Driver Attention in Automatic Transmission Cars

International Journal of Automotive Technology, Vol. 18, No. 1, pp. 179−194 (2017)

DOI 10.1007/s12239−017−0018−4

Copyright © 2017 KSAE/ 094−18

pISSN 1229−9138/ eISSN 1976−3832

179

ADAPTIVE CONTROL OF THE SHIFTING PROCESS IN AUTOMATIC

TRANSMISSIONS

G. SHI 1, 2)

, P. DONG 1, 2)*

, H. Q. SUN 1, 2)

, Y. LIU 3) , Y. J. CHENG

1, 2) and X. Y. XU

1, 2)

1)Department of Automotive Engineering, School of Transportation Science and Engineering, Beihang University, Beijing 100191, China

2)Beijing Key Laboratory for High Efficient Transmission and System Control of New Energy Resource Vehicle, Beihang University, Beijing 100191, China

3)Beijing Institute of Space Launch Technology, Beijing 100076, China

(Received 29 July 2015; Revised 30 April 2016; Accepted 28 June 2016)

ABSTRACT−This paper focuses on the way of keeping shift quality of automatic transmissions consistent in mass production

and with mileage accumulation. We investigate the main factors influencing the consistency of shift quality. Test results show

that the torque to pressure (T2P) and pressure to current (P2I) characteristics of shifting elements are easily affected. A

simulation model of an 8-speed automatic transmission is established to simulate the dynamic process of clutch-to-clutch shift.

Simulation results demonstrate that the change of T2P and P2I characteristics has a significant influence on shift quality. In

order to compensate for the influences, we develop two adaptive control strategies, i.e., the adaptive control strategies for

torque phase and inertia phase. They make use of the measured speed information and time information to evaluate shift

quality. Then the control parameters are tuned to adapt to the change of T2P and P2I characteristics. Vehicle tests verify that

the developed adaptive control strategies are effective to keep shift quality consistent in mass production and with mileage

accumulation.

KEY WORDS : Automatic transmission, Adaptive control strategy, Shift quality, Torque to pressure characteristic, Pressure

to current characteristic

1. INTRODUCTION

Thanks to the increasing requirements for CO2 reduction

and fuel economy, automatic transmissions (ATs) tend to

have more speeds in recent years, which leads to an

increase in shift operations of daily driving. In order to

have a fast and smooth shift feeling, comprehensive studies

focus on the control of the shifting process. Integrated

control with mutual communication between engine and

transmission is increasingly being applied (Narumi et al.,

1990). It enables significant improvements for shift quality

and clutch durability. Examples of such an integrated

control method can be found in the work (Lorenz et al.,

1990; Cho, 1987; Yang et al., 2001; Sawamura et al., 1998;

Goetz et al., 2004; Bai et al., 2013; Guo et al., 2014; Cheng

et al., 2015).

In the shifting process of ATs, the oil filling of the on-

coming clutch is a major source of uncertainty that makes

the pressure overlap in the torque phase a difficult task

(Sun and Hebbale, 2005). Song et al. (2011) presented a

systematic approach to evaluate the clutch filling dynamics

and to synthesize the optimal pressure. The proposed

method was validated through experimental investigation

and had a good effectiveness for the improvement of shift

quality (Song et al., 2010). Pinte et al. (2010), Depraetere

et al. (2011) and Dutta et al. (2014a, 2014b) discussed the

application of iterative learning control algorithoms for the

engagement of wet clutches, which can maintain a good

clutch filling performance despite the time-varying

dynamics of wet clutches. Meng et al. (2015a) developed

an clutch filling control strategy using both feedforward

and feedback control. Simulation results demonstrated that

the control strategy can effectively decrease the fill time

and the clutch pressure shock. Liu et al. (2016) proposed a

clutch filling method for start-stop function, which enables

a precise control of the vehicle launch.

In addition to the optimized control of clutch filling,

some other methods regarding the improvement of shift

quality are also available in open literatures. Minowa et al.

(1994, 1996, 1999) and Ibamoto et al. (1995, 1997)

developed control methods to estimate the shaft torque of

transmission. By means of the estimated shaft torque, it is

possible to detect the torque fluctuation and the start time

of inertia phase accurately. Hence shift quality can be

improved. Bai et al. (2002) developed a new technology

using a hydraulic washout technique to control the shifting

process. The test results showed that this new technology

greatly improved shift quality and reduced calibration*Corresponding author. e-mail: [email protected]

180 G. SHI et al.

work. Haj-Fraj and Pfeiffer (2000, 2001, 2004) proposed

an approach for the optimization of gear shifting operations

based on a verified mechanical model of a vehicle

powertrain. The control parameters for the clutch pressure

as well as those for the engine torque reduction were

optimized to improve shift comfort or shift spontaneity

according to two sets of optimization criteria. Küçükay et

al. (2009) automated the shift quality adjustment by

transferring the calibration process from road test to roller

dynamometer in the lab. This method was also applied

successfully by AVL and ZF (Bagot et al., 2008). They

jointly developed a methodology for the automation of a

model-based process in the calibration of shift quality on

the test rig. Meng et al. (2015b) presented an optimal

shifting control strategy for inertia phase based on dynamic

models and control objectives. Simulation results showed

that the influence induced by the disturbance could be

reduced effectively. Kim et al. (2014) developed a model

and shifting controller for the dual clutch transmission

which has similar clutch-to-clutch shifting process as ATs.

