143 Modelling, control, and hardware-in-the-loop ... Articles/Modelin… · Proc. IMechE Vol. 224 Part D: J. Automobile Engineering JAUTO1284 ... t is the transmission gear box inertia,

Modelling, control, and hardware-in-the-loopsimulation of an automated manual transmissionX-Y Song1, Z-X Sun1*, X-J Yang2, and G-M Zhu2

1Department of Mechanical Engineering, University of Minnesota, Minneapolis, Minnesota, USA2Department of Mechanical Engineering, Michigan State University, East Lansing, Michigan, USA

The manuscript was received on 3 June 2009 and was accepted after revision for publication on 16 July 2009.

DOI: 10.1243/09544070JAUTO1284

Abstract: To enable a realistic automated manual transmission (AMT) system performanceevaluation and rapid prototyping, this paper focuses on constructing a practical Simulinkmodel and a hardware-in-the-loop (HIL) real-time simulation. The working principle anddynamic characteristics of the AMT system are first explored. The driveline, the engine control,and the dry clutch are modelled and analysed. In particular, a dynamic model for the hydraulicclutch actuator that is currently used in the actual transmissions is developed. To evaluate theperformance and operation characteristics of the AMT system, the control methodology toensure desirable performance is studied. The gearshift control logic and the proportional–integral–derivative-based clutch control are analysed and implemented. Based on the dynamicmodel and the controller, a Simulink model is developed and implemented into an HIL real-time simulator to enable rapid prototyping. In addition, to realize an energy-efficient andsmooth clutch engagement, the possibility of using the dynamic programming method togenerate the optimal clutch and engine torque control inputs is investigated as well. Inparticular, the controllability of the AMT system is studied to determine the number of controlinputs necessary for optimal control. To this end, the simulation and experiment results in theHIL environment are presented.

Keywords: automated manual transmission, hardware-in-the-loop simulation, drivelinedynamics

1 INTRODUCTION

With volatile fossil fuel prices and concerns on glo-

bal warming, vehicle manufacturers put more focus

on developing fuel-efficient vehicles. The trans-

mission system, which is used to transmit the en-

gine torque and power to the vehicle, is one of the

crucial systems that affect the vehicle fuel economy

[1]. Nowadays, the two types of most widely used

transmission system are manual transmission (MT)

and automatic transmission (AT), both of which

have their advantages and disadvantages. For exam-

ple, an AT is convenient to use but has a relatively

higher fuel consumption. An MT is relatively fuel

efficient but is not easy to operate. Therefore, a new

type of transmission – automated manual transmis-

sion (AMT) (Fig. 1), which combines the benefits of

both AT and MT – represents a promising solution

since it can be considered as an inexpensive add-on

solution for classical MT systems.

A vehicle equipped with AMT should be operated

in the same way as a vehicle with AT, but the fuel

economy should be highly improved compared with

the AT system. However, a poorly designed AMT

system will cause undesired vehicle vibration dur-

ing gear shifts due to the torque interruption. This

undesirable characteristic of the AMT system is

actually the bottleneck for its wide application and

competition with the AT system in the market.

However, this technical difficulty also provides a

great research opportunity, given the volatile fuel

price and environmental concerns.

AMT [2–4] shares a similar mechanical structure

to the MT system. Different from MT, the clutch and

*Corresponding author: Department of Mechanical Engineering,

University of Minnesota, Twin Cities Campus, Minneapolis, MN

55455, USA.

email: [email protected]

143

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gearshift are controlled automatically by the AMT

microcontroller. During vehicle operation, the gear-

shift scheduling algorithm sends commands to the

transmission controller, which generates the control

signal to the actuators attached to the clutch and

gears on the AMT, and finally the actuators act on

the synchronizer and the clutch to complete the

clutch shift. The goal of the clutch engagement is to

ensure smooth connection of two rotating masses,

the flywheel and the transmission shaft, which have

different rotational speeds before engagement, and

to realize power transfer from the engine to the

vehicle driveline. The clutch engagement in the AMT

system must satisfy several performance require-

ments: short gearshift duration and smooth gearshift

with improved vehicle fuel efficiency.

To achieve those performance objectives, it is very

important to select a proper clutch actuator and

to build a dynamic model to study the dynamic

characteristics of the AMT system. Moreover, it is

also desirable to manage the control and motion

strategy of the clutch engagement, which is the key

factor for drivability and fuel consumption of the

AMT system. Specifically the control of the clutch

motion will affect the engine and the clutch speeds

during the engagement and at lock-up, which plays

an important role for both comfort and friction

losses [2–3]. The desired control method should

result in smooth clutch engagement without lurch

and should minimize energy loss due to the clutch

slip, for good fuel economy. To achieve this goal, an

advanced control methodology needs to be imple-

mented, which also adds to the complexity and

challenge of the AMT control system.

In fact, in order to achieve the above objectives,

research related to the clutch engagement during the

gearshift phase has been widely explored. In refer-

ence [2], the control method to track the reference

clutch torque was presented to achieve the desirable

performance. In reference [4], a procedure for com-

puting the desirable engine speed during gear-

shift was proposed. In reference [5], a neurofuzzy

approach was implemented. In reference [6], a

model-based back-stepping methodology was used

to design the gearshift control in the AMT system.

However, in spite of the extensive literature on

AMT control, the control methodology of the AMT

system is still not mature for its wide applications.

The main challenge lies in the clutch torque in-

terruption during engagement and the coordina-

tion of the engine and the transmission. To improve

the control design and validation process, a practical

model and rapid prototyping system is necessary. In

this paper, a Simulink AMT model is developed and

implemented in a hardware-in-the-loop (HIL) simu-

lation environment for AMT control strategy devel-

opment and validation.

