. OR 4WD ON MOT. DRIVE OFF EM RECEIVES CONTINUOUS POWER THROUGH DC BUS FROM ISA.

With each of these, the fuel efficiency increases and the emissions decrease immensely. During the idle mode, and decelerating cases the ICE is be turned off, unless recharging of the battery requires this to drive the ISA to provide the necessary power (series HEV). The fuel efficiency can increase by as much as 10% simply by eliminating fuel flow to the ICE during braking and idling situations [5]. This concept accompanies the general rule that the EM should be used during launch and immediate power request situations [6]. This is because electric actuators can deliver high torque at low speeds while emitting no environmentally harmful by-products. This general rule is satisfied during Electric Launch mode when the EM motors (MOT.) the vehicle. After a set speed, the ICE turns on during the Engine Start mode. Once the ICE is up to speed, the automatic transmission engages and the ICE becomes the primary actuator for vehicle propulsion. At this point, the vehicle enters the Normal mode. Between the Electric Launch and Normal mode, the HEV satisfies the constraints of being a parallel HEV as previously defined. Note that during Normal mode, the EM can be used to supply regenerative power to the battery; moreover, the EM can draw power

12 from the battery and assist the ICE with motoring the vehicle during four-wheel drive situations. The ISA shares similar options during Normal mode. Basically, the 4WD mode is merely a derivative of the Normal mode with the EM motoring and the ISA generating the electrical power needed (a series/parallel hybrid combination). The vehicle enters Deceleration mode when the driver uses the brakes to slow the vehicle. Here the concept of “Regenerative braking” is implemented. Regenerative braking involves the process of using the resistance between the field and armature of the EM to generate power to replenish the battery. As the driver applies the brake, for a set distance of pedal travel, the mechanical braking system does not activate and the EM absorbs torque off of the rear axle. This mechanical energy is converted to electrical energy and sent to the battery [6]. The power-split HEV solution with a charge-sustaining focus has been selected by the Ohio State Challenge X team. This particular configuration leads to alternate modes of operation all of which increase the efficiency of the vehicle. With the architecture, and components thereof, defined, modeling of the HEV can begin.

Chapter 2

Modeling

With the vehicle architecture and components selected modeling of the Challenge X HEV is performed. The entire driveline is first visually represented by a figure which leads to the development of the mathematical expressions governing the behavior of the HEV. These expressions are then configured into Simulink block diagrams for further analysis and simulation.

2.1 Model of the Driveline The dynamic model of the driveline is displayed in Figure 2. Refer to Table 3 of the Appendix for a list of the nomenclature. Only the necessary inertias are included in the model. The inertias of the smaller components (the axles, brake assemblies, and wheels) do not have a drastic effect on the dynamics of the system and can be ignored for simplicity. Unnecessary damping and spring effects such as those intrinsic to the automatic transmission and rear gearbox are also eliminated to further simplify the model. Disregarding these dynamic effects does not alter the accuracy of the model since they are insignificant in comparison to other driveline components (i.e. ICE, EM, and ISA). The equations that follow are developed by the author, as well as separately developed by others and represented in the referenced publications [2, 5, 7, 8].

Figure 2. Dynamic Model of the Driveline [8].

2.1.1 Dynamic Equations of the Front Driveline Due to the fact that the ISA is rigidly connected to the ICE, they can be considered as one lumped inertia (JICE+JISA) accelerating at the same rate as the

ICE(ω&ICE ). The torque converter divides the front driveline into two parts. The first includes the dynamic behavior of every component from the ICE and ISA to the pump side of the torque converter. This relationship is as follows:

()JJICE +=ISA ω&ICE TICE +TISA −bICEωICE −TTC _ P (1)

Here the inertias of the ICE and ISA are combined and have the same rotational

speed(ωICE ). This inertial force must be equivalent to the torque of the ICE (TICE) and

ISA (TISA), as well as the damping effect of the ICE (bICEωICE), and torque of the pump side of the torque converter (TTC_P). When the torque converter is not locked, the dynamic behavior of each component from the turbine side of the torque converter to the wheels can be modeled as:

15 TTC _T ⎛⎞xVEH ⎛vVEH ⎞ JkTRωθ&TR =−F ⎜⎟TR −−bF ⎜ωTR −⎟ (2) τTR ()gr⎝⎠F ⎝rF ⎠

The rotational inertia of the transmission accelerates ( JTRω&TR ) as a result of the excitation imposed by the following quantities. Torque from the transmission depends on the gear

ratio (τTR (g)), which in turn depends on the current gear (g). Each gear results in a different torque on the turbine side of the torque converter (TTC_T). Coming off of the

transmission are the spring (kF ) and damping (bF ) dynamic effects introduced by the front axles (half shafts). These quantities are functions the transmission rotational speed

(ωTR) and angular position (θTR). Vehicle speed (vVEH) and vehicle position (xVEH) are manipulated by the wheel radius (rF) to be used here as well. Note the dynamic effects of the front brakes have been ignored, and are only considered as a torque (TB_F). This torque is zero until the driver begins to demand stopping power. When this occurs, equation (2) becomes:

TTC _T ⎛⎞xVEH ⎛vVEH ⎞ JkTRωθ&TR =−F ⎜⎟TR −−bF ⎜ωTR −⎟−TB _ F (3) τ RF()gr⎝⎠⎝rF⎠

The above equations are derived assuming that the torque converter is not locked. When the torque converter is locked, the fluid coupler becomes a rigid link connecting the ICE and ISA inertia directly to the inertia of the automatic transmission through the gears. This also means that the torque the pump side and turbine side are equal (TTC), or:

TTTC __P = TC T = TTC (4)\

However, the specific dynamic equations for the driveline when the torque converter is locked have yet not been developed. Currently, the Ohio State Challenge X Team is not concerned with such a model. This concludes the development of the dynamic equations for the conventional (front) driveline.

16 2.1.2 Dynamic Equations of Rear Driveline The rear driveline is not nearly as complex as the front as there is no torque converter. The rotational inertia of the EM is excited ( J EM ω&EM ) by the torque of the EM

(TEM) and the intrinsic damping of the EM (bEM). The spring (kR) and damping (bR) characteristics of the axle add to the dynamic response of this component as well. Here, the angular speed (ωEM ) and angular position (θEM ) of the EM are manipulated by the ratio of the gearbox (τ GB ) and this interacts with the previously defined vehicle parameters to yield the appropriate dynamic response from the rear axle. This portion of the vehicle is modeled as follows:

⎡ ⎤ ⎛⎞xvVEH ⎛VEH ⎞ JTEM ωω&EM =−EM bEM EM −τGB ⎢kR ⎜⎟θEMτGB − +bR ⎜ωEMτGB − ⎟⎥ (4) ⎣ ⎝⎠rrRR⎝⎠⎦

Again, the dynamics of the rear brakes are disregarded and their effect is represented by a torque (TB_R). This torque is zero until the driver commands otherwise. If the brakes are being applied, then (4) becomes:

⎡⎤ ⎛⎞xvVEH ⎛VEH ⎞ JTEM ωω&EM =−EM bEM EM −τGB ⎢⎥kR ⎜⎟θEMτGB − +bR ⎜ωEMτGB − ⎟−TB _ R (5) ⎣⎦⎝⎠rrRR⎝⎠ 2.1.3 Dynamic Equation of the Vehicle The final expressions to derive are those of the vehicle. This component will be affected by not only the tractive force (F) input from the powertrain, but also the opposing forces due to aerodynamic drag (FDRAG), rolling resistance (FRR), and forces

from the road grade (FRD). These equations can be seen below.

mvVEH &VEH = FRR ++FDRAG FRD −F (6)

FmRR = VEH gCr cos(ϕ) (7)

1 F= ρ CAv2 (8) DRAG 2 AIR d f VEH

FmRD = VEH gsin(ϕ) (9)

The rolling resistance is the product of the vehicle mass (mVEH), the gravitational

acceleration due to gravity (g), the rolling resistance coefficient (Cr) and the cosine of the grade angle of the road measured from the horizontal plane (φ). Air drag on the vehicle is

represented by the standard drag equation that includes the density of air (ρAIR), the drag

coefficient of the vehicle (Cd), the frontal area of the vehicle (Af) and the vehicle velocity

(vVEH). Finally, the force resulting from the grade of the road is merely a product of the mass of the vehicle, the acceleration due to gravity, and the sine of the grade angle [6]. With all of the dynamic equations derived for the entire driveline, models can be created in Simulink for further analysis and simulation.

2.2 Dynamic Simulink Model of the Front Driveline One of the most convent ways to analyze dynamic equations such as those previously derived is with Simulink modeling software. Each of the above equations are represented by a block diagram. Each individual diagram is connected to create the entire system. Then an input can be introduced and the response of this system can be analyzed in great detail. When this Simulink model was initially developed, the Ohio State Challenge X team was considering using a manual transmission; therefore, the model presented below is slightly different than the aforementioned vehicle model. Also, the variables seen in these diagrams are different than those seen in Figure 2. This is done for programming convenience. Finally, the version of the front driveline developed here is not used for the HEV vehicle simulator discussed later; however, this model, after slight alterations, is used by another for initial testing of the control strategy that is discussed in a subsequent chapter [2]. In general, torque, or speed in some cases, flows forward through the following model component by component. The speed, or torque in some cases, and position are then fed back when necessary. This model operates on an initial torque request from the “driver.” This request acts as an input to each actuator. The particular actuator then converts this input to an output torque and a feed back speed. The output torque then

18 serves as the input of the next component in the driveline. This process continues until torque is delivered to the wheels, and vehicle speed is fed back to the “driver.” The driver is ultimately represented by a Simulink subsystem that can be seen in Figure 15. 2.2.1 ICE Model The Simulink block diagram of the ICE can be seen in Figure 3 along with the dynamic equation that governs this model. Note that the inertia of both the ICE and ISA are lumped together into one variable ( JJFI= CE+ JEM) as seen in the diagram. The first two inputs represent the torque command for the ICE (TICE) and ISA (TISA). The third input is the opposing torque coming from the clutch of the manual transmission (Tc). This torque is subtracted from the other input torques. The output from the inertia gain is

integrated twice: once for speed (ωICE ), and the other for position (θICE ) . The value of the ICE speed is sent to the clutch, but the value of ICE position is used only for observation purposes. The dynamic equation is as follows:

()JJICE +=ISA ωω&ICE TICE +TISA −bICE ICE −TC (10)

Figure 3. Simulink Diagram of ICE & ISA.

2.2.2 Clutch Model The speed and position of the ICE and ISA enter the clutch. The clutch is fairly simple and operates under the assumption that no slip occurs. This is a valid assumption for modeling purposes as predicting and modeling the magnitude of any slip presents a rather complex problem. However, provisions have been made in the model for the

19 damping (bc ) and stiffness (kc ) intrinsic to the clutch and are represented in the respective gain blocks of Figure 4. The input, γ, is a command sent to the clutch by the driver that either engages, or disengages, the clutch. This value can either be 0 to represent the clutch being disengaged, or 1 to represent the clutch being engaged. If the driver is shifting and has the clutch disengaged, the product will be zero, and no torque passes through the clutch. When the driver has the clutch engaged, the speeds will be multiplied by 1 with the product block and the torque flows through this device and onto

the gearbox. The clutch speed (ωc ) is an input here and is sent from the gearbox as a feedback. The governing equation of the clutch is:

TbcC=−γω⎣⎡( ICEωC) +kC(θICE−θC)⎦⎤ (11)

Figure 4. Simulink Diagram of the Clutch.

2.2.3 Front Gearbox Model

The torque from the clutch (Tc ) enters the front gearbox. This block diagram can be seen in Figure 5. Here the torque and speed are manipulated according to the gear and the respective gear ratio. The only inputs are the torque from the clutch, the gear

command, the feed back speed (ωT ) and position (θT ) of the transmission. These inputs will be manipulated to result in an output torque (TCT@ ), speed(ωc ) , and position(θc ) .

20 The ratios for each gear are contained within the look-up table and provide the appropriate constants for accurate speed reduction and torque increase. To ensure ideal operation, a switch allows torque to pass through the clutch if the clutch command is 1 (engaged). Otherwise, the switch will force the output torque to be zero. Torque, speed, and position are calculated as follows:

TC TCT@ = (12) τTR ()g

ωCT=τR( g )ωT (13)

θCT=τR( g )θT (14)

Figure 5. Simulink Diagram of the Front Gearbox.

2.2.4 Transmission The transmission resembles that of the ICE and is shown in Figure 6. The inertia

(JT ) and damping (bT ) affect the input torque from the gearbox. The resistive torque of the front axle is subtracted from the torque input (TCT@ ). This result is integrated for speed (ωT ) and position (θT ) respectively. These quantities are fed back to the gearbox

21 and sent on to the front axle. The dynamic equation for this process is represented in (15) below.

JTTTω& = C@1T+−TX bfωT (15)

Figure 6. Simulink Diagram of the Automatic Transmission.

2.2.5 Front Axle

The front axle is assumed to be a mass-less component that only contributes a

torsional damping (bX 1 ) and stiffness (kX 1) to the system. As seen in Figure 7, the axle is a very simple model with input speeds and positions from both the transmission and the

wheels (ωF ) . The output is merely the torque experienced at the axle(TX 1). This is somewhat backwards from the previous components, but effective for modeling this particular device. The individual expression representing the axle is shown in (16) below.

TbXX11=−(ω fωt) +kX1(θf−θt) (16)

Figure 7. Simulink Diagram of the Front Axle.

2.2.6 Front Brakes The front brakes simply apply a torque to the powertrain that counter-acts the motion of the vehicle when the driver demands to do so. As previously mentioned, beta (β), the input command from the driver, ranges from 0 to 1 corresponding to the position of the brake pedal. This value is 0 at rest and 1 when the pedal is completely depressed.