The model and controller were validated and a good

correlation was observed between simulation results and

vehicle test data.

Nevetheless, above references do not take the influences

of build-to-build and life-cycle variations into account. An

adaptive system is necessary to keep shift quality consistent

in mass production and with mileage accumulation

(Hebbale and Kao, 1995). Kim et al. (2001) developed an

adaptive compensation controller with intelligent supervisor

to achieve improved shift quality over the system variations.

However, this paper only investigated the adaptive control

for inertia phase during shifting. The adaptive control for

torque phase still remains blank, which also affects the

consistency of shift quality greatly.

In this paper, a simulation model is established for the

investigation on the influences of build-to-build and life-

cycle variations. It is found that the change of pressure to

current (P2I) and torque to pressure (T2P) characteristics

are the main reasons for the weak robustness of shift

control. Therefore, two adaptive control strategies (i.e.,

adaptive control strategies for torque phase and inertia

phase) are developed to compensate for the influences.

They evaluate shift quality according to the measured

speed information and time information in the shifting

process. Then the control parameters are tuned to improve

shift quality. The developed adaptive control strategies are

implemented into the control software of an 8-speed AT.

Vehicle tests show that they have a good effect on the

improvement of shift quality.

2. SHIFTING PROCESS

Clutch-to-clutch shifts have no power interruption because

there is a pressure overlap between the on-coming clutch

and the off-going clutch in the shifting process. The torque

is transferred from the off-going clutch to the on-coming

clutch whilst the engine speed has to be synchronized from

the current gear to the target gear. There are four main

shifting types, i.e., power on upshift, power on downshift,

power off upshift and power off downshift. Before

discussing the adaptive control strategies, it is necessary to

introduce the shifting process of different shifting types

firstly. Since power off downshift can in principle be

controlled like power on upshift and power off upshift like

power on downshift, only the shifting process of power on

upshift and power on downshift are discussed in this paper.

2.1. Shifting Process of Power on Upshift

Power on upshift happens when driver slowly accelerates

the vehicle. Figure 1 (a) shows its shifting process which

can be divided into four phases. Phase 1 ~ 2 is the

preparation phase. In this phase, the on-coming clutch is

firstly fast filled by following a high pressure command. It

is for overcoming the return spring force and the seal

friction force to eliminate the clearance of clutch pack in a

short time. Then the clutch pressure decreases to the kiss-

point where the piston comes in contact with the clutch

pack and the clearance has already been eliminated.

Meanwhile the pressure of the off-going clutch starts

decreasing. When the torque capacity is smaller than the

actual torque of the off-going clutch, a small speed

Figure 1. Shifting process of power on upshift and power

on downshift.

ADAPTIVE CONTROL OF THE SHIFTING PROCESS IN AUTOMATIC TRANSMISSIONS 181

difference between the transmission input speed and the

current gear speed appears because the off-going clutch

starts slipping. In short, the objective of the preparation

phase is to build the relationship between the clutch

pressure and the actual clutch torque.

Phase 2 ~ 3 is the torque phase in which the transmission

input torque is transferred from the off-going clutch to the

on-coming clutch. The control target of the torque phase is

to keep the slip between the transmission input speed and

the current gear speed at a small amount level. Otherwise

engine flare (a large positive speed difference between the

input speed and the current gear speed) or clutch tie-up (a

negative speed difference between the input speed and the

current gear speed) will happen to cause a shifting impact.

After the pressure of the off-going clutch decreases

below its kiss-point, the inertia phase 3 ~ 4 starts. The

transmission input speed is decelerated from the current

gear level to the target gear level by continuing increasing

the on-coming clutch pressure. A negative engine torque

intervention benefits the speed synchronization in this

phase. Before the end of the inertia phase, the pressure of

the on-coming clutch decreases a little to reduce the

shifting impact at the synchronization point. At last, the

pressure of the on-coming clutch increases to the line

pressure in phase 4 ~ 5 to finish the shifting process of

power on upshift.

2.2. Shifting Process of Power on Downshift

If driver wants to overtake or the vehicle starts climbing,

the acceleration pedal will be kicked down in a short time.

In this case transmission control unit (TCU) judges that the

vehicle needs more wheel torque to accelerate or to

overcome the climbing resistance. Then power on downshift

occurs. As shown in Figure 1 (b), the shifting process of

power on downshift is different from power on upshift. The

inertia phase 1 ~ 2 comes firstly. In this phase, the pressure

of the off-going clutch decreases to a certain level. The

engine load is reduced thus the transmission input speed

can be accelerated from the current gear level to the target

gear level. A positive engine torque intervention can

shorten the synchronization time to improve shift

spontaneity. Meanwhile, the on-coming clutch is firstly fast

filled. Then clutch pressure decreases to the kiss-point.

After reaching the kiss-point, the pressure of the on-

coming clutch will not immediately increase in phase 1 ~ 2.

It will wait until the transmission input speed exceeds the

target gear speed.

After the transmission input speed is larger than the

target gear speed, the torque phase 2 ~ 3 starts with

increasing the pressure of the on-coming clutch whilst

decreasing the pressure of the off-going clutch. The control

target of the torque phase is to keep a small slip between

the transmission input speed and the target gear speed. If

control parameters are not well calibrated, engine flare will

happen thus increasing the heat load of the on-coming

clutch. At last, the off-going clutch pressure drops below its

kiss-point and the on-coming clutch pressure increases to

the line pressure in the phase 3 ~ 4.

