Method of electronically controlling fuel injection for internal combustion engine

Fuel is injected in synchronism with the crank angle. In addition, an engine acceleration state is detected from the second-order differential value of the intake-pipe pressure, and the quantity of the asynchronous fuel injection in which fuel is injected in asynchronism with the crank angle is increased in an early stage of acceleration but is decreased after the early stage of acceleration. Moreover, no asynchronous injection is carried out in a low engine speed region. It is thereby possible to obtain an optimum air-fuel ratio in accordance with the engine acceleration state.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to a method of electronically controlling the 
fuel injection for an internal combustion engine, and more particularly, 
to a method of electronically controlling the fuel injection for an 
internal combustion engine adapted to perform a synchronous injection that 
fuel is injected at a predetermined period in accordance with the crank 
angle and an asynchronous injection that fuel is injected in asynchronism 
with the crank angle in acceleration. 
2. Description of the Prior Art 
Hitherto, such a fuel injection method is known that a fuel injection valve 
is provided on each of cylinders so as to project into an intake manifold, 
and signals fed from various sensors are processed by means of a 
microcomputer to judge an engine operating condition and inject fuel in 
amount in accordance with the operating condition. In this fuel injection 
method, a synchronous injection and an asynchronous injection are 
effected. The synchronous injection is such that fuel is injected into all 
cylinders simultaneously or for each specific cylinder at a predetermined 
period, while the asynchronous injection is such that fuel is injected in 
acceleration independently of the synchronous injection. More 
specifically, in the synchronous injection, a basic fuel injection pulse 
width is calculated in accordance with the engine load (the pressure in 
the intake pipe or the quantity of the intake air per revolution of the 
engine shaft) and the engine speed, as well as corrected by employing a 
partial lean correction coefficient, a feedback correction coefficient and 
other correction coefficient determined by the cooling water temperature 
or the like, thereby to obtain a fuel injection pulse width and a fuel 
injection valve is opened to inject fuel for a period of time 
corresponding to the fuel injection pulse width at a predetermined crank 
angle. On the other hand, the asynchronous injection during acceleration 
is effected in order to improve the engine responsiveness and the like 
during acceleration. In the asynchronous injection, a linear throttle 
sensor is attached which outputs a voltage as a linear function with 
respect to the throttle opening, and fuel is injected in accordance with 
the rate of change of the output voltage and that of the engine load 
independently of the synchronous injection. Since this asynchronous 
injection makes it possible to correct the air-fuel ratio during a 
transient period in the early stage of acceleration, driveability and the 
exhaust emission control are improved. 
In the above conventional fuel injection method, however, there is a 
disadvantage that in the case of acceleration from a light-load operation 
region, the intake-pipe pressure and the intake-air quantity exceedingly 
increase with a slight increase in the throttle opening, so that the 
air-fuel ratio during acceleration cannot be properly controlled in 
accordance with the acceleration state. 
SUMMARY OF THE INVENTION 
Accordingly, an object of the present invention is to provide a method of 
electronically controlling the fuel injection for an internal combustion 
engine, which makes it possible to improve the driveability and the 
exhaust emission control during acceleration of the engine by properly 
controlling the air-fuel ratio during acceleration in accordance with the 
acceleration state, thereby to obviate the above-mentioned disadvantage of 
the prior art. 
To this end, according to a first aspect of the present invention, there is 
provided a method of electronically controlling the fuel injection for an 
internal combustion engine wherein fuel is injected in asynchronism with 
the crank angle when a throttle valve is open and the first-order 
differential value of the engine load with respect to time takes a 
positive value, comprising the steps of: injecting a first quantity of 
fuel during the period from the point of time when the throttle valve at 
fully closed position is opened until a predetermined period of time has 
elapsed and when the second-order differential value of the engine load 
with respect to time is not less than a first reference value and the 
third-order differential value of the engine load with respect to time is 
not negative; and injecting a second quantity of fuel after the 
predetermined period of time has elapsed and when the second-order 
differential value is not less than a second reference value and the 
third-order differential value is not negative. In this case, the 
first-order differential value of the engine load with respect to time 
means the rate of change or quantity of change of the engine load with 
respect to a predetermined period of time; the second-order differential 
value of the engine load with respect to time means the quantity of change 
of the first-order differential value with respect to a predetermined 
period of time; and the third-order differential value of the engine load 
with respect to time means the quantity of change of the second-order 
differential value with respect to a predetermined period of time. 
