CN115045770B - Quantitative filtering method of air-fuel ratio control system based on binary oxygen sensor - Google Patents

Quantitative filtering method of air-fuel ratio control system based on binary oxygen sensor Download PDF

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CN115045770B
CN115045770B CN202210981069.1A CN202210981069A CN115045770B CN 115045770 B CN115045770 B CN 115045770B CN 202210981069 A CN202210981069 A CN 202210981069A CN 115045770 B CN115045770 B CN 115045770B
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赵延龙
张晓燕
张纪峰
薛文超
王颖
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
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    • F02D—CONTROLLING COMBUSTION ENGINES
    • F02D41/00—Electrical control of supply of combustible mixture or its constituents
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F02—COMBUSTION ENGINES; HOT-GAS OR COMBUSTION-PRODUCT ENGINE PLANTS
    • F02D—CONTROLLING COMBUSTION ENGINES
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Abstract

The invention provides a quantitative filtering method of an air-fuel ratio control system based on a binary oxygen sensor, which comprises the following stepsThe method comprises the following steps: 1. establishing a mathematical model of a filtering problem under a binary oxygen sensor HEGO; 2. discretizing the mathematical model in the first step to obtain a discrete form system; 3. equivalent transformation as relating to the accurate measurement output
Figure 138260DEST_PATH_IMAGE001
And a variation threshold
Figure 293910DEST_PATH_IMAGE002
A function of (a); 4. initializing assignment of a quantization filtering method; 5. sequentially obtaining system states based on the output of the binary oxygen sensor HEGO at the kth moment, namely a binary prediction value of oil film mass flow, a binary prediction value of the output value of the binary oxygen sensor HEGO and prediction error covariance; 6. correcting the binary prediction value of the system state in the step 5 to obtain a binary filtering value of the system state at the moment k; 7. and 6, obtaining a precisely output filtering value according to the binary filtering value of the system state in the step 6.

Description

Quantitative filtering method of air-fuel ratio control system based on binary oxygen sensor
Technical Field
The invention belongs to the field of filtering of an air-fuel ratio control system of an internal combustion engine, and particularly relates to a problem of filtering oil film mass flow and fuel mass flow by using measurement output of a binary oxygen sensor HEGO.
Background
Modern gasoline internal combustion engines use a variety of technologies to improve combustion efficiency while reducing pollutant emissions. Three-way catalytic (TWC) converters play a key role in reducing toxic gas emissions and pollutant emissions. Air-fuel ratio (AFR) is a key parameter in regulating the combustion process of an automotive engine to reduce exhaust emissions and fuel consumption. The lowest emissions can be achieved when the AFR is kept at the maximum efficiency of the three-way catalytic converter, i.e., near the stoichiometric air-fuel ratio (typically between 14.57 and 14.70 depending on the fuel type). Therefore, effective air-fuel ratio control is critical to ensure good combustion rate and high catalyst efficiency.
To meet this requirement, a common strategy is AFR control, i.e. to control the injectors to match the injected fuel mass flow stoichiometrically to the air mass flow entering the cylinder, see reference [1]. When the driver executes a torque request by stepping on the accelerator pedal, the Electronic Control Unit (ECU) generates a desired air mass flow set point, which the feedforward controller converts to a corresponding AFR reference. The AFR feedback controller keeps the air/fuel ratio as close as possible to this AFR reference value.
In the AFR control, in order to determine the injection quantity, the fuel mass flow of the cylinder needs to be estimated. The estimation of this value requires the use of a measurement of the Oxygen concentration in the combustion Exhaust gases in the cylinder, obtained by a specific binary Oxygen sensor HEGO (Heated Exhaust Gas Oxygen). The output of the sensor is strongly non-linear with respect to oxygen concentration, i.e., only rich or lean air/fuel mixtures can be distinguished.
Because the binary oxygen sensor HEGO cannot obtain the accurate value of the measurement output signal, only whether the measurement output signal belongs to a certain set is known, and the system state estimation task under the binary oxygen sensor HEGO becomes a nonlinear filtering problem. Therefore, the conventional kalman filter method (KF) and many modified kalman filter algorithms, such as Extended Kalman Filter (EKF), extended state-based kalman filter (ESKF) algorithms, etc., are no longer applicable.