In addition, few papers have been published that

offer a systematic approach to obtain the desired

trajectory of the clutch torque input, which is the

key for minimal energy loss control. Reference [2]

presented a method to control the clutch torque

based upon the engine and the clutch reference

velocities, but it did not provide the optimal clutch

torque for smooth gearshift without vibration.

Reference [7] provided a control strategy based on

linear quadratic control, but its cost function is a

quadratic approximation of the actual energy loss

cost function. In this paper we also explored the

possibility of using the dynamic programming (DP)

method to design the optimal clutch and engine

velocity and the clutch torque trajectory during

clutch engagement. Although the DP method re-

quires tremendous computational throughput, it is

capable of providing optimal solution based upon

non-quadratic cost function and the given non-

linear dynamic model. However, the lack of control

means that to precisely track the optimal torque tra-

jectory is another bottleneck to successfully solving

the whole optimal clutch engagement problem.

Instead of applying optimal trajectory tracking, this

paper compares the energy loss during gearshift

between the conventional proportional–integral–

derivative (PID) controller obtained during simula-

tion and the controller calculated from DP. This

comparison provides information regarding the gap

between the achievable energy efficiency using DP

and the actual performance from a conventional PID

controller.

This paper is organized as follows. In section 2,

models of the driveline, the dry clutch, and the

electrohydraulic actuator are discussed. In section 3,

four different operating phases of the AMT are ana-

lysed. The controllers corresponding to each phase

are also presented. In addition, the possibility of

Fig. 1 The AMT schematic diagram

144 X-Y Song, Z-X Sun, X-J Yang, and G-M Zhu

Proc. IMechE Vol. 224 Part D: J. Automobile Engineering JAUTO1284



using the DP method to generate the optimal clutch

torque control input is investigated. section 4 intro-

duces the Simulink model and its implementation

with respect to the HIL simulator. Simulation res-

ults of the AMT system performance and the opti-

mized clutch torque trajectory are presented in sec-

tion 5. Conclusions are provided in section 6.

2 SYSTEM MODELLING

In this section, the dynamics of the driveline sys-

tem and major subsystems of the AMT system are

modelled. In particular, the model of a hydraulic

clutch actuator that is widely used in production is

provided.

2.1 Driveline modelling

Reference [2] presented a control-oriented driveline

dynamic model, which is adopted for development.

The driveline is treated separately for the clutch-

disc-slipping condition, clutch-disk-engaged condi-

tion, and gearshift synchronization condition. When

the clutch disc is in the slipping-operating condition,

the driveline dynamics can be modelled as

Je _vve~Te{Tc(xc)

JczJeq ig, id� ��

_vvc

~Tc xcð Þ{ 1

igidktw Dhcwzbtw

vc

igid{vw

� ��

Jw _vvw~ktw Dhcwzbtwvc

igid{vw

� �{TL vwð Þ

D _hhcw~vc

igid{vw

ð1Þ

where Je is the engine inertia, Jc is the clutch inertia,

Jw is the wheel inertia, Te is the engine torque, Tc is

the clutch torque, ve is the engine rotational speed,

vc is the clutch speed, vw is the wheel speed, and xcis the throw-out bearing position. Furthermore, ig is

the gear ratio, id is the differential ratio, Jeq ig, id� �

~

Jmz 1i2g Js1zJs2zJt

i2d

� �, Js1 and Js2 are the inertias

of the two discs connected to the synchronizer, Jm is

the mainshaft inertia, Jt is the transmission gear box

inertia, TL is the load torque, hcw is the driveshaft

torsional angle, ktw is the elastic stiffness coefficient,

and btw is the friction coefficient.

When the clutch is engaged, the engine speed and

the clutch disc speed are the same. Then ve5vc

results in the driveline model as

JezJczJeq ig, id� ��

_vve

~Te{1

igidktw Dhcwzbtw

vc

igid{vw

� ��

Jw _vvw~ktw Dhcwzbtwvc

igid{vw

� �{TL vwð Þ

D _hhcw~vc

igid{vw

ð2Þ

When the clutch disc is fully disengaged from the

engine flywheel, the gears are shifted, which results

in the rotational speed difference between the

transmission gear shaft and the driveline shaft. The

speed difference introduces friction between the

collar gear and the synchronizer, which generates

the synchronization torque Ts due to friction. By

controlling the synchronization torque, the trans-

mission shaft and gear shaft could be synchronized

smoothly. During this synchronization process,

there is no torque transmitted from the engine to

the powertrain driveline. Thus the driveline dyna-

mics during this process can be modelled as

JczJeq ig, id� ��

_vvc~{Ts

ig

Jw _vvw~Tsid{TL vwð Þð3Þ

where Ts is the torque generated from the friction of

the gear synchronizer.

2.2 Clutch dynamics

The clutch packs are connected to the engine and

the main shaft respectively (the clutch disc is

connected to the main shaft, and the flywheel disc

is connected to the engine). The surfaces of the

clutch packs are covered with friction material. The

actuator controls the engagement and disengage-

ment of the clutch pack on the engine flywheel and

that on the main shaft. During the slipping-closing

phase, the clutch disc on the main shaft is moved

towards the flywheel disc until the friction between

the two discs is high enough to transmit engine

torque to the driveline. The clutch displacement

position determines the direct normal force FNbetween the flywheel disc and the clutch disc, and

therefore the torque transmission capacity of the

� �

Simulation of an automated manual transmission 145




clutches. The relationship between the direct normal

force and the torque transmission capacity is written

as

Tc~nFNmR ð4Þ

where m is the friction coefficient, n is the number of

clutch packs, and R is the clutch mean radius.

