JPH0942066A - Method and device for recirculating exhaust gas - Google Patents

Abstract

PROBLEM TO BE SOLVED: To control an EGR rate by accurately detecting oxygen concentration, and performing feedback control based on this detection. SOLUTION: A device comprises an exhaust gas recirculation means 3 for recirculating partly exhaust gas to an intake system 2, oxygen concentration sensor 5 provided in an exhaust passage 4 to detect oxygen concentration in exhaust gas and an exhaust pressure sensor 6 provided in the vicinity of the oxygen concentration sensor 5 to detect an exhaust gas pressure, and an oxygen concentration detection value VR detected by the oxygen concentration sensor 5 is corrected by an exhaust pressure detection value PT in the exhaust pressure sensor 6. A control means 7, actuating the exhaust gas recirculating means 3 so that this oxygen concentration correction value V obtains target oxygen concentration Vs of an optimum EGR rate determined in accordance with an engine operating condition, is provided.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an exhaust gas recirculation method and apparatus for appropriately controlling the exhaust gas recirculation rate of an internal combustion engine.

[0002]

2. Description of the Related Art A conventional exhaust gas recirculation system (EG
In R), in order to obtain a preset exhaust gas recirculation rate (EGR rate) depending on engine operating conditions, the EGR valve provided in the exhaust gas recirculation path is controlled by a duty solenoid, or the solenoid valve is controlled electronically. By doing so, the opening degree of the EGR valve is controlled. Further, it is difficult to finely control the opening degree of the EGR valve in accordance with the engine operating state that fluctuates greatly, because it is difficult from the structural aspect of the EGR valve. By controlling both the EGR valve opening and the EGR valve opening,
It has also been proposed to widen the range of R ratio control (for example, Japanese Utility Model Laid-Open No. 59-56364).

[0003]

By the way, the conventional EGR
The rate control only controls the operation of the valve, and in order to perform EGR with higher accuracy, it is necessary to detect the EGR rate and correct the opening of the EGR valve or the like based on the signal. In order to detect the EGR rate, it is conceivable to measure the oxygen concentration in the exhaust gas with an O ₂ sensor (for example, JP-A-58-140461 and JP-A-63).
-94061, Japanese Patent Laid-Open No. 2-118858, etc.). However, the O ₂ sensor has a large pressure dependency, and when the exhaust pressure becomes high, the oxygen concentration becomes large.
Particularly in a system with an exhaust throttle valve, the exhaust pressure is higher and fluctuates, which makes it more difficult to accurately measure the oxygen concentration by the O ₂ sensor.

[0004]

In order to solve the above-mentioned problems, the present invention provides an optimum EGR according to the operating condition of the engine.
A method of recirculating exhaust gas so that the exhaust gas recirculates so that the oxygen concentration in the exhaust gas and the exhaust pressure are detected, and the oxygen concentration detection value is corrected by the exhaust pressure detection value. The exhaust gas recirculation is feedback-controlled based on the concentration correction value. By this method
The EGR rate can be controlled by accurately detecting the oxygen concentration and performing feedback control based on the detected oxygen concentration. Further, the present invention is an apparatus for carrying out this method, comprising an exhaust gas recirculation means for recirculating a part of exhaust gas to an intake system, and an oxygen recirculation device provided in an exhaust passage for detecting an oxygen concentration in exhaust gas. An oxygen concentration sensor, an exhaust pressure sensor for detecting exhaust pressure provided near the oxygen concentration sensor, and an oxygen concentration detection value detected by the oxygen concentration sensor are corrected by the exhaust pressure detection value by the exhaust pressure sensor. And a control means for operating the exhaust gas recirculation means so that the oxygen concentration correction value becomes the target oxygen concentration of the optimum EGR rate determined according to the operating state of the engine.

