JP2008144744A - Control device for internal combustion engine - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To properly adapt to the secular change of engine characteristics and the change of operating environment when an ignition timing is controlled and suppress the delay of the control in an ignition timing control device of an internal combustion engine. <P>SOLUTION: This control device comprises a feed-forward controller 56 for calculating the ignition timing according to an ignition timing model, a feedback controller 58 for correcting the ignition timing to be near an MBT, and an ignition timing model learning means 62 which learns the ignition timing after the feedback correction and updates ignition timing model parameter vectors according to a calculation method in which the Kalman filter theory is used. A covariance calculation means 72 calculates the covariance matrix of differential vectors between the ignition timing model parameter vectors and their averaged value. The ignition timing model learning means 62 updates the ignition timing model parameter vectors by using the covariance matrixes of the differential vectors. A deterioration determination means 74 determines the deterioration of the internal combustion engine according to the differential vectors. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a control device for an internal combustion engine.

  In order to improve the fuel efficiency and emission performance of the internal combustion engine and to prevent knocking, it is important to control the ignition timing. Therefore, conventionally, it is generally performed that the optimum ignition timing according to the engine operating state is checked in advance and stored in an ECU (Electronic Control Unit) as a map, and the ignition timing is controlled in a feed-forward manner according to the map. It has been broken.

  However, the optimal ignition timing also changes according to the deterioration with time of the internal combustion engine or the change of the operating environment. The map control as described above cannot cope with such a change.

  On the other hand, in Japanese Patent Laid-Open No. 9-317522, a target combustion ratio at a predetermined crank angle is set according to the operating state, and the ignition timing is fed back so that the actual combustion ratio at the predetermined crank angle becomes the target combustion ratio. An apparatus for controlling is disclosed.

JP-A-9-317522

  According to the ignition timing feedback control disclosed in the above publication, it is possible to cope with a change in the optimal ignition timing caused by the deterioration of the internal combustion engine over time or the change in the operating environment. However, in the case of ignition timing feedback control, the ignition timing is not corrected unless there is a deviation between the target combustion state and the actual combustion state. That is, there is a problem that a delay in control cannot be avoided and the responsiveness is not good.

  The present invention has been made to solve the above-described problems. When controlling the ignition timing, the present invention can appropriately cope with deterioration with time of the internal combustion engine, changes in the operating environment, and the like, and delays in control. It is an object of the present invention to provide a control device for an internal combustion engine that can suppress the above-described problem.

In order to achieve the above object, a first invention is a control device for an internal combustion engine,
Ignition timing feedforward control means for calculating the ignition timing according to the operating state of the internal combustion engine according to the ignition timing model;
Combustion state detection means for detecting the combustion state;
Ignition timing feedback for correcting the ignition timing calculated by the ignition timing feedforward control means based on the combustion state detected by the combustion condition detecting means so that the combustion condition of the internal combustion engine approaches the target combustion condition Control means;
By learning the ignition timing corrected by the ignition timing feedback control means, the Kalman filter theory is adjusted so that the ignition timing calculated according to the ignition timing model is close to the ignition timing that realizes the target combustion state. Ignition timing model learning means for updating a parameter vector of the ignition timing model based on an applied calculation method;
An average value calculating means for calculating an average value of the ignition timing model parameter vector;
Covariance calculating means for calculating a covariance matrix of a difference vector between the ignition timing model parameter vector updated by the ignition timing model learning means and the ignition timing model parameter vector average value calculated by the average value calculating means;
With
The ignition timing model learning means performs calculation for updating the ignition timing model parameter vector using the covariance matrix of the difference vector calculated by the covariance calculation means.

The second invention is the first invention, wherein
When the function vector having the operating state of the internal combustion engine as a variable is φ _k , the ignition timing model parameter vector is θ ^ _k, and the subscript k of each symbol represents the cycle number of the internal combustion engine The ignition timing calculated by the ignition timing model is represented by φ _k ^T θ ^ _k ,
Ignition timing model parameter vector update formula used by the ignition timing model learning means when the ignition timing corrected by the ignition timing feedback control means is SA _k , Kalman gain is K _k , D is a vector, and Q and R are scalars Is the following equation: θ ^ _{k + 1} = θ ^ _k + K _k (SA _k −φ _k ^T θ ^ _k )
K _k = P _k φ _k (R + φ _k ^T P _k φ _k ) ^-1
P _k = P _k-1 + DQD ^T −P _k-1 φ _k-1 (R + φ _k-1 ^T P _k-1 φ _k-1 ) ^-1 φ _k-1 ^T P _k-1 (I)
Represented by
The ignition timing model learning means uses the covariance matrix of the difference vector calculated by the covariance calculating means as the matrix DQD ^T in the above equation (I).

The third invention is the first or second invention, wherein
The apparatus further includes a determination unit that determines deterioration or abnormality of the internal combustion engine based on the difference vector.

The fourth invention is the first to third invention,
The average value calculating means acquires the ignition timing model parameter vector for each trip of a vehicle on which the internal combustion engine is mounted, and calculates the average value.

The fifth invention is the first to fourth inventions,
The average value calculating means calculates an average value of the ignition timing model parameter vector using a forgetting factor.

  According to the first invention, the ignition timing feedforward control means for calculating the ignition timing according to the ignition timing model and the ignition timing feedback control means for correcting the ignition timing so that the combustion state approaches the target combustion state. In the timing control device, the ignition timing model parameter vector is updated so that the ignition timing calculated according to the ignition timing model is close to the ignition timing that achieves the target combustion state by learning the ignition timing after feedback correction. can do. Thereby, as the learning progresses, the ignition timing model is improved, so that the ignition timing calculated by the ignition timing model becomes closer to the ignition timing for realizing the target combustion state. That is, the ideal ignition timing can be calculated by the feedforward control means without using the feedback control. For this reason, according to the first aspect of the invention, it is possible not only to realize an ideal ignition timing by adapting to the deterioration with time of the internal combustion engine and the change of the operating environment, but also to suppress the control delay due to the feedback control. be able to. Therefore, even when the operating state changes, the ignition timing can be quickly controlled to an ideal ignition timing.

  In addition, according to the first invention, the ignition timing model parameter vector can be updated by a calculation method applying the Kalman filter theory. According to the knowledge of the present inventors, the ignition timing after feedback correction has a variation that accurately matches the normal distribution. According to the first invention, by applying the Kalman filter theory, it is possible to learn the ignition timing after feedback correction after appropriately filtering the above-described variation in the ignition timing after feedback correction. For this reason, the ignition timing model parameter vector can be appropriately updated without being adversely affected by variations inherent in the ignition timing after feedback correction. For this reason, the ignition timing model parameter vector can be optimized smoothly and reliably.