Many researches focus on the control of clutch-to-clutch

shifts aiming to achieve a consistent shift quality. Generally,

there are two kinds of control strategies. One is the open-

loop control strategy. The other is the closed-loop control

strategy which has a target slip in the torque phase and a

target speed trajectory in the inertia phase. Both control

strategies require a good calibration of control parameters.

However, shift quality is difficult to maintain consistent

with only the two control strategies.

3. PROBLEM FORMULATION

No matter which control strategy is applied, the robustness

of shift control is always a key issue. The main reason

comes from the uncertainties of physical characteristics.

Figure 2 shows a pilot control system of shifting element.

The proportional solenoid valve provides a low pilot

pressure which is controlled by the current command.

However, the multi-plate shifting element requires a high

clutch pressure. Therefore, a slide valve is added to amplify

the low pilot pressure to the high clutch pressure. In this

way, the pressure of shifting element can be controlled by

means of the current of proportional solenoid valve. Then

the relationship between control current and clutch pressure

is established. It is an important physical characteristic

which is called the P2I characteristic.

Figure 2. Pilot control system of shifting element.

182 G. SHI et al.

The clutch pressure pushes the piston of shifting element

to clamp the clutch pack. The friction torque is calculated

according to Equation (1).

(1)

where “µd” is the dynamic friction coefficient; “pSE” is the

pressure of the shifting element; “pkiss” is the kiss-point

pressure; “A” is the piston area; “r” is the equivalent

friction radius; “z” is the number of friction surface; “Δω”

is the angular speed difference between the two halves of

the shifting element. Equation (1) builds the relationship

between the friction torque and the clutch pressure. It is

another important physical characteristic which is called

the T2P characteristic.

TCU needs to know above two physical characteristics

accurately for a precise control of the shifting process. Both

characteristics are either calibrated manually in prototype

phase or tested automatically in mass production. Figure 3

shows the flow chart of the control loop. The target clutch

torque is calculated by the control strategy in each time

step. Then it is converted to the current signal according to

the measured T2P and P2I characteristics. TCU sends the

current command to the proportional solenoid valve to

obtain the actual clutch pressure. Then we can obtain the

actual clutch torque based on Equation (1). In this control

loop, deviation between the target clutch torque and the

actual clutch torque inevitably exists because the P2I and

T2P characteristics are easily affected by tolerances, wear,

driving conditions and so on.

3.1. Deviation of T2P Characteristic

In Equation (1), parameters “A”, “r”, “z” are determined in

the design phase. Parameter “pSE” is tuned to control the

shifting process. The dynamic friction coefficient “µd” and

kiss-point pressure “pkiss” are the main reasons for the

deviation of T2P characteristic.

Dynamic friction coefficient is easily affected by driving

conditions. It changes continuously. Generally, friction

coefficient depends on the following factors:

(1) Friction linings (material, design, quality, aging and

wear);

(2) Automatic transmission fluid (ATF) (base oils, additives,

quality, aging and wear);

(3) Temperature of ATF and friction plates;

(4) Slipping speed, especially at micro slip;

(5) Surface pressure on the friction plate.

Figure 4 shows the test results of an ATF’s “μ-v” friction

characteristic. The tests are conducted according to the

Japanese Automobile Standard “JASO M-349”, in which

detailed test methods and test conditions are listed. It can

be seen that the dynamic friction coefficient changes with

the slipping speed. The range of variation is especially

wider at low speed. Meanwhile, temperature also has a

significant influence on the dynamic friction coefficient.

Figure 5 shows the durability test results of two different

ATFs. Test methods and test conditions are detailed

described in the Japanese Automobile Standard “JASO M-

348”. It can be seen that the dynamic friction coefficient

varies irregularly with the increasing driving cycle. It is the

reason for the change of T2P characteristic throughout the

transmission service life. Furthermore, different ATFs

show different dynamic friction characteristics although

the friction material is the same.

Kiss-point pressure is a physical characterisitc which

changes easily with mileage accumulation. Accurate kiss-

point pressure lays a solid foundation for precise shift

control. However, it is usually different in different shifting

elements and different builds because of the manufacture

and assembly tolerances.

Figure 6 depicts the load characteristic of a disc spring in

SE d SE kiss ( ) sign( )T p p A r zμ Δω= ⋅ − ⋅ ⋅ ⋅ ⋅

Figure 3. Flow chart of the control loop.

Figure 4. Test results of “μ-v” friction characteristic.

Figure 5. Durability test results of dynamic friction

coefficient.

ADAPTIVE CONTROL OF THE SHIFTING PROCESS IN AUTOMATIC TRANSMISSIONS 183

an 8-speed AT. It can be seen that this disc spring has a

tolerance range from about 100 N to about 200 N at

different height. According to the design parameters of

corresponding shifting element, this tolerance causes a

change of kiss-point pressure from 0.2 bar to 0.3 bar. In

addition, the wear of friction plates increases the spring

stroke, which thus results in an increase of the kiss-point

pressure.

Clutch seal also affects the kiss-point pressure. The

friction force of seal is difficult to know because of aging.

Furthermore, the oil centrifugal force should also be

considered in the calibration of kiss-point pressure for

clutch design without a balance chamber. All above factors

make the kiss-point pressure become an uncertain physical

characteristic.