For the filtering problem, the measurement signal of the binary oxygen sensor HEGO has the following 2 disadvantages compared to the accurate measurement sensor: 1) Available information is reduced, uncertainty of the system to deal with is greatly increased, and the effect of system state estimation is seriously influenced; 2) The output of the binary oxygen sensor HEGO is in a nonlinear form, and the existing filtering method is not applicable. Therefore, how to design an effective quantization filtering method to process the state estimation of the system under the output of the binary oxygen sensor HEGO becomes an urgent problem to be solved.
Reference [1] is as follows:
Gagliardi G, Mari D, Tedesco F, et al. An air-to-fuel ratio estimation strategy for turbocharged spark-ignition engines based on sparse binary HEGO sensor measures and hybrid linear observers[J]. Control Engineering Practice, 2021, 107: 104694。
disclosure of Invention
The technical problem solved by the invention is as follows: aiming at the problem of air-fuel ratio control of the internal combustion engine, under the condition that the measurement output of a binary oxygen sensor HEGO is a binary signal and the system is noisy, a quantitative filtering method is designed to obtain the state of the system, namely a filtering value of oil film mass flow, and then an estimated value of fuel oil mass flow is obtained, and a control law is further designed. The flow chart of the present invention is shown in fig. 1, wherein,
Figure DEST_PATH_IMAGE001
as a reference signal, to be used as a reference signal,
Figure DEST_PATH_IMAGE002
for passing the HEGO pair system of binary oxygen sensor
Figure DEST_PATH_IMAGE003
Is estimated.
Therefore, the invention provides a quantitative filtering method of an air-fuel ratio control system based on a binary oxygen sensor, which mainly comprises two stages of 'forecasting' and 'correcting'. The block diagram of the quantization filtering method of the present invention is shown in fig. 2.
The invention relates to a quantitative filtering method of an air-fuel ratio control system based on a binary oxygen sensor, which comprises the following 7 steps:
step (I): and establishing a mathematical model of the filtering problem under the binary oxygen sensor HEGO. The fuel injected into the cylinder is composed of fuel vapor flow and fuel film flow, and under the condition of noise, a simplified system state transition model and an accurate output model are as follows:
Figure DEST_PATH_IMAGE004
wherein, t is a time,
Figure DEST_PATH_IMAGE005
is oilThe mass flow rate of the film is controlled,
Figure DEST_PATH_IMAGE006
is the derivative of oil film mass flow with respect to time t,
Figure DEST_PATH_IMAGE007
is the injection flow of the injector,
Figure DEST_PATH_IMAGE008
is the mass flow of fuel into the cylinder,
Figure DEST_PATH_IMAGE009
and
Figure DEST_PATH_IMAGE010
respectively, process noise and measurement noise at time t, wherein,
Figure DEST_PATH_IMAGE011
and
Figure DEST_PATH_IMAGE012
as process noise
Figure DEST_PATH_IMAGE013
And measuring noise
Figure DEST_PATH_IMAGE014
Known standard deviation of;
Figure DEST_PATH_IMAGE015
is the time constant of the evaporation of the oil film,
Figure DEST_PATH_IMAGE016
is the fuel deposit coefficient. When the engine is at maximum efficiency, take
Figure DEST_PATH_IMAGE017
。
Step (II): discretizing the model in the step (I) to obtain a discrete form system
Figure DEST_PATH_IMAGE018
Figure DEST_PATH_IMAGE019
Wherein the oil film mass flow at the k-th time
Figure DEST_PATH_IMAGE020
The system state at the k time of the system and the oil film mass flow at the k-1 time
Figure DEST_PATH_IMAGE021
Is the system state at the k-1 time of the system, and the fuel injection flow of the fuel injector at the k time
Figure DEST_PATH_IMAGE022
For the control input at time k of the system, the mass flow of fuel into the cylinder at time k
Figure DEST_PATH_IMAGE023
For the precise measurement and output at the kth time,
Figure DEST_PATH_IMAGE024
is the process noise at time k and,
Figure DEST_PATH_IMAGE025
is the measurement noise at time k;
to simplify the calculation, the system parameters after the dispersion are recorded as
Figure DEST_PATH_IMAGE026
Wherein h is the discretization step length; process noise at time k
Figure DEST_PATH_IMAGE027
And measuring noise
Figure DEST_PATH_IMAGE028
Are all independently and simultaneously distributed, and
Figure DEST_PATH_IMAGE029
、
Figure DEST_PATH_IMAGE030
and system state at time 0
Figure DEST_PATH_IMAGE031
Are independent of each other.
