Method for estimating fuel injection quantity of high-pressure common rail system based on kalman filter and cascade closed-loop control method

Abstract

The application discloses a method for estimating fuel injection quantity of a high-pressure common rail system based on Kalman filtering and a cascade closed-loop control method, and belongs to the technical field of diesel engine fuel system control. The method for adjusting fuel injection quantity based on rail pressure considers noise, uncertain interference and model nonlinearity in engineering application, and the application adopts a cascade closed-loop control method. The cascade control comprises fuel injection quantity closed loop and rail pressure closed loop. In the fuel injection quantity closed loop, the method based on Kalman filtering is used to estimate fuel injection quantity in real time, and the real-time estimated fuel injection quantity is used as feedback for fuel injection quantity closed loop control. Meanwhile, the target rail pressure is calculated through the real-time estimated fuel injection quantity, and the target rail pressure is used as input to control the rail pressure closed loop. The pressure of the common rail is the output and feedback of the rail pressure closed loop. The application can realize fuel injection quantity closed loop control of the high-pressure common rail system under different working conditions, thereby effectively guaranteeing the consistency and reliability of cycle fuel injection performance.

Description

Technical Field

[0001] This invention belongs to the field of diesel engine fuel system control technology, specifically relating to a novel closed-loop control method for fuel injection quantity applicable to high-pressure common rail fuel systems in diesel engines. Background Technology

[0002] With increasingly stringent international emission regulations, the demand for improved fuel economy and emissions performance of diesel engines, as the primary power source for ships, is becoming increasingly urgent. High-pressure common rail fuel injection technology has broad application prospects in the field of marine diesel engines. Currently, the injection quantity control of high-pressure common rail systems is based on open-loop control using experimentally calibrated injection quantity MAP diagrams, indirectly adjusting the injection process through rail pressure closed-loop and speed closed-loop control. However, due to the complex hydraulic influences of high-pressure common rail systems, changes in the working environment and operating conditions, and the degradation of system structural parameters, this method struggles to guarantee the consistency and reliability of cyclic injection performance during diesel engine operation.

[0003] In a high-pressure common rail system, there are two ways to change the injection quantity: one is to change the injection pulse width by controlling the opening time of the needle valve through a solenoid valve; the other is to change the rail pressure, as the injection quantity will also change due to the change in injection pressure. Changing the injection pulse width requires designing a separate closed-loop control system for the injection quantity, while changing the rail pressure can be done without changing the original rail pressure control system structure.

[0004] To achieve closed-loop control of fuel injection quantity, obtaining real-time fuel injection quantity information is crucial. Currently, commonly used methods for testing fuel injection quantity include momentum method, volumetric method, and displacement method. However, these methods require modification of the original mechanical structure of the diesel engine and cannot be applied to the actual operation of the diesel engine. Summary of the Invention

[0005] To address the aforementioned problems in the existing technology, this invention proposes a method for adjusting the injection quantity of a high-pressure common rail fuel system based on Kalman filter estimation, and a cascade closed-loop control method for the injection quantity, applicable to high-pressure common rail fuel systems of diesel engines.

[0006] The specific technical solution adopted in this invention is as follows:

[0007] The method for estimating the fuel injection quantity of a high-pressure common rail system based on Kalman filtering comprises the following specific steps:

[0008] 1) Based on the fuel system flow process, establish a nonlinear mathematical model of the fuel injection law based on instantaneous common rail pressure:

[0009] The nonlinear mathematical model of the fuel injection law based on instantaneous common rail pressure is as follows:

[0010]

[0011] In equation (1), p is the instantaneous pressure of the common rail, and Q inj This refers to the fuel injection rate;

[0012]

[0013] In equation (2), C leak V is the fuel leakage coefficient, taken as a constant; c ΔV(p) represents the common rail volume; ΔV(p) represents the change in common rail volume, which is related to the instantaneous pressure p of the common rail.

[0014] 2) Constructing the state-space model:

[0015] Select common rail pressure p and injection rate Q inj Rate of change of fuel injection rate The three variables are used as state variables, namely x1 = p, x2 = Q. inj , It is approximately a constant, therefore we have According to equation (7), the nonlinear equation of the system can be obtained:

[0016]

[0017] In equation (3), y is the measured output of the system, i.e., the instantaneous pressure p;

[0018] Equation (3) can be written in state-space form as follows:

[0019]

[0020] 3) Discretize the continuous state-space model (4):

[0021] Let the sampling step size be Δt, and the state variable x at time t k-1 The derivative at time t can be approximated as:

[0022]

[0023] t k t k-1 Replacing k and k-1, equation (5) can be written as:

[0024] x(k)=x(k-1)+Δt·f(x(k-1)) (6)