3.2. Deviation of P2I Characteristic

Proportional solenoid valve has tolerance and hysteresis,

which affect the accuracy of P2I characteristic. Figure 7

shows the P2I characteristic of a proportional solenoid

valve. It can be seen that the minium tolerance is 0.4 bar. In

addition, the pressure does not follow the same line when

increasing and decreasing with the current because of

hysteresis. In a pilot control system, there is an additional

slide valve for each solenoid to amplify the low pilot

pressure to the high clutch pressure. Therefore, the

tolerance of slide valve also affects the P2I characteristic.

The operating temperature of ATF is from – 20 °C to

+ 120 °C. The kinematic viscosity of ATF changes a lot in

this range, which has a significant influence on the P2I

characteristic. Figure 8 shows the test results of P2I

characteristic of a shifting element at 20 °C and 90 °C. A

large deviation of pressure difference exists between the

two P2I characteristics. In order to control the shifting

process precisely, the influence of temperature has to be

compensated.

In mass production, the T2P and P2I characteristics of

each shifting element are obtained from the end-of-line

test. It is an efficient way to reduce the influence of

tolerance at beggining. However, these two characteristics

change greatly under different driving conditions and with

mileage accumulation. The real T2P and P2I characteristics

will inevitably deviate from the beggining. It is impossible

to know the exact characteristics timely. In addition to the

T2P and P2I characteristics, there are also many other

uncertainties, such as measurement errors from the speed

sensor and the engine torque. All these factors will affect

the control accuracy of the shifting process.

4. MODELING OF SHIFING PROCESS

In order to investigate the influences of T2P and P2I

characteristics, a powertrain model is established to simulate

the shifting process. The control strategies of the shifting

process are the same as in TCU. Therefore, this simulation

model also has a virtual tuning capability for calibration

work.

Figure 9 (a) shows the schematic representation of the

simulation model including an engine, a hydraulic torque

converter with input torsion damper, an 8-speed AT, a

driveline’s spring-damper system and the driving resistance.

The engine output torque is expressed as a function of the

throttle opening degree and the engine speed based on an

Figure 6. Load characteristic of a disc spring.

Figure 7. P2I characteristic of a proportional solenoid

valve.

Figure 8. P2I characteristics of a shifting element at 20 °C

and 90 °C.

184 G. SHI et al.

engine map. The pump and turbine of the torque converter

are assumed to be connected mechanically in the shifting

process, which does not consider the hydraulic damping for

the shifting impact. In order to improve the computational

efficiency, two equivalent spring-damper systems located

at the transmission input and output side are taken into

account. The first spring-damper sytem at the input side

represents the torsion damper in the torque converter. The

second spring-damper sytem at the output side represents

the spring-damper characteristic of the driveline. Since this

paper concentrates on the adaptive control of the shifting

process, the modeling of the 8-speeed AT is detailed

introduced as follows.

4.1. Modeling of the 8-speed AT

Figures 9 (b) and (c) show the scheme and the shifting

logic of the 8-speed AT. It has four transfer gear sets (i.e.,

“TG610, TG47, TG58, TG211”), three planetary gear sets

(i.e., “PG1, PG2, PG3”) and five shifting elements (i.e.,

“B1, C1, C2, C3, C4”). In order to analyze the AT dynamic

behavior in the shifting process, the transmission kinetics

and kinematics needs to be determined firstly.

Every shaft of the transmission is considered as a

separate inertia. According to the scheme, each component

has several torque nodes on corresponding shafts. We

develop a method to encode the torque nodes simply and

easily. For example, in the code of torque node “Tx_i”, “x”

means the component and “i” means the shaft number.

According to the scheme of the 8-speed AT, there are

fourty-six unknown variables including all the torque

nodes and the acceleration of each shaft, as shown in

Figure 10. In addition, “Ji” represents the inertia of the ith

shaft; “αi” represents the angular acceleration of the ith

shaft.

Fourty-six linear equations are necessary to solve the

unknown variables. Newton method is applied to formulate

all the linear equations. The kinetic equations for all

transmission shafts and housing are formulated as follows.

Figure 9. (a) Schematic representation of the powertrain model; (b) Scheme of the 8-speed AT; (c) Shifting logic of the 8-

speed AT.

Figure 10. Unkonwn variables including shaft acceleration and torque nodes.

ADAPTIVE CONTROL OF THE SHIFTING PROCESS IN AUTOMATIC TRANSMISSIONS 185

Housing: (2)

Shaft 1: (3)

Shaft 2: (4)

Shaft 3: (5)

Shaft 4: (6)

Shaft 5: (7)

Shaft 6: (8)

Shaft 7: (9)

Shaft 8: (10)

Shaft 9: (11)

Shaft 10: (12)

Shaft 11: (13)

The torque equations for all planetary gear sets and

transfer gear sets are formulated as follows. In order to

facilitate the computer programming, the transfer gear set

is assumed to have a carrier like the planetary gear set. This

carrier has no rotational speed thus is considered to be

connected with the housing.

PG1: (14)

(15)

PG2: (16)

(17)

PG3: (18)

(19)

TG47: (20)

(21)

TG58: (22)

(23)

TG610: (24)

(25)

TG211: (26)

(27)

where “ix” is the stationary ratio of each gear set. The

kinematic constraints of all gear sets are formulated from

Equation (28) to Equation (35). The acceleration of

housing should be 0.