When the clutch packs are in slipping phase, the

transmitted clutch torque capacity is also the

transmitted torque Tc, which is determined via a

non-linear relationship. In the present simulation,

the non-linear characteristic of the clutch pack is

based on the data reported in reference [2]. When

the clutches are in the engagement phase, the clutch

torque Tc transmitted could be calculated directly

from the driveline model for the engagement phase.

However, if the calculated Tc is greater than the

clutch torque transmission capacity, the clutch will

slip.

2.3 Hydraulic clutch actuator model

In the AMT system, the electrohydraulic actuator is

mainly composed of a hydraulic piston, a housing,

and return springs. The piston is controlled by the oil

flow which determines the force on the actuator. In

this section, a dynamic model for the hydraulic

clutch actuator that is currently used in the actual

transmissions is developed. This model is necessary

for further study of the AMT design.

A simplified schematic diagram of the electrohy-

draulic clutch actuation system is shown in Fig. 2,

where ps is the supply pressure command and also

the control input to the system, pp is the pressure

inside the clutch chamber, and xp is the clutch

piston displacement. The pressurized fluid flows into

the clutch chamber and pushes the clutch piston to

the right; finally it contacts and engages with the

clutch pack. This process is called clutch fill and

engagement. The dynamics associated with clutch

engagement can be modelled as [8, 9]

_xx1~x2

_xx2~1

MpAp x3zPc{Patmð Þ{Dpx2

{Fdrag x3zPcð Þ tanh x2a

�{Kp x1zxp0

� �{FN

i

_xx3~b

V0zApx1sgn u{x3ð ÞCdAorifice

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2 u{x3j j

r

s{Apx2

" #

ð5Þ

with

x1~xp

x2~ _xxp

x3~pp

u~ps

26664

37775,

x1 0ð Þx2 0ð Þx3 0ð Þ

264

375~

0

0

u 0ð Þ

264

375

where Mp is the effective mass of the piston, Ap is

the piston surface area, Dp is the clutch damping

coefficient, Fdrag is the piston seal drag force which is

defined as

Fdrag x3zPcð Þ~0:0006 x3zPcð Þz30 ð6Þ

Pc is the centrifugal-force-induced pressure gener-

ated by the rotational motion of the clutch system,

Patm is the atmospheric pressure, a is the piston seal

damping coefficient, Kp is the return spring constant,

xp0 is the spring preload, b is the fluid bulk modulus,

V0 is the chamber volume, Cd is the discharge

coefficient, Aorifice is the orifice area, and r is the

fluid density. The direct normal force FN in equation

(4) also affects the hydraulic actuator dynamics in

the clutch engagement process and is calculated

from equation (4) by

FN~Tc

mnRð7Þ

The international system of units is used for all the

above variables. In addition, the fluid pressure distri-

bution Pct due to the centrifugal force at any radius

r can be expressed as

Pct~r

2v2 r2{r2st

� � ð8ÞFig. 2 Schematic diagram of electrohydraulic clutchactuation system

i





where v is the clutch system rotational speed, and

the fluid level starts at rst, as shown in Fig. 3.

Therefore the average fluid centrifugal pressure Pc

on the effective piston area Ap could be expressed as

Pc~

Ðrporpi

Pct2pr dr

Apð9Þ

where rpi and rpo are the inner and outer radius

respectively of the piston.

3 AMT CONTROL SYSTEM

The AMT system has four operating phases: en-

gaged, slipping opening, synchronization, and slip-

ping closing; these are shown in Fig. 4. During

normal operating conditions, the AMT is in the

engaged phase, and the clutch is engaged. When a

gearshift is requested on the basis of the gearshift

scheduling logic, the clutch pack on the main shaft

moves away from the flywheel on the engine. This

case is considered as the slipping-opening phase.

When the clutches are fully opened, a new gear can

be engaged and the synchronization phase starts.

The clutch disc and the mainshaft speed quickly

change to a speed value corresponding to the new

gear ratio because of the friction of the synchronizer.

During the synchronization phase, the vehicle speed

is assumed constant, and the engine speed also

starts to decrease. When the gearshift finishes, the

slipping-closing phase starts. In this phase, the

clutch pack on the main shaft moves towards the

fly wheel disc and then the clutch packs are

squeezed. When the clutch and flywheel reach the

same speed, they are locked up and a new engaged

phase of the AMT starts.

The control schematic diagram is shown in Fig. 5.

The main task of the controllers is to control the

engine speed and the clutch speed in order to meet

the smooth clutch shift requirement.

3.1 Engine control

The torque output of the engine is a function of the

throttle and engine speed. The controlled engine

torque in the simulation is determined by a pre-

calibrated engine map, which is a look-up table with

the throttle and the engine speed as inputs and the

engine torque as output.

3.2 Gearshift logic control

The gearshift control logic determines the time to

perform a gearshift during a driving cycle for the best

vehicle fuel economy. Some studies have been

conducted to find the optimal gearshift strategies.

Most of these are based on the vehicle speed and the

amount of throttle. Once the gearshift command is

initiated, the clutch starts to disengage and the

appropriate gears will be shifted. In this paper, the

gearshift logic is implemented in a Stateflow finite

state machine in a MATLAB/Simulink environment

Fig. 3 Fluid pressure distribution and load due to the centrifugal force

Fig. 4 The clutch operation diagram





for a four-gear AMT with gear ratios [2.393 1.450

1.000 0.677] from the first to the fourth gear.