When exhaust gas recirculation of the internal combustion engine is performed by the exhaust gas recirculation device of the above-mentioned means, the control means determines the target oxygen concentration which becomes the optimum EGR rate according to the operating state of the engine, and The detected oxygen concentration value is corrected by the detected exhaust pressure value to obtain an oxygen concentration correction value. Then, the exhaust gas recirculation means is feedback-controlled so that the oxygen concentration correction value becomes the target oxygen concentration. As the control means, an engine control module including a storage section, a calculation processing section, etc. is used. The exhaust gas recirculation means is composed of a single EGR valve or an EGR valve and an exhaust throttle valve. For driving the EGR valve, a duty solenoid valve or the like for controlling the opening thereof in multiple stages is used, and for driving the exhaust throttle valve, Japanese Patent Laid-Open No. 12910/1993.
A multistage air cylinder as disclosed in Japanese Patent No. 9 is used. A sensor using a zirconia element or the like is used as the oxygen concentration sensor. As the exhaust pressure sensor, a strain gauge or the like that detects the absolute pressure in the exhaust passage is used. A rotation speed sensor, a load sensor, a timing sensor, etc. are used to grasp the operating state of the engine.

[0006]

BEST MODE FOR CARRYING OUT THE INVENTION Next, embodiments of the present invention will be described in detail with reference to the accompanying drawings. FIG. 1 shows an exhaust gas recirculation device to which the present invention is applied. This exhaust gas recirculation device is provided in an exhaust gas recirculation means 3 for recirculating a part of exhaust gas of the engine 1 to an intake pipe 2 which is an intake system, and an exhaust pipe 4 which defines an exhaust passage, and oxygen in the exhaust gas is provided. An oxygen concentration sensor 5 for detecting the concentration, and an exhaust pressure sensor 6 provided near the oxygen concentration sensor 5 for detecting the pressure of exhaust gas.
And an engine control module (ECM) 7 that feedback-controls the exhaust gas recirculation means 3 based on the outputs of these sensors 5 and 6.

The exhaust gas recirculation means 3 connects the exhaust pipe 4 and the intake pipe 2 to an EGR pipe 8 which defines a recirculation path of exhaust gas, and E
It is composed of an EGR valve 9 provided in the middle of the GR pipe 8 and a butterfly type exhaust throttle valve 10 provided in the exhaust pipe 4. The EGR valve 9 includes a housing 11 that defines a gas passage 61 that is appropriately bent, and the gas passage 6 of the housing 11.
1 and a valve body 12 which is seated on a valve seat portion formed in No. 1, and is provided with an actuator 13 for opening and closing the valve body 12. The actuator 13 is the rod 1 of the valve body 12.
It comprises a diaphragm 15 connected to the head of No. 4 and a case 16 which defines a control pressure chamber 75 for operating the diaphragm 15 by positive pressure. Case 1 has piston 1
A spring 17 for urging the valve 5 in the valve closing direction is provided, and an air tank 18 is provided to drive the valve 5 in the valve opening direction.
An air pipe 19 that guides the compressed air from is connected. The duty solenoid valve 2 is provided in the middle of the air pipe 19.
0 is provided. Duty solenoid valve 20
Is designed to control the driving force of the actuator 13, that is, the lift amount (opening degree) of the valve body 12 in 10 steps by changing the air pressure step by step according to the duty ratio of the supplied current. The exhaust throttle valve 10 is provided on the downstream side of the branch position of the exhaust pipe 4 with the EGR pipe 8, and its opening is adjusted stepwise by expansion and contraction of the multistage air cylinder 21. The multi-stage air cylinder 21 is provided with three ports 22, and by opening and closing the solenoid valve 23, compressed air from the air tank 18 is supplied to each port 22, so that the piston rod 24 advances and retreats in eight stages, and exhaust air is exhausted. The opening of the throttle valve 10 is changed.

The oxygen concentration sensor 5 is formed of a zirconia element, generates an electromotive force according to the difference in oxygen concentration between standard air and exhaust gas, and corresponds to the detected oxygen concentration as shown in FIG. and it outputs an electrical signal (sensor real output V _R). The exhaust pressure sensor 6 is a strain gauge that converts the deformation of the pressure receiving portion such as a semiconductor into an electric signal and outputs the electric signal, and detects the absolute pressure in the exhaust pipe 4 (exhaust pressure detection value P _T). ).