PG1: (28)

PG2: (29)

PG3: (30)

TG47: (31)

TG58: (32)

TG610: (33)

TG211: (34)

Housing: (35)

The torque on both halves of every shifting element

should be the same, as expressed from Equation (36) to

Equation (40).

Brake B1: (36)

Clutch C1: (37)

Clutch C2: (38)

Clutch C3: (39)

Clutch C4: (40)

The transmission input torque is known from the engine

side. The transmission output load is known from the

calculation of the driving resistance.

Input: (41)

Output: (42)

where “TTurbine” represents the input torque from the turbine

of the hydraulic torque converter; “TL” represents the

output torque from the differential.

Above equations are the same for different shift

simulations. Additional five equations are necessary to

calculate the unknown variables. They are derived from the

shifting logic in Figure 9 (c). For example, when shifting

from the second gear to the third gear, clutch C3 and C4 are

the engaged shifting elements. Both halves of these two

shifting elements have the same angular acceleration.

Clutch C3: (43)

Clutch C4: (44)

Clutch C2 is the disengaged shifting element. It doesn’t

transmit any torque.

Clutch C2: (45)

Brake B1 is the off-going shifting element and clutch C1

is the on-coming shifting element. In the shifting process,

they transmit friction torque which can be controlled by

means of pressure.

Brake B1:

(46)

TG47_0 TG58_0 TG610_0 TG211_0

B1_0 0 0 0 0

T T T T

T T J α

+ + + +

+ − =

PG1_1 C1_1 in_1 1 1 = 0T T T J α+ + −

PG2_2 PG3_2 TG211_2 2 2 = 0T T T J α+ + −

PG1_3 C4_3 B1_3 3 3 = 0T T T J α+ + −

PG1_4 TG47_4 C3_4 4 4 = 0T T T J α+ + −

TG58_5 C1_5 C3_5 5 5 = 0T T T J α+ + −

TG610_6 C4_6 6 6 = 0T T J α+ −

PG2_7 TG47_7 7 7 = 0T T J α+ −

PG3_8 TG58_8 C2_8 8 8 = 0T T T J α+ + −

PG2_9 C2_9 9 9 = 0T T J α+ −

PG3_10 TG610_10 10 10 = 0T T J α+ −

TG211_11 out_11 11 11 = 0T T J α+ −

PG1_4 PG1 PG1_3 = 0T i T+

PG1_4 PG1_3 PG1_1 = 0T T T+ +

PG2_9 PG2 PG2_7 = 0T i T+

PG2_9 PG2_7 PG2_2 = 0T T T+ +

PG3_10 PG3 PG3_8 = 0T i T+

PG3_10 PG3_8 PG3_2 = 0T T T+ +

TG47_7 TG47 TG47_4 = 0T i T+

TG47_7 TG47_4 TG47_0 = 0T T T+ +

TG58_8 TG58 TG58_5 = 0T i T+

TG58_8 TG58_5 TG58_0 = 0T T T+ +

TG610_10 TG610 TG610_6 = 0T i T+

TG610_10 TG610_6 TG610_0 = 0T T T+ +

TG211_11 TG211 TG211_2 = 0T i T+

TG211_11 TG211_2 TG211_0 = 0T T T+ +

3 PG1 4 PG1 1 ( 1) = 0i iα α α− + −

7 PG2 9 PG2 2 ( 1) = 0i iα α α− + −

8 PG3 10 PG3 2 ( 1) = 0i iα α α− + −

4 TG47 7 TG47 0 ( 1) = 0i iα α α− + −

5 TG58 8 TG58 0 ( 1) = 0i iα α α− + −

6 TG610 10 TG610 0 ( 1) = 0i iα α α− + −

2 TG211 11 TG211 0 ( 1) = 0i iα α α− + −

0 = 0α

B1_3 B1_0 = 0T T+

C1_1 C1_5 = 0T T+

C2_8 C2_9 = 0T T+

C3_4 C3_5 = 0T T+

C4_3 C4_6 = 0T T+

in_1 Turbine T T=

out_11 L T T=

4 5 α α=

3 6 α α=

C2_8 = 0T

B1_3 d B1 kiss_B1 B1 B1 B1 B1 ( ) sign( )μ Δω= ⋅ − ⋅ ⋅ ⋅ ⋅T p p A r z

186 G. SHI et al.

Clutch C1:

(47)

Equations (43) ~ (47) change depending on different

shift simulations. The program will automatically

supplement these five equations according to the specific

shift. All the unknown variables are solved by means of

matrix operation of the linear equation system, which

forms a good basis for the development of a general-

purposed program.

It is noted that the friction coefficient “µd” is modeled by

means of an inverse tangent function which eliminates the

discontinuity at the point of zero slipping speed. It makes

the simulation run fast by reducing the oscillation in the

vicinity of the discontinuity point. A positive slope “µ-v”

friction characteristic is formulated by Equation (48). A

negative slope “µ-v” friction characteristic is formulated by

Equation (49). Their characteristic curves are shown in

Figure 11.

Positive slope: (48)

Negative slope:

(49)

where “µmax” represents the maximum value of the friction

coefficient; “Δn” represents the slipping speed; “nα, nβ, nγ,

nδ” represent the speed scaling factors which are used to

change the shape of the friction curves.