3.3 Synchronization control

During the synchronization phase, the clutches are

disengaged, and no torque is transferred from the

engine to the driveline system. The rotational speed

of the gear to be connected to the driveline shaft is

different from the driveline shaft rotational speed,

and it therefore needs to be synchronized. The

synchronization is realized by controlling the friction

torque between the new gear and the synchronizer

collar gear, which is fixed on the driveline shaft. The

synchronization controller is realized by the PID

control presented in reference [10].

3.4 Clutch control

The most important and difficult phase for the AMT

operation is the slipping-closing clutch engagement.

Improper control of the clutch velocity and torque

will lead to driveline vibration and poor fuel

economy. Even worse, the energy loss during the

clutch engagement generates heat, and excessive

heat could damage the clutch. The critical part for

clutch control and operation is to control the

displacement of the electrohydraulic actuator pis-

ton, which squeezes the clutch pack and therefore

determines the clutch torque transferred to the

driveline system. The transferred clutch torque to-

gether with the engine torque will affect the engine

and clutch speed. Note that the speed difference

between engine and clutch is proportional to the

energy loss. Therefore, it is critical to have both an

optimal clutch and engine torque trajectories that

enable a smooth and efficient torque transfer. In

fact, although previous work [7] is reported to have

designed the optimal torque trajectory, the asso-

ciated cost function is an approximation of the

actual energy loss during clutch engagement. The

main reason is due to the non-quadratic energy loss

function, which is difficult to apply the linear

quadratic regulator controller. Furthermore, to avoid

driveline oscillation, it is necessary not only to con-

sider the possible vibration at the end of clutch

engagement but also to reduce the vibration during

the entire process of clutch engagement. In addition,

it is also important to ensure the smoothness of the

reference clutch torque; otherwise it will be difficult

for the controller to track. However, so far there has

been limited research work that takes all the above

three criteria into account to generate the optimal

torque trajectory. In a later section, a systematic way

to obtain the optimal torque trajectory based on the

DP method will be presented.

Before applying the DP method to the slipping-

closing clutch control, first the clutch system con-

trollability is investigated; this determines the num-

ber of control inputs required to control the engine

speed and clutch speed independently in order to

meet the optimal clutch engagement requirement. If

the clutch torque Tc is the only control input, based

on the dynamic model (1) the controllability matrix

is

{1 0 0 0

1 {btw

igidð Þ2 C23 C24

0 btwigid

C33 C34

0 1igid

C43 C44

2666664

3777775 ð10Þ

where

Fig. 5 The control scheme of the AMT system





Note that the controllability matrix is not full rank.

This indicates that the clutch speed and the engine

speed cannot be controlled independently by the

single control input Tc. With a similar approach, it

can be verified that the above controllability matrix

is full rank and the system is controllable if Te and Tc

are both control inputs. Therefore, to control the

energy loss and the driveline vibration efficiently,

both Te and Tc are regarded as control inputs for the

DP design.

3.5 Optimal clutch and engine torque duringclutch engagement

In this section, the possibility of using the DP meth-

od to obtain the optimal torque trajectory during

clutch engagement is investigated, and the result

from DP will be used as a benchmark to compare

with the result using the feedforward and PID con-

trollers.

3.5.1 Formulation of the clutch engagementoptimal control problem

To enable smooth clutch engagement control, the

clutch torque transmitted to the driveline system

should not induce vibration. In fact, the most critical

point is at the moment of the engagement. Accord-

ing to reference [2], to avoid the lurch problem, it is

desirable that _vve tf{ð Þ{ _vvc tf

{ð Þ is as small as

possible. Also, at the final time tf, the velocity dif-

ference between ve and vc must be zero to complete

the engagement, and it is desirable that the clutch

torque Tc(tf) is larger than the load torque TL(tf) to

continue accelerating after engagement.

These requirements can be translated into a set of

final state conditions that the system must satisfy

according to

min _vve tf{ð Þ{ _vvc tf

{ð Þj jð Þve tfð Þ{vc tfð Þ~0

Tc tfð ÞwTL tfð Þð11Þ

whereve(tf) andvc(tf) are the final state variables, and

Tc(tf) and TL(tf) are the clutch torque control input

and the load torque respectively at the final state.

Among the controls that can realize the clutch

engagement, consider the control that has minimum

energy loss. The energy dissipated during the engage-

ment can be written as

Ed~

ðtf0

ve(t){vc(t)½ �Tc(t)dt

In addition, to realize independent control of vc and

ve, the engine torque Te is assumed to be controllable

in the DP algorithm. The control inputs Tc and Te

obtained from DP should be continuous and smooth

enough to ease the future tracking control. Therefore

the derivatives of Tc and Te are constrained to be

small values during the clutch engagement process.

Moreover, this constraint on the clutch torque

derivative also avoids a high-frequency input to the

driveline system and will therefore prohibit driveline

system vibration during the clutch engagement.

Now the clutch engagement control problem can

be formulated as an optimization problem based on

the above control objectives. The cost function of the

C23~{{b2

tw{b2

twigid� �2

zktw igid� �2

igid� �4

C24~btw {b2

tw{2b2

twigid� �2

z2ktw igid� �2

{ igid� �4

b2twz2ktw igid

� �4h iigid� �6

C33~{b2

tw{b2

twigid� �2

zktw igid� �2

igid� �3

C34~{btw {b2

tw{2b2

twigid� �2

z2ktw igid� �2

{ igid� �4

b2twz2ktw igid


C43~{btw 1z igid


C44~{ {b2

tw{2b2

twigid� �2

zktw igid� �2

{ igid� �4

b2twzktw igid






optimization problem is

g~l1

ðtf0

ve(t){vc(t)½ �Tc(t)dtzl2

ðtf0

_TT c(t)� �2

dt

zl3

ðtf0

_TT e(t)� �2

dtzl4 _vve tf{ð Þ{ _vvc tf

{ð Þj j

zl5 ve tfð Þ{vc tfð Þj j ð12Þ

In particular, the first term of the cost function

ensures minimum energy dissipation during the

clutch engagement process. The second and third

terms set constraints to the trajectory of the clutch

torque and the engine torque to ensure smoothness.