According to the first aspect of the present invention, an engine 
acceleration state is detected from the second-order differential value of 
the engine load with respect to time, and the asynchronous injection is 
effected when the third-order differential value of the engine load with 
respect to time is not negative. It is, therefore, possible to obtain such 
a characteristic advantage that the asynchronous injection is effected 
only in the early stage of acceleration, and a proper air-fuel ratio can 
be obtained in accordance with the acceleration state. 
Further, according to a second aspect of the present invention, there is 
provided a method of electronically controlling the fuel injection for an 
internal combustion engine wherein fuel is injected in asynchronism with 
the crank angle when a throttle valve is open and the rate of change of 
the engine load takes a positive value, comprising the steps of: injecting 
a first quantity of fuel during the period from the point of time when the 
throttle valve at fully closed position is opened and until a 
predetermined period of time has elapsed and when the rate of change of 
the change rate of the engine load is not less than a first reference 
value; and injecting a second quantity of fuel after the predetermined 
period of time has elapsed and when the rate of change of the change rate 
of the engine load is not less than a second reference value. 
According to the second aspect of the present invention, an engine 
acceleration state is detected from the rate of change of the change rate 
of the engine load, and the fuel injection quantity is made to differ 
between the engine operation in the early stage of acceleration and that 
after the acceleration early stage. It is, therefore, possible to obtain 
such a characteristic advantage that an engine acceleration state can be 
detected with a high accuracy, and a proper air-fuel ratio can be obtained 
in accordance with the acceleration state. 
Furthermore, according to a third aspect of the present invention, there is 
provided a method of electronically controlling the fuel injection for an 
internal combustion engine wherein fuel is injected in asynchronism with 
the crank angle when a throttle valve is open and the rate of change of 
the engine load takes a positive value, comprising the steps of: obtaining 
a time based on the point of time when the throttle valve at fully closed 
position is open, as well as determining a reference value which is 
increased with the time; injecting a first quantity of fuel when the 
above-mentioned time is not exceeding a predetermined period time and the 
rate of change of the change rate of the engine load is not less than the 
reference value; and injecting a second quantity of fuel when the 
above-mentioned time exceeds the predetermined period of time and the rate 
of change of the change rate of the engine load is not less than the 
reference value. 
According to the third aspect of the present invention, an engine 
acceleration state is detected from the rate of change of the change rate 
of the engine load, and the reference value in the early stage of 
acceleration is made small, while the reference value after the 
acceleration early stage is made large. It is, therefore, possible to 
obtain such a characteristic advantage that the number of times of 
asynchronous injections in the acceleration early stage is increased, and 
a proper air-fuel ratio can be obtained in accordance with the 
acceleration state. 
Moreover, according to the present invention, the above-mentioned reference 
value is determined so as to be increased in accordance with a time based 
on the point of time when the throttle valve at fully closed position is 
opened, and further increased after the injection of fuel, thereby to 
effect the above-mentioned fuel injection control. Accordingly, the 
reference value is increased after the asynchronous injection, and hence, 
the number of times of asynchronous injections is reduced. Thus, it is 
possible to obtain a proper air-fuel ratio in accordance with the engine 
acceleration state. 
The above-mentioned engine load can be detected from the intake-pipe 
pressure, the intake-air quantity per revolution of the engine shaft, the 
throttle opening and the fuel injection pulse width. Further, in the 
present invention, it is preferable to set the first quantity as a 
predetermined quantity and increase the second quantity in accordance with 
the rate of change of the change rate of the engine load. In addition, the 
reference value may be further increased in the low engine speed region.