Output from the precise measurement at the k-th time
Figure DEST_PATH_IMAGE032
The air-fuel ratio at the kth time is obtained as follows:
Figure DEST_PATH_IMAGE033
in the formula,
Figure DEST_PATH_IMAGE034
the air-fuel ratio at the time k,
Figure DEST_PATH_IMAGE035
is the mass flow rate of air at time k,
Figure DEST_PATH_IMAGE036
is a theoretical air-fuel ratio value;
the sensor of the system is a binary oxygen sensor HEGO, and a measurement output equation under the binary oxygen sensor HEGO is as follows:
Figure DEST_PATH_IMAGE037
in the formula,
Figure DEST_PATH_IMAGE038
is the measurement output of the binary oxygen sensor HEGO at the moment k. When air-fuel ratio
Figure DEST_PATH_IMAGE039
When the value is more than or equal to the threshold value 1, the measurement output of the binary oxygen sensor HEGOIs 1, otherwise is 0.
Step (three): the air-fuel ratio in the binary oxygen sensor HEGO in the step (two) is compared
Figure DEST_PATH_IMAGE040
Is equivalently transformed into a signal related to the accurate measurement output
Figure DEST_PATH_IMAGE041
And a variation threshold
Figure DEST_PATH_IMAGE042
The function of (a), namely the measurement output equation under the equivalent binary oxygen sensor HEGO, is as follows:
Figure DEST_PATH_IMAGE043
（5）
wherein,
Figure DEST_PATH_IMAGE044
is the threshold value at the k-th time.
Step (IV): carrying out initialization assignment on a quantization filtering method; selecting system state, i.e. oil film mass flow
Figure DEST_PATH_IMAGE045
Is initially of
Figure DEST_PATH_IMAGE046
Selecting the covariance initial value of the filtering error as
Figure DEST_PATH_IMAGE047
Wherein E is an expected value; the standard deviation of the selected process noise and the measured noise is respectively
Figure 191507DEST_PATH_IMAGE011
And
Figure DEST_PATH_IMAGE048
。
step (V): the "prediction" stage of the quantization filtering method. And sequentially obtaining a system state prediction value based on the output of the binary oxygen sensor HEGO, a binary prediction value of the output value of the binary oxygen sensor HEGO and a prediction error covariance at the kth moment. The 3 quantities obtained above are ready for the "correction" phase of the next quantization filtering method. Specifically, the 3 quantities at the k-th time are obtained in the following order:
(1) The system state, namely the binary prediction value of oil film mass flow:
Figure DEST_PATH_IMAGE049
;
(2) The binary prediction value of the output value of the binary oxygen sensor HEGO:
Figure DEST_PATH_IMAGE050
;
(3) Prediction error covariance:
Figure DEST_PATH_IMAGE051
；
wherein,
Figure DEST_PATH_IMAGE052
at time k to system state, i.e. oil film mass flow
Figure DEST_PATH_IMAGE053
The binary forecast value of (1);
Figure DEST_PATH_IMAGE054
is the k-1 time to the system state, namely the oil film mass flow
Figure DEST_PATH_IMAGE055
The binary filtered value of (a);
Figure DEST_PATH_IMAGE056
the predicted value output by the binary oxygen sensor HEGO at the kth moment;
Figure DEST_PATH_IMAGE057
is composed of
Figure DEST_PATH_IMAGE058
A distribution function of (a);
Figure DEST_PATH_IMAGE059
predicting the covariance of the error for the kth time;
Figure DEST_PATH_IMAGE060
covariance of the filtering error at time k-1;
step (six): the "correction" stage of the quantization filtering method. Using the 3 quantities at time k obtained in step (five), the gain and innovation of the quantization filtering method at time k are obtained
Figure DEST_PATH_IMAGE061