The other input is rotational speed of the front wheels (ωF ) . Using these values along

with the damping coefficient of the brakes (bBF ) , results in an output torque from the

front brakes (TBF ) . This torque is sent to the wheels. Figure 8 is the Simulink model while (17) is the mathematical representation of this figure.

TbBF = BFωF β (17)

Figure 8. Simulink Diagram of the Front Brakes.

23 2.2.7 Front Wheels The model of the wheels is displayed in Figure 9. The front wheels convert the

torque from the axle and potential torque from the brakes into a tractive force (Ff ) that is sent to the vehicle. The vehicle speed (vF ) and position (xF ) are used to provide an output rotational speed and position for feed back to the brakes and axle. The effect of the

front differential ratio (diff ) is considered along with the wheel radius (RF ) . Equations 18, 19 and 20 represent this process mathematically.

⎛⎞11⎛⎞ FF=⎜⎟⎜⎟(TX1 −TBF) (18) ⎝⎠diff ⎝⎠RF

diff θF= xF (19) RF

diff ωF= vF (20) RF

Figure 9. Simulink Model of the Front Wheels and Differential.

24 2.3 Dynamic Simulink Model of the Rear Driveline The development of an acceptable model for the rear driveline of the chosen vehicle architecture is the one of the main thrusts of this thesis. Each model seen below was developed specifically for the simulators discussed in a Chapter 3. Because of this, the nomenclature seen in the figures to follow is significantly different than that of the models previously discussed. The nomenclature of the models developed for the rear driveline matches that of the early versions of cX-SIM and cX-DYN (See Chapter 3). The nomenclature also differs from that of the previously seen dynamic equations for convenience during programming. Each component is modeled as dynamic, but only the more dominant dynamic characteristics are considered. Hence, the inertia of the axle is once again ignored due to the smaller magnitude of this quantity when compared to that of the EM. 2.3.1 Electric Motor The electric motor, seen in Figure 10, is modeled identically to the ICE. There is an input torque command (TEM ) from the “driver” that is affected by a gain equal to that

of the inertia of the EM (J EM ) . This value is then integrated twice for position (θEM ) and

speed(ωEM ) . The intrinsic damping of the EM (bEM ) is included. The output of the EM

diagram is rotational speed (ωEM ) and position(θEM ) . The feed back to the EM is the torque from the rear gearbox (TRGB ) . The green box is another method of signal routing in Simulink that is utilized to simplify the appearance of the system model seen in Figure 15. The dynamic equation for this component is (21).

JTEM ω&EM = EM −−TRGB bEM ωEM (21)

Figure 10. Simulink Diagram of the Traction Motor.

2.3.2 Rear Gearbox The speed of the EM enters the gearbox and is reduced according to the gear ratio

(τ GB ) as seen in Figure 11. From the data given to Ohio State by General Motors, the reduction ratio was found to be 10.946. The third input to this block is the torque from

the rear axle (TRGB ) . After applying the ratio to these inputs, gearbox rotational speed

(ωRGB ) and position (θRGB ) , as well as torque, become outputs. This process is modeled with the following equations. Note the rear gearbox is far less complex than the front counterpart. This is because the gearbox attached to the EV1 motor has only one reduction and no “driver selectable” gears to be considered. The EM is either motoring, regenerating, or off depending on commands received by this device.

TRGB = τ GBTRAxle (22)

ωEM ωRGB = (23) τ GB

θEM θRGB = (24) τ GB

Figure 11. Simulink Block Diagram of the Rear Gearbox.

2.3.3 Rear Axle The rear axle is an exact replica of the front axle as seen in Figure 12. Assumed to be mass- less, the axle only contributes a damping (bRAxle ) and stiffness (kRAxle ) to the dynamics of the rear driveline. Inputs to the rear axle match that of the outputs of the gear box. By implementing the appropriate damping and stiffness values, the rear gearbox speed and position are converted to an output torque (TRAxle ) .This torque is sent to the rear brakes and fed back to the rear gearbox as previously stated. The values of stiffness and damping have yet to be determined. Expression (25) mathematically represents the process seen in Figure 12.

TbRAxle =−RAxle ()ωωRGB RBrake +kRAxle (θθRGB −RBrakes ) (25)

Figure 12. Simulink Diagram of the Rear Axle.

2.3.4 Rear Brakes The rear brakes behave exactly as the front brakes. They are considered to have no mass, and only impose a torque (TRBrake ) that will resist the torque driving the vehicle. There are differences in this model when compared to the front counterpart as seen in Figure 13. For modeling purposes, the actual damping coefficient of the brakes is a very difficult number to estimate. Keeping this in mind, the brake torque is determined by

multiplying the brake command from the driver by a proportional gain (λRBrakes). This result is subtracted from the incoming torque to the brakes. This effectively reduces the torque flowing between the rear axle and the wheels. The value of the gain is simply the percentage of the total braking power that is provided by the rear brakes. In this case the value equals 40%, or 0.4. The incoming brake command, determined by the control strategy, accurately provides a value that is manipulated by this gain. The simple expression representing this process is:

TRBrakes = βλRBrakesTRAxle (26)

Figure 13. Simulink Diagram of the Rear Brakes.

2.3.5 Rear Wheels The model of the rear wheels provides semblance to that of the model of the front wheels. However, no differential is included here since this does not exist on the Chevrolet Equinox. The only reduction of the rear driveline occurs at the gearbox attached to the EM. This model uses the inputs of brake torque (TRBrake ) , vehicle

speed(vVEH ) , and vehicle position(θVEH ) , and creates the three outputs using the wheel

radius (rRWheel ) as seen in Figure 14. The outputs include wheel rotational speed (ωRWheel ) and position(θRWheel ) , as well as, the tractive force (FRWheel ) to be given to the vehicle. The wheel radius is determined from the specifications of the Equinox released by General Motors for this competition. The dynamics of the wheels are relatively small compared to the other dynamic phenomena present in the rear driveline. Thus, the stiffness and damping of the wheels are not considered in the following model. The effects of the wheel are mathematically represented in the equations below.

TRBrakes FRWheel = (27) rRWheel

θRWheel = rRWheel xVEH (28)

ωRWheel = rRWheel vVEH (29)

Figure 14. Simulink Diagram of the Rear Wheels.

The individual components of the driveline have been represented both mathematically and by Simulink diagrams. Each of these can now be connected together to create a model of the entire vehicle powertrain. Completing this task results in the creation of two HEV simulators that will be extensively used to evaluate the performance of the hybrid Equinox.

Chapter 3

Simulation Results

With all of the modeling complete, two comprehensive HEV simulators are created. One is a quasi-static simulator that is effective for monitoring energy consumption. The other is a dynamic simulator for the evaluation of the drivability of the HEV. Both work together in conjunction with a graphics program that is developed here. These three items give the Ohio State Challenge X team extensive capability to study of all aspects of HEV operation.

