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Int. J. Powertrains, Vol. 2, No. 1, 2013 1
Copyright © 2013 Inderscience Enterprises Ltd.
Powertrain control parameter optimisation using HIL simulations of a heavy-duty vehicle
Yuming Wang Department of Mechanical and Vehicular Engineering, Beijing Institute of Technology, 5 South Zhongguancun Street, Haidian District, Beijing 100081, China E-mail: [email protected]
Guoming Zhu* Department of Mechanical Engineering, Michigan State University, MI 48824, USA E-mail: [email protected] *Corresponding author
Fujun Zhang Department of Mechanical and Vehicular Engineering, Beijing Institute of Technology, 5 South Zhongguancun Street, Haidian District, Beijing 100081, China E-mail: [email protected]
Abstract: This paper studies the potential fuel economy improvement that can be achieved by optimising powertrain control parameters without modifying its hardware. A real-time powertrain model was developed and implemented in Simulink. It consists of a simple diesel engine model, an automatic transmission (AT) model with a torque converter, a vehicle dynamic model, and an integrated controller for both the engine and transmission. In particular, a dynamic gearshift clutch model was developed for the AT gearbox. A hardware-in-the-loop (HIL) simulation environment was also established to simulate the developed real-time powertrain model, along with a simplified vehicle model under the federal test procedure (FTP), US06, and urban driving cycles. To evaluate the proposed control parameter optimisation process for a heavy-duty vehicle, the fuel consumptions of the FTP, US06, and urban driving cycles were used as the evaluation criterion, based upon different gear shifting control parameters and throttle slope angle. The HIL simulation results show that about 2% fuel economy can be gained by optimising the throttle slope angle; and simulation results also demonstrated that the optimised gearshift schedule provides the fuel economy improvement between 2.11% and 7.6% over the traditional gearshift schedule, where the most significant improvement was obtained for the urban driving cycle.
Keywords: heavy-duty vehicle; automatic transmission; AT; parameter optimisation; hardware-in-the-loop simulation.
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Reference to this paper should be made as follows: Wang, Y., Zhu, G. and Zhang, F. (2013) ‘Powertrain control parameter optimisation using HIL simulations of a heavy-duty vehicle’, Int. J. Powertrains, Vol. 2, No. 1, pp.1–25.
Biographical notes: Yuming Wang is an Engineer with the Department of System and Function Development at United Automotive Electronic Systems Corporation (UAES), a joint venture of Robert Bosch GmbH and Zhong-Lian Automotive Electronics Corporation, Shanghai, China. He received his PhD, MS and BS degrees from Beijing Institute of Technology, Beijing, China, in 2011, 2006 and 2003, respectively. His current research interests focus on the control of automatic transmission (AT), dual clutch transmission (DCT) and continuously variable transmission (CVT).
Guoming (George) Zhu is an Associate Professor at the Department of Mechanical Engineering (ME) and the Department of Electrical and Computer Engineering (ECE) at Michigan State University, East Lansing. He received his PhD in Aerospace Engineering from Purdue University, West Lafayette, IN, in 1992. His current research interests include closed-loop combustion control, engine system modelling and identification, hybrid powertrain control and optimisation, linear parameter varying control. He has authored or co-authored over 100 refereed technical papers and received 40 US patents. He was an Associate Editor for ASME Journal of Dynamic Systems, Measurement and Control. He is also an ASME Fellow.
Fujun Zhang is a Professor at the Department of Mechanical Engineering (ME), Beijing Institute of Technology, Beijing, China. His current research interests include powertrain modelling and control, new concept power set and system, etc. He has authored or co-authored over 70 refereed technical papers, received six Chinese patents and five Government Ministry Prize of Advancement of Science and Technology. He was a reviewer of the National High Technology Research Programme of China (863 programme) and the National Basic Research Programme of China (973 programme), and members of the Chinese Society for Internal Combustion Engine and Society of Automobile Engineers of China.
1 Introduction
With the limited fossil fuel resources and the concern about the global warming, automotive manufactures nowadays emphasise more and more on improving the vehicle fuel economy with reduced emissions. There are a few ways to improve fuel economy, such as optimising the vehicle aerodynamics, improving the engine combustion efficiency, increasing the transmission efficiency, etc. However, for the heavy duty vehicle applications, the powertrain system efficiency is also one of the key factors of improving fuel economy.
In the past decade, many vehicle powertrain system technologies have been developed to improve vehicle fuel economy with reduced emissions. For instance, homogeneously charged compression ignition (HCCI) (Chiang and Stefanopoulou, 2007; Yang and Zhu, 2012) has been developed for improved engine combustion efficiency and so does the hybrid powertrain system (Gao et al., 2009). For powertrain transmissions, there are many existing technologies such as manual transmission (MT),
Powertrain control parameter optimisation using HIL simulations 3
automated manual transmission (AMT), automatic transmission (AT), continuously variable transmission (CVT) and dual clutch transmission (DCT) (Sun and Hebbale, 2005).