DETAILED DESCRIPTION OF THE INVENTION 
An example of an internal combustion engine (referred to as simply 
"engine", hereinafter) to which the present invention is applied will be 
described hereinunder in detail with reference to FIG. 1. An intake-air 
temperature sensor 2, which detects the temperature of the intake air and 
delivers an intake-air temperature signal, is provided on the downstream 
side of an air cleaner (not shown). On the downstream side of the 
intake-air temperature sensor 2 is disposed a throttle valve 4, which is 
equipped with a throttle switch 6 which is interlocked with the throttle 
valve 4 and adapted to be made ON when the throttle valve 4 is at fully 
closed position and made OFF when the throttle valve 4 is opened. On the 
downstream side of the throttle valve 4 is provided a surge tank 8, which 
is equipped with a pressure sensor 10 which detects the intake-pipe 
pressure on the downstream side of the throttle valve 4 and delivers an 
intake-pipe pressure signal. The surge tank 8 is communicated with a 
combustion chamber 14 in the engine through an intake manifold 12. The 
intake manifold 12 has a fuel injection valve 16 provided for each of 
cylinders. The combustion chamber 14 in the engine is communicated with a 
catalytic converter (not shown) filled with a three-way catalyst through 
an exhaust manifold. Further, the engine block is equipped with a water 
temperature sensor 20 which detects the temperature of water for cooling 
the engine and delivers a water temperature signal. The end of a spark 
plug 22 is projected into the combustion chamber 14 in the engine, and a 
distributor 24 is connected to the spark plug 22. The distributor 24 is 
provided with a cylinder discriminating sensor 26 and an engine speed 
sensor 28 each constituted by a pickup secured to the distributor housing 
and a signal rotor secured to the distributor shaft. The cylinder 
discriminating sensor 26 delivers a cylinder discriminating signal every 
720.degree. CA, for example, to a control circuit 30 constituted by a 
microcomputer or the like, while the engine speed sensor 28 delivers a 
crank angle signal every 30.degree. CA, for example, to the control 
circuit 30. In addition, the distributor 24 is connected to an ignitor 32. 
It is to be noted that a reference numeral 34 denotes an O.sub.2 sensor 
which detects the residual oxygen concentration in an exhaust gas and 
delivers an air-fuel ratio signal. 
The control circuit 30 includes, as shown in FIG. 2, a central processing 
unit (CPU) 36, a read-only memory (ROM) 38, a random-access memory (RAM) 
40, a backup RAM (BU-RAM) 42, an input/output port (I/O) 44, an 
anlalog-to-digital converter (ADC) 46 and buses, such as a data bus and a 
control bus for connecting these components to each other. Fed into the 
I/O 44 are the cylinder discriminating signal, the crank angle signal, the 
air-fuel ratio signal, and the throttle signal delivered from the throttle 
switch 6. Delivered from the I/O 44 are a fuel injection signal for 
controlling the opening/closing timings of the fuel injection valve 16 
through a driving circuit and an ignition signal for controlling the 
ON/OFF timings of the ignitor 32. Further, the intake-pipe pressure 
signal, the intake-air temperature signal and the water temperature signal 
are fed into the ADC 46 and converted into digital signals, respectively. 
The crank angle signal is fed into the I/O 44 through a waveform shaping 
circuit. From the crank angle signal, a digital signal representative of 
the engine speed is formed. The cylinder discriminating signal is fed into 
the I/O 44 in the same manner as the above and converted into a digital 
signal. The cylinder discriminating signal, together with the crank angle 
signal, is utilized to form an interruption request signal for calculation 
of a basic fuel injection pulse width, a fuel injection start signal and 
so forth. The ON/OFF signal from the throttle switch 6 is fed into a 
predetermined bit position in the I/O 44 and temporarily stored therein. 
Moreover, the I/O 44 is provided therein with a known fuel injection 
control circuit including a presettable counter and a register. The fuel 
injection control circuit forms, from binary data on the injection pulse 
width fed thereinto from the CPU 36, an injection pulse signal having the 
injection pulse width, and feeds the injection pulse signal to the fuel 
injection valves 16 successively or simultaneously, thereby to energize 
the injection valves 16. As a result, fuel in quantity in accordance with 
the pulse width of the injection pulse signal is injected synchronously or 
asynchronously. The ROM 38 has previously stored therein a main processing 
routine program, an interruption processing routine program for 
calculation of the fuel injection pulse width, an interruption processing 
routine program for calculation of coefficients, such as a partial lean 
correction coefficient, other programs, and various data necessary for 
each of the above operational processings. The ROM 38 further has 
previously stored therein data on first and second quantities, first and 
second reference values L.sub.1, L.sub.2 and so forth for the asynchronous 
fuel injection. In addition, a reference numenal 48 denotes a counter. 