3.1 cX-SIM The first simulator is called cX-SIM and the top layer of this Simulink model can be seen in Figure 15. This is a quasi-static HEV simulator, meaning the dominant dynamics of the system are solely the vehicle. The vehicle reacts much slower than every other component in the system thus the time constant of the vehicle is quite large. This fact allows for the time constants of all other components to be assumed zero [6]. However, there is one caveat; the inertia of the ICE is included to ensure proper operation of the dynamic model of the torque converter. With only these two dynamic characteristics included, this simulator is computationally inexpensive and the results are acquired in a rather timely fashion. This is ideal for monitoring fuel consumption and energy usage. Since the models of the previous chapter result in a convoluted system when integrated together, they are each converted into a subsystem. This collects of the

31 various parts of the aforementioned models into one block. These are the subsystems seen in cX-SIM.

Figure 15. cX-SIM Top Layer.

3.1.1 Driver As shown in Figure 15, cX-SIM is divided into three main parts. The first represents the Driver. Contained within this subsystem are all of the components that mimic the behavior of an actual vehicle operator. There is an input velocity profile that can be set to match that of the Federal Urban Driving Cycle (FUDS) or Federal Highway Driving Cycle (FHDS). This input enters a PID controller, which receives a feedback signal of the actual velocity from the vehicle. The controller minimizes the discrepancy between the desired and actual vehicle velocity. Not only is the difference in velocity rectified, but also two signals are generated and sent from the driver subsystem. The first signal, alpha (α), represents the accelerator pedal position. The second represents the brake pedal position, beta (β). These commands are then sent to the HEV Powertrain subsystem.

32 3.1.2 HEV Powertrain The diagram of the HEV Powertrain subsystem is shown in Figure 16. Here, the models seen in the previous chapter are integrated together to effectively represent the driveline of the Ohio State Challenge X Equinox. The driver commands, α and β, enter the controller bock. Within this subsystem lies the control strategy. The inputs from the driver are manipulated to create torque requests for each of the actuators, as well as, state commands, the gear command, and the brake command. The torque request enters the appropriate component and the conversion of torque and speed according to the characteristic of the device begins. Note that the axles of the driveline have been removed because these dynamics are being ignored for this particular simulator. Moreover, the inertias of the EM and the AT have also been ignored for the reasons previously described. A look-up table containing the appropriate data is included in place of the inertia. The result from this subsystem, as mentioned in Chapter 2, is a tractive force from both the front and rear driveline, which are summed together and sent on to the vehicle.

Figure 16. cX-SIM Powertrain Subsystem.

33 3.1.3 Vehicle The final subsystem in cX-SIM is the Vehicle. The contents of this subsystem are merely the Simulink block representations of equations 6-9. Forces due to air drag, vehicle rolling resistance, and road grade are subtracted from the total tractive force given to the vehicle from the powertrain. Also, the inertia of the vehicle is included to give cX- SIM the quasi-static classification previously defined. Once all of the force effects on the vehicle have been calculated, and output vehicle speed is sent from this subsystem back to driver. This entire process then repeats throughout the predetermined driving cycle.

3.2 cX-DYN A quasi-static simulator cannot effectively analyze vehicle dynamics, particularly drivability. So a second HEV simulator is created to accomplish this. The second simulator is called cX-DYN and is used primarily to analyze the drivability of the vehicle. Drivability refers to the vibrations felt by the operator. In order to maintain consumer favorability and fulfill one of the competition goals, this detail must be precisely controlled. cX-DYN allows for this type of control, as well as the ability to monitor all dynamic responses of the vehicle. The construction of cX-DYN resembles that of cX-SIM. As can be seen in Figure 17, there are three main parts: Driver, HEV Powertrain, and Vehicle. The functions of the driver and vehicle subsystems are exactly the same as those in the quasi-static counterpart. However, the HEV Powertrain includes additional components to make the simulator more dynamic. Mainly the dynamics of the axles and inertias of the EM and AT are included. Figure 18 displays the HEV Powertrain of cX-DYN with these additional components included.

Figure 17. cX-DYN Top Layer.

Figure 18. cX-DYN Powertrain Subsystem.

35 One main disadvantage to cX-DYN is that the included vehicle dynamics make this simulator computationally more expensive. Therefore, this simulator must be run in Simulink’s “Accelerator” mode in order to obtain results in a more time efficient manner. Both cX-SIM and cX-DYN have their advantages and disadvantages, but they are used together to analyze all aspects of HEV operation.

3.3 cX Graphics In order to obtain visual knowledge of the functions of the Challenge X Equinox after running one of the aforementioned simulators, a graphical user interface program is developed. The interface of this program is shown in Figure 19. Appropriately named cX Graphics, this program can monitor every quantity of the HEV and visually represent them. Moreover, the user has the option of selecting which exactly quantities to view. This is done by dividing the data into the “Set layout for plots” categories as seen in Figure 19: Driver, Vehicle, Acceleration, HEV Operation, Conventional Powertrain, and Electric Powertrain. Statistical information of some of the quantities within these categories can be viewed as well. A key feature of cX Graphics is that the user can select to view their particular quantity is English, or SI units. This is done to increase the versatility of this program; as well as, to enhance the Challenge X simulation analysis experience by giving the users of cX-SIM, or cX-DYN, a detailed visual link between the simulated operation of the HEV and the occurrences therein.

Figure 19. cX Graphics Top Layer.

3.3.1 Set Layout for Plots Driver The plot options for the Driver are seen in Figure 20. Here, the accelerator and brake pedal positions can be viewed over the entire drive cycle. Also, the commands from the PID controller within the driver block can be monitored. The pedal positions reflect how an actual driver behaves in order to match the velocity profile of the set driving cycle being simulated. The output of the PID controller will be continuously adjusted to in order to meet the desired velocity command.

Figure 20. Driver Plot Options Screen.

3.3.2 Set Layout for Plots Vehicle Plot options for the vehicle are displayed in Figure 21. The actual velocity of the vehicle can be generated, as well as the desired vehicle velocity according to the driver. Both of the curves can be graphed together to analyze the error. The user also has the option of setting a customized range for both the horizontal and vertical axis. The default values are maximums and minimums of the particular simulation. Not only can the speed be displayed, but also the desired and actual power at the wheels can be visualized. Statistical data such as the rms, maximum and minimum deviations for the velocities and powers can be also displayed.

Figure 21. Vehicle Plot Options Screen. 3.3.3 Set Layouts for Plots Acceleration Test Prior to running the simulator, the user has the option of selecting an Acceleration Test. After the simulation is complete, the user can then open the appropriate plot options screen in cX Graphics (Figure 22) and define the parameters of this test. Once the cX Graphics program is executed, the results appear in both a figure and table. The figure shows the actual velocity and the table will contain the statistical information previously aforementioned. The units for this can also be interchanged between SI and English.

Figure 22. Acceleration Test Parameter Selection Screen.

3.3.4 Set Layout for Plots HEV Operation Since the main output signal of the control strategy is the torque request for each driveline component, the most important aspect of analyzing this HEV is monitoring these requests and device output. Thus, every torque request and output torque for each actuator in the driveline can be visualized with cX Graphics. Figure 23 shows the plot options for HEV operation. Deviations of the actual torque and torque request, as well as, the shifting schedule can also be displayed if desired. Once the control strategy is implemented, the options to see the potential for energy recuperation and Sankey Diagrams will be fully developed. These options make cX Graphics a vital tool for energy management analysis. Such an analysis leads to minimal fuel consumption, fulfilling one of the primary goals of Challenge X.