A smooth and efficient torque conversion of a powertrain transmission is critical for the vehicle fuel economy. This requires accurate control (or coordination) between the engine and transmission. Some studies focused on solving the problem by optimising the engine operation. For instance, Pettersson and Nielsen (2000) introduced an active engine control method, or virtual clutch control, of the AMT automatic clutch using closed loop engine speed control; and Amisano et al. (2001) presented a method of calculating engine speed reference during the torque holding phase of the gear shifting and a control strategy for the engine to track the reference speed trajectory.
On the other side, the transmission clutch/actuating-piston control is essential for most of the transmissions, especially for the AMTs. Most research focused on improving smooth gear shifting and efficient torque transmission using the advanced control technologies (Glielmo et al., 2004; Glielmo and Vasca, 2000; Garofalo et al., 2001). In Glielmo et al. (2004), to eliminate the performance deviations due to the clutch wear, the AMT clutch operation was divided into the following five statuses: engaged, slipping-opening, synchronisation, go-to-slipping, and slipping-closing; and three cascaded feedback control loops were used respectively to control speed, torque and throw-out bearing position. The transmission control is formulated in Glielmo and Vasca (2000) as a finite horizon time optimal control problem, in which the optimal solution consists of a time-varying state feedback control gain that depends on the duration of clutch engagement and a feedforward control that is used to compensate the unknown initial condition and engine torque input. In Garofalo et al. (2001), the driveline dynamics were proposed as a set of the piecewise linear time-invariant models due to the presence of the clutch. In this case, the slip control strategy is based on the speed difference between the driven disk and engine crankshaft.
As discussed above, the improvement of the powertrain control focuses on optimising either engine control or transmission clutch control during gear shifting to reduce torque output perturbation of the powertrain, and hence, to improve driving comfort and vehicle handling with very little improvement of the fuel economy. In Glielmo et al. (2006), a control method of tracking reference clutch torque is employed to achieve the desired performance. In Hayashi et al. (1993), a neuro-fuzzy approach was used, and in Fredriksson and Eardt (2000), a model-based back stepping non-linear control methodology was used to control the gearshift in an AMT system. A Simulink AMT model was developed in Song et al. (2009) and implemented into a hardware-in-the-loop (HIL) simulation environment. The possibility of using dynamic programming method to obtain the optimal clutch/engine speed and the clutch trajectory during clutch engagement was discussed.
However, in most of existing studies, the powertrain engine is simplified as a steady state output torque map based upon the engine throttle and speed and the engine dynamic characteristics, especially engine fuel economy as a function of load and speed, is not used for optimising the drive-train efficiency. To develop an optimal control strategy for a powertrain with the best fuel economy possible, the engine and the transmission must be considered as an integrated system. An example of using integrated approach for powertrain optimisation can be found in Assanis et al. (1999), in which a simulation method was presented for a heavy-duty truck consisting of a diesel engine, its driveline
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and vehicle dynamic models. But the transmission model is relatively simple with basic gearshift logic as a function of engine speed.
A well designed HIL simulation environment can be used to validate the control strategies with the reduced development time and cost. Kim et al. (2007) described a method of developing throttle-gearshift maps that satisfy driver’s power demand with optimised fuel economy based on the environment protection agency (EPA) driving cycle. Note that the fuel consumption modelling is critical for evaluating the fuel economy. Giannelli et al. (2005) provided an example of a fuel consumption model of a heavy-duty diesel vehicle based on vehicle driving conditions and the powertrain system parameters. This paper intends to study the fuel economy improvement by optimising the control parameters of a heavy-duty powertrain such as gearshift speeds and throttle slope angle.
The paper is organised as follows: Section 2 presents the powertrain system model of a heavy-duty truck, Section 3 discusses an HIL simulation environment with the developed powertrain model, simulation results are presented in Section 4, and conclusions are drawn in the last section.
2 Powertrain model
2.1 Powertrain system architecture
In this section, we study a powertrain system of a 16-ton heavy-duty vehicle equipped with a diesel engine and a four-speed AT; see Figure 1 for the transmission system diagram.
Figure 1 Powertrain system diagram (see online version for colours)
Powertrain control parameter optimisation using HIL simulations 5
The Deutz 11.9 Liter V6 turbocharged diesel engine is equipped with an in-line fuel pump and the fuel injection process is controlled by an electronic engine governor, where fuel injection timing mass can be precisely controlled. The diesel engine is rated for 290 kW at 2,100 rpm.
The AT was developed by Beijing Institute of Technology and it bridges the Deutz engine and the driving wheel. This transmission consists of a torque converter, gearbox, planetary drive, and side drive. The gearbox has three axes and five clutches. The clutches on axis 1 are CL, CH and CR, see Figure 1; the clutches on axis 3 are C1 and C2, and there is no clutch on axis 2. The steady state clutch states, corresponding to the given transmission gear position, are shown in Table 1, where the dots indicate that the corresponding clutches are engaged. Table 1 Clutch control logic
Clutches engaged Gear
CL CH CR C1 C2 1st ● ● 2nd ● ● 3rd ● ● 4th ● ● R ● ●
Note: The locations of five clutches (CL, CH, CR, C1 and C2) are shown in Figure 1.