The asynchronous injection routine in accordance with a first embodiment of 
the present invention will be explained hereinunder with reference to 
FIGS. 3 to 5. It is to be noted that since the synchronous injection 
routine is the same as the conventional one, the description thereof is 
omitted. Referring now to FIG. 3, which shows a main routine, a judgement 
is made in a step S2 as to whether the throttle switch 6 is ON or OFF, 
that is, whether the throttle valve is open or closed, in accordance with 
the throttle signal. If the throttle switch is ON, the process proceeds to 
a step S3 in which a flag XLL is reset, and then proceeds to the next 
routine. If the throttle switch is OFF, a judgement is made in a step S4 
as to whether the flag XLL, which is set when the throttle switch is OFF, 
is reset or not. If the flag XLL is set, the process proceeds to the next 
routine. If the flag XLL is reset, that is, if the throttle switch is ON 
the last time, the counter is cleared in a step S6, and the flag XLL is 
set in a step S8. Accordingly, the counter counts at all times and is 
cleared at the point of time when the throttle switch changes from ON to 
OFF. In other words, the counter counts a period of time based on the 
point of time when the throttle switch changes from ON to OFF, that is, 
the throttle valve at fully closed position is opened. 
FIG. 4 shows a routine for incrementing the counter every predetermined 
period of time. In this embodiment, the count C is incremented every 4 
msec in a step S12. It is to be noted that the overflow of the counter is 
prevented by limiting the count C by the counter to a maximum value MAX in 
a step S10 and a step S14. 
FIG. 5 shows a routine for calculating a pulse width TAU of the fuel 
injection signal in the asynchronous injection through judgement of an 
engine acceleration state. This routine is interrupted when the AD 
conversion of the intake-pipe pressure PM is completed. It is to be noted 
that the AD conversion of the intake-pipe pressure PM is executed every 12 
msec. In a step S16, calculation is carried out to obtain the difference 
between an intake-pipe pressure PMn measured this time and an intake-pipe 
pressure PMn-2 measured before the last time, that is, 24 msec before, to 
calculate the quantity of change of the intake-pipe pressure during 24 
msec, that is, the change rate .DELTA.PMn. This change rate .DELTA.PMn is 
equivalent to the first-order differential of the intake-pipe pressure PM 
with respect to time. In a step S18, calculation is carried out to obtain 
the difference between the change rate .DELTA.PMn calculated this time and 
the change rate .DELTA.PMn-1 calculated the last time, that is, 12 msec 
before to calculate the quantity of change in the change rate during 12 
msec, that is, the rate .DELTA..DELTA.PMn of change of the change rate of 
the intake-pipe pressure. This change rate .DELTA..DELTA.PMn is equivalent 
to the second-order differential of the intake-pipe pressure PM with 
respect to time. 
Accordingly, in the following description, the change rates .DELTA.PMn, 
.DELTA..DELTA.PMn will be referred to as "first-order differential value" 
and "second-order differential value", respectively. 
In a step S20, a judgement is made as to whether the throttle switch is ON 
or OFF, and a judgement is made in a step S22 as to whether the 
first-order differential value .DELTA.PMn of the intake-pipe pressure is 
negative or not. Only when the throttle switch is OFF and the first-order 
differential value .DELTA.PMn is not less than zero, the following steps 
are executed. Accordingly, when the first-order differential value 
.DELTA.PMn is negative, that is, during deceleration, no asynchronous 
injection is effected. In a subsequent step S24, a judgement is made as to 
whether the count C by the counter exceeds a predetermined value (six, for 
example) or not. If the count C is not exceeding six, the process proceeds 
to a step S26. If the count C exceeds six, the process proceeds to a step 
S30. 
In the step S26, a judgement is made as to whether the second-order 
differential value .DELTA..DELTA.PMn of the intake-pipe pressure is not 
less than the first reference value L.sub.1 (a positive value). Only when 
the second-order differential value .DELTA..DELTA.PMn is not less than the 
first reference value L.sub.1, the process proceeds to a step S28 in which 
the asynchronous injection pulse width TAU is set at a predetermined value 
(2 msec, for example). As a result, the first quantity of fuel 
corresponding to the asynchronous injection pulse width (2 msec) is 
asynchronously injected during an acceleration period from the point of 
time when the throttle valve at fully closed position is opened until a 
predetermined period of time (24 msec) has elapsed. 