And (4) correcting the system state in the step (five), namely the binary prediction value of the oil film mass flow, so as to obtain the system state at the moment k, namely the filtering value and the filtering error covariance of the oil film mass flow. Specifically, the 3 quantities at the k-th time are obtained in sequence according to the following formulas:
(1) Gain:
Figure DEST_PATH_IMAGE062
；
(2) System state, i.e. oil film mass flow
Figure DEST_PATH_IMAGE063
The filtered value of (c):
Figure DEST_PATH_IMAGE064
；
(3) Filtering error covariance:
Figure DEST_PATH_IMAGE065
；
wherein,
Figure DEST_PATH_IMAGE066
is the gain at time k;
Figure DEST_PATH_IMAGE067
is the system state at the k-th moment, i.e. oil film mass flow
Figure DEST_PATH_IMAGE068
The two-value filtered values of (a) are,
Figure DEST_PATH_IMAGE069
is the covariance of the filtering error at time k.
Step (seven): from the system state in the step (six), i.e. oil film mass flow
Figure DEST_PATH_IMAGE070
Filtered value of
Figure DEST_PATH_IMAGE071
Bring-in system
Figure DEST_PATH_IMAGE072
The accurate output model obtains a filtering value of accurate output, and the specific formula is as follows:
Figure DEST_PATH_IMAGE073
；
wherein,
Figure DEST_PATH_IMAGE074
for precise output of filtered value at time k, i.e. fuel mass flow
Figure DEST_PATH_IMAGE075
An estimate of (d).
Therefore, the binary oxygen sensor HEGO output value is utilized
Figure DEST_PATH_IMAGE076
Through the steps, the mass flow of the oil film at the moment k is obtained according to a quantitative filtering method
Figure DEST_PATH_IMAGE077
Two-value predicted value of
Figure DEST_PATH_IMAGE078
And the filtered value
Figure DEST_PATH_IMAGE079
Further obtaining the fuel mass flow in the cylinder at the k moment
Figure DEST_PATH_IMAGE080
Real-time estimate of
Figure DEST_PATH_IMAGE081
. On the basis of this estimated value, the air-fuel ratio AFR control law can be designed.
Compared with the prior art, the invention has the advantages that:
1. aiming at the problem of air-fuel ratio control, the invention provides a quantitative filtering method under the output of a binary oxygen sensor HEGO, so that the system state at each moment, namely the real-time estimation of the oil film mass flow is obtained, and further the accurate output, namely the estimated value of the fuel oil mass flow is obtained;
2. binary oxygen sensor HEGO output at time k
Figure DEST_PATH_IMAGE082
And its predicted value
Figure DEST_PATH_IMAGE083
The error of (2) is used as the innovation of a binary filtering algorithm;
3. the requirement of the Kalman filtering algorithm on the measurement precision is greatly reduced.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a block diagram of the quantization filtering method of the present invention.
Fig. 3 is a diagram showing the effect of estimating the oil film mass flow rate in case 1 according to the present invention.
FIG. 4 shows the mean square error of the estimated value of oil film mass flow under the condition 1.
FIG. 5 is a graph illustrating the effect of the present invention on fuel mass flow estimation in case 1.
Fig. 6 is a diagram showing the effect of estimating the oil film mass flow rate in case 2 according to the present invention.
FIG. 7 shows the mean square error of the estimated oil film mass flow under condition 2.
Fig. 8 is a graph showing the effect of the estimation of the fuel mass flow rate in case 2 of the present invention.
Detailed Description
In order to illustrate the applicability of the present invention to systems under various dynamics, a specific implementation of the quantized filtering method using the binary oxygen sensor HEGO in the field of system state estimation for AFR control is described below by taking several systems with different in-cylinder fuel dynamics equations as an example.
