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SAE TECHNICAL
PAPER SERIES
2003-01-3266
MBT Timing Detection and its Closed-Loop
Control Using In-Cylinder Pressure Signal
Guoming G. Zhu, Chao F. Daniels and James Winkelman
Visteon Corporation
Reprinted From: Experimental Investigation of Compression Ignition and
Spark Ignition Engines
(SP–1804)
Powertrain & Fluid Systems
Conference & Exhibition
Pittsburgh, Pennsylvania USA
October 27-30, 2003
400 Commonwealth Drive, Warrendale, PA 15096-0001 U.S.A. Tel: (724) 776-4841 Fax: (724) 776-5760 Web: www.sae.org
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Copyright © 2003 SAE International
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2003-01-3266
MBT Timing Detection and its Closed-Loop Control Using InCylinder Pressure Signal
Guoming G. Zhu, Chao F. Daniels and James Winkelman
Visteon Corporation
Copyright © 2003 SAE International
ABSTRACT
MBT timing for an internal combustion engine is also
called minimum spark timing for best torque or the spark
timing for maximum brake torque. Unless engine spark
timing is limited by engine knock or emission
requirements at a certain operational condition, there
exists an MBT timing that yields the maximum work for a
given air-to-fuel mixture. Traditionally, MBT timing for a
particular engine is determined by conducting a spark
sweep process that requires a substantial amount of
time to obtain an MBT calibration. Recently, on-line MBT
timing detection schemes have been proposed based
upon cylinder pressure or ionization signals using peak
cylinder pressure location, 50 percent fuel mass fraction
burn location, pressure ratio, and so on. Because these
criteria are solely based upon data correlation and
observation, both of them may change at different
engine operational conditions. Therefore, calibration is
still required for each MBT detection scheme. This paper
shows that MBT timing can be achieved by locating the
maximum net pressure acceleration point at top dead
center. This result is developed based upon the physical
aspects of the combustion process, and therefore, it
should be independent of engine operational conditions
and valid for all spark-ignited engines that have one
peak heat release rate during the combustion process.
Experimental validation of this result over certain engine
operational conditions is completed, and validation of
this result over whole engine operational map is the
subject of future work.
The second part of this paper develops an MBT timing
closed-loop control using the detected MBT timing
criteria as a feedback signal. The benefit of closed loop
control of MBT timing is improved robustness over openloop MBT timing calibration with respect to engine-toengine variations, engine aging, engine operational
conditions, etc. A two-way filtering algorithm, combined
with the derivative calculation, is developed to improve
the robustness of MBT timing detection scheme without
the penalty of filter phase delay. A PI (proportional and
integral) controller is used to illustrate closed-loop
control of MBT timing, where the reference signal is
used to control the engine ignition timing at its set point.
The closed-loop control system is implemented in
dSpace and prototyped on a two liter four cylinder
engine. The test results show that the closed-loop MBT
timing controller based upon the maximum net pressure
acceleration point not only maintains the engine average
ignition timing at its MBT timing but also reduces the
cycle-to-cycle variations. For comparison purpose, three
MBT timing feedback signals are used in the study: peak
cylinder pressure location, 50 percent burn location, and
maximum net pressure acceleration location.
INTRODUCTION
Traditionally, MBT timing is determined by conducting a
spark timing sweep. Almost every calibration point
needs a spark sweep to see if the engine can be
operated at the MBT timing condition. If not, a certain
degree of safety margin is needed to avoid pre-ignition
or knock during engine operation. Open-loop spark
mapping usually requires a tremendous amount of effort
and time to achieve a satisfactory calibration.
In recent years, various closed loop spark timing control
schemes have been proposed based upon cylinder
pressure measurements [1,3,5-8] or spark ionization
sensing [9]. Based on test data, it has been found that
the peak cylinder pressure usually occurs around 15
o
ATDC at MBT timing. The 50% mass fraction burned
point generally occurs from 8 to 10 oATDC when MBT
timing is achieved, see [4]. The algorithm published in
[3] controls PR(10) (normalized pressure ratio of incylinder and motoring pressure at 10 oATDC) around
0.55 to obtain the MBT timing. Because these criteria
are solely based upon observations and may change at
different operating conditions, each algorithm still
requires some calibration effort.
It is clear that the
combustion process has to be matched with the engine
cylinder volume change to attain the best torque.
However, there is no sound theory to support the
rational that peak cylinder pressure must occur around
15 oATDC or that 50% burned must happen around 9
o
ATDC for the MBT timing conditions.
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Mass Fraction Burned and Its Derivatives
1
Mass Fraction Burned
1st Derivative (20 tim es)
2nd Derivative (200 tim es)
Xb
0.8
dXb/d θ *20
b
Mass Fractio n B urned (X )
0.6
0.4
0.2
0
-0.2
-0.4
d 2 Xb/d θ 2 *200
-0.6
-20
-10
0
10
20
30
40
50
60
Crank Angle (Degree ATDC )
Figure 1 mass fraction burned and its derivatives
One may view a combustion process as both a chemical
process and a physical process. It is usually described
by mass fraction burned (MFB) versus crank angle. The
mass fraction burned not only signifies how much
chemical energy is released at each crank angle during
the combustion, but also how fast the chemical energy is
released. When graphed, MFB has a characteristic Sshape and changes from zero to one from the beginning
to the end of combustion. Figure 1 shows a typical mass
fraction burned for an engine operating at MBT and its
first and second derivatives. The first derivation of MFB
can be treated as the rate of heat release or the velocity
of the combustion process, while the second derivative
can be treated as the acceleration of the combustion
process.