In the step S30, on the other hand, a judgement is made as to whether the 
second-order differential value .DELTA..DELTA.PMn of the intake-pipe 
pressure is not less than the second reference value L.sub.2 (a positive 
value). Only when the second-order differential value .DELTA..DELTA.PMn is 
not less than the second reference value L.sub.2, the process proceeds to 
a step S32 in which the asynchronous injection pulse width TAU is 
determined by the following equation: 
##EQU1## 
It is to be noted that in the above equation the coefficients 0.51, 24 are 
determined through experiments, while the coefficient 1000 is a constant 
for converting the asynchronous injection pulse width TAU into a time in 
the unit of msec. As a result, after the above-mentioned predetermined 
period of time has elapsed, the second quantity of fuel is injected 
corresponding to the asynchronous injection pulse width TAU proportional 
to the second-order differential value .DELTA..DELTA.PMn of the 
intake-pipe pressure. 
It is to be noted that since the reference values L.sub.1, L.sub.2 are set 
to be positive, no asynchronous injection is carried out during the 
stationary traveling state (.DELTA.PM=0) and a slow acceleration 
(.DELTA.PM=constant) in which .DELTA..DELTA.PM is zero. 
A second embodiment of the present invention will be explained hereinunder. 
Since the main routine and 4 msec routine in accordance with this 
embodiment are the same as those shown in FIGS. 3 and 4, respectively, the 
description thereof is omitted. The ROM 38 has previously stored therein 
data on the first and second quantities for the asynchronous fuel 
injection and a map shown in FIG. 6. This map is employed for 
determination of a reference value L with respect to the count C by the 
counter for counting a period of time based on the point of time when the 
throttle valve at fully closed position is opened, and is determined so 
that the reference value L stepwisely increases as the count C increases. 
FIG. 7 shows a reference value processing routine for varying the reference 
value L in accordance with the engine speed NE. In a step S9, a judgement 
is made as to whether the engine speed NE is not less than a predetermined 
value (1,800 r.p.m., for example). Only when the engine speed is less than 
the predetermined value, the process proceeds to a step S11 in which a 
positive predetermined value A is added to the reference value L to 
increase the latter. This is intended to prevent the execution of any 
asynchronous injection in the low engine speed region, since the ripple of 
the intake-pipe pressure due to the fluctuation of the engine speed is 
large in the region, even during the stationary traveling state, not to 
mention a transient period of the engine. From this point of view, as 
shown in FIG. 6, the reference value L is increased in accordance with 
time from the point of time when the throttle switch changes from ON to 
OFF and further increased in the low engine speed region and is then 
stored at a given address in the RAM. 
FIG. 8 shows a routine for calculating the pulse width TAU of the fuel 
injection signal during the asynchronous injection through the judgement 
of an engine acceleration state. Since FIG. 8 is similar to FIG. 5, the 
like portions are denoted by the like reference numerals, and the 
description thereof is omitted. However, the routine in FIG. 8 is 
additionally provided with steps S25, S27 for reading out the reference 
value L from the RAM. Since the reference value L differs according to the 
count C by the counter, a reference value when C&lt;6 is defined as a first 
reference value L.sub.1, and a reference value when C.gtoreq.6 is defined 
as a second reference value L.sub.2. Increasing the reference value in the 
low engine speed region as described above prevents any asynchronous 
injection from taking place in the low engine speed region, resulting in 
an improvement in driveability. 
A third embodiment of the present invention will be explained hereinunder. 
Since the main routine and 4 msec routine in accordance with this 
embodiment are the same as those shown in FIGS. 3 and 4, respectively, the 
description thereof is omitted. The ROM 38 has previously stored therein 
data on the first and second quantities for the asynchronous fuel 
injection and the map shown in FIG. 6. 
FIG. 9 shows a routine for calculating the pulse width of the fuel 
injection signal in the asynchronous injection through the judgement of an 
engine acceleration state. Since FIG. 9 is similar to FIG. 5, the like 
portions are denoted by the like reference numerals, and the description 
thereof is omitted. However, FIG. 9 is additionally provided with steps 
S34, S36 and S38. It is to be noted that the reference values L.sub.1 and 
L.sub.2 for the steps S26 and S30 are obtained from the map shown in FIG. 
6 in the same manner as that in the second embodiment. 
In the step S34, a predetermined value (six, for example) is added to the 
count C obtained by the counter, and a judgement is made in a step S36 as 
to whether the count C exceeds a maximum value MAX or not. If the maximum 
value MAX is exceeded, the count C is set at the maximum value MAX in the 
step S38. Thus, since after the asynchronous injection is executed in the 
steps S28 and S32, the count C by the counter is incremented and the 
reference value is set so as to increase in accordance with the count C, 
the reference value is consequently increased after the asynchronous 
injection, so that the number of times of asynchronous injections is 
reduced with the elapse of time. 