  Further, according to the first invention, an average value of the ignition timing model parameter vector is calculated, and further, a covariance matrix of a difference vector between the average value and the updated ignition timing model parameter vector is calculated, A calculation for updating the ignition timing model parameter vector can be performed using the covariance matrix of the difference vector. That is, it is possible to detect the degree of variation actually generated in the ignition timing model parameter vector and reflect it in the update processing of the ignition timing model parameter vector applying the Kalman filter theory. For this reason, the ignition timing model parameter vector can be updated more appropriately, and can be optimized more smoothly and reliably. In addition, since it is not necessary to set the degree of variation occurring in the ignition timing model parameter vector in advance, it is possible to reduce the number of conforming man-hours at the development stage.

According to the second invention, the function vector having the operating state of the internal combustion engine as a variable is φ _k , the ignition timing model parameter vector is θ ^ _k , the ignition timing after feedback correction is SA _k , the Kalman gain is K _k , D Is a vector, Q and R are scalars, and the ignition timing model parameter vector update formula is: θ ^ _{k + 1} = θ ^ _k + K _k (SA _k −φ _k ^T θ ^ _k )
K _k = P _k φ _k (R + φ _k ^T P _k φ _k ) ^-1
P _k = P _k-1 + DQD ^T −P _k-1 φ _k-1 (R + φ _k-1 ^T P _k-1 φ _k-1 ) ^-1 φ _k-1 ^T P _k-1 (I)
The difference vector covariance matrix can be used as the matrix DQD ^T in the above equation (I). As a result, the ignition timing model parameter vector θ ^ _k can be updated more appropriately, and can be optimized more smoothly and reliably. In addition, since it is not necessary to set the matrix DQD ^T in the formula (I) in advance, it is possible to reduce the number of matching man-hours in the development stage.

  According to the third invention, it is possible to determine the deterioration or abnormality of the internal combustion engine based on the difference vector between the ignition timing model parameter vector and its average value. If the characteristics of each part change due to changes with time of each part of the internal combustion engine, for example, deterioration of the spark plug or accumulation of oil sludge, the combustion state changes. The change in the combustion state is remarkably reflected in the ignition timing model parameter vector through the update process applying the Kalman filter theory. For this reason, when the internal combustion engine is deteriorated or abnormal with time, the ignition timing model parameter vector changes greatly, and the difference vector between the ignition timing model parameter vector and its average value increases. Therefore, it is possible to determine with high accuracy deterioration with time or abnormality occurring in the internal combustion engine based on the difference vector.

  According to the fourth aspect of the invention, when calculating the average value of the ignition timing model parameter vector, the ignition timing model parameter vector is obtained for each trip of the vehicle on which the internal combustion engine is mounted, and the average value is calculated. it can. As a result, the calculation load of the ECU can be reduced, and the average value of the ignition timing model parameter vector from a relatively long-term viewpoint can be calculated with high accuracy.

  According to the fifth aspect, the average value of the ignition timing model parameter vector can be calculated using the forgetting factor. As a result, the new ignition timing model parameter vector can be averaged so that the weight is larger and the older ignition timing model parameter vector is smaller, so that a more appropriate ignition timing model parameter vector average value can be calculated. it can.

Embodiment 1 FIG.
[Description of system configuration]
FIG. 1 is a diagram for explaining a system configuration according to the first embodiment of the present invention. As shown in FIG. 1, the system of this embodiment includes a spark ignition type internal combustion engine 10. The internal combustion engine 10 is used as a power source of a vehicle, for example. The number of cylinders and the cylinder arrangement of the internal combustion engine 10 are not particularly limited.

  An intake passage 12 and an exhaust passage 14 communicate with the cylinder of the internal combustion engine 10. An air flow meter 16 that detects an intake air amount Ga is disposed in the intake passage 12. A throttle valve 18 is disposed downstream of the air flow meter 16. The opening degree of the throttle valve 18 is adjusted by the operation of the throttle motor 20. In the vicinity of the throttle valve 18, a throttle position sensor 22 for detecting the throttle opening is disposed. An accelerator position sensor 24 that detects the accelerator opening is provided in the vicinity of the accelerator pedal.

  A fuel injector 26 for injecting fuel into the intake port 11 is disposed in the cylinder of the internal combustion engine 10. The internal combustion engine 10 is not limited to the port injection type as shown in the figure, but may be a direct injection type that directly injects fuel into the cylinder, and also performs port injection and in-cylinder injection. It may be used in combination. The cylinder of the internal combustion engine 10 is further provided with an intake valve 28, a spark plug 30, and an exhaust valve 32.

  A crank angle sensor 38 is attached in the vicinity of the crankshaft 36 of the internal combustion engine 10. According to the output of the crank angle sensor 38, the crank angle and the engine speed NE can be detected.

  Further, the internal combustion engine 10 is provided with an in-cylinder pressure sensor 40 that detects a pressure (combustion pressure) Pc in the cylinder.

  The system of the present embodiment further includes an ECU (Electronic Control Unit) 50. The ECU 50 is connected to the various sensors and actuators described above. The ECU 50 controls ignition timing, fuel injection amount, throttle opening, and the like based on the output of each sensor.

  FIG. 2 is a functional block diagram showing a part of the functions of the ECU 50. As shown in FIG. 2, the ECU 50 performs a change over time of a real-time control unit 52 that controls the ignition timing of the internal combustion engine 10 in real time for each cycle and an ignition timing model parameter vector described later from a relatively long-term viewpoint. A function as a temporal change detection unit 54 for detection is provided.

(Real-time control unit 52)
Hereinafter, first, the real-time controller 52 will be described. The real-time control unit 52 shown in FIG. 2 controls the ignition timing to be MBT (Minimum advance for the Best Torque). MBT is an ignition timing at which the torque is maximized, that is, an ignition timing at which the thermal efficiency is the best. The MBT not only changes according to the engine speed NE and the engine load, but also changes according to a change with time of the internal combustion engine 10, a change in operating environment, and the like.

  As shown in FIG. 2, the real-time control unit 52 includes a feedforward controller 56, a feedback controller 58, a combustion ratio calculation unit 60, an ignition timing model learning unit 62, and a covariance calculation unit 64. It is.