The last two terms will lead the system to reach the

specified final conditions in the required time tf. l1,

l2, l3, l4, and l5 are the weighting factors.

As the cost function and the dynamic model are

non-linear, it is difficult to use the traditional quad-

ratic optimal control method to solve this problem.

Therefore, it is proposed to apply the DP method to

find the desired clutch and the engine speeds or, in

other words, the optimal input clutch torque tra-

jectory. A systematic solution to the above optimiza-

tion problem can be determined recursively via

Bellman’s Dynamic Programming [11]. Since the

system model is non-linear, an analytical solution

cannot be obtained. Instead a numerical solution

will be provided. However, first it is necessary to

discretize the system model to carry out the nu-

merical DP method.

3.5.2 System model discretization

To alleviate the computational throughput for DP, it

is desirable to have a low-order system model that

captures the major system dynamics of equation (1).

Therefore, by assuming that vc; igidvw, combin-

ing the vehicle inertia with the main shaft [2] leads

to a second-order model. This reduced-order model

is used for the DP algorithm, and the discretized

second-order system model is

ve kz1ð Þ~ Te kð Þ{Tc kð Þ½ �DtJe

zve kð Þ ð13Þ

vc kz1ð Þ~ Tc kð Þ{TL kð Þ½ �DtJv

zvc kð Þ

~Tc kð Þ{Br vc= igid

� �� 2n oDt

Jvzvc(k)

ð14Þwhere Dt refers to the sampling time interval, B is theresistance coefficient, and r is the tyre radius.

N5T/Dt is defined as the number of steps from

the initial state to the final state, and the cost

function (12) becomes

g xð Þ~l1XN{1

k~1

ve kð Þ{vc kð Þ½ �Tc kð ÞDt

zl2XN{1

k~1

Tc kz1ð Þ{Tc kð Þ½ �2Dt

zl3XN{1

k~1

Te kz1ð Þ{Te kð Þ½ �2Dt

zl5 ve Nð Þ{vc Nð Þj j

zl4ve Nð Þ{ve N{1ð Þ

Dt{

vc Nð Þ{vc N{1ð ÞDt

ð15Þ

Consequently, the optimal control problem is to find

the optimal control inputs Tc and Te to minimize the

cost function

J xð Þ~minu[U

g xð Þ ð16Þ

3.5.3 Application of dynamic programming to theoptimal clutch engagement control

In this section, the application of the conventional

numerical DP for the clutch engagement control

problem is discussed. To convert DP into a finite

computational problem, the standard method is to

use state space quantization [8, 11–13]. By applying

this approach, the state space is discretized into

finite grids according to

vc kð Þ[ v1c kð Þ,v2

c kð Þ, . . . ,vic kð Þ, . . . ,vL

c kð Þ� �ve kð Þ[ v1

e kð Þ,v2e kð Þ, . . . ,vi

e kð Þ, . . . ,vLe kð Þ� �

ð17Þ

Define X(k)5 [ve(k),vc(k)]T and Xij kð Þ~ vi

c kð Þ,vje kð Þ .

Therefore, in each step, ve(k) and vc(k) are discre-

tized into L discrete values respectively, and X(k)

has L6L possible discrete values in the step k.

For the clutch engagement problem, the initial

states are unknown because they depend on the

driving condition. The final state of the clutch

velocity vc is not specified either. To formulate this

problem for DP, it is necessary to specify the final

states first. As the final state value of the velocity

difference ve2vc is required to be zero for clutch

engagement, then the only final state value that it is

� �





necessary to specify is the clutch velocity vc. In fact,

the range of vc(tf) can be predetermined, as the

vehicle velocity range is restricted given the specific

gear shift ratio. Then the vc(tf) range interval can be

evenly partitioned into a number of discrete vc(tf)

values. During the DP searching process, the discrete

states at step N2 1 as shown in Fig. 6 will choose the

optimal final states respectively, based on the cost

function. In fact, as the driveline inertia is much

larger than the engine inertia Je, vc does not change

much during the clutch engagement process com-

pared with the change in ve. Consequently in the DP

searching process, the range of the state vc is

restricted, and therefore the computation burden is

alleviated.

The DP process ends at step 2 rather than step 1,

as the initial states are unknown. All the discretized

states in step 2 will be assigned an optimal cost value

and the corresponding optimal trajectory towards

the final states. Then all the states and optimal

trajectory will be stored in a look-up table. During

the real-time driving, the initial states at the clutch

engagement will be known. Therefore, on the basis

of the initial state, an optimal trajectory can be

selected from the look-up table.

Then the spatial discretization yields the following

general step of the DP algorithm. Step N2 1, for

1( i( L, and for 1( j(L, is

JN{1 vie,v

jc

� �~ min

1¡s¡Ll5 vs

e Nð Þ{vsc Nð Þ� �2

zl4vs

e Nð Þ{vie N{1ð Þ

Dt{

vsc Nð Þ{v

jc N{1ð Þ

Dt

" #29=;

ð18Þ

Step k, for 0( k,N2 1, for 1( i(L, and for

1( j(L, is

Jk vie,v

jc

� �~ min

1¡s¡L1¡h¡L

l1 ve kð Þ{vc kð Þ½ �Tc kð ÞDt

zl2 Ts,hc kz1ð Þ{Tc kð Þ� �

zl3 Ts,he kz1ð Þ{Te kð Þ� �

zJkz1 vse kz1ð Þ,vh

c kz1ð Þ� ��ð19Þ

where Tc(k) and Te(k) can be calculated from equa-

tions (13) and (14) given specific vie kð Þ, v

jc kð Þ,

vse kz1ð Þ, and vh

c kz1ð Þ. The optimal control policy

minimizes the cost in equations (18) and (19).