FIG. 10 shows the change with time of the throttle opening, the actual 
intake-pipe pressure P, the intake-pipe pressure PM detected by the 
pressure sensor, the first-order differential value .DELTA.PM of the 
intake-pipe pressure PM, the second-order differential value 
.DELTA..DELTA.PM of the intake-pipe pressure PM and the driving voltage 
for the fuel injection valve during an engine acceleration in each of the 
above-described embodiments. During the period when the driving voltage is 
at a low level, the fuel injection valve is maintained at open position to 
inject fuel. When acceleration of the engine is started at a time t.sub.1, 
the throttle opening increases from 0.degree.. Consequently, the actual 
intake-pipe pressure P increases, and the intake-pipe pressure PM as a 
value detected by the pressure sensor also increases. The intake-pipe 
pressure PM has an overshoot. A pulse Ib represents a synchronous 
injection in which fuel is injected in synchronism with the crank angle. 
The synchronous injection quantity corresponds to a quantity obtained by 
correcting the basic injection quantity, which is determined in accordance 
with the intake-pipe pressure PM and the engine speed, by the 
engine-cooling water temperature and the like. A pulse Ic represents an 
asynchronous acceleration fuel injection effected with the execution of 
the step S28, in which a first quantity of fuel corresponding to the 
asynchronous injection pulse width (2 msec) is injected during the period 
after the throttle valve at fully closed position is opened until a 
predetermined period of time has elapsed and when .DELTA..DELTA.PMn is not 
less than the first reference value L.sub.1. A pulse Id represents an 
asynchronous acceleration fuel injection effected with the execution of 
the step S30, in which a second quantity of fuel corresponding to the 
asynchronous injection pulse width obtained in the step S32 is injected 
when .DELTA..DELTA.PMn is not less the second reference value L.sub.2 
after the asynchronous injection by the pulse Ic. Since .DELTA..DELTA.PM 
is larger than .DELTA.PM in rise at the start of acceleration, the start 
of acceleration can be speedily and accurately detected to effect the 
asynchronous acceleration fuel injection. In addition, since the increase 
in .DELTA..DELTA.PM excellently reflects the increase in the throttle 
opening, it is possible to effect the asynchronous acceleration fuel 
injection in accordance with the engine acceleration state. 
The following is the description of a fourth embodiment of the present 
invention. Since the main routine and 4 msec routine in accordance with 
this embodiment are the same as those in FIGS. 3 and 4, respectively, the 
description thereof is omitted. The ROM 38 has previously stored therein 
data on the first and second quantities for the asynchronous injection and 
the map shown in FIG. 6. 
FIG. 11 shows a routine for calculating the pulse width TAU of the fuel 
injection signal in the asynchronous injection through the judgement of an 
engine acceleration state as well as for calculating the acceleration 
correction coefficient ETC in the synchronous injection. This routine is 
interrupted when the AD conversion of the intake-pipe pressure PM is 
completed. It is to be noted that the AD conversion of the intake-pipe 
pressure PM is carried out every 12 msec. In a step S126, calculation is 
performed to obtain the difference between the intake-pipe pressure PMn 
measured this time and the intake-pipe pressure PMn-2 measured before the 
last time, that is, 24 msec before to calculate the quantity of change, 
that is, the change rate .DELTA.PMn of the intake-pipe pressure during 24 
msec. This change rate .DELTA.PMn is equivalent to the first-order 
differential of the intake-pipe pressure PM with respect to time. In a 
step S118, calculation is carried out to obtain the difference between the 
change rate .DELTA.PMn calculated this time and the change rate 
.DELTA.PMn-1 calculated the last time, that is, 12 msec before to 
calculate the quantity of change of the change rate, that is, the rate 
.DELTA..DELTA.PMn of change of the change rate of the intake-pipe pressure 
during 12 msec. This change rate .DELTA..DELTA.PMn is equivalent to the 
second-order differential of the intake-pipe pressure PM with respect to 
time. In a step S119, calculation is carried out to obtain the difference 
between the change rate .DELTA..DELTA.PMn calculated this time and the 
change rate .DELTA..DELTA.PMn-1 calculated the last time, that is, 12 msec 
before to calculate the quantity of change of the change rate, that is, 
the rate D3PMn of change of the change rate of the change rate of the 
intake-pipe pressure during 12 msec. This change rate D3PMn is equivalent 
to the third-order differential of the intake-pipe pressure PM with 
respect to time. 