Figure 23. HEV Operation Plot Options Screen.

3.3.5 Set Layout Plots for Conventional Operation The user has the option of only viewing the results from the conventional powertrain with the options seen in Figure 24. These options include only those variables that are related to the ICE. Again, the torque request and actual torque delivered by the ICE can be examined. To enhance this comparison, statistical data between these two values can also be shown. Not only can the speed and torque be viewed independently, but they can also be displayed on the efficiency and fuel consumption map for the Fiat 1.9L diesel engine. Features like this, and others shown below, give cX Graphics the capability to extensively audit the functions of the conventional powertrain. Unlike the electric actuators, the ICE is only capable of delivering positive torque, hence why only

41 the first quadrant of the torque, speed, and efficiency/fuel consumption map is shown when this option is selected (see Figure 30).

Figure 24. Conventional Powertrain Plot Options Screen.

3.3.6 Set Layout Plots for Electric Powertrain Not only can the conventional powertrain be independently viewed, but the electric powertrain can be as well. Figure 25 displays the plot options screen for this task. All aspects of the battery—voltage, current, and state-of-charge—can be analyzed. However, all of the limits for these quantities are still being investigated by other members of the Ohio State Challenge X team. These limits will be properly implemented here once conclusive values have been obtained. The next component that can be monitored is the EM. Speed and torque can be viewed independently, as well as on the efficiency map for the EV1 motor. Of course, the statistical deviations between actual and desired torque can also be shown. Displaying the power used by the EM is an option as well. It is important to note that the speed listed

42 here is that of only the EM, the angular speed seen at the half shafts is this value divided by the gearbox ratio of 10.946. As previously stated, the EM is capable motoring the vehicle and absorbing kinetic energy from the vehicle to replenish the battery. Thus, both positive and negative torque, as well as power, is seen here throughout any given driving cycle (see Figure 31). The final set of options includes presenting the quantities produced by the ISA. However, the efficiency map of the ISA does not currently exist since the Ohio State Challenge X team has not yet received the actual device. The operating data of this component is a modified version of a similar ISA that has been analyzed by others. Once the actual ISA is been received and examined, the appropriate changes will be made in cX-SIM and cX-DYN, as well as cX Graphics, to reflect this. Nonetheless, the delivered torque and torque request can be viewed along with the statistics that quantify their differences. The efficiency and power of this component are also display options. Keep in mind that this component, just like the EM, can deliver torque (positive power) and absorb torque (negative power) to recharge the battery. Therefore, both positive and negative torque and power values will appear here.

Figure 25. Electric Powertrain Plot Options Screen.

The quasi-static cX-SIM is developed for the task of monitoring energy and fuel consumption while the dynamic cX-DYN is used to the study drivability of the HEV. An in-depth visual analysis is performed by cX Graphics once the simulators produce results. Now that the vehicle can be actively simulated and analyzed, preliminary results are obtained and verified to ensure the simulators are accurate to the designed vehicle.

Chapter 4

Results & Model Verification

As discussed in the previous chapter, both a quasi-static and dynamic simulator are being developed. At the present time, only cX-SIM is functional and only a few of the modes of operation are available. Therefore, the results presented here are preliminary. Additional work on these simulators will continue until both are fully capable of providing the Ohio State Challenge X team with the appropriate analysis. Techniques to verify of these simulators are developed and also presented.

4.1 cX-SIM Only the Idle, Launch, Engine Start and Deceleration modes of operation are functional when the preliminary results from cX-SIM are obtained. cX Graphics is then used to create the figures seen below. Using a Federal Urban Driving Cycle (FUDS), a simulation was performed for approximately the first 3 minutes of the cycle. Figure 26 shows the actual and desired velocity curves. In a perfect system, the two curves would lay precisely on top one another; however, since this system design mimics the behavior of an actual driver, the discrepancy seen in Figure 26 is very realistic. Nonetheless, the deviation between the desired and actual velocity is not that outlandish. Figure 27 shows the screen shot of the statistical data created by cX Graphics. The rms deviation is only ~2.0 kph-- an acceptable value given the nature of this simulation.

Figure 26. Actual & Desired Velocity from cX-SIM Preliminary Simulation.

Figure 27. Deviation of Actual & Desired Vehicle Speed of cX-SIM Simulation.

Using the Set Layout Plots HEV Operation option of cX Graphics the sum of the total torque desired from the powertrain (ICE, ISA and EM combined) as well as the total torque delivered from the powertrain is visually represented in Figure 28. The total torque request can never be negative because the control strategy lacks the appropriate algorithms for this case. In order for negative torque to be requested from the powertrain,

46 the battery state-of-charge must be approaching the acceptable lower bound. Since no state-of-charge control is effectively implemented to date, the control strategy never requests torque to replenish the battery. However, this does not mean that the powertrain cannot deliver negative torque. As the vehicle slows down, the EM and ISA, as seen by the resulting output torque curve of Figure 28, absorb the kinetic energy of the vehicle. This results in the rather high deviations between total torque request and total torque output seen in Figure 29.

Figure 28. Total Output and Requested Torque during the cX-SIM Preliminary Simulation.

Figure 29. Deviations Between Actual & Desired Torque of HEV Powertrain.

The operating points of the ICE as selected by the current control strategy can be viewed in Figure 30. Keep in mind that these are not necessarily sequential, and the control strategy selects the operating points of the ICE based only one of the three control strategy objectives (See Chapter 5). Further more, the appearance of this figure will be different once the complete control strategy is integrated into cX-SIM. However, the Fiat ICE proves to be an efficient choice. As long as the torque of the ICE remains above ~50 Nm, the efficiency of this device never decreases below 33%-- a favorable result for the Ohio State Challenge X team. However, as the torque demand increases the efficiency reaches values in the upwards of 41%-- a good value for ICE’s.

Figure 30. ICE Operating Points during cX-SIM Preliminary Simulation.

The components of the electrical powertrain are also analyzed after the preliminary simulation. Figure 31 displays the operating points of the EM on the efficiency map on the EV1 motor. Again, these points are not necessarily sequential, and are selected by the control strategy according to Figure 43 (See Chapter 5). The operating points do appear to lie more so in the negative torque (regeneration) region than the positive torque (motoring) region. This is another result of the incomplete control strategy. The operating points seen in Figure 31 are not optimal for minimal fuel consumption and SOC control as a completed control strategy forces them to be. Nonetheless, the EM tends to operate in the 60-75% efficiency region throughout this particular driving cycle.

Figure 31. Operating Points of the EM during the cX-SIM Preliminary Simulation.

Since no efficiency map of the ISA exists to date, the power of the ISA is shown below. Note that the ISA power is zero, until the control strategy moves from Launch mode into Engine Start mode. At this point, the power will spike as seen at ~15 seconds into the drive cycle. Here, the ISA turns ON in order to start the ICE. The negative power seen in Figure 32 represents the ISA being driven by the ICE in order to generate electrical power. As previously aforementioned, this figure will also look differently once the complete control strategy is implemented.