The simulation was performed under the following 2 system parameter values, respectively.
Case 1: taking the mass flow of air in the cylinder at time k
Figure DEST_PATH_IMAGE084
Theoretical air-fuel ratio
Figure DEST_PATH_IMAGE085
Time constant of oil film evaporation
Figure DEST_PATH_IMAGE086
Coefficient of fuel oil deposition
Figure DEST_PATH_IMAGE087
Discretizing step size
Figure DEST_PATH_IMAGE088
Bring into a discrete system
Figure DEST_PATH_IMAGE089
Model, obtaining system
Figure DEST_PATH_IMAGE090
The parameters of (A) are as follows:
Figure DEST_PATH_IMAGE091
process noise
Figure DEST_PATH_IMAGE092
And measuring noise
Figure DEST_PATH_IMAGE093
Has a standard deviation of
Figure DEST_PATH_IMAGE094
And
Figure DEST_PATH_IMAGE095
。
case 2: taking the mass flow of air in the cylinder at time k
Figure DEST_PATH_IMAGE096
Theoretical air-fuel ratio
Figure DEST_PATH_IMAGE097
Time constant of oil film evaporation
Figure DEST_PATH_IMAGE098
Coefficient of fuel oil deposition
Figure DEST_PATH_IMAGE099
Discretizing step size
Figure DEST_PATH_IMAGE100
Bringing into a discrete system
Figure DEST_PATH_IMAGE101
Model, obtaining system
Figure DEST_PATH_IMAGE102
The parameters of (A) are as follows:
Figure DEST_PATH_IMAGE103
(ii) a Process noise
Figure DEST_PATH_IMAGE104
And measuring noise
Figure DEST_PATH_IMAGE105
Has a standard deviation of
Figure DEST_PATH_IMAGE106
And
Figure DEST_PATH_IMAGE107
。
and (3) respectively carrying out oil film mass flow estimation and fuel mass flow estimation of the system according to the following steps on the 2 different fuel dynamic equations.
Step (I): and establishing a mathematical model of the filtering problem under the binary oxygen sensor HEGO. The fuel injected into the cylinder is composed of a fuel vapor flow and a fuel film flow, and under the condition of noise, the simplified system state transition model and the accurate output model are as follows:
Figure DEST_PATH_IMAGE108
step (II): discretizing the model to obtain a discrete form system
Figure DEST_PATH_IMAGE109
:
Figure DEST_PATH_IMAGE110
Output from the precise measurement at the kth time
Figure DEST_PATH_IMAGE111
The air-fuel ratio at the k-th time is obtained as follows:
Figure DEST_PATH_IMAGE112
the sensor of the system is a binary oxygen sensor HEGO, and the measurement output equation under the sensor is as follows:
Figure DEST_PATH_IMAGE113
in the formula,
Figure DEST_PATH_IMAGE114
the measurement output of a binary oxygen sensor HEGO at the moment k is obtained, when the air-fuel ratio is greater than or equal to a threshold value 1, the output of the binary oxygen sensor HEGO is 1, otherwise, the output is 0;
step (three): the air-fuel ratio under the binary oxygen sensor HEGO in the step (II)
Figure DEST_PATH_IMAGE115
Output equivalence of (1) is transformed into a method for accurately measuring output
Figure DEST_PATH_IMAGE116
And a variation threshold
Figure DEST_PATH_IMAGE117
The function of (a), namely the measurement output equation under the equivalent binary oxygen sensor HEGO is as follows:
Figure DEST_PATH_IMAGE118
wherein,
Figure DEST_PATH_IMAGE119
is the threshold value at the k-th time.