The key event associated with the combustion process
begins with the spark event. After the spark discharge,
the flame kernel starts to form. Once the flame kernel
becomes stable, it develops very fast and the
combustion process reaches its maximum acceleration
point. Then the rapid burning period starts and reaches
its maximum heat release velocity very quickly. After this
point, the combustion process slows down and attains
its maximum deceleration point. Because the
combustion cannot complete instantaneously and the
chamber volume is constantly changing, choice of
alignment of these critical points versus crank angle may
have significant impact on how much useful work can be
accomplished during the combustion process. If one
ignites the mixture too soon, the pressure increase due
to the heat release before the Top Dead Center (TDC)
would generate negative work. If one doesn't ignite the
mixture on time, the heat release process would not be
efficient enough to utilize the small volume advantages
at TDC. Therefore, the decision on where to ignite the
combustion mixture becomes a critical factor of
obtaining best torque. In this paper, an MBT timing
criterion based upon maximum acceleration of mass
fraction burned (MAMFB) is developed and validated.
The desired engine spark timing is a function of MBT,
misfire and knock spark timing limits, as well as engine
physical limitations, etc. For this paper, we concentrated
mainly on closed-loop MBT spark timing controller
development. For the closed-loop MBT timing control
strategy, individual cylinder pressure was sampled at
every crank degree and processed every combustion
event to generate both MBT timing criterion and closedloop MBT timing control output. The final spark time in
o
BTDC (Degrees Before Top Dead Center) was limited
by both advance and retard bounds that were
dynamically modified by both misfire and knock limit
managers. The closed-loop MBT timing control
strategies were validated using a two-liter four-cylinder
engine in a dynamometer located at the Visteon
Dearborn Technical Center. A dSpace expansion box
was used for controlling engine spark timing in closedloop and the dynamometer controller controls engine
speed, load, fueling, EGR, etc.
The closed-loop MBT spark control was demonstrated
using three feedback control criteria: peak cylinder
pressure (PCP) location, 50% mass fuel burn (MFB50%)
location, and maximum acceleration location of mass
fraction burn (MAMFB). Test results show stable MBT
timing control for all three closed-loop control strategies
(PCP, MFB50%, and MAMFB) in both transient and
steady state operation. The MBT spark timing was
achieved over the complete engine operational map
when MAMFB remains at zero, while MFB50% and PCP
locations varies within several crank degrees over
engine map when MBT spark is achieved.
MBT TIMING DETECTION
The mass fraction burned is mostly determined by the
well-known Rassweiler-Withrow [2] method established
in 1938 through pressure measurement. It uses the
chamber volume at the ignition as a reference and
calculates the net pressure increase at every crank
angle for the whole combustion process, then
normalizes the pressure by the maximum pressure
increase at the end of combustion. The procedure
ignores the heat loss and mixture leakage during the
combustion. Each percentage of pressure increase
signifies the percentage of mass fraction of fuel burned
at the corresponding crank angle.
In this study, instead of using the mass fraction burned,
we used the net pressure P and its first and second
derivatives to represent the distance, velocity and
acceleration of the combustion process. If we normalize
the net pressure by the overall net pressure increase at
the end of the combustion, the result is mass fraction
burned. Note that the pressure difference P(i+1)-P(i),
where i represents the current crank angle, is caused by
two parts. One is the pressure change due to volume
change that can be found through the difference
P(i)*(V(i)/V(i+1))1.3 – P(i), assuming the pressure
undergoes isentropic compression or expansion. The
other is the pressure difference resulting from
combustion between two crank angles that can be
represented by P(i+1) – P(i)*(V(i)/V(i+1))1.3, that is
evaluated at volume V(i). In order to know the net
pressure without any volume change since the ignition,
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the difference should be compared with the volume at
the ignition point as if the combustion undergoes
constant volume combustion. Therefore, the net
pressure change between two crank angles is:
(Eq. 1)
S T = 3 2 o BTD C
S T = 3 0 o BTD C
2
S T = 2 8 o BTD C
Acceleration of Net Pressure
1 .3

 V (i )    V (i ) 
∆P(i ) =  P(i + 1) − P(i ) ⋅ 

 ⋅ 

V (i + 1)    V Ig 
MBT Sp ark Tim ing Se arch (2 50 0 R PM with 6.9 bar BMEP )
2 .5
1 .5
S T = 2 6 o BTD C
1
S T = 2 2 o BTD C
S T = 2 4 o BTD C
0 .5
0
-0 .5
-1
-1 .5
and the net pressure at each crank angle is
-2
PNET (i ) = PNET (i − 1) + ∆P(i) ,
-2 .5
-3 0
(Eq. 2)
-2 0
-1 0
0
10
20
30
C rank A ngle (D e gre e ATD C )
40
50
60
Figure 3 Pressure accelerations
where P is pressure, V is volume and Vig is the chamber
volume at the ignition point.
Engine Brake Torque vs. S park Tim ing
92.6
92.4
Engine Brake Torque (ft-lb)
92.2
92
91.8
91.6
91.4
91.2
After the maximum pressure acceleration is reached, the
crank angle taken for the flame propagating to the peak
velocity point is mainly determined by the flame speed,
see Figure 4. When the fuel is leaner or EGR rate is
higher, the flame speed will be slower. Therefore, it will
take a longer time for the flame to propagate and the
peak pressure velocity point will occur later. At low load
conditions, because the pressure and temperature are
relatively lower, the flame speed is also slower and the
peak velocity point happens later. As the engine speed
increases, the turbulence becomes stronger and the
flame speed is faster, and the peak pressure velocity
point occurs slightly earlier.