The feedforward controller 56 sets the ignition timing SA ₀ according to the ignition timing model expressed by the following equation for each cycle of the internal combustion engine 10 according to the operating state of the internal combustion engine 10 (engine speed NE and charging efficiency KL). calculate.
SA ₀ = φ ^T θ ^ (1)

  In the above equation (1), φ is a function vector determined by the engine speed NE and charging efficiency KL, and θ ^ is a vector composed of parameters that affect the characteristics of the ignition timing model. Hereinafter, this vector θ ^ is referred to as an ignition timing model parameter vector. Further, in the present specification, including the above formula (1), the superscript T means transposition.

Specifically, for example, the following equation can be used as the equation (1). In this case, the function vector φ and the ignition timing model parameter vector θ ^ can be expressed as follows, respectively.

  Note that a, b, c, and d in the above equation (2) are respectively predetermined constants. The charging efficiency KL is an index corresponding to the load of the internal combustion engine 10, and is based on the intake air amount Ga detected by the air flow meter 16 and the engine speed NE, or an intake pressure sensor (not shown). It can be calculated based on the intake pressure detected in step (1).

In the example shown in the above equation (2), the ignition timing model parameter vector θ ^ is a four-dimensional vector composed of four elements (parameters) of θ ₀ , θ ₁ , θ ₂ and θ ₃ . As will be described later, the ignition timing model parameter vector θ ^ is updated by the ignition timing model learning means 62 for each cycle of the internal combustion engine 10.

The feedback controller 58 corrects the ignition timing SA ₀ calculated by the feedforward controller 56. This corrected ignition timing is hereinafter referred to as “ignition timing after feedback correction”. In the present system, the ignition timing after the feedback correction is made the actual ignition timing by the spark plug 30. That is, a voltage is applied to the spark plug 30 at the ignition timing after feedback correction.

  The feedback controller 58 of the present embodiment corrects the ignition timing so as to approach the MBT by the following method.

  In the internal combustion engine 10, a combustion state in which the combustion rate is 50% when the crank angle is 8 ° after top dead center (hereinafter referred to as “8 ° ATDC”) is the most efficient combustion state. Is known empirically. Therefore, it can be determined that the ignition timing at which the combustion rate when the crank angle is 8 ° ATDC (hereinafter referred to as “8 ° ATDC combustion rate”) is 50% is MBT. Therefore, if the 8 ° ATDC combustion ratio is detected during operation of the internal combustion engine 10 and the ignition timing is corrected so that the 8 ° ATDC combustion ratio approaches 50%, the ignition timing can be brought close to MBT.

  In order to realize the feedback control as described above, the combustion ratio calculation means 60 calculates an 8 ° ATDC combustion ratio for each cycle of the internal combustion engine 10 based on the output of the in-cylinder pressure sensor 40. Hereinafter, the calculation method will be described.

The combustion rate calculating means 60 first calculates the heat generation rate in the cylinder. The heat generation rate in the cylinder can be calculated thermodynamically by the following equation.

  In the above equation (3), q is the amount of heat generated in the cylinder, P is the in-cylinder pressure, V is the in-cylinder volume, ψ is the crank angle, and κ is the specific heat ratio. The in-cylinder volume V and the rate of change dV / dψ are functions of the crank angle ψ, and the function is geometrically determined according to the bore, crank radius, connecting rod length, and the like. The specific heat ratio κ is a value determined based on the composition of the combustion gas, but may be simplified to κ = 1.32.

  The combustion ratio calculation means 60 samples the in-cylinder pressure Pc detected by the in-cylinder pressure sensor 40 at every predetermined crank angle (for example, every 1 ° CA). Next, by substituting P and dP / dψ obtained from the sampled data into the above equation (3), the heat release rate dq / dψ is calculated for each crank angle. The total heat generation amount is calculated by integrating the heat generation rate dq / dψ until the end of combustion. Further, the heat generation rate up to 8 ° ATDC is calculated by integrating the heat generation rate dq / dψ up to 8 ° ATDC. Then, the 8 ° ATDC combustion ratio can be calculated by dividing the calorific value up to 8 ° ATDC by the total calorific value.

  The combustion rate calculation means 60 may calculate the 8 ° ATDC combustion rate by the method described in JP-A-2005-351147, that is, the following method, instead of the above method.

It is known that the product PV ^{κ of the} in-cylinder pressure P and the in-cylinder volume V to the κ power and the calorific value q are correlated. Using this, P at crank angle ψ is P (ψ), V ^κ at crank angle ψ is V ^κ (ψ), a predetermined crank angle before the start of combustion is ψ ₁ , and a predetermined crank angle after the end of combustion is When the angle is ψ ₂ , the combustion ratio (MFB) at the crank angle ψ ₀ can be approximately calculated by the following equation.

By setting ψ ₀ to 8 ° ATDC in the above equation (4), the 8 ° ATDC combustion ratio can be calculated. That is, in this case, the 8 ° ATDC combustion ratio can be calculated only by detecting the in-cylinder pressure Pc at the three crank angles of ψ ₁ , 8 ° ATDC, and ψ ₂ . Therefore, the calculation load of the ECU 50 can be greatly reduced.

The feedback controller 58 corrects the ignition timing so that the 8 ° ATDC combustion ratio detected as described above approaches 50%. That is, the feedback controller 58 is based on the deviation between 50% (0.5), which is the target value of the 8 ° ATDC combustion rate, and the actual 8 ° ATDC combustion rate calculated by the combustion rate calculating means 60. A feedback correction amount dSA is calculated. The feedback correction amount dSA is added to the ignition timing SA ₀ calculated by the feedforward controller 56, whereby the ignition timing is corrected. That is, when the detected 8 ° ATDC combustion ratio is less than 50%, the ignition timing is corrected to be advanced, and when the detected 8 ° ATDC combustion ratio exceeds 50%, the ignition is performed. The time is corrected in the direction of becoming late.

According to such a feedback controller 58, even when the ignition timing SA ₀ calculated by the feedforward controller 56 is deviated from MBT, it can be brought closer to the actual ignition timing to MBT.

  However, there is of course a delay in feedback control. That is, when the MBT changes due to a change from one operating state to another operating state, it takes time for the feedback controller 58 to bring the ignition timing closer to the MBT again. Therefore, fuel consumption deteriorates during that time. In view of this, it is ideal that the ignition timing for MBT can be directly calculated from the operating state by the feedforward controller 56 (ignition timing model).