[0009] Engine control module 7 includes an input unit 25 for inputting the detected value of the oxygen concentration sensor 5 and the exhaust pressure sensor 6, the exhaust pressure oxygen concentration value detected by the oxygen concentration sensor 5 (V _R) by the exhaust pressure sensor 6 The oxygen concentration correction value V and the target oxygen concentration (optimum EGR rate) V _S are compared with each other by the detection value P _T , and the duty solenoid valve 20 and the solenoid valve 23 are output via the output unit 26.
It is mainly configured by an arithmetic processing unit 27 that operates the. A rotation speed sensor 28, a load sensor 29, and a timing sensor 30 for detecting the engine operating state are connected to the input unit 25. The rotation speed sensor 28 is
The pickup is arranged so as to face the crank gear 31, and one rotation of the crank outputs pulses corresponding to the number of teeth of the crank gear 31 (engine speed Ne). The load sensor 29 is a potentiometer that detects the amount of displacement of the control lever 33 of the fuel injection pump 32, and outputs an electric signal (load L) corresponding to the engine load. The timing sensor 30 is arranged to face the timing plate 34 mounted on the cam shaft of the fuel injection pump 32, generates a pulse at the compression top dead center of each cylinder, and detects the compression top dead center of each cylinder. It is like this. The arithmetic processing unit 27 is provided with a first storage unit (ROM) 35 provided with maps I, II and III for determining the valve opening and correction of detected values, and memories I and II for feedback control. Second storage unit (RAM) 36
Are provided, and the opening degree of the exhaust throttle valve 10 and the EGR valve 9 is controlled by these maps and memory.

As shown in FIG. 4, the map I is a combination of the basic openings m and n of the exhaust throttle valve 10 and the EGR valve 9 in the EGR region (hatched portion) determined by the load L and the engine speed Ne. Is written. Further, in map II, as shown in FIG. 5, in the EGR region (hatched portion) determined by the load L and the engine speed Ne, the oxygen concentration corresponding to the target EGR rate, that is, the target of the oxygen concentration sensor 5 is shown. The output (target oxygen concentration V _S ) is written. And Map III
6, the relationship between the exhaust pressure ΔP and the oxygen concentration sensor output correction amount ΔV, which is a positive correlation, is written. Further, in the memory I, the basic opening m, n of the exhaust throttle valve 10 and the EGR valve 9 thus obtained are written, and when the control is executed, it is compared with the control immediately before that and a different basic opening is performed. If it is degree, it is updated to that value. In the memory II, the execution openings M and N of the exhaust throttle valve 10 and the EGR valve 9 are written, and the values are updated to the values after executing the control.

Next, the exhaust gas recirculation method of the present invention will be described assuming that the EGR control is performed by the above-mentioned exhaust gas recirculation device. As shown in FIG. 2, the engine control module 7 first detects each sensor 28, 29, 5, 6
The engine speed Ne, the load L, the oxygen concentration sensor actual output V _R , and the exhaust pressure sensor detection value P _T, which are the detection values from, are input (ST 1). Previous next from the map I, reads the basic opening n ₁ of basic opening m ₁ and the EGR valve 9 of the exhaust throttle valve 10 corresponding to the detected load L and the engine speed Ne (ST 2), from memory I Exhaust throttle valve 10 under control of
The basic opening m ₀ and the basic opening n ₀ of the EGR valve 9 are read (ST 3). And these basic openings m ₁ , m ₀ ,
It is determined whether n ₁ and n ₀ are equal to each other (ST 4).
If they are different, the basic opening m is used as the execution opening M of the exhaust throttle valve 10 and the basic opening n is used as the execution opening N of the EGR valve 9 (ST 5), which is stored in the memory I. The basic openings m ₀ and n ₀ are replaced with these basic openings m ₁ and n ₁ (ST 6), and drive signals corresponding to these execution openings M and N are supplied to the solenoid valve 23 and the duty solenoid valve 20, respectively. Output (ST21). The duty solenoid valve 20 supplies compressed air corresponding to the current duty ratio as a drive signal to the actuator 13,
The valve 9 is operated so as to reach its execution opening N. The solenoid valve 23 is opened and closed to open the multi-stage air cylinder 21.
The exhaust air throttle valve 10 is operated so as to reach the execution opening degree M by appropriately introducing compressed air into the port 22 of the above. Then, the previous execution openings M ₀ and N ₀ stored in the memory II are replaced with the execution openings M ₁ and N ₁ of this time (ST22), and the next control is executed.