From the above analysis, a heavy computational

burden associated with the DPmethod is expected. In

addition, the lack of control means that precise track-

ing of the optimal torque control trajectory is ano-

ther bottleneck in solving the optimal engagement

problem. Therefore, in the Simulink and HIL model

developed in the next section, the torque trajectory

result from DP cannot be implemented, and it is used

to show the difference between the conventional PID

control and the possible optimal control. The clutch

engagement controller in the Simulink and the HIL

model is based on a PID controller that is not

optimized for minimal energy loss during clutch

engagement. However, instead of developing the

control tools to track the trajectory, this paper tries

to compare the energy loss between the PID controller

used in the Simulink model and that calculated from

DP. This comparison will give us insight on the

achievable energy efficiency if the clutch engagement

tracks the optimal torque trajectory obtained fromDP.

Fig. 6 DP algorithm

9=;

�





4 DEVELOPMENT OF THE SIMULINK AND THEHIL MODEL

4.1 Development of the Simulink model

Based on the mathematical system dynamic model,

a simulation model is developed in the MATLAB/

Simulink environment. As shown in Fig. 7, the Simu-

link model consists of four parts: the engine model,

the gearshift logic model, the transmission driveline

model, and the transmission controller model. The

controllers are separated from the driveline dyna-

mics since it will be implemented in a real-time con-

troller later for HIL simulation.

The engine model provides the engine speed and

torque based on the input throttle. The engine

torque in the simulation is obtained from the pre-

calibrated engine map, which is interpolated from a

series of discrete throttle values and engine speed

values.

The gearshift logic is programmed using Stateflow

in Simulink and is obtained on the basis of the

gearshift scheduling map, which provides the opti-

mal gearshift schedule based upon the current

vehicle speed and throttle. Once the gearshift com-

mand is initiated from the gearshift logic model, the

clutch controller is triggered.

The clutch controllers include the engagement

controller, the slipping-opening controller, the syn-

chronization controller, the go-to-slipping control-

ler, and the slipping-closing controller. The con-

trollers switch between each other by triggering the

proper controller in the specific operating phase.

When no gearshift is requested, the engagement

controller maintains a high-pressure control signal

to the hydraulic actuator to maintain the clutch

engagement. Once the gearshift becomes active, the

clutch control switches to the slipping-opening

controller followed by the gearshift clutch control-

lers. This control sequence is carried out in the

Simulink strategy by selecting the operating period

right after the gearshift for different controllers and

detecting the specific time period. On the one hand,

the ‘detect change’ function block in Simulink is

used to capture the gearshift request event. The

starting time ts of the gearshift event is recorded.

On the other hand, the controller switching module

implemented in Simulink keeps updating the differ-

ence tc2 ts between the current time tc and ts. As

shown in Fig. 8, when tc2 ts is between 0 s and

0.2 s, the slipping-opening controller is activated and

the input pressure control signal to the hydraulic

actuator decreases to disengage the clutches. When

tc2 ts is greater than 0.2 s and less than 0.4 s, the

synchronization controller is triggered. When tc2 tsis greater than or equal to 0.4 s and less than 1.1 s,

the controller switches to the go-to-slipping and

then the slipping-closing controller to engage the

clutches. When tc2 ts is greater than or equal to 1.1 s,

the engagement controller is again activated to

maintain the clutch engagement. In the future, if a

new gearshift is requested, the starting time ts is

reset and the sequence is repeated. As discussed

before, the hydraulic pressure controller implemen-

ted in Simulink is a combination of feedforward and

PID controllers, which does not guarantee the

optimal clutch torque. The optimal torque trajectoryFig. 7 Simulink model blocks

Fig. 8 Controller switch logic





based on the DP is not implemented in the Simulink

model owing to the heavy computational through-

put and lack of control means to track the optimal

torque trajectory precisely.

The control signals generated from the AMT

controller are then sent to the AMT transmission

and the driveline system model block. This block is

composed of the hydraulic clutch actuator dynamics

model, the clutch torque physics module, and the

driveline dynamics model. The clutch torque deter-

mination module simulates the clutch torque phys-

ical characteristic. The clutch torque is the sliding

friction torque when the clutches are slipping, while

it becomes static friction torque when the clutches

are engaged. The clutch torque determination mod-

ule will select different equations (equations (1) to

(3)) to describe the different friction torques. The

driveline dynamics block consists of the engage-

ment driveline dynamics, the slipping-closing dy-

namics, and the synchronization. Similar to the

controllers, the driveline dynamics also need to

switch in different operating phases. The parts of

the model that change with different AMT operating

phases are implemented on the basis of the event-

control method. For instance, the commutation

from the slipping-closing phase to the engaged

phase is obtained with the event ‘ve5vc’.

4.2 Hardware-in-the-loop simulation

After the AMT control strategy has been validated in

Simulink simulation, together with the AMT model,

HIL simulation was used. The HIL real-time simu-

lation of the developed AMT system and control

models is performed. For the HIL real-time simu-

lation, the AMT system is split into two independent

subsystems: the AMT plant model and controller.

The AMT plant is implemented in an HIL simulation

platform, and the AMT control strategy is imple-

mented into a rapid control prototyping electronic

control module (ECM) supplied by Mototron. The

HIL simulation is a necessary step in developing an

automotive controller for reduced development cost

and development cycle in a flexible development

environment.