Step (IV): and (4) carrying out initial assignment on the filtering algorithm. Selecting the system state, i.e. the oil film mass flow and the initial value of the filter thereof are respectively
Figure DEST_PATH_IMAGE120
And
Figure DEST_PATH_IMAGE121
selecting the initial covariance value of the filtering error as
Figure DEST_PATH_IMAGE122
；
Step (V): the "prediction" phase of the quantization filtering method. Sequentially obtaining: at the kth moment, the oil film mass flow prediction value based on the output of the binary oxygen sensor HEGO, the binary prediction value of the output value of the binary oxygen sensor HEGO and the prediction error covariance are as follows:
(1) The two-value prediction value of the oil film mass flow is as follows:
Figure DEST_PATH_IMAGE123
(2) The binary prediction value of the output value of the binary oxygen sensor HEGO:
Figure DEST_PATH_IMAGE124
;
(3) Prediction error covariance:
Figure DEST_PATH_IMAGE125
and (5) obtaining an oil film mass flow predicted value output by the binary oxygen sensor HEGO through the step (V), and preparing for obtaining a filtering value of the oil film mass flow in the next step.
Step (six): the "correction" stage of the quantization filtering method, namely, the gain and innovation of the quantization filtering method are obtained by using the 3 quantities obtained in the step (five) at the k-th time
Figure DEST_PATH_IMAGE126
And (5) correcting the system state in the step (V), namely the predicted value of the oil film mass flow, so as to obtain a filtering value and a filtering error covariance of the oil film mass flow at the moment k. Specifically, the 3 quantities at the k-th time are obtained according to the following equations:
(1) Gain:
Figure DEST_PATH_IMAGE127
;
(2) The filtered value of the oil film mass flow is as follows:
Figure DEST_PATH_IMAGE128
;
(3) Filtering error covariance:
Figure DEST_PATH_IMAGE129
；
step (seven): from the filtered value of the oil film mass flow in the step (VI)
Figure 283309DEST_PATH_IMAGE067
And (3) bringing the data into an output model of the system to obtain a filtering value of the accurate fuel mass flow value:
Figure DEST_PATH_IMAGE130
；
therefore, the output value of the binary oxygen sensor HEGO is utilized through the 7 steps
Figure DEST_PATH_IMAGE131
First, the mass flow of the oil film at the moment k is obtained
Figure DEST_PATH_IMAGE132
Is predicted value
Figure DEST_PATH_IMAGE133
And the filtered value
Figure DEST_PATH_IMAGE134
And further obtaining the fuel mass flow in the cylinder at the k moment
Figure DEST_PATH_IMAGE135
Real-time estimate of
Figure 232941DEST_PATH_IMAGE081
。
1000 times of simulation experiments are carried out aiming at random values of process noise and measurement noise to obtain oil film mass flow
Figure DEST_PATH_IMAGE136
And fuel mass flow
Figure DEST_PATH_IMAGE137
The estimated simulation results are as follows:
for case 1, get the oil film mass flowMeasurement of
Figure DEST_PATH_IMAGE138
And fuel mass flow
Figure DEST_PATH_IMAGE139
The estimation results of (a) are shown in fig. 3 to 5.
For case 2, get the oil film mass flow
Figure DEST_PATH_IMAGE140
And fuel mass flow
Figure DEST_PATH_IMAGE141
The estimation results of (2) are shown in fig. 6 to 8.
Fig. 3 and fig. 6 show the estimation effect of the quantization filtering method on the oil film mass flow in case 1 and case 2, respectively, where the solid line is the real value and the dotted line is the estimation value of the quantization filtering method. As can be seen from fig. 3 and 6, in case 1 and case 2, the quantitative filtering method can obtain a good estimation effect on the oil film mass flow at a limited time.
Fig. 4 and 7 show mean square estimation errors of oil film mass flow obtained by performing 1000 times of simulations by using a quantization filtering method in case 1 and case 2, respectively. As can be seen from fig. 4 and 7, in both cases 1 and 2, the estimation error of the oil film mass flow obtained by the quantization filtering method can be converged within a finite time in the mean square sense.
Fig. 5 and 8 are graphs comparing the estimated value and the actual value of the fuel mass flow rate using the quantization filtering method in case 1 and case 2, respectively. In the figure, the solid line represents a true value, and the dotted line represents an estimated value thereof by using a quantization filtering method. As can be seen from fig. 5 and 8, in case 1 and case 2, a good estimation effect on the fuel mass flow can be obtained by estimating the oil film mass flow by using a quantization filtering method.