91
90.8
90.6
18
20
22
24
26
28
Spark Tim ing (Degree BTD C)
30
32
Net Prssure and Its First and Second Derivatives
34
600
Net P ressure (P sia) and Its D e rivatives
Figure 2 Engine brake torque vs spark timing
Figure 2 shows engine torque output at different spark
timing when operating at 2500 RPM with 7.86 bar
BMEP, and Figure 3 shows the corresponding pressure
acceleration curves with different spark timing. The
calculation is based upon the average pressure signal
over 300 combustion cycles. It is clear from Figure 2 that
the MBT timing occurs around 28 oBTDC. The peak
acceleration points shown in Figure 3 gradually
advances as the spark timing advances. At 28 oBTDC,
the peak acceleration of pressure is located very close
to TDC. Based on Figure 3, at 28 BTDC, the pressure
velocity reaches its maximum at about 9 oATDC and the
net pressure at this point is about 50% of the total net
pressure. As we have mentioned earlier, locating 50%
mass fraction burned at 9 oATDC is often used as an
indicator for MBT timing.
dP/d θ *20
Net Pressure
1st Derivative (20 tim es)
2nd Derivative (100 tim es)
500
Net Pressure
400
300
200
100
0
d 2 P/d θ 2 *100
-100
-200
-300
-20
Early flam e
form ation
-10
Rapid
flam e
developm ent
0
10
20
30
Crank Angle (Degree ATDC )
40
50
60
Figure 4 Net pressure acceleration vs. crank angle
Figure 5 shows the BMEP changes with the spark timing
when the engine operates at 1500 RPM with 2.62 bar
BMEP and different EGR rates for the two-liter fourcylinder engine. The MBT timing can be found for each
EGR condition. Figure 6 shows the acceleration curves
at different EGR rates. The spark timing at each
condition associated with the maximum acceleration
point locating at TDC and the spark timings found
through torque measurement are listed in Table I.
37.5
0%EGR
10% EGR
5% EGR
15% EGR
37
36.5
36
22 24 26 28 30
26 28 30 32 34
32 34 36 38 40
38 40 42 44 46
Spark Timing (BTDC)
Figure 5 BMEP, spark timing, and EGR rate
Table 1 MBT timing and maximum acceleration
EGR
0%
5%
10%
15%
20%
MBT timing
(Max BMEP)
28
32
34-36
42
47
o
Spark timing ( BTDC) when
[Max (d2PNET /dθ2) at TDC]
28
32
34 or 36
40
46
Test data has shown that MBT timing occurs when the
maximum net pressure acceleration point is located at
TDC. The question is: is this phenomenon only true for
several operating conditions or is it true for all operating
conditions? As mentioned before, the combustion
process has its distinctive footprint that is signified by the
mass fraction burned. The whole combustion process
can be compared to a distance runner entering a race.
Deciding where to attain maximum acceleration and
when and where to reach peak velocity will determine
how well the runner finishes in the race. It is well known
that the work generated before the top dead center
(TDC) is wasted in a fight with the moving piston and
produces heat. However, it is a necessary step for the
flame to establish itself for further flame development.
The useful work is done after TDC. If we go back to
Figure 1, we can see that the combustion process
reaches its maximum acceleration point at a relatively
early stage, which indicates that the early flame
preparation is finished at this point and the combustion
is ready to start the rapid burning period. If we achieve
this maximum acceleration point before TDC, some of
the rapid burning period will be wasted before the TDC.
If we attain the maximum acceleration point after the
TDC, the rapid burning period right after the maximum
acceleration point will occur at a bigger cylinder volume
and that results in lower combustion efficiency.
Therefore, it is reasonable to start the rapid burning
period right at the top dead center, which maximizes the
useful work. In other words, when the spark timing is
advanced to the point where the maximum acceleration
point aligns with the top dead center, we can obtain the
most useful work out of the combustion process and we
achieve MBT timing.
2nd D erivative of Net Pressure (d 2P/d θ 2) for C ylinder #1
BMEP (psi)
38
2nd D erivative of Net Pressure (d 2P/d θ 2) for C ylinder #1
38.5
2nd D erivative of Net Pressure (d P /d θ 2) for C ylinder #1
39
2nd D erivative of Net Pressure (d 2P/d θ 2) for C ylinder #1
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MBT Spark Tim ing Search (1500 R PM, 2.62 Bar BMEP, 0% EG R )
0.8
ST = 22 o BTDC
ST = 24 o BTDC
0.6
ST = 26 o BTDC
ST = 28 o BTDC
0.4
ST = 30 o BTDC
0.2
0
-0.2
-0.4
-0.6
-0.8
-30
-20
-10
0
10
20
30
C rank Angle (D egree ATD C )
40
50
60
MBT Spark Tim ing Search (1500 R PM, 2.62 Bar BMEP, 5% EG R )
0.6
ST = 22 o BTDC
ST = 24 o BTDC
0.4
ST = 26 o BTDC
ST = 28 o BTDC
0.2
ST = 30 o BTDC
0
-0.2
-0.4
-0.6
-0.8
-30
-20
-10
0
10
20
30
C rank Angle (D egree ATD C )
40
50
60
MBT Spark Tim ing Search (1500 R PM, 2.62 Bar BMEP, 10% EG R )
0.5
ST = 22 o BTDC
0.4
ST = 24 o BTDC
ST = 26 o BTDC
0.3
ST = 28 o BTDC
ST = 30 o BTDC
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
-40
-30
-20
-10
0
10
20
C rank Angle (D egree ATD C )
30
40
50
60
MBT Spark Tim ing Search (1500 R PM, 2.62 Bar BMEP, 15% EG R )
0.4
ST = 22 o BTDC
ST = 24 o BTDC
0.3
ST = 26 o BTDC
ST = 28 o BTDC
0.2
ST = 30 o BTDC
0.1
0
-0.1
-0.2
-0.3
-0.4
-50
-40
-30
-20
-10
0
10
C rank Angle (D egree ATD C )
20
30
40
50
Figure 6 Net pressure acceleration at different EGR
rates
In Figure 7, acceleration curves for all four cylinders are
plotted for the two-liter four-cylinder engine operated at
3000 RPM with 7 bar BMEP. The IMEP reading for
cylinder one starts to drop at spark timing 24 oBTDC,
while the rest of the cylinders have not reached the
maximum IMEP. Therefore, setting the spark timing for
all cylinders at 24 oBTDC will limit the maximum torque
that can be delivered from the engine. Since cylinder
one starts to experience some minor knock, it would be
ideal for this cylinder to have later spark timing than the
rest of the cylinders, and the rest of the cylinders can
have slightly advanced spark timing to achieve the
maximum torque.