In a step S120, a judgement is made as to whether the throttle switch is ON 
or OFF, and a judgement is made in a step S122 as to whether the 
first-order differential value .DELTA.PMn of the intake-pipe pressure is 
negative or not. Only when the throttle switch is OFF and the first-order 
differential value .DELTA.PMn is not less than 0, the following steps are 
executed. Accordingly, no asynchronous injection is effected when the 
first-order differential value .DELTA.PMn is negative, that is, during 
deceleration. In a subsequent step S124, a judgement is made as to whether 
the count C by the counter exceeds a predetermined value (six, for 
example) or not. If the count C is not exceeding six, the process proceeds 
to a step S126 in which the reference value L is set at one, and then 
proceeds to a step S130. If the count C exceeds six, in a step 128, a 
reference value L corresponding to the count is read out from the map in 
the ROM, and then the process proceeds to the step S130. Since this 
reference value L differs according to the count C by the counter as shown 
in FIG. 6, a reference value when C.ltoreq.6 is defined as L.sub.1, while 
a reference value when C&gt;6 is defined as L.sub.2. 
In the step S130, a judgement is made as to whether the second-order 
differential value .DELTA..DELTA.PMn of the intake-pipe pressure is not 
less than the reference values L.sub.1, L.sub.2. If the second-order 
differential value .DELTA..DELTA.PMn is not less than the reference values 
L.sub.1, L.sub.2, a judgement is made in a step S132 as to whether the 
third-order differential value D3PMn of the intake-pipe pressure is 
negative or not. Only when the third-order differential value D3PMn of the 
intake-pipe pressure is not negative, a judgement is made in a step S134 
as to whether the count C by the counter exceeds a predetermined value 
(six, for example) or not. 
When the count C is not exceeding six, the process proceeds to a step S136 
in which the asynchronous injection pulse width TAU is set at a 
predetermined value (2 msec, for example). As a result, the first quantity 
of fuel corresponding to the asynchronous injection pulse width TAU is 
asynchronously injected during an engine acceleration period from the 
point of time when the throttle valve at fully closed position is opened 
until a predetermined time (24 msec) has elapsed. 
On the other hand, when the count C exceeds six, process proceeds to a step 
S138 in which the asynchronous injection pulse width TAU is determined by 
the above-mentioned equation (1). 
As a result, the second quantity of fuel corresponding to the asynchronous 
injection pulse width TAU proportional to the second-order differential 
value .DELTA..DELTA.PMn of the intake-pipe pressure is injected after the 
predetermined period of time has elapsed. 
It is to be noted that since the reference value L is set to be positive 
and no asynchronous injection is effected when the third-order 
differential value D3PMn is negative, no asynchronous injection is 
conducted during the stationary travel (.DELTA.PMn=0) and a slow 
acceleration (.DELTA.PMn=constant) in which .DELTA..DELTA.PMn is zero, and 
after the acceleration early stage when D3PMn is negative. 
The synchronous injection in accordance with this embodiment will be 
described hereinunder. In this synchronous injection, fuel is injected 
from the fuel injection valve every crank angle of 360.degree., and the 
synchronous injection pulse width TAU therefor is determined by the 
following equation: 
EQU TAU=TP.times.f(k).times.(1+FTC) (2) 
where, TP represents a basic fuel injection time width determined by the 
intake-pipe pressure PM and the engine speed NE; f(k) a correction 
coefficient determined by the intake-air temperature signal, the air-fuel 
ratio signal, etc; and FTC a correction coefficient in acceleration of the 
engine. 
The acceleration correction coefficient FTC is determined by the following 
equation (3): 
EQU FTC=Max (FTCLL, FTCDDPM, FTCPM) (3) 
where, Max denotes a function representing a maximum value; FTCLL a 
constant acceleration coefficient at the point of time when the throttle 
switch changes from ON to OFF; FTCDDPM an acceleration coefficient with 
respect to the second-order differental value .DELTA..DELTA.PMn; and FTCPM 
an acceleration coefficient with respect to the first-order differential 
value .DELTA.PMn. The acceleration coefficients ETCDDPM, FTCPM are 
determined by the following equations, respectively: 
EQU FTCDDPM=.SIGMA..DELTA..DELTA.PMn.times.KTC (4) 
EQU FTCPM=.SIGMA..DELTA.PMn.times.KTC (5) 
In addition, the above-mentioned constant KTC is varied so as to decrease 
as the engine-cooling water temperature T rises, as shown in FIG. 12. This 
constant KTC is previously stored in the ROM in the form of a map. 