[0025] Here vector at this time,

[0026]

[0027] The discrete state-space model can then be expressed as:

[0028]

[0029] 4) Considering process noise w(k) and measurement noise v(k) in the model, equation (8) can be written as:

[0030]

[0031] In equation (9), w(k) and v(k) are uncorrelated zero-mean Gaussian white noise, and w(k) = [w1(k) w2(k) w3(k)] T Let v(k) be a scalar; define the covariance matrices of w(k) and v(k) as Q and R, respectively, where Q is a 3×3 diagonal matrix, Q = diag[q1 q2 q3], and R is a scalar, R = r; let the estimated value of x(k) be... According to the Kalman filter algorithm,

[0032] 5) Linearize the nonlinear model:

[0033] At sampling time k, let the estimated value of x(k) be... According to the Kalman filter algorithm, Divided into prior estimates and posterior estimate

[0034] The posterior estimate of the state variable x(k) at time k-1 Therefore in At w(k-1)0=0, performing a Taylor series expansion on x(k)=g(x(k-1),w(k-1)), omitting terms of second order and above, yields an approximately linearized expression of the state equation:

[0035]

[0036] In equation (10), A(k-1) and M(k-1) are the values ​​of x(k) in the equation. The Jacobian matrix at that point, i.e.:

[0037]

[0038] Substituting equation (7) into equation (11), we get

[0039]

[0040] M(k-1) is a constant:

[0041]

[0042] 6) Optimal estimation of fuel injection quantity for high-pressure common rail system based on Kalman filtering:

[0043] Set initial values and P(0) + The covariance matrices are Q and R, respectively. First, time updates are performed starting from time k=1:

[0044] ① Calculate the prior estimate using the discrete state-space model (8)

[0045]

[0046] ②In At point A, calculate the Jacobian matrices A(k-1) and M(k-1);

[0047] ③ Calculate the covariance matrix P(k) of the prior estimates. - :

[0048] P(k) - =A(k-1)P(k-1) + A(k-1) T +M(k-1)·Q·M(k-1) T (15)

[0049] ④ Calculate the Kalman filter gain

[0050] K(k)=P(k) - C(k) T [C(k)P(k) - C(k) T +R] -1 (16)

[0051] ⑤ At time k, the measured value y(k) and the prior estimate The difference is used as feedback to correct the optimal estimation system and obtain the posterior estimate.

[0052]

[0053] Equation (17) yields the posterior estimate at time k. In That is, the optimal estimate of the fuel injection rate:

[0054]

[0055] ⑥ Calculate the posterior estimation error covariance matrix P(k) + :

[0056] P(k) + =(IK(k)C(k))P(k) - (IK(k)C(k)) T +K(k)·R·K(k) T (19)

[0057] The posterior estimate is continuously updated by iterating through equations (14) to (19). And the posterior estimation error covariance matrix P(k) + ;

[0058] 7) Real-time online estimation of fuel injection quantity:

[0059] Based on the estimated fuel injection rate The estimated amount of fuel injected is obtained by summing the values ​​during the fuel injection phase.

[0060]

[0061] Where k1 is the start time of fuel injection, k2 is the end time of fuel injection, and Δt = k2 - k1 is the duration of fuel injection.

[0062] The cascade closed-loop control method consists of a fuel injection quantity closed loop and a rail pressure closed loop. The specific steps of the control method are as follows:

[0063] Step S1: Periodically acquire the pressure signal of the common rail pipe in the high-pressure common rail system;

[0064] Step S2: Using the common rail pressure p output from the rail pressure closed loop as the input to the Kalman filter, the method of estimating the injection quantity of the high-pressure common rail system based on Kalman filtering is applied to obtain the observed value of the injection quantity.

[0065] Step S3, with the estimated fuel injection quantity This feedback loop forms a closed loop for the fuel injection quantity, which is the target fuel injection quantity V. obj Compared with the estimated fuel injection quantity The difference is subtracted, and the resulting fuel injection quantity error ΔV is input into the fuel injection quantity closed-loop controller. The output of the fuel injection quantity closed-loop controller is the change in target rail pressure ΔP. obj ;

[0066] Step S4, the change in target rail pressure ΔP obj Adding the initial rail pressure P0, we obtain the current target rail pressure P. obj ;

[0067] Step S5, target rail pressure P obj The difference between the common rail pressure p and the feedback is input to the rail pressure controller. The output of the rail pressure controller is the opening degree of the fuel metering valve, which controls the fuel to pass through the fuel injection pump and then to the common rail. The common rail pressure p is the output and feedback of the rail pressure closed loop.