2.2 Powertrain system model
2.2.1 Engine model
The engine model used for this study consists of a simplified rigid crankshaft dynamic model with an engine fuel efficiency map. The engine speed (or crankshaft speed), ne, is calculated by:
0
( ) ( )( )t b l
ee
T τ T τn t dτJ−
= ∫ (1)
where Tb is the engine brake torque as a function of the injected fuel mass and the current engine speed; Tl is the engine load torque, which is equal to the input torque of the torque converter; and Je is the crankshaft moment of inertia.
For a heavy-duty diesel engine, the variances of parameters at each steady working condition are very small. As a result, this paper simplifies the transient operation of the diesel engine to a composition of each steady working point. This means that the engine fuel consumption model is calculated based on a steady lookup table, which is a function of the engine brake torque (engine indicated torque Ti minus friction torque Tf) and engine speed. This map (a 2D lookup table) can be obtained through the engine mapping process in an engine dynamometer. Figure 2 shows the engine map used in this study.
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Figure 2 Engine brake specific fuel consumption (see online version for colours)
10001500
20002500
0
500
1000
1500
200
300
400
500
600
Engine Speed /rpmEngine Torque /Nm
Eng
ine
Bra
ke S
peci
fic F
uel C
onsu
mpt
ion
/g⋅(k
Wh)
-1
2.2.2 Torque converter model
Since the transmission used in this study consists of four forward gears, it is almost impossible to develop a gearshift strategy without interrupting continuous torque output. Therefore, a torque converter is used and located between the internal combustion engine and the transmission. The torque converter can be modelled using the following steady state relationships by omitting the transient dynamics:
t
p
nin
= (2)
1( )λ f i= (3)
2 ( )K f i= (4)
2 5( )p pT n λ ρ g D= × × × × (5)
t pT K T= × (6)
where nt is the turbine speed; np is the pump speed; i is the speed ratio of the torque converter; λ is the performance factor of the torque converter; K is the torque ratio of the torque converter (shown in Figure 3); ρ is the mass density of the working fluid; D is the diameter of the torque converter; Tp is the pump torque which equals to the engine load torque Tl; and Tt is the turbine torque which is the input torque of the gearbox.
Powertrain control parameter optimisation using HIL simulations 7
Figure 3 Torque converter performance characteristics
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
2
4
6
8
10
Speed Ratio
Per
form
ance
Fac
tor λ⋅1
0-6 &
Tor
que
ratio
k
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.2
0.4
0.6
0.8
1
Effi
cacy
η
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.2
0.4
0.6
0.8
1k
λ⋅10-6
η
2.2.3 Gearbox model
The gearshift is realised through operating five gearshift clutches. The structure of the gearshift clutch is shown in Figure 4 (Zhang, 2007).
Figure 4 Transmission gearshift clutch structure
When the clutch is engaged, the high pressure transmission oil flows into the corresponding oil flow path and into the clutch cylinder. As the transmission oil pressure
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builds up in the clutch cylinder, the oil pressure overcomes the spring force, which causes the piston to move and makes the steel disc tightly contact with the friction disc, leading torque transmission from the drive shaft to the drive gear.
Two coefficients, coP and coS, ranging between zero and one are used in our clutch model to reflect the percentage of the torque transmitted by the clutch based on speed ratio. The relationship between input torque TS and output torque TG of each clutch can be described as:
G S P ST T co co= × × (7)
where the first coefficient, coP, describes the torque transmission efficiency between the friction disc torque and the torque induced by the oil pressure established within the clutch cylinder; and the second coefficient, coS, represents the torque transmission efficiency of the clutch friction pair and the friction pair rotating speed differential.
Figure 5 Simplified clutch system diagram
Figure 5 shows a simplified structural diagram of a single clutch system used in this paper. The clutch system is divided into two parts: torque input and output subsystems. The torque input subsystem (left side) consists of an oil cylinder, a drive shaft, a piston, and a steel disc. The drive shaft, the piston, and the steel disc are rotating as one part. The torque output subsystem (right side) has a friction disc mounted with a drive gear. Based upon the clutch system diagram, coefficient coP represents the torque transmitting efficiency of the input portion subsystem (left side) of the clutch and coefficient coS represents the torque transmitting efficiency of the output subsystem (right side) of the clutch.
Coefficient coP is a function of the controlled oil pressure; and PCtrl = f(t), shown in Figure 6, is a function of time. The piston motion is controlled by the oil pressure in the forward direction and by spring force in the opposite (backward) direction.