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Four C ylinder Net Pressure Acceleration (3000 RPM, 7.0 Bar BMEP, SA=24 o BTDC )
3
Cylinder
Cylinder
Cylinder
Cylinder
2
#1
#2
#3
#4
d 2P /d Θ 2
1
0
It is also worth mentioning that the method of finding
MBT timing developed in this study should be coupled
with knock detection to yield the best and safest spark
timing for the engine operation.
-1
-2
-3
-20
-10
0
10
20
30
Crank Angle (Degree ATDC)
40
50
60
Figure 7 Acceleration curves for individual cylinders
Figure 8 shows the net pressure and its derivatives for a
gasoline direct injection engine. The figure shows some
differences between PFI engine combustion and GDI
engine stratified combustion. For a GDI engine operated
in a stratified mode, the diffusion flame needs a very
short time to achieve the maximum acceleration. The
combustion happens extremely fast until about 70% of
fuel is consumed. Then the combustion becomes
relatively slow compared to the earlier part of the
process due to the leaner air-to-fuel mixture toward the
end of the combustion. For the first case, it only takes
about 10 degrees of crank angle to reach about 50%
burned, while it usually takes more than 30 degrees for a
PFI engine to reach 50% burned. For the engine
condition shown in Figure 8, the spark timing setting at
12 oBTDC is more reasonable because the majority of
the pressure increase happened after TDC.
D irect Injection Engine Stratified Mode (1300 RP M, 330 NMEP, SA=12 o B TDC )
2500
Net Pressure (Kpa) and Its Derivatives
2000
2nd D erivative (100 tim es)
Net Pressure
1st Derivative (20 tim es)
1500
1000
500
0
-500
-1000
-20
process of the combustion does not change, the
interaction between the combustion energy release and
the cylinder volume change will still be the same. For a
gasoline direct injection engine, if the multiple injection
schemes are not adopted, lining up the peak
acceleration point at the TDC will still yield the MBT
timing. However, this hypothesis needs to be validated
with the help of extensive test data.
-10
0
10
20
C rank Angle (Degree ATD C)
30
40
50
Figure 8 GDI engine net pressure and its derivatives
For any internal combustion engine, if the heat release
rate or the velocity of the net pressure has only one
peak, using the acceleration of pressure to determine
the MBT timing should work because the physical
process for the combustion is the same no matter how
fast the combustion develops. The whole process
always reaches the early maximum acceleration first,
then the peak velocity, and then the late minimum
acceleration. In other words, as long as the physical
AN MBT DETECTION ALGORITHM
In order to implement the MBT detection criterion using
the location of maximum acceleration (MAMFB), a
detection algorithm was developed. The MBT detection
algorithm can be divided into the following steps.
Step 1: Net Pressure Calculation
Net pressure is calculated based upon the sampled
pressure signal during engine compression and
expansion stroke, using the formulae defined in (Eq. 1)
and (Eq. 2). The purpose of using net pressure instead
of actual pressure is to exclude pressure variation due to
piston compression and expansion. A typical net
pressure curve can be found in Figure 4.
It is worth mentioning that the calculated net pressure
can be used to calculate mass fraction burned location.
For instance, 50% burn location can be found by
detecting the crank-angle when net pressure rises to
50% of its peak during compression and expansion
strokes.
Step 2: Double net pressure derivative calculation
Net pressure points between 15 oBTDC and 15 oATDC
are used to calculate the double net pressure derivative.
Due to the fact that derivative operation is very sensitive
to noise, a special filtering technique, called two-way low
pass filtering, is used along with the derivative
calculation. The off-line calculation between combustion
events makes it possible. A key factor in using this
filtering technique for double derivative calculation is
minimization of the phase shift, which is directly
associated with the accuracy of MBT timing detection.
The first derivative (difference) is calculated using the
following transfer function,
dPNET (z)
PNET (z)
= FB (z) ⋅ FF (z) ⋅ D(z)
=
1− a
1− a
⋅
⋅ ( 1 − z −1 ),
1 − a ⋅ z 1 − a ⋅ z −1
(Eq. 3)
where a is the digital filter parameter associated with the
low pass filter bandwidth, and FB(z), FF(z), and D(z) are
first order backward, first order forward, and first order
difference transfer functions, respectively. Note that the
complete transfer function can be rewritten as follows,
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dPNET ( z )
(1 − a) 2 ⋅ (1 − z −1 )
=
.
PNET ( z ) (1 + a 2 ) − a( z + z −1 )
(Eq. 4)
Similarly, the second derivative is defined as follows,
CONTROL ARCHITECTURE AND STRATEGY
= FB ( z ) ⋅ FF ( z ) ⋅ D ( z )
(Eq. 5)
1− a
1− a
=
⋅
⋅ (1 − z −1 ).
1 − a ⋅ z 1 − a ⋅ z −1
Note that the discrete transfer function of the two-way
low pass filtering algorithm can be lumped together as
follows,
GF ( z) =
1− a
1− a
(1 − a) 2
.