Claims (5)

1. A quantitative filtering method of an air-fuel ratio control system based on a binary oxygen sensor is characterized by comprising the following steps: the method comprises the following steps:
step (I): establishing a mathematical model of a filtering problem under a binary oxygen sensor HEGO; under the condition of noise, the simplified system state transition model and the accurate output model are specifically as follows:
Figure 472149DEST_PATH_IMAGE001
wherein, t is a time,
Figure 248344DEST_PATH_IMAGE002
is the mass flow of the oil film,
Figure 496923DEST_PATH_IMAGE003
is the derivative of oil film mass flow with respect to time t,
Figure 436672DEST_PATH_IMAGE004
is the oil injection flow of the oil injector,
Figure 110099DEST_PATH_IMAGE005
is the mass flow of fuel into the cylinder,
Figure 401403DEST_PATH_IMAGE006
and
Figure 12644DEST_PATH_IMAGE007
respectively, process noise and measurement noise at time t, wherein,
Figure 8282DEST_PATH_IMAGE008
and
Figure 146002DEST_PATH_IMAGE009
as process noise
Figure 483574DEST_PATH_IMAGE010
And measuring noise
Figure 706745DEST_PATH_IMAGE011
Is known as the standard deviation of the measured signal,
Figure 302811DEST_PATH_IMAGE012
is the time constant for the evaporation of the oil film,
Figure 295038DEST_PATH_IMAGE013
is the fuel deposition coefficient;
step (II): discretizing formula (1) to obtain a discrete form system
Figure 272353DEST_PATH_IMAGE014
Figure 107453DEST_PATH_IMAGE015
Wherein the oil film mass flow at the k-th time
Figure 116998DEST_PATH_IMAGE016
The mass flow of the oil film at the k-1 th moment is the system state at the k-th moment of the system
Figure 107606DEST_PATH_IMAGE017
Is the system state at the k-1 time of the system, and the fuel injection flow of the fuel injector at the k time
Figure 239510DEST_PATH_IMAGE018
For the control input at time k of the system, the mass flow of fuel into the cylinder at time k
Figure 437273DEST_PATH_IMAGE019
For the accurate measurement output at the k-th time,
Figure 125875DEST_PATH_IMAGE020
is the process noise at time k and,
Figure 92694DEST_PATH_IMAGE021
is the measurement noise at time k;
output from the precise measurement at the k-th time
Figure 661078DEST_PATH_IMAGE022
The air-fuel ratio at the k-th time is obtained as follows:
Figure 955925DEST_PATH_IMAGE023
in the formula,
Figure 572851DEST_PATH_IMAGE024
the air-fuel ratio at the time k,
Figure 722072DEST_PATH_IMAGE025
is the mass flow rate of air at time k,
Figure 8828DEST_PATH_IMAGE026
is a theoretical air-fuel ratio value;
the measurement output equation under the binary oxygen sensor HEGO is as follows:
Figure 915604DEST_PATH_IMAGE027
in the formula,
Figure 195276DEST_PATH_IMAGE028
is the measurement output of the binary oxygen sensor HEGO at the moment k;
step (three): equivalently transforming equation (4) to output for accurate measurements
Figure 136687DEST_PATH_IMAGE029
And a variation threshold
Figure 794677DEST_PATH_IMAGE030
A function of (a);
step (IV): carrying out initialization assignment on a quantization filtering method; selecting system state, i.e. oil film mass flow
Figure 313383DEST_PATH_IMAGE031
Is initially of
Figure 272112DEST_PATH_IMAGE032
Selecting the initial value of the covariance of the filtering error as
Figure 677817DEST_PATH_IMAGE033
Wherein E is an expected value;
step (V): the 'forecasting' stage of the quantization filtering method; sequentially obtaining a system state based on the output of the binary oxygen sensor HEGO at the kth moment, namely a binary prediction value of oil film mass flow, a binary prediction value of the output value of the binary oxygen sensor HEGO and a prediction error covariance; the method prepares for the next correction stage of the quantization filtering method; the method comprises the following specific steps:
the system state, namely the binary prediction value of oil film mass flow:
Figure 758905DEST_PATH_IMAGE034
；
the two-value prediction value of the output value of the two-value oxygen sensor HEGO:
Figure 905853DEST_PATH_IMAGE035
；
prediction error covariance:
Figure 278059DEST_PATH_IMAGE036
；
wherein,
Figure 928483DEST_PATH_IMAGE037
at time k to system state, i.e. oil film mass flow
Figure 914894DEST_PATH_IMAGE038
The binary forecast value of (1);
Figure 158925DEST_PATH_IMAGE039
is the k-1 time to the system state, namely the oil film mass flow
Figure 459456DEST_PATH_IMAGE040
The binary filtered value of (a);
Figure 354600DEST_PATH_IMAGE041
the predicted value output by the binary oxygen sensor HEGO at the kth moment;
Figure 253855DEST_PATH_IMAGE042
is composed of
Figure 109815DEST_PATH_IMAGE043
A distribution function of (a);
Figure 338671DEST_PATH_IMAGE044
predicting the covariance of the error for the kth time;
Figure 698109DEST_PATH_IMAGE045
covariance of filtering error at the k-1 th moment;
step (six): a 'correction' stage of the quantization filtering method; obtaining the gain and innovation of the quantization filtering method under the k moment by using the 3 formulas under the k moment obtained in the step (five)
Figure 42633DEST_PATH_IMAGE046
Correcting the system state in the step (V), namely the two-value forecast value of the oil film mass flow, so as to obtain the system state at the moment k, namely the filtering value and the filtering error covariance of the oil film mass flow; the method specifically comprises the following steps:
gain:
Figure 244945DEST_PATH_IMAGE047
；
system state, i.e. oil film mass flow
Figure 152858DEST_PATH_IMAGE048
The filtered value of (a):
Figure 507747DEST_PATH_IMAGE049
；
filtering error covariance:
Figure 944544DEST_PATH_IMAGE050
；
step (seven): from the system state in step (six), i.e. oil film mass flow
Figure 837414DEST_PATH_IMAGE051
Filtered value of
Figure 158805DEST_PATH_IMAGE052
Carry-in system
Figure 492835DEST_PATH_IMAGE053
The accurate output model obtains a filtering value of accurate output, and the specific formula is as follows:
Figure 428429DEST_PATH_IMAGE054
；
wherein,
Figure 618715DEST_PATH_IMAGE055
for precise output of filtered value at time k, i.e. fuel mass flow
Figure 337272DEST_PATH_IMAGE056
An estimate of (d).
2. A binary-based method according to claim 1A quantization filtering method of an air-fuel ratio control system of an oxygen sensor, characterized in that: in the step (one), taking
Figure 119283DEST_PATH_IMAGE057
。
3. The quantization filtering method of the binary oxygen sensor-based air-fuel ratio control system according to claim 1, wherein: in the second step, the discretized system parameters are recorded for simplifying the operation
Figure 38829DEST_PATH_IMAGE058
Wherein h is the discretization step length; process noise at time k
Figure 906291DEST_PATH_IMAGE059
And measuring noise
Figure 428539DEST_PATH_IMAGE060
Are all independently and simultaneously distributed, and
Figure 612527DEST_PATH_IMAGE061
、
Figure 827608DEST_PATH_IMAGE062
and system state at time 0
Figure 713524DEST_PATH_IMAGE063
Are independent of each other.
4. The quantization filtering method of the binary oxygen sensor-based air-fuel ratio control system according to claim 1, characterized in that: in the step (two), when the air-fuel ratio is higher than the predetermined value
Figure 118092DEST_PATH_IMAGE064
And when the value is larger than or equal to the threshold value 1, the measurement output of the binary oxygen sensor HEGO is 1, otherwise, the value is 0.
5. The quantization filtering method of the binary oxygen sensor-based air-fuel ratio control system according to claim 1, characterized in that: in the step (III), the measurement output equation under the equivalent binary oxygen sensor HEGO is as follows:
Figure 281220DEST_PATH_IMAGE065
wherein,
Figure 791835DEST_PATH_IMAGE066
is the threshold value at the k-th time.
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