  In order to realize the above ideal, the ignition timing model learning means 62 determines the ignition timing after feedback correction, that is, the ignition timing after being corrected to be close to MBT, and the operating state (engine speed NE and charging efficiency KL). ) To update the ignition timing model parameter vector θ ^.

  Incidentally, as is well known, the internal combustion engine 10 has combustion fluctuations for each cycle. That is, even if the operating state of the internal combustion engine 10 has not changed, the state of combustion of the air-fuel mixture in the cylinder (flame propagation) changes from cycle to cycle. The main cause of this is that the air-fuel ratio in the cylinder, the amount of unburned gas remaining in the previous cycle remaining in the cylinder, and the mixing (disturbance) of the air-fuel mixture in the cylinder change randomly from cycle to cycle. It is to do.

  Due to the presence of the combustion fluctuation as described above, even if the operation state including the ignition timing is the same, the actual 8 ° ATDC combustion ratio varies from cycle to cycle. Therefore, when the feedback controller 58 corrects the ignition timing so that the 8 ° ATDC combustion ratio detected for each cycle approaches 50%, the corrected ignition timing varies for each cycle.

  That is, the ignition timing after feedback correction input to the ignition timing model learning unit 62 for each cycle has a variation, and its average value accurately matches the MBT, but deviates from the average value. It cannot be said that the input accurately matches the MBT. For this reason, learning is performed from the standpoint that all the ignition timings after feedback correction input to the ignition timing model learning means 62 are equal and correct, and the ignition timing model parameter vector θ ^ is updated according to the learning result. It is not appropriate to do so.

  Therefore, the ignition timing model learning means 62 of the present embodiment updates the ignition timing model parameter vector θ ^ by applying the Kalman filter theory.

  The Kalman filter theory is a filtering theory generally used for estimating the state of a system. According to the Kalman filter theory, when noise (white noise) is added to the system or observation, the noise can be appropriately filtered, so that optimum state estimation can be performed.

  According to the knowledge of the present inventors, the variation (noise) generated in the ignition timing after feedback correction is the same type as the noise that can be filtered by the Kalman filter theory. That is, since the variation in the ignition timing after the feedback correction is caused by random combustion fluctuations as described above, the variation substantially matches the normal distribution. For this reason, according to the ignition timing model learning means 62 to which the Kalman filter theory is applied, the variation inherent in the ignition timing after the feedback correction can be appropriately filtered when learning the ignition timing after the feedback correction. Therefore, it is possible to appropriately update the ignition timing model parameter vector θ ^ without being adversely affected by variations inherent in the ignition timing after feedback correction.

The update rule of the ignition timing model parameter vector θ ^ applying the Kalman filter theory is expressed by the following equation.
θ ^ _{k + 1} = θ ^ _k + K _k (SA _k −φ _k ^T θ ^ _k ) (5)

In the symbols used in this specification including the above expression (5), the subscript k indicates the value of the kth cycle of the internal combustion engine 10. In the equation (5), K _k is Kalman gain, and SA _k is the ignition timing after feedback correction.

In the above equation (5), (SA _k −φ _k ^T θ ^ _k ) is the ignition timing SA _k after feedback correction and the ignition timing φ _k ^T θ calculated by the feedforward controller 56 according to the above equation (1). ^ Indicates the error from _k (hereinafter referred to as “prediction error”). The above equation (5) is _obtained by adding the prediction error multiplied by the Kalman gain K _k to the ignition timing model parameter vector θ ^ _k of the current cycle, thereby obtaining the ignition timing model parameter vector θ ^ _{k + 1} of the next cycle. Is calculated.

Hereinafter, the process of deriving the Kalman gain K _{k in} the above equation (5) will be described.
When the true value of the ignition timing model parameter vector θ ^ (optimum ignition timing model parameter vector that cannot be actually known) is θ, the true value θ of the ignition timing model parameter vector is a change with time of the characteristics of the internal combustion engine 10. In addition, it can be considered that the cycle changes depending on the operating environment. This is expressed by the following equation.
θ _{k + 1} = θ _k + Dw _k (6)

In the above equation (6), Dw _k corresponds to the cycle-by-cycle change in the true value θ of the ignition timing model parameter vector due to the above-described change over time, environmental change, and the like. Of this Dw _k , D is a vector of the same dimension as θ ^, and w _k is a variable (scalar).

In addition, the ignition timing to be calculated by the ignition timing model using the true value θ of the ignition timing model parameter vector (optimum ignition timing that cannot be actually known) φ _k ^T θ _k and the ignition timing SA after feedback correction _When an error existing between _k and n _k is defined, the following equation is defined.
SA _k = φ _k ^T θ _k + n _k (7)

From the above, the error (hereinafter referred to as “model error”) θ˜ between the true value θ of the ignition timing model parameter vector and the actual ignition timing model parameter vector θ ^ is expressed as follows.
θ ~ _{k + 1} = θ _{k + 1} −θ ^ _{k + 1}
= Θ _k + Dw _k − {θ ^ _k + K _k (SA _k −φ _k ^T θ ^ _k )}
= Θ ~ _k + Dw _k −K _k (φ _k ^T θ _k + n _k −φ _k ^T θ ^ _k )
_{= (I-K k φ k} T) θ ~ k + Dw k -K k n k ··· (8)

  The above formulas (5), (6) and (7) were used for the formula transformation in the formula (8).

According to the knowledge of the present inventors, the change Dw _k of the true value θ of the ignition timing model parameter vector can be considered as a random walk. Further, the error _nk in the above equation (7) is considered to be a random disturbance caused by the combustion fluctuation and the measurement noise as described above. Therefore, w _k and n _k are assumed to have independent normal distributions having an average value of 0 and covariances Q and R. In other words, it is defined as:
E [w _k ^T w _k ] = Q (9)
E [n _k ^T n _k ] = R (10)

  In addition, in this specification including Eqs. (9) and (10), E [] represents an average value (expected value).