⋅
=
1 − a ⋅ z 1 − a ⋅ z −1 (1 + a 2 ) − a( z + z −1 )
(Eq. 6)
The Bode plot of the two-way filtering transfer function
FB(z)FF(z) is shown in Figure 9. It is clear that the first
order two-way filter is equivalent to a second order filter
without phase delay. Also notice that the two-way filter is
anti-causal (i.e., it can not be realized in real time since
the back filter uses future information), and the
combined two-way filtering transfer-function cannot be
used directly since it is an unstable filter transfer function
(one is inside the unit circle and one is outside the unit
circle, i.e., a and a-1). The two-way filter defined in (Eq.
6) can only be realized off-line to ensure a stable filtering
calculation, that is, filtering the raw signal using the first
order stable forward filter FF(z) defined in (Eq. 3),
reversing the order of the filtered signal, and then
filtering the reversed-order signal using the same
forward filter to have a stable backward filter. The last
two steps guarantee the numerical stability of backward
filtering.
The purpose of closed-loop MBT timing control is twofold: keeping the engine running at its MBT spark timing,
if it is not knock limited, and reducing the cycle-to-cycle
combustion variation through closed-loop spark timing
control. The closed-loop control architecture of MBT
timing is limited by knock constraints within engine
controller. Instead of controlling engine spark timing
using calibrated tables as function of engine speed,
load, etc., an engine ignition timing control is generated
by a closed-loop PI (Proportional and Integral) controller
using information derived from in-cylinder pressure as
the feedback signal.
In the rest of this paper, "closed-loop MAMFB MBT
timing controller" refers to the closed-loop MBT timing
controller using Maximum Acceleration location of Mass
Fraction Burned (MAMFB). "Closed-loop PCP MBT
timing controller" refers to the closed loop controller
using PCP location, and "closed-loop MFB50% MBT
timing controller" refers to the closed-loop controller
using 50% mass fraction burned (MFB50%). The results
of the three closed loop MBT timing controllers (MAMFB,
PCP, and MFB50%) will be compared.
Cylinder pressure
vector
Knock Intensity
Engine speed
and load
MBT estim ation
knock/m isfire detection
d 2 PNET ( z )
dPNET ( z )
For comparison purpose, two other MBT timing criteria
are used for closed-loop spark time control in this study.
They are 50% burn location (MFB50%) and Peak
Cylinder Pressure (PCP) location.
MBT
Reference
Advance
lim it
m anager
PI MBT
tim ing
controller
Lim it
m anagement
Desired
spark
tim ing
Retard
lim it
m anager
B od e Plo t of F irst O rd er T wo -W ay F ilter T ransfer F unctio n (R P M = 15 00 , a = 0 .9 )
Magnitude (db)
0
Figure 10 Closed-loop MBT timing control architecture
-2 0
-4 0
-6 0
1
10
10
2
10
3
10
4
Phase (deg)
1 00
50
Cylinder pressure vector:
0
-5 0
-1 00
1
10
The inputs to the closed-loop MBT timing controller are
the individual in-cylinder pressure signals, the
conditioned knock intensity signal, and the current
engine operational information such as the engine
speed, load, etc., see Figure 10.
10
2
10
3
10
4
Fre que ncy (Hz)
Figure 9 Bode diagram of two-way filter transfer function
Step 3: MAMFB location calculation:
After the double derivative is calculated using the twoway filter technique, the MAMFB location can be found
by locating the maximum over the double derivative
signal.
The individual cylinder pressure signal is sampled at a
one crank degree resolution for all cylinders. Only the
compresion and expansion cycles of the in-cylinder
pressures are sampled. The sampled cylinder pressure
signal is available for closed-loop control right after
engine expension stroke for each corresponding
cylinder.
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Conditioned knock intensity:
The knock intensity is calculated using cylinder pressure
signal over a specific window, typically right after the
peak cylinder pressure location. The pressure signal
over the knock window is filtered by a bandpass filter,
and then integrated using absolute value of the
bandpass filtered signal. Because knock frequency is
relatively high compared with one crank degree
sampling resolution at low engine speed, the knock
intensity is obtained through an analog circuit.
Engine speed and load:
Engine speed and load are lookup table inputs for
setting hard timing advance and retard limits for advance
and retard limit managers, see Figure 10.
For closed-loop MAMFB MBT timing control, the MBT
estimation block in Figure 10 calculates the engine net
pressure based upon (Eq. 1) and (Eq. 2). The calculated
net pressure is differentiated twice using (Eq. 3) and
(Eq. 4). Note that forward and backward filtering
techniques are used to reduce noise with minimal
filtering phase shift. Finally, the crank angle associated
with the maximum acceleration location of the net
pressure or mass fraction burned (also called MAMFB)
is calculated as the MBT feedback signal. For closedloop PCP MBT timing control, peak cylinder pressure
location is detected and used as the MBT feedback
signal, and for MFB50% control, 50% MFB location is
used as the MBT feedback signal.
The MBT estimation block also calculates the misfire
index using the calculated net pressure. Misfire of the
corresponding cylinder is declared if the net pressure is
below a threshold as a function of engine speed and
load. The knock index is determined using the knock
intensity input. Both advance and retard limit managers
use the engine knock and misfire index, obtained from
the MBT estimation block, to generate both advance and
retard timing bounds.
The closed-loop spark MBT timing control is realized
using a PI (Proportional and Integral) controller. The
error between MBT reference and the MBT feedback
signal is used as an input to the PI controller. The MBT
reference signal is a function of MBT timing control
method being tested. For MAMFB approach, the MBT
reference is zero, for PCP approach, MBT reference is
around 15 oATDC, and for 50% MFB approach, aound 9
o
ATDC.
The limit management block passes through the desired
ignition timing from PI controller if the signal is within the
advance and retard limits. Otherwise, the output of the
PI controller will be saturated by either the advance or
retard spark timing limit.