Powertrain control parameter optimisation using HIL simulations 9
Figure 6 Controlled oil pressure PCtrl as a function of time (see online version for colours)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
2
4
6
8
10
12
14
Time [s]
Pct
rl [bar
]
The forward force, FO, applied on piston due to the oil pressure within the clutch cylinder can be calculated as:
O Ctrl PF P A= × (8)
where AP is the area of the friction disc. The return force, FS, due to the return spring can be calculated as:
( )0S S PF k x x= × − (9)
where kS is the spring coefficient; xP is the position of the piston, and x0 is its initial displacement. When the driving force FO overcomes the return spring force, FS, the piston begins to move towards friction disc. The piston movement is governed by the following dynamic equation:
0 1,O S P P O P PF F m x B x x x x− = + ≤ < (10)
where mP is the total mass of the drive shaft, the piston, and the steel disc; BO is the damping coefficient of the oil in clutch cylinder; and x1 is the maximum position of the piston. As soon as the piston displacement reaches x1, the steel and friction discs begin to engage, and as a result, the torque from the drive shaft starts transmitting to the drive gear via the friction pair. It is worth to mention that equation (10) is used for all gear shifts.
It is also assumed in this paper that the engaging-clutch is activated only after the releasing-clutch is fully disengaged, and therefore, clutch-to-clutch shifting is not considered. Since a torque converter is used in the front of the gear box, most of the
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powertrain vibration is absorbed by the torque converter. Due to the fact that the time spent on gear shifting (in seconds) occupies only a small portion of the overall driving cycle [e.g., thousand seconds for the federal test procedure (FTP) cycle], as a result, the vibration effect to the overall fuel economy is very small and it is ignored in this study for simplicity. The engagement force of the friction pair, FF, can be calculated as:
( )0 1
1 0 1
0,,
PF
O S P
x x xF
F k x x x x≤ <⎧
= ⎨ − − =⎩ (11)
Torque TF, generated by the fiction disk pair, is a function of the friction coefficient and the friction pair engagement force FF; and it is shown below:
F d F F FT μ F n R= × × × (12)
where μd is the friction coefficient of the friction pair; nF is the number of friction pairs; and RF is the radius of the friction disc. From the above equations, when there is no oil pressure applied to the piston, the piston rests at its minimum displacement position due to the spring return force. In that case, coefficient coP will be scaled down to zero, which means that no torque is transmitted through the input side of the clutch. On the other hand, as long as the controlled oil pressure follows the same trajectory, the torque output, applied to the piston steel disc set, will only be a function of the controlled oil pressure, which means that coefficient coP can be scaled up to one that corresponds to the maximum torque transmitted via the input side of the clutch. Therefore, the characteristics of coefficient coP can be simplified as shown in Figure 7.
Figure 7 Coefficient coP and controlled oil pressure PCtrl (see online version for colours)
0 2 4 6 8 10 12 140
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Pctrl [bar]
coP
Powertrain control parameter optimisation using HIL simulations 11
For the second coefficient, coS, in order to eliminate the inference of the controlled oil pressure, coP is assumed equal to one. Assume that the steel and friction discs are a damper-mass system with two block masses; see the output subsystem (left side) of the clutch system in Figure 4. Once the friction pair is tightly engaged, the torque transmitted through the clutch depends on two factors: the friction torque between friction pair (either static or dynamic friction torque) and the damping torque due to speed difference of the friction pair. In this case, coS can be calculated as:
( )43
1,
0.95 ,S G
S GS c n n
S G
n n δco
c e n n δ× −
⎧ − ≤⎪= ⎨+ × − >⎪⎩
(13)
where coS, equal to one, is for the case that static friction coefficient is used when there is no relative movement between the friction pair; coS, equal to 0.95, is for the dynamic friction coefficient case; c3 and c4 are both used to describe the simplified damping function of the friction pair; nS is the rotational speed of drive shaft (that equals the rotational speed of clutch piston and steel disc) and nG is the rotational speed of drive gear (same as the friction disc).
The torque transmission in the gearbox passes through all three axis and clutch combinations that depend on the gear selection. Taking the first gear as an example, the engine torque is transmitted from crankshaft to the pump for the torque convertor, through the torque convertor to the turbine side. Then, the turbine torque Tt is transmitted through the first axial, CL clutch, the second axial, C1 clutch, the third axial, and finally it is transmitted to the planetary drive and the gearbox output shaft. Therefore, the gearbox model describes the dynamics between the turbine torque and the output torque. The rotation speed of the first axis can be calculated as:
231
1 12
10 1
( )
v
t ttL
T icoT i i
con t dtJ
×× − ×
= ∫ (14)
where n1 is the rotational speed of axis 1; it1 is the speed ratio between turbine and axis 1; Tv is the load from vehicle dynamic side; i12 is the speed ratio between axis 1 and axis 2; i23 is the speed ratio between axis 2 and axis 3; coL is the torque transmission coefficient of CL clutch; co1 is the torque transmitting coefficient of C1 clutch; and J1 is the moment inertia from the turbine to axis 1. The turbine speed nt can be calculated as:
1 1t tn n i= × (15)
The rotational speed of axis 2, n2, can be calculated as:
1 12 231
20 2
( )
vt t Lt
TT i co i icon t dt
J
× × × − ×= ∫ (16)
where the notations used in equation (16) are similar to those in equation (15). The rotation speed of axis 3, n3, can be calculated as:
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( )31,000 1
60 2 p sn v i iπr
⎛ ⎞= × × × ×⎜ ⎟⎝ ⎠
(17)
where v is the velocity of the vehicle; r is the radius of the drive wheel; ip is the speed ratio of the planetary gear; and is is the side ratio. The output torque of the gearbox To can be calculated as:
113
1
t t
Lo
T i icoT
co
××
= (18)
Note that To is the input torque of vehicle dynamic model.