Further, in the comparison judgment (ST 4) of the basic opening m, n, when the basic opening m ₀ , n ₀ of the previous control and the basic opening m ₁ , n _{1 of the present} control are equal, Basic opening m
It is checked whether the EGR rate by the control based on ₀ or n ₀ is the target EGR rate. In this inspection, first, the previous execution openings M ₀ and M ₀ are read from the memory II (ST 7), and the target EGR rate (V _S ) is read from the map II (ST 8). Then, by subtracting the atmospheric pressure P _O from the output value (P _T ) of the exhaust pressure sensor 6, the actual exhaust pressure ΔP
(= _{PT- PO} ) is calculated (ST9). Then Map III
The oxygen concentration sensor output correction amount ΔV corresponding to the exhaust pressure ΔP is obtained (ST10), and the actual output V _R of the oxygen concentration sensor 5 is calculated.
This output correction amount ΔV is subtracted from
(= V _R -ΔV) to calculate the (ST11). Then, this oxygen concentration correction value V is compared with the target oxygen concentration V _S (ST1
2). As a result of this comparison, if they are equal (V =
V _S), is regarded that there is no need for modifications, by directly using run opening M _0, M ₀ of the previous control as executed opening M _1, N ₁ of the current control (ST13), they perform opening M ₁ , N ₁ is output to maintain the previous control (ST21), and the execution openings M ₀ and M ₀ of the memory II are updated (ST22).

Comparison judgment of oxygen concentrations V and V _S (ST12)
If the two are different from each other, it is further judged which is larger (ST14). If the oxygen concentration correction value V is smaller than the target oxygen concentration V _S (V <V _S ), EGR
If the rate is considered to be excessive, it is possible to reduce the previous execution opening degree N ₀ of the EGR valve 9, that is, the opening degree "1".
Is larger (ST15), and if it is larger (N ₀ > 1), the execution opening M ₀ of the exhaust throttle valve 10 is left as it is and the execution opening N ₁ of the EGR valve 9 is set. Decrease by one step from the previous execution opening N ₀ (ST16). This execution opening N ₁
By driving corresponding to (= N ₀ −1) (ST21), EGR
The valve body 12 of the valve 9 operates toward the closing side, the opening degree thereof becomes small, and the recirculation amount of exhaust gas is reduced. If the previous execution opening of the EGR valve 9 is "1", E
The execution opening N ₁ of the GR valve 9 remains the previous opening N ₀ , and the execution opening M ₁ of the exhaust throttle valve 10 is changed to the previous execution opening M _0.
Lower by one step (ST17). This execution opening M ₁ (= M
By opening and closing the solenoid valve 23 corresponding to ₀ −1) (ST21),
The multi-stage air cylinder 21 is driven in one stage and the exhaust throttle valve 1
The throttle of 0 is relaxed, the amount of exhaust gas guided from the exhaust pipe 4 to the EGR pipe 8 is reduced, and the recirculation amount is reduced. Further, the execution openings M ₀ and M ₀ of the memory II are updated (ST2
2).

Then, the oxygen concentration correction value V and the target oxygen concentration V
_If the oxygen concentration correction value V is larger than the target oxygen concentration V _S (V> V _S ) in the determination of the magnitude of _S (ST14), EG
Considering that the R ratio is insufficient, it is judged whether or not it is possible to increase the execution opening degree N ₀ of the EGR valve 9 at the previous time, that is, it is smaller than the opening degree "10" (ST18). If so (N ₀ <10), the execution opening M ₀ of the exhaust throttle valve 10 is left unchanged and the execution opening N ₁ of the EGR valve 9 is raised by one step from the previous execution opening N ₀ (ST19). This execution opening N
By driving ₁ (= N ₀ +1), the opening degree of the EGR valve 9 is increased and the recirculation amount of exhaust gas is increased. If the previous execution opening of the EGR valve 9 is "10", E
The execution opening degree N ₁ of the GR valve 9 is left unchanged, and the execution opening degree M ₁ of the exhaust throttle valve 10 is raised by one step from the previous execution opening degree M ₀ (ST20). The exhaust throttle valve 10 is throttled by the drive (ST21) corresponding to this execution opening M ₁ (M ₀ +1), and E
The amount of exhaust gas guided to the GR pipe 8 increases, and the exhaust gas recirculation amount increases. Then, the execution openings M ₀ and M ₀ of the memory II are updated (ST22). The above control is repeatedly executed each time a pulse is input from the timing sensor 30, that is, each cylinder reaches the compression top dead center.