TEST CONFIGURATION
The closed-loop MBT timing controller was validated in
an engine dynamometer. A two-liter four-cylinder engine
was used for the validation test. The four-cylinder engine
was controlled by the dynamometer controller except for
engine spark timing. All engine sensors were connected
to the dynamometer controller. The dynamometer
controller controlled the engine throttle position, EGR
rate, and fuel injection. It also controlled the engine
speed and load. A dSpace PX-10 expansion box was
used for both open-loop and closed-loop spark timing
control. Kistler pressure sensors were installed in every
cylinder for estimating MBT criterion used for closedloop feedback control.
The dSpace PX-10 expansion box, used for closed loop
MBT timing control, consists of a main processor card, a
fast A/D card, a digital waveform capture card, and a
digital waveform output card.
The digital waveform capture card generates the
interrupt based upon the crankshaft encoder pulse, that
triggers the data sampling process. The interrupt also
calculates current crank angle, synchronized by the
camshaft sensor, to arrange the sampled pressure
signal into an array during compression and expansion
cycle of the corresponding cylinder. The crank angle
also generates software interrupt to enable combustion
event-based closed-loop spark control calculation.
The dSpace data sampling and control scheme is eventbased. The cylinder pressure signals are sampled every
crank-degree and the spark timing command is
calculated during exhaust stroke of the corresponding
cylinder to make sure that the spark control commands
are available at intake stroke for corresponding cylinder.
As a summary, two crank-based processes are running
in the dSpace main processor. The first runs every crank
angle that is trigged by crankshaft encoder, and the
second runs every 180 crank degrees (for a four cylinder
engine) that is trigged by the first crank based process
through software interrupt. The first process has a higher
priority than the second one so that the data sampling
and current crank angle calculation is guaranteed.
As mentioned before, the first process samples
individual cylinder pressure signals and arranges them
into a data array using compression and expansion
stroke data. The other main task is to send digital
ignition signal through the digital waveform output card
based upon the ignition command generated by the
closed-loop MBT timing control algorithm during the
second process.
The second dSpace process runs the closed-loop MBT
timing control strategy. For the two-liter four-cylinder
engine used for control concept validation, the closedloop MBT timing control algorithm, shown in Figure 10,
runs every 180 crank degrees.
The closed-loop MBT timing control strategy shown in
Figure 10 is implemented in Simulink environment
utilizing the dSpace hardware. The closed-loop MBT
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timing control strategy implemented in Simulink allows
controlling the MBT timing using three MBT timing
criteria as feedback signals. They are MAMFB, PCP,
and MFB50%. The purpose is to compare the test
results of the three closed-loop control approaches.
TEST RESULTS AND ANALYSIS
Before the closed-loop MBT timing control is evaluated,
the MAMFB MBT timing estimation is validated in
dynamometer tests. Figure 11 shows the three MBT
timing criteria with open-loop (or fixed) engine spark
timing control. The engine was running at 1500 RPM
with 34.5 NM load. The data shown in Figure 11 is 100
cycles of data for cylinder three only. It is obvious that
the engine is not running at its MBT timing since all three
MBT timing criteria show that the engine is almost three
degrees advanced from its MBT timing. For example,
the mean PCP location is around three degree ahead
from its MBT timing location (15 oATDC). The ranges of
three MBT timing criteria (PCP, MFB50%, and MAMFB)
vary over a 12 degree window for the 100 engine cycle
data shown in Figure 11.
(0.8920, 0.8926, 0.8798, and 0.9373) than PCP location
(0.8554, 0.8368, 0.7863, and 0.9018) for all four
cylinders. This implies that there is no significant
difference between MBT timing criteria PCP and
MFB50% locations and MAFMB criterion is less
correlated with the PCP and MFB50% criteria.
Figure 12 shows the responses of three MBT timing
criteria (PCP top line with "o", MFB50% middle line with
"U", and MAMFB bottom line with "¡") when the engine
ignition timing is controlled in a closed-loop manor using
MAMFB MBT timing criterion as feedback signal. Both
proportional and integral gains are set to 0.2. The engine
operation condition is the same as the open-loop control
case shown in Figure 11. It is clear that that with the
help of the closed-loop MBT timing control, the engine
operates at it MBT timing. This can be validated by
checking three MBT timing criteria shown in Figure 12.
The mean of three MBT timing criteria are 14.9, 9.14,
and 0 for PCP, MFB50%, and MAMFB locations,
respectively. That is close to desired location for all three
MBT timing criteria (PCP 15 oATDC, MFB50% 9 oATDC,
and MAMFB 0 oATDC).
15 00 R P M, 34.5 N-M, λ = 1.0, C L C ontrol
15 00 R P M, 34.5 N-M, λ = 1.0, ST = -30 o A T D C
40
C yl. #1 PCP, MFB50% , and MAMFB Location (o ATDC )
C yl. #1 PCP, MFB50% , and MAMBT Location (o ATDC )
20
P C P Location
MF B 50 % Lo catio n
MA MB T Location
15
10
5
0
-5
-10
30
20
10
0
-10
-20
0
10
20
30
40
50
60
E ng ine C yc le Num be r
70
80
90
10 0
Figure 11 MBT criteria based upon test data (open-loop)
P C P Loc ation
MF B 50 % Lo catio n
MA MB T Loc ation
0
50
10 0
15 0
20 0
E ng ine C yc le Num be r
25 0
30 0
Figure 12 Closed-loop controlled MBT criteria
Table 2 Correlation matrices of PCP, MFB50%, MAMFB
Cylinder #1
Cylinder #2
1.0000 0.9716 0.8554 1.0000 0.9589 0.8368
0.9716 1.0000 0.8920 0.9589 1.0000 0.8926
0.8554 0.8920 1.0000 0.8368 0.8926 1.0000
Cylinder #3
Cylinder #4
1.0000 0.9535 0.7863 1.0000 0.9753 0.9018
0.9535 1.0000 0.8798 0.9753 1.0000 0.9373
0.7863 0.8798 1.0000 0.9018 0.9373 1.0000
Closed-loop MBT timing control using the other two MBT
timing criteria PCP and MFB50% locations were also
conducted and similar response to Figure 12 were
obtained. The main difference is that the MBT reference
for MAMFB approach remains constant at zero for all
engine operational conditions, while the references for
the other two feedback criteria (PCP and MFB50%
locations) have to be adjusted for the test engine to
operate at its MBT timing over the whole engine speed
and load range.