2.3 Simple vehicle dynamic model
Besides the driving torque from the output shaft of the gearbox, the vehicle speed is also affected by wind resistance, friction resistance, and road gradient resistance that can be calculated using the following equations:
sing v SF m g= × × α (19)
f vF m g μ= × × (20)
2aF c v A= × × (21)
where Fg is the gradient resistance; Ff is the tyre rolling resistance; Fa is the vehicle aerodynamic resistance; mv is the vehicle weight; μ is the rolling resistance friction coefficient; and αS is the slope of the road. The vehicle velocity, v, can be calculated by:
o sv g r a b
T iF F F F Fr×
= − − − − (22)
0
t v
v
Fv dtm
= ∫ (23)
where Fv is the net driving force of the vehicle; and Fb is the brake force that comes from the driver model.
3 HIL simulation environment
The HIL simulation environment consists of an Opal-RT system (a PC-based real-time simulation system) and a Mototron real-time production powertrain control module. The powertrain and vehicle models described in the previous section were implemented into the Opal-RT real-time simulation system and the proposed powertrain control algorithm was implemented in the Mototron powertrain control module. The HIL simulation was realised through the control area network (CAN) communication between the Opal-RT real-time simulator and the Mototron controller.
Powertrain control parameter optimisation using HIL simulations 13
3.1 Driver behaviour model
In order to simulate the vehicle operation behaviour under a given driving cycle, such as FTP, US06 or urban, a driver behaviour model is required. A simple driver behaviour model was integrated into the console block of the Opal-RT HIL system. The purpose of this driver model is to generate the drive inputs to the vehicle and powertrain model, implemented in the Opal-RT real-time simulation system, to achieve the desired vehicle speed required to track the given driving cycle such as the FTP driving cycle. The inputs to the driver behaviour model are the target vehicle speed and the actual vehicle speed; and the outputs are the acceleration pedal position and desired brake torque that is proportional to braking pedal position. Two independent proportional and integral (PI) controllers were used in the driver behaviour model to control both acceleration pedal position and braking force (brake pedal). The PI controller can be described by the following transfer function:
( )( )
p iK s KU sE s s
+= (24)
where U(s) is the control output; E(s) is the error between the target and feedback variables; and Kp and Ki are two constant PI gains. Figure 8 shows the PI controller used for throttle control, where a saturation block was used to saturate the throttle output signal between zero and one. The braking PI control has the same architecture as the throttle one. The driver model is also responsible for the gearbox mode selection between manual and automatic operations. When the gearbox is set to the manual mode, driver behaviour controller takes over the transmission gear selection from the powertrain controller.
Figure 8 Control diagram of the driver behaviour model (see online version for colours)
Target vehicle speed
Simulated vehicle speed
Throttle
- PK
IK 1s
3.2 Powertrain controller
The powertrain control strategy is implemented in the Mototron ECM (electronic control module) and it generates the desired torque output of the engine and gear selection of the gearbox model. The desired engine torque at a given engine speed is selected to be a straight line over the engine speed and torque map for a given acceleration pedal position (or throttle percentage). Figure 9 shows the throttle table, where the engine controller interprets the desired engine torque based upon current engine speed and throttle position. Define the throttle slope angle, α, between the throttle and horizontal lines as indicated in Figure 9. Note that all throttle lines from 0% to 100% are parallel. Therefore, throttle angle α is the same for all throttle lines in Figure 9. The dot-line in Figure 9 represents the maximum engine output torque as the function of engine speed.
14 Y. Wang et al.
Figure 9 Engine reference torque characteristics (see online version for colours)
Engine speed
Engi
ne to
rque
0% Throttle
α
In order to study vehicle performance under different reference throttle characteristics (or different throttle slope angle α), a relationship between the throttle position and speed-torque slope can be established as:
max0
maxmax
0
, 0°tan
, 90°tan
PT
nP
α αα
α αα
⎧ ≤ <⎪⎪= ⎨⎪ ≤ <⎪⎩
(25)
( )maxbasic idle idlen n n n th= + − × (26)
( )peak peak eT f n= (27)
( )0, 0
tan , 0,
r
c basic e r peak
peak peak r
TT n n T T
T T Tα
≤⎧⎪= − × < <⎨⎪ ≤⎩
(28)
where nmax is the theoretical maximum engine speed; TPmax is the engine torque when the engine is operated at the maximum (or rated) power point; Pmax is the maximum power of the engine; α is the throttle slope of the speed-torque line; nidle is the idle speed; th is the percentage of the pedal position; Tr and Tc are the reference torque obtained from throttle table in Figure 9 and engine command torque, respectively; Tpeak and Tpeak is the peak engine torque at corresponding speed. Note that nmax is calculated based upon two different equations of α and it is guaranteed that both the maximum torque point and the maximum power point will be covered within the speed and torque characteristics.