Figure 32. ISA Power during the cX-SIM Preliminary Simulation.

The final component analyzed during this preliminary simulation is that of the battery. Figure 33 displays the SOC of the battery throughout the driving cycle. This figure does not accurately represent how the SOC behaves during a given driving cycle, as no SOC control is provided. However, this figure does display how the SOC increases during replenishment, and decreases during power demand. The current limits of 60% and 80% are initial boundaries set with the knowledge of past HEV development research at Ohio State [6]. These limits will be optimized to accommodate the batteries being used in the Ohio State Challenge X Equinox.

Figure 33. Battery SOC during cX-SIM Preliminary Simulation.

4.2 cX-DYN No preliminary results for cX-DYN have been acquired to date. Since cX-SIM is a more efficient simulator, computationally speaking, for optimizing two of the main parts of the control strategy, the primary focus has been directed toward completing the quasi-static simulator. Key deadlines for the Challenge X competition (reports and Year 1 competition) have also shifted the focus on gaining full functionally of cX-SIM prior to cX-DYN. However, once cX-SIM is fully operational, the changes to be made in order to make cX-DYN operational will be trivial.

4.3 Rolling Chassis In order to validate the modeling and simulations mentioned in Chapters 2 and 3, the Ohio State Challenge X team has created a Rolling Chassis. One of the obsolete future truck vehicles was taken and cut down to only the floor pan, firewall, frame, axles and wheels. The driver seat and steering wheel were left as well. This serves as a

52 platform on which all of the components described in Chapter 1 will be mounted for initial testing. Once all of the actuators are assembled and the control strategy hardware and software is installed, the complete verification process will begin. This will not only verify the simulators, but also the ability for each of the aforementioned components to be integrated together and behave according to the desired vehicle architecture. 4.3.1 Launch Test Currently, only the EM is ready for testing and validation. The EM is attached to the rolling chassis, and placed on a dynamometer as seen in Figure 34. Tests have been conducted to analyze the effectiveness of the EM during electric launch. The figures that follow show speed data from one such test. The pedals of the rolling chassis are used to accelerate and decelerate the EM on the dynamometer. This approach accurately resembles the accelerator pedal positions during the launch of the actual vehicle. With the inertial and frictional values of the Equinox programmed into the dynamometer, the accelerator pedal is pushed to the maximum position to generate a replication of a vehicle launch. In order to preserve the mechanical integrity of each device involved, there is a torque request limit placed on the system. One of the tests has a limit of 40% torque request. The second has a limit of 50%. This means that when the accelerator pedal is completely depressed, only 40% of the total torque capacity of the EM is available for delivery to the dynamometer. Figure 35 shows the EM motor speed during the 40% limited test. Figure 36 displays the vehicle speed generated throughout the duration of this test. The vehicle reaches a speed of ~24 kph (~15mph) in just under 10 seconds. The launch is also performed with the torque output limit of 50%. Figure 37 and 38 show the EM motor speed and vehicle speed, respectively, for this experiment. The vehicle reaches a speed of approximately 37kph (~23 mph) in approximately 15 seconds. Recall that the EM only provides motoring torque during launch for a short period of time (Launch Mode), and then the ICE is started (Engine Start Mode) and then reigns as the primary motoring device (Normal Mode). Considering the output of the EM is limited, initial observations would suggest this actuator is capable of being a part of the system to meet the goals specified in Table 1.

53 There are a few factors that exist which alter the data seen below. The most prominent involves the experimental set-up. Doing a repeated launch test is very taxing to the battery, so a power supply is used. However, the DC output of this power supply fluctuates immensely. In order to stabilize this output, the power supply is connected in parallel to a lead-acid battery pack. The pack serves as an “electrical shock absorber”, or large capacitor. This configuration stabilizes the voltage going into the EM at rest; however, when the launch is performed, the power oscillates slightly. This oscillation is reflected in the speed figures seen below. The torque request is constant, but the speed fluctuates due to a changing power input. Since the pack can respond more rapidly than the power supply, as the launch initially begins the battery pack supplies the electrical energy until the power supply “catches up.” Once the power supply is up to speed, it provides more than the requested power in order to charge the battery, as well as run the EM. The battery absorbs this “overshoot” and the power supply then decreases output to the point where the battery once again supplies power. The power supply detects this drop in the battery and once again provides an “overshoot” of energy. This process would repeat until a steady-state supply environment is reached between the two sources. However, the launch test is not performed for this length of time.

54 Lead-Acid Battery Pack

EV1 Motor & Inverter

Rolling Chassis

Chassis Dynamometer

Figure 34. Rolling Chassis Experimental Set-Up.

Figure 35. Launch Test EM Motor Speed -40% Torque Limit.

Figure 36. Launch Test Vehicle Speed- 40% Torque Limit.

Figure 37. Launch Test EM Motor Speed--50% Torque Limit.

Figure 38. Launch Test Vehicle Speed-- 50% Torque Limit.

4.3.2 Model Verification & Mapping The EM was originally the propulsion device for the EV1 electric car as previously mentioned. After deciding to use this component for Challenge X, the Ohio State team sent this drive unit to be rebuilt. When the rebuilt unit arrived testing began. However, there is no method of requesting an exact torque from the EM, but merely a rough percentage of the maximum torque capacity. Therefore, a series of tests will be conducted to create a map, so that known torque requests can be sent to the EM during operation. Once this extensive “torque mapping” exercise is completed, a modified version of cX-SIM will investigated for simulator accuracy. The mapping process will be quite extensive. Unfortunately, the chassis dynamometer is not calibrated correctly to yield an accurate power reading. Thus, the torque mapping procedure involves varying the friction coefficient of the dynamometer and running the EM at certain torque requests. Once the chassis reaches steady-state speed, the torque being provided by the EM can be found. Effectively, the result of this procedure will be the torque-speed map of the EM. The dynamometer specifies 3

57 coefficients that make up the total load that is placed on the vehicle. However, these coefficients are represented by the horsepower at 50 miles per hour and require some manipulation to be used for this mapping. The general expression of the dynamometer load is:

Friction = A ++B C (30)

where A is the rolling resistance, B is the intrinsic friction, and C is the air drag. The variable of interest is the friction coefficient, B. Each of these variables has units of HP@50 mph [10]. Knowing this fact we can relate this horsepower at a rated speed to the force of the dynamometer, Fdyno (N):

Bλ Fdyno = (31) vSS

In this expression, λ represents all of the conversion factors necessary and vSS is the found steady-state speed (mph). This force, along with the wheel radius, rwheel, is used to find the torque at the wheel, Twheel:

TFwheel = dynorwheel (32)

Using the gear ratio, τGB, the torque of the EM (TEM :) can be found.