Through observation of Figure 11 it is clear that three
MBT criteria are highly correlated. That is, when one
MBT timing criterion moves in an advance direction, the
other two follow. Table 2 shows the correlation matrices
of PCP, MFB50%, and MAMFB for all four cylinders. It is
clear that the highest correlation is between the PCP
and MFB50% for all cylinders (0.9716, 0.9589, 0.9535,
and 0.9753 for cylinders one to four), and MAMFB
location has higher correlation to MFB50% location
Another aspect of analyzing closed-loop control of
engine MBT timing is from a stochastic perspective. It is
well known that for a linear system with a stationary
stochastic process input, closed-loop controllers, such
as an LQG (Linear Quadratic Gaussian) controller, are
able to reduce system output variances. Figure 13
shows output variances of three MBT timing criteria for
both open-loop and closed-loop system using MAMFB
control. The engine operation condition is the same as
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the open-loop control case shown in Figure 11. It is clear
that closed-loop control using MAMFB MBT timing
criterion reduces all three MBT timing criteria variances
shown in Figure 13. One conclusion from Figure 13 is
that closed-loop MAMFB MBT timing control reduces
variances of PCP, MFB50%, and MAMFB locations,
hence, reduces combustion cycle-to-cycle variation.
O p en /clo sed -lo o p v arian ce co m p ariso n
Variances of PCP, M FB50%,
M AM FB Criteria
8
7
6
5
O p en-loop
4
CL - MAMFB
3
2
1
0
(PCP)
(MFB50% )
(MAMFB)
The same variances of three MBT timing criteria are
shown in Figure 14 for the case of closed-loop PCP
MBT timing control when the engine was operated at the
same condition as the closed-loop MAMFB MBT timing
control case shown in Figure 13 with the selected PI
control gains equal to half of MAMFB ones. It is clear
that the variance improvement is not uniform, compared
to the case of closed-loop MAMFB MBT timing control.
Figure 15 shows the same variances of three MBT
timing criteria for the case of closed-loop MFB50% MBT
timing control when the engine was operated at the
same condition as the closed-loop MAMFB MBT timing
control case shown in Figure 13 with the same PI control
gain as MAMFB case. Similar to the case of closed-loop
PCP MBT timing control, the variance improvement of
MBT criteria is not uniform.
Recall that, as illustrated in the correlation matrices of
Table 2, the MBT timing criteria PCP and MFB50%
locations have very high correlations (above 0.9535) for
all cylinders. It is not surprising that the performance of
both PCP and MFB50% MBT timing control is similar in
stochastic sense.
Figure 13 Open/closed-loop variance comp. (MAMFB)
Coola nt Te m p (o C)
CL M BT S T Co n tro l Usin g DDP
7
6
5
Cyl. #1
1
0
(MAMFB)
Figure 14 Open/closed-loop variance comparison (PCP)
Cyl. #3
O p en /clo sed lo o p v arian ce co m p ariso n
7
Cyl. #4
Variances of PCP, M FB50%,
M AM FB criteria
8
6
5
O p en -loop
4
CL - MFB50
36
50
R PM = 2 0 0 0 L o a d = 4 4 N -m
40
35
34
30
18
16
2
(MFB50% )
37
60
CL - PCP
3
(PCP)
38
O p en-loop
Ave ra ge
4
= 0 w / T ra n sie n t En g in e T e m p e ra tu re
70
20
Cyl. #2
Variances of PCP, M FB50%,
M AM FB criteria
8
ne t
80
C o o lan t T em p
33
MBT ST
0
2000
4000
6000
8000
32
10000
0
2000
4000
6000
8000
10000
0
2000
4000
6000
8000
10000
0
2000
4000
6000
8000
10000
0
2000
4000
6000
8000
10000
0
2000
4000
6000
En g in e Cycle #
8000
10000
M BT S T (o BTDC )
O p en /clo sed -lo o p v arian ce co m p ariso n
14
12
18
16
14
12
18
16
14
12
18
16
14
12
18
16
14
12
3
Figure 16 CL control for transient temperature (PCPL)
2
1
0
(PCP)
(MFB50%)
(MAMFB)
Figure 15 Open/closed-loop variance comp. (MFB50%)
The transient performance of closed-loop MBT timing
control was also studied. Figure 16 and Figure 17 show
the results of closed-loop MAMFB MBT timing control
during engine warm up process. The engine was
running at 2000 RPM with 44 NM load. The whole
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process lasted for about 10 minutes and resulted in ten
thousand engine cycles. The starting engine coolant
temperature is about 34 oC and the ending temperature
is about 78 oC. The top graphs of both Figure 16 and
Figure 17 show the relationship between engine coolant
temperature and engine MBT timing. In order to keep
the maximum acceleration location of mass fuel burned
at around TDC location, the ignition timing has to be
advanced to compensate relatively slow burn when
engine is cold. It is clear that during the ten-minute
warm-up process, the MBT timing controller moves the
spark timing in a retard direction from around 37 oBTDC
to 32 oBTDC. During this warm up process, the burn-rate
increases and the corresponding MBT spark timing
moves back in a retard direction.