As described above, the oxygen concentration and pressure in the exhaust gas are measured by the oxygen concentration sensor 5 and the exhaust pressure sensor 6, and the detected oxygen concentration value V _R is the output correction amount ΔV determined by the exhaust pressure ΔP. Since the EGR rate is feedback-controlled based on the calculated oxygen concentration correction value V, the actual oxygen concentration can be calculated even if the oxygen concentration sensor 5 affected by the exhaust pressure change due to the exhaust throttle is used. It can be accurately grasped and the valve opening control according to the operating state can be executed. That is, the optimum EGR rate according to the engine operating state can be realized, and NOx reduction of exhaust gas can be reliably achieved.

Further, in this embodiment, in the feedback control, the valve opening N of the EGR valve 9 is first adjusted,
Since only the EGR valve 9 was set to operate the exhaust throttle valve 10 when not reached the target value (V _S), without the exhaust gas pressure varies excessively, stable control is achieved.

Next, referring to FIG. 7, an example of the EGR valve 9 in FIG. 1 will be described in detail. A valve seat 62 serving as a valve seat portion is provided in the housing 11 that defines the gas passage 61, and the outer peripheral edge of the valve body 12 is seated on the inner side surface of the valve seat 62. The rod 14 attached to the valve body 12 extends along the axial direction, and
Through the insertion hole 63 formed in the actuator 13
The case 16 is extended. A bush 65 that slidably holds the rod 14 is provided in the insertion hole 63, and a filter 66 that is separated from the gas passage 61 is provided below the bush 65.
Is attached. The case 16 is formed by joining the upper case 16a and the lower case 16b to each other with bolts 68 at the flange 67, and the peripheral edge of the diaphragm 15 is sandwiched between the joint surfaces. A cylindrical portion 76 that guides the rod 14 is erected on the bottom surface of the lower case 16b, and a bush 64 is provided at the tip thereof. A spring guide 69 for holding one end of the spring 17 is provided on the outer bottom surface of the cylindrical portion 76. Further, a bolt hole is formed on the bottom surface, and the case 16 is attached to the housing 11 with a bolt 70 passing therethrough. A spring holder 71 sandwiched vertically in the axial direction is provided at the axial center position of the diaphragm 15, and the spring 17 is interposed via the spring holder 71.
The other end of is abutted. Further, the head of the rod 14 penetrates the diaphragm 15 and the spring holder 71, and is nut-fastened to them. Air A on the upper case 16a
A nipple 72 that serves as an inlet for
A position sensor 73 for detecting the position of the rod 14 (valve body 12) is provided. Position sensor 7
3 is attached by a screw 78 via a flange plate 77. A nipple 74, which serves as a discharge port for closing the quick valve, is provided at a position opposite to the introduction port, and is normally closed by an electromagnetic valve (not shown). With such a configuration, the air pressure supplied to the control pressure chamber 75 is changed stepwise, the diaphragm 15 is deformed according to the air pressure, and the rod 14 is moved up and down in the figure to move the valve body. The opening degree of 12 can be controlled in multiple stages.

Next, an example of the multistage air cylinder 21 in FIG. 1 will be described in detail with reference to FIG. This multi-stage air cylinder 21
Are three pistons 42, 43, 4 inside the housing 41.
4 is provided in series, and the base 45 of the first piston 42 with the piston rod 24 extending from the housing 41
The head 46 of the second piston 43, the base 47 of the second piston 44, the head 48 of the third piston 44, and the base 49 of the third piston 44 on the housing bottom wall 50. 51 are slidably inserted in the respective axial directions. The first piston 42 is provided with a spring 52 that biases the rod in the rod retracting direction. Each piston 42 ... 4
Compressed air chambers 53, 54, 55 are defined between the outer peripheral surfaces of the bases 45, 47, 49 of FIG. 4 and the inner peripheral surface of the housing 41. Ports for introducing air into these compressed air chambers 53 ... 55. 22a, 22b, 22c are housing 4 respectively
1 side by side. That is, when air pressure is supplied to each of the pressure chambers 42 ...
44 are pushed by an amount that allows them to slide with each other, the second piston 43 is the first piston 42, and the third piston 44 is the second and first pistons 43, 42.
Is pushed.