In order to simulate the dynamic response of the engine torque output, a first order transfer function is used to calculate the engine output torque:
Powertrain control parameter optimisation using HIL simulations 15
( ) 1( ) 1
e
c
T sT s τs
=+
(29)
where τ is a time constant as the function of engine speed; and Te is engine output torque. When the gearbox is set to the automatic mode, the powertrain controller is responsible for the gear selection based on a 2D look-up table using vehicle speed and acceleration pedal position as inputs. The details of the look-up table are discussed in Section 4.
3.3 HIL simulation environment
In order to develop an optimal control strategy of coordinating the engine and transmission operations for the studied heavy-duty vehicle powertrain, an HIL simulation platform is developed. The HIL simulation platform, see Figure 10, consists of an Opal-RT real-time simulation system for simulating both powertrain and vehicle and a Mototron rapid prototyping electronic control module for control strategy simulation. Based upon the powertrain system structure shown in Figure 1, the vehicle model described in Section 2 was implemented into the Opal-RT HIL simulator in Simulink. The vehicle model consists of both powertrain and vehicle dynamics. And the powertrain model is divided into three parts, engine system model, transmission torque converter and gearbox models.
To make the vehicle follow the given driving cycle, such as the FTP driving cycle, the driver behaviour model that controls both acceleration and brake pedals is also implemented in the Opal-RT simulation environment. Meanwhile, the powertrain system control strategy was also developed in Simulink and implemented into the Mototron ECM. The controller generates the desired engine torque and transmission gear selection to the vehicle model simulated in Opal-RT via a CAN bus.
Figure 10 HIL simulation platform (see online version for colours)
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4 HIL simulations and case study
This section studies the AT gearshift strategy. In order to obtain the optimal gearshift logic for a given engine torque-speed (or throttle) slope angle α, the gearbox is set to the manual mode and the gear is selected by the driver behaviour model.
By operating the vehicle under a set of vehicle accelerations (see Figure 11), a set of vehicle speed-fuel consumption curves for each given gear can be obtained. Figure 12 shows the speed-fuel consumption curves for the acceleration of 0.4 mph/s with throttle slope angle α equal to 75°.
Three intersection points, shown in Figure 12, represent the corresponding optimal up-shift and down-shift points under the given vehicle speed and acceleration for the best fuel economy without hysteresis. The up-shift and down-shift logic can be obtained by transferring the up-shift set points under different vehicle speeds and accelerations into a function of the acceleration pedal position and vehicle velocity look-up table (see discrete points in Figure 13) since the acceleration rate at a given vehicle speed in miles per hour (MPH) can be associated with a given throttle position. The three straight lines are curve-fitted to these discrete points to form the three gear shifting lines, see Figure 13. The major difference of the proposed gearshift strategy is to use both vehicle speed and throttle position variables for gearshift, instead of only using the engine speed. The benefit of the proposed strategy will be discussed later.
Figure 11 Target vehicle speed in HIL simulations
0 5 10 15 20 25 30 35 400
10
20
30
40
50
60
Time [s]
Veh
icle
spe
ed [m
iles
per h
our]
0.2(mph)/s0.4(mph)/s0.6(mph)/s0.8(mph)/s1.0(mph)/s2.0(mph)/s3.0(mph)/s
Powertrain control parameter optimisation using HIL simulations 17
Figure 12 Vehicle fuel consumption for 0.4 (mph)/s under different gears
0 5 10 15 20 25 30 35 40 45 500
10
20
30
40
50
60
Vehicle speed [miles per hour]
Fuel
con
sum
ptio
n [k
g pe
r hou
r]
1st Gear
2nd Gear
3rd Gear
4th GearGear 1-2Gear 2-3Gear 3-4
Figure 13 Shifting schedule based upon curve fitting
0 5 10 15 20 25 300
10
20
30
40
50
60
70
80
90
100
Vehicle speed [MPH]
Thro
ttle
[%]
1st Gear to 2nd
2nd Gear to 3rd
3rd Gear to 4th
18 Y. Wang et al.
By varying throttle slope angle α, defined in Figure 9, a family of the up-shift and down-shift lines can be obtained and they are shown in Figure 14, where the solid line with circles indicates shifting between the first and second gear; dash-dotted line with squares between the second and third gear; and dashed line with squares between the third and fourth gear. Note that each set of gear shift curves (for instance, solid lines for gear shifting between the first and second gear) contains eight up-shift (down-shift) lines for α (throttle slope angle) equal to 5° to 85° with an increment of 10°. The throttle slope angle is used in this paper as an optimisation parameter for the powertrain control strategy. Note that the up-shift (or down-shift) lines shown in Figure 14 are slightly different from these shown in Figure 13. To have reasonable drivability, the minimal up-shift vehicle speed was limited according to engine idle speed and speed ratio of the up-shift gear. This is mainly used to eliminate excessive gearshift when the vehicle is operated under low speed or light load.