In Kalman filter theory, the covariance matrix of the model error theta ~ _k as (hereinafter referred to as "model error covariance matrix") P _k is minimized, determining the Kalman gain K _k. The model error covariance matrix P _k is expressed by the following equation.
P _k = E [θ ~ _k θ ~ _k ^T ] (11)

Using the above equations (8), (9) and (10), the model error covariance matrix P _{k + 1} can be calculated as follows.
P _{k + 1} = E [θ ~ _{k + 1} θ ~ _{k + 1} ^T ]
= E [{θ ~ _k + Dw _k −K _k (n _k + φ _k ^T θ ~ _k )} {θ ~ _k + Dw _k −K _k (n _k + φ _k ^T θ ~ _k )} ^T ]
＝ E [θ ~ _k θ ~ _k ^T ] + DQD ^T −E [θ ~ _k θ ~ _k ^T ] φ _k K _k ^T −K _k φ _k ^T E [θ ~ _k θ ~ _k ^T ]
+ E [K _k (n _k + φ _k ^T θ ~ _k ) (n _k + θ ~ _k ^T φ _k ) K _k ^T ]
＝ E [θ ~ _k θ ~ _k ^T ] + DQD ^T −E [θ ~ _k θ ~ _k ^T ] φ _k K _k ^T −K _k φ _k ^T E [θ ~ _k θ ~ _k ^T ]
−K _k (E [n _k n _k ] + φ _k ^T E [θ ~ _k θ ~ _k ^T ] φ _k ) K _k ^T
= P _k + DQD ^T −P _k φ _k K _k ^T −K _k φ _k ^T P _k −K _k (R + φ _k ^T P _k φ _k ) K _k ^T
= P _k + DQD ^T −P _k φ _k (R + φ _k ^T P _k φ _k ) ^-1 φ _k ^T P _k
+ {K _k −P _k φ _k (R + φ _k ^T P _k φ _k ) ⁻¹ } (R + φ _k ^T P _k φ _k ) {K _k ^T − (R + φ _k ^T P _k φ _k ) ⁻¹ φ _k ^T P _k }
(12)

From the above equation (12), it can be seen that the Kalman gain K _k may be determined as follows to minimize the model error covariance matrix P _{k + 1} .
K _k = P _k φ _k (R + φ _k ^T P _k φ _k ) ⁻¹ (13)

In that case, the model error covariance matrix P _{k + 1} is expressed by the following equation.
P _{k + 1} = P _k + DQD ^T −P _k φ _k (R + φ _k ^T P _k φ _k ) ⁻¹ φ _k ^T P _k (14)

The above equation (14) can be modified as the following equation.
P _k = P _k-1 + DQD ^T −P _k-1 φ _k-1 (R + φ _k-1 ^T P _k-1 φ _k-1 ) ^-1 φ _k-1 ^T P _k-1 (15)
Using the equation (15), P _k in the equation (13) can be calculated.

(Covariance R)
As shown in the above equation (13), in order to obtain the Kalman gain K _k , it is necessary to determine the value of the covariance R of n _k . The covariance R of n _k is a value representing the degree of variation in the ignition timing SA _k after feedback correction, as can be seen from the definition of the above equation (7). The value of this covariance R may be set in advance as an appropriate value obtained empirically, or the covariance actually occurring in the ignition timing SA _k after feedback correction is obtained and the value is calculated. The Kalman gain K _k may be obtained using the covariance R. In the system shown in FIG. 2, the covariance calculating means 64 obtains the covariance actually generated at the ignition timing SA _k after feedback correction. Hereinafter, specific processing of the covariance calculation unit 64 will be briefly described.

Covariance calculation unit 64 calculates the covariance of the ignition timing SA _k after the feedback correction of the last N cycles of the internal combustion engine 10. Here, N, so that the number of cycles that can be calculated ignition timing after the feedback correction covariance SA _k with sufficient accuracy, are set in advance.

In general, the covariance V _k for the past N variables x _k can be calculated by the following equation.

The covariance calculation means 64 stores the ignition timing SA _k after feedback correction for the past N cycles, and substitutes these values for x _k in the above equation (16), thereby changing the covariance value to the cycle. Calculate every time. The covariance value thus calculated by the covariance calculation means 64 is input to the ignition timing model learning means 62 and used as the covariance R.

  The covariance calculation means 64 may calculate the covariance by using a movement calculation method in order to reduce the calculation load, instead of executing the calculation of the above equation (16) as it is. .

(Matrix DQD ^T )
Further, as shown in the above equations (13) and (15), in order to obtain the Kalman gain K _k , it is necessary to obtain the model error covariance matrix P _k , and in order to obtain this P _k It is necessary to define the matrix DQD ^T. The matrix DQD ^T, as shown in the following equation, is equal to the covariance matrix of Dw _k (autocorrelation _{matrix) E [Dw k (Dw k} ) T].
E [Dw _k (Dw _k ) ^T ] = E [Dw _k ^T w _k D ^T ]
＝ DE [w _k ^T w _k D ^T ] D ^T
= DQD ^T (17)

Dw _k covariance matrix _{E [Dw k (Dw k)} T], i.e. the matrix DQD ^T is representative of the variation degree of the true value θ of the ignition timing model parameter vector. In this embodiment, as will be described later, the covariance matrix actually generated in the ignition timing model parameter vector θ ^ _k is obtained, and the Kalman gain K _k is obtained using the covariance matrix as the DQD ^T. It is said.

  Hereinafter, specific processing when the ignition timing model learning unit 62 updates the ignition timing model parameter vector θ ^ according to the update rule of the above equation (5) will be described. FIG. 3 is a flowchart of a routine executed by the ECU 50 as the ignition timing model learning means 62 in the present embodiment. This routine is executed every cycle of the internal combustion engine 10.

According to the routine shown in FIG. 3, first, a function vector φ _k is calculated based on the engine speed NE and the charging efficiency KL (step 120). Each element of the function vector φ is composed of a predetermined function as exemplified in the above equation (2). A function vector φ _k is calculated by substituting the values of the engine speed NE and the charging efficiency KL into the variables of the function.

Subsequently, a model error covariance matrix P _k is calculated based on the above equation (15) (step 122). In step 122, the values calculated in the previous cycle are substituted for φ _k-1 and P _k-1 in the above equation (15). Further, the covariance R of n _k, calculated by the covariance calculation unit 64, values of the covariance of the ignition timing SA _k after the feedback correction for the past N cycles is substituted. The method for obtaining DQD ^{T in} the equation (15) will be described later.

Following the processing of step 122, the Kalman gain K _k is calculated based on the above equation (13) (step 124). In this case, the function vector φ _k calculated in step 120, the covariance R calculated by the covariance calculation means 64, and the model error covariance matrix P _k calculated in step 122 are the above (13 ) Is assigned to each expression.