The sliding range between the pistons 42 ... 44 increases toward the cylinder base end side, and when the piston rod 24 is most retracted,
The distance S ₁ between the flange surface of the head portion 46 of the second piston 43 and the locking surface of the base portion 45 of the first piston 42 that abuts against this is the flange surface of the head portion 48 of the third piston 44 and this. Is half the distance S ₂ between the second piston 43 and the engaging surface of the base 47 of the second piston 43 (S ₂ = 2 × S ₁ ).
The distance between the flange surface of the head portion 51 of the housing bottom wall 50 and the locking surface of the base portion 49 of the third piston 44 is three times the first distance S ₁ (S ₃ = 3 × S). ₁ ). Therefore, if the first spacing S ₁ is, for example, 3 mm, the second spacing S ₂ is 6 mm, the third spacing S ₃ is 12 mm, and each port 2
Depending on which of 2a, 22b and 22c the air pressure is introduced to, the amount of protrusion from 0 mm to full stroke 21 mm (S ₄ )
Eight strokes can be obtained in 3 mm increments.
That is, the exhaust throttle valve 10 of FIG. 1 described above is connected to the piston rod 24 of the multi-stage air cylinder 21, so that the rotation angle around the axis is changed by the stroke, and the valve opening degree (throttle) is divided into eight stages. Is to be adjusted.

[0020]

In summary, according to the present invention, the oxygen concentration can be accurately grasped even if the exhaust pressure changes, and the feedback control of the valve opening degree according to the operating condition can be executed. That is, the optimum EGR rate according to the engine operating state can be surely realized, and NOx reduction of the exhaust gas can be surely achieved.

[Brief description of drawings]

FIG. 1 is a configuration diagram of an exhaust gas recirculation device showing an embodiment of the present invention.

FIG. 2 is a flow chart of an exhaust gas recirculation method showing an embodiment of the present invention.

FIG. 3 is a relationship diagram between oxygen concentration and sensor output in the oxygen concentration sensor of FIG.

FIG. 4 is a diagram showing a map I of FIG.

5 is a diagram showing a map II of FIG.

FIG. 6 is a diagram showing Map III in FIG.

FIG. 7 is a side sectional view showing an example of the EGR valve of FIG.

8 is a cross-sectional view showing an example of the multi-stage air cylinder of FIG.

[Explanation of symbols]

1 engine 2 intake pipe (intake system) 3 exhaust gas recirculation means 4 exhaust pipe (exhaust passage) 5 oxygen concentration sensor 6 exhaust pressure sensor 7 engine control module (control means) 8 EGR pipe 9 EGR valve 10 exhaust throttle valve 13 actuator 20 duty Solenoid valve 21 Multi-stage air cylinder 23 Solenoid valve V _R Oxygen concentration detection value (actual output of oxygen concentration sensor) ΔV Oxygen concentration sensor output correction amount V Oxygen concentration correction value V _S Target oxygen concentration P _T Exhaust pressure detection value P _O Atmospheric pressure ΔP Exhaust pressure m Exhaust throttle valve basic opening degree M Exhaust throttle valve execution opening degree n EGR valve basic opening degree N EGR valve execution opening degree

Claims (2)

[Claims] 1. An optimum EG according to an engine operating condition
An exhaust gas recirculation method in which exhaust gas is recirculated so as to have an R ratio, in which the oxygen concentration in the exhaust gas and the exhaust pressure are detected, and the oxygen concentration detection value is corrected by the exhaust pressure detection value. An exhaust gas recirculation method, wherein feedback control of exhaust gas recirculation is performed based on an oxygen concentration correction value. 2. An exhaust gas recirculation means for recirculating a part of exhaust gas to an intake system, an oxygen concentration sensor for detecting an oxygen concentration in exhaust gas provided in an exhaust passage, and an oxygen concentration sensor near the oxygen concentration sensor. An exhaust pressure sensor provided to detect the exhaust pressure and the oxygen concentration detection value detected by the oxygen concentration sensor are corrected by the exhaust pressure detection value detected by the exhaust pressure sensor, and this oxygen concentration correction value changes to the operating state of the engine. An exhaust gas recirculation apparatus comprising: a control unit that operates the exhaust gas recirculation unit so that a target oxygen concentration of an optimum EGR rate that is determined accordingly is obtained.