Figure 14 Shifting schedule of an automatic gearbox
0 5 10 15 20 25 30 35 40 45 500
10
20
30
40
50
60
70
80
90
100
Vehicle speed [MPH]
Thro
ttle
[%]
1st Gear to 2nd
2nd Gear to 3rd
3rd Gear to 4th
In summary, the gearshift schedule for a fixed throttle slope angle, α, is obtained by finding the gearshift vehicle speed under constant vehicle acceleration and generating the throttle and vehicle speed map shown in Figure 14. The next step is to optimise throttle slope angle α for the best fuel economy.
The objective of this simulation study is to find the fuel economy measure for the given throttle slope angle, α, while the vehicle speed tracks the reference speed provided by the given driving cycle. Three different driving cycles (FTP, US06 and urban) were used as the evaluation driving cycles. As discussed in the last section, a driver behaviour model was implemented into the console module of the Opal-RT HIL simulator. The two PI controllers (acceleration pedal and brake pedal controls) of the driver behaviour model
Powertrain control parameter optimisation using HIL simulations 19
were used to control the vehicle to follow the target vehicle speed for the given driving cycle.
Figure 15 shows the vehicle speed tracking performance of the driver model, where the solid line is the reference vehicle speed of the FTP driving cycle and the dots represents the actual vehicle speed simulated in the Opal-RT HIL simulator. From Figure 15, one can see that the tracking error between target and simulated vehicle speeds is fairly small.
Figure 15 Target and simulated vehicle speeds of the FTP driving cycle
0 500 1000 1500 2000 2500 3000 35000
10
20
30
40
50
60
Time [s]
Veh
icle
Spe
ed [M
PH
]
Target vehicle speedSimulated vehicle speed
The HIL simulation is then conducted for each throttle slope angle α with its corresponding gearshift lines. The throttle slope varied between 5° and 85° with a ten-degree increment.
Figure 16 shows the transient fuel consumption of the FTP driving cycle. The solid line stands for the case of α = 65°, while the dash line stands for α = 5°. Simulation results show that engine throttle slope angle has a significant influence on the vehicle’s fuel consumption.
Figure 17 shows the fuel consumptions under the FTP, US06, and urban driving cycles as a function of the throttle slope angle α. Simulation results show that the best economy associated with the engine throttle slope angle for the studied heavy-duty vehicle under each driving cycles are different, and the fuel economy improvement varies from about 2% to 6%. However, considering all three simulation results together, a range of the engine throttle slope angle from 65° to 85° provide the best fuel consumption. Since the smaller the slope is, the better the drivability, Figure 17 provides a trade-off between the vehicle drivability and engine throttle-speed slope. Therefore, considering the simulation results for all three driving cycles, it is reasonable to select the engine
20 Y. Wang et al.
throttle slope angle around 65°, which provides a minimum of 2% fuel economy improvement under the three driving cycles.
Figure 16 Transient fuel consumption of the FTP driving cycle for α = 5°, 65°
0 500 1000 1500 2000 2500 3000 35000
10
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30
40
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90
100
Time [s]
Tran
sien
t Fue
l Con
sum
ptio
n [m
pg]
Figure 17 Fuel consumption under the FTP driving cycle (see online version for colours)
5 15 25 35 45 55 65 75 85
96
98
100
FTP
5 15 25 35 45 55 65 75 8590
95
100
Fuel
con
sum
ptio
n pe
r driv
ing
cycl
e[%
]
US06
5 15 25 35 45 55 65 75 85
96
98
100
Engine torque-speed slope[degree]
Urban
Powertrain control parameter optimisation using HIL simulations 21
To study the fuel economy benefit of the optimised gearshift schedule as a function of vehicle speed and throttle position, a traditional engine speed-based gearshift schedule, with the up-shift and down-shift engine speeds shown in Table 2, was used as the baseline gearshift schedule. Two sets of the HIL simulations were conducted with throttle slope angles of 40° and 65°, where the throttle slope angle of 40° is similar to a traditional universal speed governor of diesel engines and 65° is the optimised slope angle obtained through HIL simulations. The fuel economy simulation results are shown in Table 3. It can be observed that with the throttle slope angle of 40° the fuel economy improvement is between 2.44% and 7.6%, and with the throttle slope angle of 65° the improvement ranges from 2.11% to 6.6%. From the simulation data, it can be concluded that the best fuel economy of the optimised gearshift schedule is achieved for urban or FTP cycles, or in other words, for urban typed driving. From Table 3, it is clear that the throttle slope angle selection is dependent on the driving cycle. For the real-world application, the throttle slope shall be selected based upon a preselected driving cycle that represents the vehicle drive pattern. For instance, for a city bus, the ‘urban’ drive cycle shall be used. Table 2 Baseline gearshift speeds
Gearshift between
1 and 2 2 and 3 3 and 4 Up shift 1,300 rpm 1,500 rpm 1,800 rpm Down shift 700 900 1,000
Table 3 Fuel economy study of optimised gearshift speeds
Fuel economy improvement (%) Throttle slop angle α
FTP US06 Urban 40° 7.6% 2.44% 7.1% 65° 6.6% 2.11% 6.08%
Note that the results of both throttle slope angles 40° and 65° in Table 3 are the fuel economy improvement of the proposed approach over the traditional universal speed governor of diesel engines with the normal manual gearshift schedule shown in Table 2; while these normalised results shown in Figure 17 are obtained based on the optimised slope angle with the corresponding gearshift schedule. That is why there are significant the differences between the results shown in Table 3 and Figure 17.