Finally, the ignition timing model parameter vector θ ^ _{k of the} current cycle is updated to the ignition timing model parameter vector θ ^ _{k + 1 of} the next cycle based on the update rule of the above equation (5) (step 126). ). In this case, the ignition timing SA _k after feedback correction of the current cycle, the ignition timing model parameter vector θ ^ _{k of the} current cycle, the function vector φ _k calculated in step 120, and the Kalman calculated in step 124 above. The gain K _k is assigned to the above equation (5).

  As described above, according to the routine processing shown in FIG. 3, it is possible to learn the ignition timing after feedback correction and update the ignition timing model parameter vector θ ^. For this reason, as the learning progresses, the ignition timing model parameter vector θ ^ is improved, and the ignition timing calculated by the ignition timing model of the above equation (1) becomes closer to MBT than before. Therefore, the ignition timing close to MBT can be calculated in the feedforward controller 56 without using the feedback control of the feedback controller 58. As a result, it is possible to solve the problem of the control delay of the accessory in the feedback control. Therefore, not only can the MBT change appropriately due to the deterioration of the internal combustion engine 10 and the change of the operating environment, but also the ignition timing can be made to follow the MBT quickly according to the change of the MBT accompanying the change of the operation state. it can. As a result, excellent fuel efficiency can be obtained.

  Further, according to the present embodiment, as described above, the ignition timing model parameter vector θ ^ can be updated by applying the Kalman filter theory. As described above, according to the knowledge of the present inventors, the ignition timing after feedback correction has a variation that accurately matches the normal distribution. In this embodiment, by applying the Kalman filter theory, it is possible to learn the ignition timing after feedback correction after appropriately filtering the variation inherent in the ignition timing after feedback correction. Therefore, it is possible to appropriately update the ignition timing model parameter vector θ ^ without being adversely affected by variations inherent in the ignition timing after feedback correction. As a result, the ignition timing model parameter vector θ ^ can be optimized more smoothly and reliably.

  Further, according to the present embodiment, as the learning by the ignition timing model learning means 62 proceeds, the ignition timing model parameter vector θ ^ can be brought closer to the optimum form. For this reason, the ignition timing model parameter vector θ ^ at the time of factory shipment does not require so high accuracy. Therefore, the number of conforming man-hours at the development stage can be reduced, and the development cost and development period can be reduced.

Incidentally, resulting in the ignition timing SA _k after feedback correction covariance (variation degree) depends on the operating conditions. On the other hand, in the present embodiment, as described above, the covariance actually generated in the ignition timing SA _k after feedback correction for the past N cycles is sequentially calculated, and the value is calculated as the ignition timing model parameter vector based on the Kalman filter theory. It is used as the covariance R necessary for the update process of θ ^. For this reason, it is possible to appropriately reflect the change in the covariance generated in the ignition timing SA _k after the feedback correction depending on the operating conditions in the update processing of the ignition timing model parameter vector θ ^. Therefore, the ignition timing model parameter vector θ ^ can be learned with higher accuracy.

(Time-change detector 54)
Next, the temporal change detection unit 54 shown in FIG. 2 will be described. The temporal change detector 54 is provided to detect temporal changes of the ignition timing model parameter vector θ ^ from a relatively long-term viewpoint. In order to achieve the object, the temporal change detection unit 54 calculates the average value θ ^ _mean of the ignition timing model parameter vector θ ^ from a relatively long-term viewpoint as follows.

  The ignition timing model parameter vector θ ^ updated by the ignition timing model learning means 62 is intermittently (periodically) input to the temporal change detection unit 54 for each trip. “Every trip” in this case refers to the travel distance of the vehicle even at a predetermined time interval (for example, every 10 hours, every 100 hours, or every week in the calendar of the internal combustion engine 10). A predetermined interval (for example, every 100 km or 200 km) may be used. The trip from the start to the stop of the internal combustion engine 10 may be one trip. In this case, it is assumed that the ignition timing model parameter vector θ ^ obtained last in each trip is input to the temporal change detection unit 54.

Hereinafter, the ignition timing model parameter vector θ ^ input to the j-th change detection unit 54 is represented by the symbol θ ^ _(j) . Then, when this θ ^ _(j) is input, the temporal change detection unit 54 calculates the ignition timing model parameter vector average value θ ^ _{mean (j-1)} calculated previously and a new input θ ^ _{( From j)} , a new average value θ ^ _{mean (j)} is calculated. In this case, in this embodiment, the ignition timing model parameter vector θ ^ is averaged using the forgetting factor α. That is, the following relationship is established between the previous average value θ ^ _{mean (j-1)} , the new input θ ^ _(j), and the new average value θ ^ _{mean (j)} .
θ ^ _{mean (j)} = αθ ^ _{mean (j-1)} + (1−α) θ ^ _(j) (18)

The forgetting factor α is a predetermined positive number smaller than 1. In the above equation (18), when calculating a new average value θ ^ _{mean (j)} , the previous average value θ ^ _{mean (j−1)} is forgotten at a ratio of the forgetting factor α and a new input θ ^ means that _(j) is multiplied by the remaining weight (1-α). The value of the forgetting factor α is not particularly limited, but can be, for example, about 0.95 to 0.99.

The temporal change detection unit 54 does not use the equation (18) as it is, but performs the calculation as follows. First, when a new ignition timing model parameter vector θ ^ _(j) is input from the ignition timing model learning means 62, as shown in FIG. 2, the new input θ ^ _(j) and the delay calculator A difference vector dθ _{(j) from the} previous average value θ ^ _{mean (j−1)} held by 66 is calculated. That is, the difference vector dθ _(j) is expressed by the following equation.
dθ _(j) = θ ^ _(j) −θ ^ _{mean (j-1)} (19)

When the above equation (19) is used, the above equation (18) can be modified as follows.
θ ^ _{mean (j)} = αθ ^ _{mean (j-1)} + (1−α) θ ^ _(j)
= Αθ ^ _{mean (j-1)} + (1−α) (θ ^ _{mean (j-1)} + dθ _(j) )
= Θ ^ _{mean (j-1)} + (1−α) dθ _(j) (20)

The temporal change detection unit 54 calculates the ignition timing model parameter vector average value θ ^ _{mean (j)} according to the above equation (20). That is, the difference vector dθ _(j) calculated by the above equation (19) is input to the forgetting calculator 68 as shown in FIG. The forgetting calculator 68 multiplies the input dθ by (1−α) to calculate (1−α) dθ. Then, by adding (1−α) dθ and the previous average value θ ^ _{mean (j−1)} held by the delay computing unit 70, a new average represented by the above equation (20) is obtained. The value θ ^ _{mean (j)} is calculated.