Twheel TEM = (33) τ GB

Figure 39 represents the vehicle speed of one such test. Notice how the vehicle reaches a steady-state speed of approximately 8 kph (~5mph). To ensure this is in fact the steady- state speed the derivative of this curve, acceleration, is found. In order to do this, a second order polynomial was fit to the speed data and is shown in Figure 39. The derivative of this curve is shown in Figure 40. The derivative approaches zero toward the

58 end of the test, meaning the vehicle speed has reached a quasi-steady state value that can be used in the aforementioned calculations. The result of this particular test is an EM torque of 313.9 Nm.

Figure 39. EM Torque Mapping Test: Vehicle Speed (B=30).

Figure 40. EM Torque Mapping Test: Acceleration (B=30).

This process will be repeated over a large range of friction coefficients and torques to create a very detailed map. These output torques will be entered, with their corresponding percentage torque request, into a look-up table. This will allow for an input torque value in standard units (e.g. Nm) to be sent to the EM for operation. Once this table is implemented, the verification of the model will be done with the modified form of cX- SIM. 4.3.3 cX Test This version of cX-SIM is called cX-Test and can be seen in Figure 41. Basically, this model is the rear driveline and vehicle cut from the parent simulator. The vehicle is included because the dynamometer simulates vehicle drag, rolling resistance, and grade resistance. Here, a torque request is sent to the EM, and the model reacts accordingly. This simulation is analyzed with the condensed version of cX Graphics seen in Figure 42—cX-Test Graphics. The same torque request is given to the actual EM on the rolling chassis, and the resulting data is compared to the cX-Test data to ensure the model is valid.

Figure 41. cX Test Top Layer.

Figure 42. cX -Test Graphics.

Preliminary results from cX-SIM have been obtained and visually represented using cX Graphics. Once cX-SIM is fully functional, cX-DYN will be brought on-line as well. Verifying both simulators is done via the rolling chassis; however, this task could not be completed before the conclusion of this thesis. Not only will finishing the simulators and verification be a task of the future, developing and integrating a robust control strategy also needs to be completed.

Chapter 5

Control Strategy Development

Future work includes performing the mapping and verification described in the previous chapter, as well as developing a fully functional control strategy. With cX-SIM nearing completion, and cX-DYN soon to follow, a suitable control strategy must be implemented so the verification process can continue. The basics of the currently considered control strategy are presented here. The ultimate design and fabrication of the controllers necessary is left for future work on this project.

5.1 Overview The primary focus of this research is modeling and simulation of the rear driveline of the Ohio State Challenge X Equinox. Development of the control strategy is a task being pursued by other members of the OSU Challenge X team. However, the literature has been investigated in regards to control of HEVs and the author has participated in the development of the control strategy for the Hybrid Equinox. Therefore, a brief summary of the control strategy is presented here. The main objective of the control strategy is to reduce fuel consumption and emissions while maximizing drivability by taking advantage of the multiple vehicle modes. This is achieved by the potential energy recovery during braking, as well as the availability of the additional degrees of freedom with respect to the power split to satisfy

62 driver demand [7]. The control strategy being developed for the Ohio State Challenge X Equinox is divided into two parts: primary control and secondary control. The primary control strategy commands the drivetrain components in real time as dependent on driver requests, the state of each component, and of course the control strategy algorithm. The secondary control monitors the state of each component, such as temperature, to ensure safe operation [5]. The focus here is on the primary control strategy. This control signal is decomposed into three “decoupled” signals: ECMS, Battery State-of-charge, and Drivability [2, 5]. Each are considered independently and then summed together to create the final control signal. The process for obtaining the ultimate control signal is described by Figure 43 below.

Figure 43. Control Strategy Schematic.

5.2 ECMS The first factor considered by the control strategy is fuel consumption. Compliant with the goals of Challenge X, the objective is to minimize this quantity. To accomplish this, Ohio State chooses to use the Equivalent Consumption Minimization Strategy (ECMS). The basis of ECMS is that all energy consumed by the vehicle comes from the fuel tank [2]. In the case of HEVs, two fuel tanks are considered. The first is the conventional fuel storage tank and the second is the battery, or some other energy storage device. For ECMS purposes, the battery is modeled as a reversible fuel tank that can exist in two states. First, the battery could be recharging, so fuel must be consumed, or kinetic energy absorbed, to replenish this electrical energy. The second state is the battery could

63 be using electrical energy to alleviate some of the load from the ICE to save fuel [4]. The governing equation for ECMS is as follows:

xuij mx& *,()iju = (34) η*,()xuijQLHV

where mx& *,()iju is the mass flow of “fuel” for component *, η*,(xiju ) is the efficiency of component *, and QLHV is known as the low-heating value of fuel. The quantity xi is a state vector that includes the speeds of the ICE, AT, EM, and vehicle, as well as, the positions of the AT, EM and vehicle. The control vector ui contains the torque of each of the three actuators [2]. At any time during vehicle operation, the entire range of operating points for ICE, ISA, and EM will be examined and equivalent flows will be found [4]. The point which minimizes the total equivalent fuel consumption—the sum of each

mx& *,()iju -- will be chosen as the ECMS control input.

5.3 Battery State-of-Charge One of the most important aspects to consider for effective HEV operation is battery state-of-charge. The capacity of the battery as stated by the manufacturer cannot reflect the change in this quantity due to usage. By maintaining the SOC, the degradation of the battery capacity as a result of use can be significantly slowed. The SOC is defined as the ratio of the used amp-hour capacity of the battery and the total amp-hour capacity of the battery.

USEDCAP(t +δt) SOC ()t +=δt 1− (35)) CAP()t +δt

Here, USEDCAP represents the energy used (Ah) and CAP is the total capacity of the battery (Ah) [1]. Keeping this value within a certain range not only preserves battery life, but also allow for additional “room” to absorb excess power and deliver additional power when necessary. The acceptable range varies according to the type of battery being used.

64 Ohio State is currently investigating this range for the Nickel Metal-hydride batteries to be used for Challenge X. In Figure 26, ECMS and SOC control are grouped together. This is due to the fact that ECMS and SOC control cannot be completely decoupled from one another. The battery state-of-charge has a large impact on ECMS because if the SOC falls too low, diesel fuel would need to be consumed in order to replenish the battery. Built into ECMS is a penalty function that shifts the optimal power split up or down according to the actual SOC and the SOC range. This penalty function shifts the power split according to three possible SOC cases. The first requires that the SOC is within the range and the selected power split operating point is valid. The second case involves the SOC being too high, thus the power split is shifted to promote discharging of the battery. Finally, the SOC could be too low and the operating point is shifted to emphasize battery recharging. Others have stated that in a charge sustaining control strategy the net consumption of electrical power is zero [4]. This is not true due to the set range of battery SOC. For example, a given drive cycle begins with a SOC of 75% and the acceptable range is between 60% and 80% SOC. The drive cycle could easily end with the battery SOC being 63%, meaning more electrical power was consumed, rather than replenished, over the cycle. Hence, the net consumption of electrical power over this drive cycle is not zero. Since the control strategy keeps the SOC within a range, the net consumption of the electrical power over a given driving cycle does not necessarily have to be zero and most likely will not be.