It is to be noted that the above-mentioned acceleration coefficients FTCLL, 
FTCDDPM, FTCPM are attenuated with time. 
As the result of determination of the acceleration correction coefficient 
FTC as described above, the correction coefficient FTC becomes equal to 
the acceleration coefficient FTCLL at the point of time when the throttle 
valve changes from ON to OFF, and is then varied in accordance with the 
second-order differential value .DELTA..DELTA.PMn as well as the 
engine-cooling water temperature, and the first-order differential value 
.DELTA.PMn as well as the engine-cooling water temperature. 
After the execution of the above-described asynchronous injection, in a 
step S140 shown in FIG. 11, the correction coefficient FTC for the present 
acceleration is obtained by adding the correction coefficient FTC for the 
previous acceleration to a value obtained by multiplying the constant KTC 
read out from the map in the ROM in accordance with the engine-cooling 
water temperature T and the second-order differential value 
.DELTA..DELTA.PMn of the intake-pipe pressure obtained in the step S118. 
Then, the fuel injection pulse width TAU in the synchronous injection is 
obtained through the above-mentioned equation (2) to inject fuel. It is to 
be noted that this synchronous injection is applicable to the first 
embodiment to the third embodiment. 
FIG. 13 shows the change with time of the throttle opening, the actual 
intake-pipe pressure P, the intake-pipe pressure PM detected by the 
pressure sensor, the first-order differential value .DELTA.PM of the 
intake-pipe pressure PM, the second-order differential value 
.DELTA..DELTA.PM of the intake-pipe pressure PM, the third-order 
differential value D3PM, the correction coefficient FTC and the driving 
voltage for the fuel injection valve during acceleration of the engine in 
this embodiment. During the period when the driving voltage is at a low 
level, the fuel injection valve is maintained at open position to inject 
fuel. When acceleration of the engine is started at a time t.sub.1, the 
throttle opening increases from 0.degree.. In consequence, the actual 
intake-pipe pressure P increases, and the intake-pipe pressure PM as a 
value detected by the pressure sensor also increases. The intake-pipe 
pressure PM has an overshoot. A pulse Ia represents an asynchronous 
acceleration fuel injection effected when the throttle switch changes from 
ON to OFF. A pulse Ib represents a synchronous acceleration fuel injection 
carried out when it is corrected by the acceleration coefficient FTCDDPM. 
In addition, a pulse Ic represents an asynchronous acceleration fuel 
injection conducted with the execution of the steps S136 and S138. Since 
.DELTA..DELTA.PM is larger than .DELTA.PM in rise at the start of 
acceleration, the start of acceleration can be speedily and accurately 
detected to carry out the asynchronous acceleration fuel injection. 
Further, since the increase in .DELTA..DELTA.PM excellently reflects the 
increase in the throttle opening, it is possible to effect the 
asynchronous acceleration fuel injection in accordance with the engine 
acceleration state. 
It is to be noted that although in each of the above embodiments the 
invention has been described through the engine in which the basic fuel 
injection quantity is calculated based on the intake-pipe pressure and the 
engine speed, the invention is applicable to an engine in which the basic 
fuel injection quantity is calculated based on the intake-air quantity Q 
per revolution of the engine shaft and the engine speed. In this case, 
PMn, .DELTA.PMn, .DELTA..DELTA.PMn and D3PMn are replaced by Qn, 
.DELTA.Qn, .DELTA..DELTA.Qn and D3Qn, respectively. In addition, it is 
also possible to determine the asynchronous injection timing from the 
differential value of function with the throttle opening and the fuel 
injection pulse width taken as variables, in the same manner as that in 
the described embodiment. 
Since each of the described embodiments does not employ any linear throttle 
sensor but a contact-type throttle sensor, the structure is simplified and 
the cost is reduced, advantageously. Moreover, driveability is improved, 
since the synchronous acceleration fuel injection quantity is increased in 
accordance with the second-order differential value of the intake-pipe 
pressure in the cold state of the engine.