For this paper an ADI PCI-Engine HIL simulation

platform [14] was selected for simulating the AMT,

engine, and vehicle dynamics since it provides

sufficient real-time throughput, inputs, and outputs

for the AMT, engine, and vehicle plant model. The

pulse-width modulated (PWM) inputs, outputs, and

pulse measurements of the PCI-Engine are used for

signal exchange between the AMT system model

implemented in PCI-Engine and the AMT control

strategy running in a production ECM. The control

hardware used in this HIL simulation system is a

production ECM (MotoTron’s ECM-0565-128-0701)

(see the photograph in Fig. 9). To implement the

control strategy inMATLAB/Simulink to the ECM, the

control strategy was discretized with a 1ms sample

period, autocoded, and flashed into the ECM.

Figure 9 shows an integrated simulation environ-

ment of the AMT controller (Mototron ECM) with

the HIL simulator (PCI-Engine). The control and

feedback signals are communicated using PWM

signals.

Fig. 9 Integrated AMT control and simulation system





Two host laptops were used for the ADI HIL

simulator andMotoTron AMT controller respectively.

A monitor is connected to the PCI-Engine simulator

directly to show the status of the AMT simulation in

real time. Key AMT and engine system parameters

such as the clutch speed, hydraulic piston displace-

ment, and engine speed are communicated to AMT

controller using PWM signals generated by the ADI

PCI-Engine, and the AMT control signals are in the

form of PWM signals, converted in the ADI PCI-

Engine simulator to AMT control inputs. Similarly,

the AMT control ECM also communicates with the

ADI HIL through PWM signals. Figure 10 shows the

PWM signal connections between the ADI HIL

simulator with AMT and powertrain models and

Mototron ECM with the AMT controller.

5 SIMULATION RESULTS AND CASE STUDY

In this section, simulation results of a few practical

AMT operation cases for the automated manual

transmission in MATLAB/Simulink are presented.

The AMT modelling parameters are shown in

Table 1.

Figure 11 shows the engine throttle input and the

gearshift scheduling for the simulation example.

Figure 12 shows the corresponding simulation res-

ults. The gear ratio is shifted from 1 to 2, and later

from 2 to 3. During each gearshift, the clutch torque

first drops to zero, then stays for a while, and finally

increases. The gearshift is realized when there is no

clutch torque transferred, and the vehicle speed

continuously increases.

Fig. 10 Hardware linkage for system integration

Table 1 The AMT system dynamic model parameters

Mp 0.4 kg r 813.79 kg/m3

xp0 0.003 57m rpo 63.9572mmKp 151 180N/m rpi 43.0022mmDp 30N/m/s rst 37.3126mmAp 0.007 04m2 Pc 2.81646104 Paa 1m/s T 1 sV0 0.000 05m3 Dt 0.02 sb 17 000bar Aorifice 3.4076106m2

Cd 0.7 m 0.13Patm 1bar n 3Je 0.2 kgm2 R 0.065mid 3.94 Jw 133 kgm2

Jc + Jeq 0.04 kgm2 btw 295Nm (rad/s)ktw 6200Nm/rad

Fig. 11 The throttle input and gearshift scheduling





The real-time HIL AMT simulation is completed

on the basis of a US 06 driving cycle. This driving

cycle covers the drive conditions of both city and

highway, as shown in Fig. 13; the target vehicle

speed ranges from 0mile/h to around 80mile/h.

Simulation based on such a driving cycle is capable

of validating all the functionalities of the AMT

system. Figure 14 also shows that the simulated

vehicle speed with the AMT system follows the target

speed fairly well. The gear shift, engine speed, and

clutch speed responses also perform well, as shown

in Figs 14 and 15.

A simulation to obtain the optimal torque trajec-

tory using DP was also conducted. The optimal

velocity and the optimal torque trajectories are also

compared with those obtained from the feedforward

and PID control results in the Simulink and the HIL

simulation. To make a fair comparison, the initial

conditions ve_initial and vc_initial, which are defined

as the speeds after synchronization and right before

engagement of both the optimal engagement and

non-optimal engagement, are the same. In addition,

both of the engagements can be realized within the

same time period. The gearshift is from gear 1 to

gear 2. The simulation shows only the clutch

synchronization and engagement process, which

starts from the end of clutch disengagement and

ends once the clutch plates are engaged. Figure 16

shows the trajectory of the clutch velocity vc and

the engine velocity ve. The first 0.2 s is the synchron-

ization phase. During gear synchronization, the clutch

plates are totally disengaged, and therefore no clutch

Fig. 12 The AMT simulation results





torque Tc is transferred. The clutch velocity vc is

dragged down by the driveline inertia during

synchronization. On the other hand, the engine

torque is assumed to be close to zero during syn-

chronization, and the engine velocity ve does not

change much during synchronization. Therefore the

initial speed difference ve_initial2vc_initial before the

clutch engagement is larger than zero. During the

clutch engagement phase, the clutch velocity does

not change much owing to the heavy inertia of the

vehicle body, but the engine velocity ve decreases

until the clutches are fully engaged.

Figure 17 shows the speed difference ve2vc. For

the optimal engagement obtained from DP, the

Fig. 13 Vehicle speed response in the HIL simulation

Fig. 14 Engine and clutch speed responses in the HILsimulation

Fig. 15 Gear shift action in the HIL simulation





speed difference decreases during clutch engage-

ment. At the final time, the change in the speed

difference becomes smaller as the derivative of ve is

constrained to be close to that of vc near the final

time of the clutch engagement. Figure 18 shows the

clutch torque Tc during the clutch engagement. Both

of the clutch torque trajectories start from 0Nm. For

the optimal clutch torque trajectory, the maximum

torque difference in each step is limited to be smaller

than 20Nm. The clutch torque controlled in the

Simulink model is almost a ramp signal, which is

easier to control by the feedforward and PID

controller. Figure 19 exhibits the engine torque Te.