5.4 Drivability Drivability refers to the smooth operation of the vehicle. In this case, the control strategy maximizes drivability by ensuring the shift from one operating mode to another does not result in any undesirable vibrations or jerks. Such anomalies are also minimized as the vehicle shifts gears. Drivability is to be evaluated by cX-DYN; however, no drivability control has been implemented at this point. Fuel consumption minimization and emissions reduction are two of the primary goals of Challenge X. Drivability is also a primary goal being considered. All three of

65 these aspects of the HEV Equinox will be controlled to meet the standards of the competition, as well as consumer standards. Many unforeseen technical difficulties hindered the progress of this research. However, once all of these issues have been resolved and the experiments detailed herein are conducted, the model of the Ohio State Challenge X HEV will prove to be valid and accurate. Moreover, both simulators will also be validated using the rolling chassis once the control strategy is in place.

66 References

[1] X. He and J. W. Hodgson, “Modeling and Simulation for Hybrid Electric Vehicles—Part I: Modeling,” in IEEE Transactions on Intelligent Transportation Systems, vol. 3, no. 4, pp. 235-243, 2002.

[2] O. Barbarisi, E.R. Westervelt, G. Rizzoni, and F. Vasca, “ Power Management Decoupling Control for a Hybrid Electric Vehilce,” 2005.

[3] X. He and J. W. Hodgson, “Modeling and Simulation for Hybrid Electric Vehicles—Part II: Simulation,” in IEEE Transactions on Intelligent Transportation Systems, vol. 3, no. 4, pp. 244-251, 2002.

[4] G. Paganelli, G. Ercole, A. Brahma, Y. Guezennec, and G. Rizzoni, “A General Formulation for the Instantaneous Control of the Power Split in Charge Sustaining Hybrid Electric Vehicles,” 2001.

[5] F. Ohlemacher, G. Rizzoni, and A. Soliman, “Challenge X 2005 Report #3: Control System Hardware and Software Development”, submitted to the Challenge X organizers March 2005.

[6] C. Musardo and Benedetto Staccia, “Energy Management Strategies for Hybrid Electric Vehicles,” Doctor of Philosophy Dissertation, 2003.

[7] F. Ohlemacher, G. Rizzoni, and A. Soliman, “Challenge X 2005 Report #2: Vehicle Architecture Selection for the Challenge X Competition”, submitted to the Challenge X organizers November 2004.

[8] F. Ohlemacher, G. Rizzoni, and A. Soliman, “Challenge X 2005 Report #4: Control System Development”, submitted to the Challenge X organizers November 2004.

[9] “Challenge X website,” 2005 www.challengex.org.

[10] Horiba Dynamometer Operation Manual, June 1992.

67 Appendix

Table 3. Nomenclature.

Abbreviation Description HEV Hybrid Electric Vehicle ICE Internal Combustion Engine EM Electric Machine MG Motor/Generator ISA Integrated Starter/Alternator AT Automatic Transmission MOT Motoring, or providing propulsion power 4WD Four Wheel Drive JICE Inertia of the ICE JISA Inertia of the ISA JTR Inertia of the AT JEM Inertia of the EM TICE Torque of the ICE TISA Torque of the ISA TTC_P Torque on Pump Side of Torque Converter TTC_T Torque on Turbine Side of Torque Converter TTC Torque of Torque Converter (locked case only) TF, TX1 Torque of Front Axle TB_F Torque of Front Brakes TEM Torque of the EM TR, TRAxle Torque of Rear Axles TB_R, TRbrakes Torque of Rear Brakes TC Torque of the Clutch TC@T Torque at Manual Transmission TRGB Torque of Rear Gearbox Twheel Torque of Wheel on Dynamometer Jf JICE + JISA

ω& ICE Angular Acceleration of the ICE

ω&TR Angular Acceleration of the AT

ω& EM Angular Acceleration of the EM ωICE Rotational Speed of the ICE ωTR, ωt Rotational Speed of the AT ωF Rotational Speed of Front Axle ωEM Rotational Speed of the EM ωR Rotational Speed of the Rear Axle ωC Rotational Speed of the Clutch

68 ωRGB Rotational Speed of Rear Gearbox ωRbrakes Rotational Speed of Rear Brakes ωRwheel Rotational Speed of Rear Wheel ωwheel Rotational Speed of Wheel on Dynamometer bICE Damping of the ICE bF, bX1 Damping of Front Axle bEM Damping of the EM bR, bRaxle Damping of Rear Axle bC Damping of Clutch kF, kX1 Spring Constant of Front Axle kR, kRaxle Spring Constant of Rear Axle kC Spring Constant of Clutch τTR(g) AT Gear Ratio τGB Gear Ratio of Rear Gearbox rF, Rf Radius of Front Wheels rR, rRwheel Radius of Rear Wheels mVEH Mass of the Vehicle vVEH,, vf Velocity of the Vehicle FRD Frictional Force of the Road FRR Force due to Rolling Resistance FDRAG Force due to Air Drag F Tractive Force from Powertrain Ff Tractive Force of Front Wheel FRwheel Tractive Force of Rear Wheel Fdyno Force of Dynamometer θTR, θt Angular Position of AT θEM Angular Position of the EM θICE Angular Position of the ICE θF Angular Position of Front Axle θC Angular Position of the Clutch θRGB Angular Position of Rear Gearbox θRbrakes Angular Position of Rear Brakes θRwheel Angular Position of Rear Wheel xVEH, xf Distance Traveled by Vehicle

&&xVEH Acceleration of the Vehicle g Acceleration due to Gravity Cr Frictional Coefficient of Rolling Resistance φ Road Grade Angle ρAIR Density of Air Cd Drag Coefficient of the Vehicle Af Frontal Area of the Vehicle α Accelerator Position/Command β Brake Pedal Position/Command γ Clutch Command

69 λRbrakesB B Rear Brake Proportional Constant diff Front Differential Ratio cX-SIM Quasi-Static HEV Simulator cX-DYN Dynamic HEV Simulator cX Graphics Graphical User Interface for simulators cX-Test Quasi-Static Model of Rear Driveline PID Proportional, Integral, Derivative ECMS Equivalent Consumption Minimization Strategy SOC State-Of-Charge FUDS Federal Urban Driving Cycle FHDs Federal Highway Driving Cycle Friction Load of the Chassis Dynamometer A Rolling Resistance of dynamometer B Friction Coefficient of Dynamometer C Air Drag Coefficient of Dynamometer λ Conversion Factor from HP to lb using Speed

vSSB B Steady-state Speed Governing equation of ECMS representing mxu& * ()ij, equivalent mass fuel flow from component *

xi State vector including { ωICEB B ωTRB BωEMB vB VEHB θB TRB

θB EMB xB BVEH }B

u j Control Vector including { TICEB BTISAB B TEMB }B B B Efficiency of component * η* ()xij,u

QLHV Low-heating value of fuel CAP Specified total capacity of the battery (Ah) USEDCAP Used energy of the battery (Ah) t Time (s) δt Interval of time (s)