The vehicle parameters used in the simulation model are

listed in Table 1, which are also the parameters of the test

vehicle.

C1_1 d C1 kiss_C1 C1 C1 C1 C1 ( ) sign( )μ Δω= ⋅ − ⋅ ⋅ ⋅ ⋅T p p A r z

d max

α

2n arctan

n

Δ μ μ

π

⎛ ⎞ = ⎜ ⎟

⎝ ⎠

β

d max 3 α δ γ

2 sign( )

( )

n / nn arctan n

n n / n n

ΔΔ μ μ Δ

π Δ

⎡ ⎤⎛ ⎞ = + ⋅⎢ ⎥⎜ ⎟

+⎢ ⎥⎝ ⎠⎣ ⎦

Figure 12. Simulation results of the influences of the kiss-point pressure.

Figure 11. Positive and negative friction characteristics.

Table 1. List of the vehicle parameters.

Parameters Value

Vehicle mass 1,850 kg

Gear ratios

1st gear: 4.17; 2nd gear: 2.65; 3rd gear: 1.69; 4th gear: 1.43; 5th gear: 1.17; 6th gear: 1.00; 7th gear: 0.84; 8th gear: 0.64.

Final drive ratio 3.56

Aerodynamic drag coefficient

0.37

Effective frontal area 2.48 m2

Wheel radius 0.35 m

ADAPTIVE CONTROL OF THE SHIFTING PROCESS IN AUTOMATIC TRANSMISSIONS 187

4.2. Discussion of Simulation Results

We assume that there is no pressure response delay in the

simulation because it does not affect our discussion about

the influences of P2I and T2P characteristics on shift

quality.

Figure 12 illustrates the influences of the kiss-point

pressure. In the first simulation (graph (a) and graph (b)),

the clutch pressure is equal to its real kiss-point pressure at

Figure 13. Simulation results with a small and a large dynamic friction characteristic.

188 G. SHI et al.

the end of clutch filling. The difference between the

transmission input speed and the current gear speed is

positive and small.

If the clutch pressure is much bigger than the real kiss-

point pressure, over fill happens. The pressure increase of

the on-coming clutch starts from a higher level at the

beginning of the torque phase. Consequently, as shown in

graph (c), the pressure becomes larger at the end of the

Figure 14. Simulation results with accurate and inaccurate P2I characteristic.

ADAPTIVE CONTROL OF THE SHIFTING PROCESS IN AUTOMATIC TRANSMISSIONS 189

torque phase. In this case, clutch tie-up easily happens. It

can be seen that the input speed has already dropped below

the current gear speed at the end of the torque phase (graph

(d)).

Conversely, if the clutch pressure is much smaller than

the real kiss-point pressure when the clutch filling is

completed, under fill happens. In this case, the pressure of

the on-coming clutch starts increasing based on a lower

level at the beginning of the torque phase. Finally, the on-

coming clutch pressure becomes smaller at the end of the

torque phase (graph (e)). The released torque of the off-

going clutch cannot be totally compensated by the on-

coming clutch. Consequently, engine flare takes place in

graph (f).

According to Equation (1), friction coefficient and

design parameters of the shifting element must be constant

to determine the linear relationship between clutch torque

and clutch pressure. However, the uncertainty of friction

coefficient breaks this linear relationship.

Figure 13 illustrates the influences of dynamic friction

coefficient on shift quality. Both simulations have the same

parameters to control the shifting process of power on

upshift from the 2nd gear to the 3rd gear. However, the first

simulation has a small dynamic friction characteristic while

the second simulation has a large dynamic friction

characteristic. Graph (a) shows that the pressure of the on-

coming clutch increases to the same level as in graph (e) in

the inertia phase. However, since the second simulation has

a large dynamic friction characteristic, the friction torque

of the on-coming clutch is larger than it is in the first

simulation. Thus the transmission input speed decreases to

the target gear level more quickly in graph (g) compared

with graph (c). Meanwhile, the vehicle acceleration drops

more sharply at the end of the shifting process in graph (h)

than in graph (d) because of the large dynamic friction

characteristic. A larger vehicle jerk (derivative of the

vehicle acceleration) can be found in graph (h) at the end of

the shifting process.

The influences of inaccurate P2I characteristic can also

be observed through simulation. Figure 14 shows two

simulations both of which consider the P2I characteristic as

the red curve in Figure 8. However, the real P2I

characteristic for the second simulation is the blue curve.

All the other control parameters are the same in the two

simulations.

The first simulation has a good shift quality because the

P2I characteristic is accurate and the control parameters are

well calibrated. In the second simulation, we assume that

TCU considers the P2I characteristic as the red curve,

according to which the target clutch pressure is converted

to the current command. However, the actual clutch

pressure follows the blue curve when the current command

is sent out. Accordingly, the second simulation has a bad

shift quality because the cluch pressure is not controlled as

desired.

Firstly, the pressure at kiss-point is smaller than its real

kiss-point pressure (graph (e)). Under fill takes place

leading to engine flare in the shifting process (graph (g)).

Correspondingly, the vehicle acceleration has a larger

decrease in graph (h) than in graph (d) at about 0.6 s.

Driver and passengers will have a feeling of traction loss.

Secondly, the pressure of the on-coming clutch is lower

than the desired level in the inertia phase. The time

duration of the inertia phase thus is much longer in the

second simulation than it is in the first simulation.