The temporal change detection unit 54 further includes covariance calculation means 72 that calculates the covariance matrix E [dθ _(j) dθ _(j) ^T ] of the difference vector dθ _(j) . It can be said that the covariance matrix E [dθ _(j) dθ _(j) ^T ] of the difference vector dθ _(j) represents the degree of variation of the ignition timing model parameter vector θ ^. Therefore, this covariance matrix E [dθ _(j) dθ _(j) ^T ] is substantially equal to E [Dw _k (Dw _k ) ^T ] representing the degree of variation of the true value θ of the ignition timing model parameter vector, that is, DQD ^T. It can be considered equivalent. Therefore, in the present embodiment, when the ignition timing model learning means 62 updates the ignition timing model parameter vector θ ^, the covariance calculated by the covariance calculation means 72 is added to DQD ^T in the above equation (15). Calculation is performed by substituting the matrix E [dθ _(j) dθ _(j) ^T ].

  As described above, in the present embodiment, the degree of variation actually generated in the ignition timing model parameter vector θ ^ is detected by the covariance calculation means 72, and the value is updated by the covariance calculation means 72. Can be reflected in the calculation. Therefore, the ignition timing model parameter vector θ ^ can be updated more appropriately, and can be optimized more smoothly and reliably. In addition, since it is not necessary to set the values of the vector D and the covariance Q in advance, it is possible to reduce the man-hours for adaptation at the development stage.

In the system of the present embodiment as described above, the ignition timing model parameter vector θ ^ is optimized as learning by the ignition timing model learning means 62 proceeds. Then, after learning by the ignition timing model learning means 62 has progressed to a certain extent, if the characteristics of the internal combustion engine 10 do not change with time, the ignition timing model parameter vector θ ^ will be compared even though there is a slight fluctuation for each cycle. From a long-term perspective, it stabilizes near the optimum value. For this reason, in this case, the difference between θ ^ input to the temporal change detection unit 54 for each trip and the average value θ ^ _mean , that is, the difference vector dθ _(j) is small.

In other words, if the difference vector dθ _(j) is smaller than a certain value, the ignition timing model parameter vector θ ^ does not change greatly, that is, the internal combustion engine 10 does not change with time (deterioration with time). Judgment can be made.

Further, since the combustion state changes when the characteristics of each part change due to the aging of each part of the internal combustion engine 10, for example, deterioration of the spark plug 30 or accumulation of oil sludge, the ignition timing model parameter vector is changed accordingly. θ ^ also changes. In this case, if the change over time of the ignition timing model parameter vector θ ^ is moderate, it can be determined that the change corresponds to a normal change over time (deterioration over time) of the internal combustion engine 10. On the other hand, when the change over time of the ignition timing model parameter vector θ ^ is abrupt, it can be determined that the characteristics of the internal combustion engine 10 have suddenly changed beyond the normal level of change over time. That is, it can be determined that an abnormality has occurred in the internal combustion engine 10. When the change over time of the ignition timing model parameter vector θ ^ is moderate, the difference vector dθ _(j) is small, and when the change over time of the ignition timing model parameter vector θ ^ is steep, the difference vector dθ _(j) is big.

According to the above-described concept, it is possible to determine the time-dependent change or deterioration of the internal combustion engine 10 by monitoring the magnitude of the difference vector dθ _(j) calculated by the time-change detecting unit 54. . Therefore, in the present embodiment, as shown in FIG. 2, the deterioration determination means 74 for determining deterioration with time of the internal combustion engine 10 based on the difference vector dθ _(j) is provided.

Hereinafter, specific processing performed by the deterioration determination unit 74 will be described. FIG. 4 is a flowchart of a routine executed by the ECU 50 as the deterioration determination means 74. This routine is executed every time the difference vector dθ _(j) is calculated, that is, every trip.

According to the routine shown in FIG. 4, first, it is determined whether or not the magnitude of the difference vector dθ _(j) calculated this time is larger than a predetermined determination value α (step 130). As a result, when it is determined that the magnitude of the difference vector dθ _(j) is larger than the determination value α, the internal combustion engine 10 is deteriorated or abnormal enough to require maintenance (repair, adjustment, parts replacement, etc.). Is determined to have occurred (step 132). In this case, for example, an indicator lamp (not shown) provided on the instrument panel of the driver's seat is turned on to notify the driver of the fact and prompt the customer to enter the maintenance shop (step 134). . Note that when the degree of deterioration or abnormality is slight, the driver may not be notified, and a record that can be confirmed by the mechanic at the next maintenance factory entry may be left.

On the other hand, if it is determined in step 130 that the magnitude of the difference vector dθ _(j) is smaller than the determination value α, the internal combustion engine 10 has not deteriorated with time so as to require maintenance. A determination is made (step 136).

If the internal combustion engine 10 is stopped after the determination in step 136 is made, that is, it is determined that the change over time occurring in the internal combustion engine 10 is within a normal range, immediately before the stop. the ignition timing model parameter vector average theta ^ _mean in _(j), it is preferred to use as the initial value theta ^ ₀ the ignition timing model parameter vector theta ^ _k when the internal combustion engine 10 is started next time. This has the following advantages.

Normally, the ignition timing model parameter vector θ ^ _k immediately before the previous engine stop is used as the initial value θ ^ ₀ of the ignition timing model parameter vector θ ^ _k at the time of engine start. In this case, a case is assumed in which the internal combustion engine 10 has been left in a biased state for a long time before the previous engine stop. Here, as an example, it is assumed that a long idling operation was performed before the previous engine stop. When the idling operation is continued for a long time, the ignition timing model parameter vector θ ^ _k is learned in a form particularly suitable for the idling operation. For this reason, when the internal combustion engine 10 is stopped as it is after the idling operation is continued for a long time, the ignition timing model parameter vector θ ^ _k has a shape particularly suitable for idling operation, that is, a slightly biased shape. Yes. Ignition timing model parameter vector theta ^ _k such biased form, the optimal ignition timing model parameter vector theta ^ _k in normal operating conditions is believed that slightly deviated. Therefore, if this slightly biased ignition timing model parameter vector θ ^ _k is used as the initial value θ ^ ₀ at the next start, the ignition timing model parameter vector θ ^ _k is learned in a truly optimal form after starting. A certain amount of time is required until this time, and it is considered that the fuel consumption slightly decreases during that time.