The optimised throttle slope is fairly large and it could affect the gearshift smoothness during the steep/hard acceleration. One solution is to use a small throttle slope angle when the engine is operated close to the gear shifting speed and the optimised throttle slop angle when the engine is operated far away from the gear shifting speed.
5 Conclusions
A Matlab/Simulink vehicle model of a heavy-duty vehicle was developed in this paper. The developed vehicle model consists of a simple diesel engine model, a torque converter model, an AT model with a dynamic gearshift clutch, a vehicle dynamic model and a
22 Y. Wang et al.
driver behaviour model. The real-time vehicle model was implemented into an HIL simulation platform that consists of an Opal-RT HIL simulator and a Mototron rapid prototyping electronic control module. A new gearshift strategy is proposed to improve the vehicle fuel economy, along with the engine throttle slope angle. The Opal-RT HIL simulator integrated with the Mototron powertrain controller was used for vehicle fuel economy simulations to optimise the gearshift parameters and the throttle slope angle under the FTP, US06 and urban driving cycles, where the real-time powertrain model was implemented into the HIL simulator and the powertrain control strategy was implemented into the Mototron powertrain control module. Simulation results show that with the proposed gear-shift schedule and optimised engine throttle slop angle, the vehicle fuel economy can be improved by a minimum of 2% through varying the throttle slope. Simulation results also demonstrated that the proposed gearshift schedule provides the minimal fuel economy improvement of 2.11% over the traditional gearshift schedule and significant improvement is achieved for the urban driving with up to 7.6% fuel economy improvement.
Acknowledgements
The authors would like to thank Mr. Xuefei Chen of Michigan State University for developing the HIL simulation platform baseline vehicle model.
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24 Y. Wang et al.
Nomenclature
AP Area of the friction disc
αS Road gradient
BO Damping coefficient of the oil in clutch cylinder co1 Torque transmitting coefficient of C1 clutch coL Torque transmit coefficient of CL clutch coP Coefficient describes the relationship between the torque from the friction disc and the
oil pressure established within the clutch cylinder coS Coefficient represents the relationship between the torque transmitted via friction pair
and the friction pair rotating speed differential. D Torque converter diameter Fa Wind resistance Fb Brake force that comes from the driver model Ff Friction resistance of the road FF Friction pair engages force Fg Gradient resistance FO Forward force applied on clutch piston FS Return force due to the return spring of the clutch Fv Net driving force of the vehicle g Gravity constant i Speed ratio of the torque converter turbine and pump speeds i12 Speed ratio between axis 1 and axis 2 i23 Speed ratio between axis 2 and axis 3 ip Speed radio of the planetary is Side ratio of the drive-train it1 Speed ratio between turbine and axis 1 J1 Moment of inertia between the turbine and axis 1 Je Crankshaft assembly moment of inertia K Converter torque ratio kS Spring stiffness mP Combined mass of the drive shaft, the piston and the steel disc mv Vehicle weight n1 Angular velocity of axis 1 n2 Angular velocity of axis 2 n3 Angular velocity of axis 3 ne Engine crank shaft speed nF Number of friction pairs nG Rotate speed of drive gear nidle Idle speed nmax Theoretical maximum engine speed
Powertrain control parameter optimisation using HIL simulations 25
Nomenclature (continued)
np Torque converter pump speed nS Rotate speed of drive shaft nt Torque converter turbine speed Pmax Maximum power of the engine RF Radius of the friction disc r Radius of the drive wheel th Percentage of the pedal position To Output torque of the gearbox Tb Engine output brake torque Tc Engine command torques Te Engine output torques TF Torque generated by the fiction disk pair TG Output torque of clutch Tl Engine load torque Tp Torque converter pump torque Tpeak Peak engine torque at corresponding speed TPmax Engine torque when engine is running at maximum (or rated) power point TS Clutch input torque Tt Torque converter turbine torque Tv Load from vehicle dynamic side v Velocity of the vehicle x0 Initial displacement of the clutch piston x1 Maximum position of the piston xP Position of the clutch piston
α Slope of the speed-torque line
Λ Torque converter performance factor μ Friction coefficient of the road μd Friction coefficient of the friction pair ρ Mass density of the working fluid τ Time constant of engine torque
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