The engine torque obtained from DP is required to

be negative at the start of the clutch engagement,

because otherwise the engine velocity will increase.

Fig. 16 Trajectories of vc and ve

Fig. 17 Optimal trajectory of ve2vc





The energy loss curves are compared in Fig. 20. The

energy loss trajectory shows the energy lost from the

initial time to the current time t1 and is given by

Ed t1ð Þ~ðt10

ve tð Þ{vc tð Þ½ �T c tð Þdt ð20Þ

It can be seen that, at the end of the clutch

engagement, the energy loss of the engagement

using DP is almost half that produced by the PID

controller. Therefore, to reduce energy loss, it is

desirable to track the torque trajectories obtained

from DP. However, the computational throughput

and lack of means of control to track the optimal

trajectory precisely make it difficult to implement

into the current Simulink and HIL model. Future

Fig. 18 Optimal trajectory of Tc

Fig. 19 Optimal trajectory of Te





research work will be focused on further reducing

the computational throughput of the DP algorithm

and developing effective control tools to track the

optimal torque trajectories from DP.

6 CONCLUSION

This paper presents a practical Simulink dynamic

model with proper complexity for an HIL simulator

of the AMT system. This AMT model provides

adequate performance for AMT control development

and validation. This is also a necessity for rapid

prototyping of an AMT controller. The developed

AMT dynamic model also includes the driveline

model, the engine model, the dry clutch model, and

the hydraulic actuator models. An AMT gearshift

control strategy is also developed that includes

gearshift control logic and clutch control method-

ology. The developed AMT dynamic model and

controller are realized in Simulink and implemen-

ted in an HIL simulator and an ECM respectively.

Simulation validation results show that the devel-

oped AMT model, together with its controller, pro-

vides adequate complexity for control system simu-

lation and development with proper throughput

for real-time simulation. In addition, to realize an

energy efficient and smooth clutch engagement, the

DP method is used to generate the optimal clutch

and engine torque control; it shows almost 50 per

cent energy saving during clutch engagement. Im-

plementing the optimal control strategy from DP is

part of future research work.

ACKNOWLEDGEMENT

The authors would like to thank Hong Kong Auto-motive Parts and Accessories Systems Research andDevelopment Center for the financial support.

F Authors 2010

REFERENCES

1 Sun, Z. and Hebbale, K. Challenges and oppor-tunities in automotive transmission control. InProceedings of the 2005 American Control Con-ference, Portland, Oregon, USA, 8–10 June 2005,pp. 3284–3289 (IEEE, New York).

2 Glielmo, L., Iannelli, L., Vacca, V., and Vasca, F.Gearshift control for automated manual transmis-sions. IEEE/ASME Trans. Mechatronics, 2006, 11(1),17–26.

3 Garofalo, F., Glielmo, L., Iannelli, L., and Vasca, F.Smooth engagement for automotive dry clutch. InProceedings of the 40th IEEE Conference on Dec-ision and control, Orlando, Florida, USA, 2001,pp. 529–534 (IEEE, New York).

4 Amisano, F., Serra, G., and Velardocchia, M.Engine control strategy to optimize a shift transientduring clutch engagement. SAE paper 2001-01-0877, 2001.

Fig. 20 Energy loss comparison, Tc(ve2vc)





5 Hayashi, K., Shimizu, Y., Nakamura, S., Dote, Y.,Takayama, A., and Hirako, A. Neuro fuzzy optimaltransmission control for automobile with variableloads. In Proceedings of the IEEE Industrial Elec-tronics, Control, and Instrumentation Conference,Maui, Hawaii, USA, 1993, vol. 1, pp. 430–434 (IEEE,New York).

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APPENDIX

Notation

Aorifice orifice area

Ap piston area of the clutch system

Cd discharge coefficient

Dp damping coefficient of the clutch

Ed energy loss during clutch

engagement

Fdrag drag force of the piston seal

FN direct normal force between the

flywheel disc and the clutch disc

id differential ratio

ig gear ratio of the transmission

Jc clutch inertia

Je engine inertia

Jm mainshaft inertia

Js inertia of the disc connected to the

synchronizer

Jt transmission gearbox inertia

Jw wheel inertia

ktw elastic stiffness coefficient

Kp return spring constant

Mp effective mass of the piston

n number of clutch packs

pp pressure inside the clutch chamber

ps supply pressure

Patm atmospheric pressure

Pc centrifugal pressure induced by

transmission rotation

Pct fluid pressure distribution

rpi inner radius of the piston

rpo outer radius of the piston

rst fluid level

R mean radius of the clutch

tf final time of clutch engagement

Tc clutch torque

Te engine torque

TL load torque

Ts synchronization torque

xc throw-out bearing position

xp0 spring preload

V0 volume of the chamber

a damping coefficient of the piston

seal

b bulk modulus of the fluid

btw friction coefficient

hcw driveshaft torsional angle

l weighting factor

m friction coefficient

r density of the fluid

v rotational speed of the clutch system

vc rotational speed of the clutch

ve rotational speed of the engine

vw speed of the wheel





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143 Modelling, control, and hardware-in-the-loop ... Articles/Modelin… · Proc. IMechE Vol. 224 Part D: J. Automobile Engineering JAUTO1284 ... t is the transmission gear box inertia,