38
37
60
36
50
R P M = 2000 L o ad = 44 N -m 35
40
34
30
Ave ra ge
Cyl. #1
14
12
10
8
6
Cyl. #2
20
14
12
10
8
6
14
12
10
8
6
14
12
10
8
6
C o o lan t T em p
0
2000
33
MBT ST
4000
6000
8000
M BT S T (o BTDC)
= 0 w / T ra n sie n t En g in e T e m p e ra tu re
70
14
12
10
8
6
Cyl. #4
ne t
80
Cyl. #3
Coola nt Te m p (o C)
CL M BT S T Co n tro l Usin g DDP
32
10000
0
2000
4000
6000
8000
10000
0
2000
4000
6000
8000
10000
0
2000
4000
6000
8000
10000
0
2000
4000
6000
8000
10000
mean MFB50% location of four cylinders, and the third
to sixth graphs from top shows the MFB50% locations
for cylinders one through four, respectively. The mean
value of MFB50% MBT criterion stays around 10 oATDC,
indicating that engine was operating at its MBT timing
during the transition. This shows that closed-loop MBT
timing control can be used to compensate the MBT
timing change during engine warm up process.
CONCLUSIONS
A new MBT timing criterion is developed using the
maximum acceleration location of mass fraction burned,
which is independent of the engine speed and load. The
concept has been validated over certain engine
operational range. The potential benefit of using this new
MBT criterion for closed-loop control is reduced
calibration and a reduced cycle-to-cycle variation. An
MBT timing detection algorithm is also developed
specially to handle the double derivatives required for
calculating the newly developed MBT timing criterion
(MAMFB). The special two-way (forward and backward)
filtering algorithm, combined with double derivative
calculation, improves numerical stability of the MBT
timing estimation algorithm.
Closed-loop MBT timing control were evaluated using
three different MBT timing criteria PCP, MFB50%, and
MAMFB locations. The engine ignition timing remains at
its MBT location when the engine is operated at the
steady condition for all three closed-loop controllers.
During engine warm up process, the closed-loop
MAMFB MBT timing controller keeps the engine
operated at its MBT timing. At the same time engine
MBT timing moves at the retard direction while the
engine coolant temperature increases.
ACKNOWLEDGMENTS
0
2000
4000
6000
En g in e Cycle #
8000
10000
Bruce Wang implemented closed-loop MBT timing
control strategy into dSpace and made dynamometer
engine tests possible.
REFERENCES
Figure 17 CL control for transient temperature (BL50%)
The five graphs below the top one of both Figure 16 and
Figure 17 validate that engine operates at its MBT
timing. Figure 16 shows both individual PCP location
and mean PCP locations of all four cylinders. The
second graph from top shows the mean PCP location of
four cylinders, and the third to sixth graphs from top
shows the PCP locations for cylinders one through four,
respectively. It can be observed that the mean PCP
location is between 15 and 16 oATDC during the engine
warm-up process. This indicates that the engine is
operating close to its MBT timing point.
Similar to Figure 16, Figure 17 shows both individual
MFB50% location and mean MFB50% locations of all
four cylinders. The second graph from top shows the
[1] J. D. Powell, M. Hubbard, and R. R. Clappier, Ignition
timing controls method and apparatus, US Patent
4063538, 1977.
[2] G. M. Rassweiler and L. Withrow, Motion picture of engine
flames correlated with pressure cards, SAE Transaction
(Vol. 42), pp185-204, May 1938.
[3] Mark C. Sellnau, Frederic A. Matekunas, Paul A. Battiston,
Chen-Fang Chang, and David R. Lancaster, Cylinderpressure-based engine control using pressure-ratiomanagement and low-cost non-Intrusive cylinder pressure
sensor, SAE 2000-01-0932, 2000.
[4] J. Cooper, Comparison between Mapping MBT versus
50% mass fraction burn MBT, Ford Motor Co. Report,
November, 1997.
[5] R. J. Hosey and J. D. Powell, Closed loop, knock Adaptive
Spark timing control based on cylinder pressure,
Transaction of ASME, Vol. 101, March, 1979,
[6] Kunifumi Sawamoto, Yoshiaki Kawamura, Toru Kita, and
Downloaded from SAE International by Brought To You Michigan State Univ, Saturday, April 04, 2015
Kenjiro Matsushita, Individual cylinder knock control by
detecting cylinder pressure, SAE 871911, 1987
[7] Yoshiaki Kawamura, Mamoru Shinshi, Hiroshi Sato,
Nobutaka Takahshi, and Masahiro Iriyama, MBT control
through individual cylinder pressure detection, SAE
881779, 1988.
[8] Rainer Muller, Martin Hart, Gerhard Krotz, Martin Eickhoff,
Anthony Truscott, Andrew Nobel, Claudio Cavalloni, and
Marco Gnielka, Combustion pressure based engine
management system, SAE 2000-01-0928, 2000.
[9] Lars Eriksson, Spark advance modeling and control, Ph.D.
Dissertation, Linkoping University, 1999.
DEFINITIONS, ACRONYMS, ABBREVIATIONS
MBT:
Torque
TDC:
o
ATDC:
o
BTDC:
PRM:
MFB:
BMEP:
IMEP:
EGR:
PFI:
GDI:
PCP:
MFB50%:
MAMFB:
PI:
A/D:
NM:
LQG:
Minimum
spark
advance
for
Best
Top Dead Center
Degrees After Top Dead Center
Degrees Before Top Dead Center
Pressure Ratio Management
Mass Fraction Burned
Brake specific Mean Effective Pressure
Indicated Mean Effective Pressure
Exhaust Gas Recirculation
Port Fuel Injection
Gasoline Direct Injection
Peak Cylinder Pressure
50% Mass Fraction Burned
Maximum Acceleration of Mass Fraction
Burned
Proportional and Integral
Analog to Digital
Newton Meter
Linear Quadratic Gaussian