Therefore, both shift comfort and shift spontaneity will get

worse if the P2I characteristic is not accurate.

5. ADAPTIVE CONTROL STRATEGIES

The change of P2I and T2P characteristics is difficult to

measure and predict. After delivering the vehicle to

customer, it is also impossible to tune control parameters

manually to adapt to the change of P2I and T2P

characteristics. Therefore, two adaptive control strategies

which make use of the speed information and time

information are proposed to keep shift quality consistent.

5.1. Adaptive Control Stragegy for the Torque Phase

Shift quality can be reflected by the deviation of

transmission input speed. It is good if the speed deviation is

small. On the contrary, a big speed deviation results in a

bad shift quality such as engine flare or clutch tie-up. In the

torque phase of power on upshift, the speed deviation is

just the difference between the transmission input speed

and the current gear speed. In the torque phase of power on

downshift, it is the difference between the transmission

input speed and the target gear speed.

As shown in Figure 15, the input speed is limited within

Figure 15. Principle of the adaptive control strategy for the

torque phase.

190 G. SHI et al.

a range by predefining the maximum speed deviation and

the minimum speed deviation in the torque phase of power

on upshift and power on downshift. If the input speed is

within this range, the adaptive control strategy will not tune

corresponding control parameters. However, corresponding

control parameters will be tuned to drive the input speed

into this range by means of an adaptive gain once the input

speed is out in a certain gear shift.

Different control parameters can be selected in the

adaptive control strategy for the torque phase. It can be

seen that TCU can increase the pressure level of the off-

going clutch in the preparation phase or increase the

pressure gradient of the on-coming clutch in the torque

phase to eliminate engine flare in power on upshift (blue

dashed line). Under fill of the on-coming clutch is the main

reason for engine flare. Therefore, the adaptive control

strategy can also increase the fast filling time of the on-

coming clutch. In power on downshift, the torque phase

follows after the inertia phase. Engine flare can be

eliminated by increasing the pressure gradient of the on-

coming clutch or by advancing the starting time of the

pressure increase (blue dashed line).

If clutch tie-up happens (red dashed line), the adaptive

control strategy tunes the control parameters in another

direction. In power on upshift, the pressure level of the off-

going clutch can be reduced in the preparation phase. Thus

the slip will increase to provide a larger buffer zone to

avoid clutch tie-up. Furthermore, the pressure increase of

the on-coming clutch can become slower or it can be

postponed for a short time. The fast filling time of the on-

coming clutch can also be shortened to avoid over fill. In

power on downshift, clutch tie-up can be eliminated by

reducing the pressure gradient of the on-coming clutch or

by postponing the starting time of the pressure increase

(red dashed line).

Figure 16 shows the block diagram of the adaptive

control strategy for the torque phase. Here we improve

shift quality of the torque phase by tuning the pressure

gradient of the on-coming clutch. In the block diagram,

“pAD” is the adaptive pressure which is assigned a value in

every gear shift. It is noted that the adaptive control

strategy is only conducted under certain operating

conditions, such as in a temperature range. If the adaptive

conditions are not satisfied or the input speed is within the

range in current gear shift, the adaptive pressue will be the

same as the value in last gear shift, i.e., “pAD_last”. If the

input speed exceeds the upper boundary, the adaptive

pressure will be updated by adding an adaptive gain “Δp”.

Conversely, the adaptive pressure will be updated by

substracting an adaptive gain “Δp” if the input speed is

smaller than the lower boundary. The new value of the

adaptive pressure is stored in the non-volatile random

access memory (NVRAM). In next gear shift under similar

operating conditions, it will be added to the pressure from

the feed-forward loop (pFD) and the feedback loop (pFB).

Thus the control pressure of the on-coming clutch “pOC”

can be corrected by a different increasing gradient in the

torque phase.

5.2. Adaptive Control Stragegy for the Inertia Phase

The adaptive control strategy for the inertia phase evaluates

shift quality according to the time duration of the inertia

phase. A long time duration leads to a big heat load in the

actuated shifting elements. In addition, it deteriorates shift

spontaneity. On the contrary, a short time duration easily

causes shifting impact which in turn deteriorates shift

comfort.

Figure 17 shows the principle of the adaptive control

strategy for the inertia phase. The time duration of the

inertia phase has a constraint between the red dashed line

(time t1) and the blue dashed line (time t2). The adaptive

control strategy will tune corresponding control parameters

to drive the time duration into this constraint once it is out.

In power on upshift, the maximum pressure level of the

on-coming clutch in the inertia phase is used as the

Figure 16. Block diagram of the adaptive control strategy

for the torque phase.

ADAPTIVE CONTROL OF THE SHIFTING PROCESS IN AUTOMATIC TRANSMISSIONS 191

adaptive control parameter. When the time duration is

shorter than t1, the on-coming clutch pressure will decrease

(red dashed line) at a certain step to extend the time

duration. Then shift comfort can be improved. When the

time duration is longer than t2, the on-coming clutch

pressure will increase (blue dashed line) at a certain step to

shorten the time duration. Then shift spontaneity can be

improved.

For the inertia phase of power on downshift, the

principle of the adaptive control strategy is essentially the

same. However, the adaptive control parameter turns into

the minimum pressure level of the off-going clutch in the

inertia phase. The off-going clutch pressure will increase

(red dashed line) at a certain step to extend the time

duration towards the desired range when it is too short.