On the other hand, the ignition timing model parameter vector average value θ ^ _{mean (j)} is an average value from a relatively long-term viewpoint, and is hardly affected by the operating state before the engine is stopped. Therefore, if the ignition timing model parameter vector average value θ ^ _{mean (j)} immediately before the previous engine stop is used as the initial value θ ^ ₀ of the ignition timing model parameter vector θ ^ _k at the next start, It is possible to prevent an unforeseen situation from occurring, and it is possible to more reliably exhibit good fuel economy performance immediately after starting.

Further, in step 130 of the routine shown in FIG. 4 described above, the deterioration of the internal combustion engine 10 is determined based on the magnitude of each difference vector dθ _(j) itself. However, in the present invention, a plurality of difference vectors are used. The deterioration determination may be performed based on a statistic obtained by performing statistical processing (calculation of average, variance, etc. _{) on} dθ _(j) .

Further, in step 130 of the routine shown in FIG. 4 described above, instead of the difference vector dθ _(j) , the ignition timing model parameter vector average value θ ^ _{mean (j)} and the initial value of the ignition timing model parameter vector θ ^ _k . It is also possible to make a deterioration determination based on whether the difference between θ ^ ₀ is large or small.

Further, when an abnormal fuel (for example, a fuel whose ignition delay is too long or too short) is supplied to the internal combustion engine 10, the value of the ignition timing model parameter vector θ ^ _k changes suddenly. Therefore, in this case as well, it is determined that the internal combustion engine 10 has deteriorated (abnormal) in the routine processing shown in FIG. That is, the deterioration (abnormality) of the internal combustion engine 10 that can be detected in the present embodiment includes an abnormality of the fuel supplied to the internal combustion engine 10.

  By the way, in Embodiment 1 mentioned above, although the combustion state of the internal combustion engine 10 is detected based on the output of the in-cylinder pressure sensor 40, this invention is not limited to this. That is, in the present invention, for example, a sensor for detecting knocking generated in the internal combustion engine 10, ion current generated in the cylinder, combustion luminance in the cylinder, or the like is provided, and the combustion state is detected based on the output of those sensors. You may do it.

  In the first embodiment described above, the feedback controller 58 performs the ignition timing feedback control with the combustion state in which the ignition timing becomes MBT as the target combustion state as an example. It is not limited to. That is, in the present invention, for example, knocking that occurs in the internal combustion engine 10 may be detected, and the ignition timing feedback control may be performed with the combustion state in which the ignition timing is advanced the most within a range where knocking does not occur as the target combustion state.

  In the first embodiment described above, the feedforward controller 56 is the “ignition timing feedforward control means” in the first invention, and the combustion rate calculation means 60 is the “combustion state detection means” in the first invention. The feedback controller 58 is the “ignition timing feedback control means” in the first invention, and the delay calculators 66 and 70 and the forgetting calculator 68 are the “average value calculating means” in the first invention. The variance calculation means 72 corresponds to the “covariance calculation means” in the first invention, and the deterioration determination means corresponds to the “determination means” in the third invention.

It is a figure for demonstrating the system configuration | structure of Embodiment 1 of this invention. It is a functional block diagram in case ECU controls the ignition timing in Embodiment 1 of this invention. It is a flowchart of the routine performed in Embodiment 1 of the present invention. It is a flowchart of the routine performed in Embodiment 1 of the present invention.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 Internal combustion engine 12 Intake passage 14 Exhaust passage 16 Air flow meter 18 Throttle valve 26 Fuel injector 30 Spark plug 40 In-cylinder pressure sensor 50 ECU
52 real-time control unit 54 time-dependent change detection unit 56 feedforward controller 58 feedback controller 60 combustion rate calculation unit 62 ignition timing model learning unit 64 covariance calculation unit 66 delay calculator 68 forgetting calculator 70 delay calculator 72 covariance calculation means

Claims (5)

Ignition timing feedforward control means for calculating the ignition timing according to the operating state of the internal combustion engine according to the ignition timing model;
Combustion state detection means for detecting the combustion state;
Ignition timing feedback for correcting the ignition timing calculated by the ignition timing feedforward control means based on the combustion state detected by the combustion condition detecting means so that the combustion condition of the internal combustion engine approaches the target combustion condition Control means;
By learning the ignition timing corrected by the ignition timing feedback control means, the Kalman filter theory is adjusted so that the ignition timing calculated according to the ignition timing model is close to the ignition timing that realizes the target combustion state. Ignition timing model learning means for updating a parameter vector of the ignition timing model based on an applied calculation method;
An average value calculating means for calculating an average value of the ignition timing model parameter vector;
Covariance calculating means for calculating a covariance matrix of a difference vector between the ignition timing model parameter vector updated by the ignition timing model learning means and the ignition timing model parameter vector average value calculated by the average value calculating means;
With
The ignition timing model learning means performs calculation for updating the ignition timing model parameter vector using the covariance matrix of the difference vector calculated by the covariance calculation means. . When the function vector having the operating state of the internal combustion engine as a variable is φ _k , the ignition timing model parameter vector is θ ^ _k, and the subscript k of each symbol represents the cycle number of the internal combustion engine The ignition timing calculated by the ignition timing model is represented by φ _k ^T θ ^ _k ,
Ignition timing model parameter vector update formula used by the ignition timing model learning means when the ignition timing corrected by the ignition timing feedback control means is SA _k , Kalman gain is K _k , D is a vector, and Q and R are scalars Is the following equation: θ ^ _{k + 1} = θ ^ _k + K _k (SA _k −φ _k ^T θ ^ _k )
K _k = P _k φ _k (R + φ _k ^T P _k φ _k ) ^-1
P _k = P _k-1 + DQD ^T −P _k-1 φ _k-1 (R + φ _k-1 ^T P _k-1 φ _k-1 ) ^-1 φ _k-1 ^T P _k-1 (I)
Represented by
2. The internal combustion engine according to claim 1, wherein the ignition timing model learning means uses a covariance matrix of the difference vector calculated by the covariance calculating means as a matrix DQD ^T in the equation (I). Control device.   The control apparatus for an internal combustion engine according to claim 1 or 2, further comprising a determination unit that determines deterioration or abnormality of the internal combustion engine based on the difference vector.   4. The average value calculating means obtains the ignition timing model parameter vector for each trip of a vehicle on which the internal combustion engine is mounted, and calculates the average value. A control device for an internal combustion engine according to claim.   5. The control apparatus for an internal combustion engine according to claim 1, wherein the average value calculating means calculates an average value of the ignition timing model parameter vector using a forgetting factor.

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