Conversely, when the time duration of the inertia phase is

too long, the off-going clutch pressure will decrease (blue

dashed line) to shorten it towards the desired range.

Figure 18 shows the block diagram of the adaptive

control strategy for the inertia phase. If the adaptive

conditions are not satisfied or the time duration is within

the constraint in current gear shift, the adaptive pressue will

be the same as the value in last gear shift. If the time

duration is longer than t2, the maximum pressure level of

the on-coming clutch in power on upshift will be updated

by adding an adaptive gain. In power on downshift, the

minimum pressure level of the off-going clutch will be

updated by substracting an adaptive gain. However, if the

time duration is shorter than t1, the maximum pressure

level of the on-coming clutch in power on upshift will be

reduced by an adaptive gain. The minimum pressure level

of the off-going clutch will be increased by an adaptive

gain in power on downshift.

The updated adaptive pressure is used in next gear shift

under similar operating conditions to correct “pOC” or “pOG”

in Figure 18, i.e., the maximum pressure level of the on-

coming clutch or the minimum pressure level of the off-

going clutch in the inertia phase.

6. VEHICLE TESTS

The two adaptive control strategies are verified through

tests. Figure 19 shows a picture of the test vehicle, which

data are the same as in the simulation model as shown in

Table 1. The test data are timely read through the

calibration software CANape. Test conditions are listed in

Table 2. Oil temperature varies within the range of the

normal operating temperature. The line pressure of the

hydraulic system changes depending on the engine torque.

The sampling time of the TCU is set as 10 ms. The tests are

conducted on a flat blacktop road.

Figure 20 shows the test results of the adaptive control

strategy for the torque phase. Small engine flare appears in

power on upshift from the fourth gear to the fifth gear, as

Figure 17. Principle of the adaptive control strategy for the

inertia phase.

Figure 18. Block diagram of the adaptive control strategy

for the inertia phase.

192 G. SHI et al.

shown in graph (a). The time window from t1 to t2 is 80

ms. In this short time interval, the pressure command of the

on-coming clutch increases from the kiss-point pressure to

about 4.1 bar. The TCU finds the input speed exceeds the

constraint and thus starts tuning the pressure increasing

gradient of the on-coming clutch.

After some miles of adaptive driving, graph (b) shows

that the small engine flare has been eliminated in the shift

under similar operating conditions. It can be seen that the

time window from t3 to t4 is still 80 ms. However, the

pressure command of the on-coming clutch increases to 4.6

bar which is bigger than it is before adaptive tuning.

Figure 21 shows the test results of the adaptive control

strategy for the inertia phase. In this case, power on

downshift from the third gear to the second gear is

performed to show the control effect. It is observed that the

time duration of the inertia phase is 0.8 s before adaptive

tuning in graph (a). Correspondingly, the minimum

pressure level of the off-going clutch is 2.8 bar in the

inertia phase. Since the time duration is too long, this

Figure 19. Test vehicle.

Table 2. Test conditions.

Item Conditions

Oil temperature 85 °C ~ 95 °C

Line pressure 8 bar ~ 20 bar

Sampling time 10 ms

Road Flat track (Blacktop)

Figure 20. (a) Small engine flare before adaptive tuning;

(b) No engine flare after adaptive tuning.

Figure 21. (a) Long time duration of inertia phase before

adaptive tuning; (b) Suitable time duration of inertia phase

after adaptive tuning.

ADAPTIVE CONTROL OF THE SHIFTING PROCESS IN AUTOMATIC TRANSMISSIONS 193

pressure level is reduced shift by shift through the adaptive

control strategy.

After some miles of adaptive driving, graph (b) shows

that the minimum pressure level of the off-going clutch

decreases to 2.2 bar in the inertia phase. The time duration

of the inertia phase is shortened from 0.8 s to 0.5 s

correspondingly. Shift spontaneity thus is improved by the

adaptive control strategy for the inertia phase.

7. CONCLUSION

This research focused on how to keep shift quality consistent

in mass production and with mileage accumulation.

Conclusions are summarized as follows:

(1) The influences on the consistency of shift quality were

investigated. Test results show that the T2P and P2I

characteristics are easily affected in build-to-build and

life-cycle variations.

(2) A simulation model was developed to simulate the

shifting process of multi-speed ATs. Simulation results

verified that the change of T2P and P2I characteristics

have a great influence on the consistency of shift

quality.

(3) In order to compensate for the change of T2P and P2I

characteristics, adaptive control strategies for the

inertia phase and the torque phase were proposed. They

evaluate shift quality according to the speed information

and the time information in the shifting process.

Control parameters are tuned shift by shift to respond

to the variations of T2P and P2I characteristics.

(4) Test results verified that the two adaptive control

strategies can improve shift quality automatically. In

order to maintain shift quality consistent in mass

production and with mileage accumulation, it is

necessary to integrate adaptive control strategies into

TCU.

ACKNOWLEDGEMENT−We would like to acknowledge the

financial supports from the National Natural Science Foundation

of China (Grant Number: 51405010), the Fundamental Research

Funds for the Central Universities, the Innovation Foundation of

Beihang University for Ph.D. Graduates, and Beijing Key

Laboratory for High-efficient Power Transmission and System

Control of New Energy Resource Vehicle.

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