[0068] Furthermore, the fuel injection quantity closed-loop controller mentioned in step S3 is a PI controller, and the controller outputs the change in target rail pressure ΔP. obj The method is as follows:

[0069] △P obj =k p ·△V+k i ·∫△Vdt (21)

[0070] In the formula, k p k is the proportionality coefficient. i is the integral coefficient.

[0071] The beneficial effects of this invention are:

[0072] 1. A closed-loop control method for fuel injection quantity applicable to diesel engine fuel systems is proposed. This method adds an outer-loop closed-loop control of fuel injection quantity without changing the original rail pressure control system. By adjusting the target rail pressure, the fuel injection quantity is adjusted. This method includes a fuel injection quantity closed loop and a rail pressure closed loop, forming a cascade structure of the control system.

[0073] 2. A real-time fuel injection quantity estimation method based on Kalman filtering is incorporated into the fuel injection quantity cascade control system to provide feedback for the closed-loop control of fuel injection quantity. This method can solve problems such as measurement noise, uncertainty interference, and model nonlinearity, and is suitable for engineering applications.

[0074] 3. In engineering applications, the original rail pressure control system of the engine can be retained, and an outer ring of fuel injection quantity and a Kalman filter can be added without changing the engine structure or adding sensors, making it simple, easy to implement and low in cost. Attached Figure Description

[0075] To more clearly illustrate the technical solution of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. All other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0076] Figure 1 Block diagram of fuel injection quantity cascade closed-loop control

[0077] Figure 2 Real-time fuel injection quantity estimation and closed-loop control flowchart

[0078] Figure 3 Measured rail pressure and estimated pressure at 100MPa 1.0ms

[0079] Figure 4 Measured and estimated injection rates at 100 MPa and 1.0 ms

[0080] Figure 5 Measured and estimated fuel injection quantity at 100MPa and 1.0ms

[0081] Figure 6Fuel injection quantity output response of closed-loop control system

[0082] Figure 7 Output response of fuel injection quantity controller Detailed Implementation

[0083] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other implementations obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0084] This invention provides a cascade closed-loop control method for fuel injection quantity in a high-pressure common rail system, and incorporates a Kalman filter into the cascade control, the structure of which is as follows: Figure 1 As shown, the fuel injection quantity closed-loop cascade control system includes two closed loops: an outer loop fuel injection quantity control and an inner loop rail pressure control.

[0085] Injection quantity closed loop: based on the estimated injection quantity This feedback loop forms a closed loop for the fuel injection quantity, which is the target fuel injection quantity V. obj Compared with the estimated fuel injection quantity The difference is subtracted, and the resulting fuel injection quantity error ΔV is input into the fuel injection quantity controller (controller 1). The output of controller 1 is the rail pressure change ΔP. obj .

[0086] Rail pressure closed loop: ΔP obj The new target rail pressure P is formed by adding it to the set rail pressure P0. obj The target orbital pressure P obj Subtracting the measured rail pressure p from the actual rail pressure yields the rail pressure difference Δp, which is input into the rail pressure controller (controller 2). The output of controller 2 is the opening degree of the fuel metering valve, which controls the fuel to pass through the fuel injection pump and then to the common rail. The pressure p of the common rail is the output of the inner loop, thereby realizing closed-loop control of the rail pressure.

[0087] Furthermore, the Kalman filter in the outer loop takes the measured rail pressure p as input and uses the Kalman filtering algorithm to achieve real-time estimation of the fuel injection quantity. The Kalman filter output is the estimated fuel injection quantity.

[0088] Real-time fuel injection quantity estimation and closed-loop control process as follows Figure 2 As shown. Includes the following steps:

[0089] Step S1: Acquire the pressure signal p of the common rail pipe in the high-pressure common rail system;

[0090] Step S2: Using the measured common rail pressure p as the input to the Kalman filter, the Kalman filtering algorithm is applied to obtain the injection rate. The optimal estimate;

[0091] Step S3, the real-time estimated fuel injection rate The estimated injection quantity is obtained by summing the values ​​at each injection point.

[0092] Step S4, with the estimated fuel injection quantity This feedback loop forms a closed loop for the fuel injection quantity, which is the target fuel injection quantity V. obj Compared with the estimated fuel injection quantity The difference is used to obtain the fuel injection quantity error ΔV, which is then input into controller 1. The output of controller 1 is the change in target rail pressure ΔP. obj ;

[0093] Step S5, the change in target rail pressure ΔP obj Adding the initial rail pressure P0, we obtain the current target rail pressure P. obj The target rail pressure P is input into the inner loop of the rail pressure control system. obj Subtracting the measured rail pressure p from the measured rail pressure yields the rail pressure difference Δp, which is input to controller 2. The output of the rail pressure controller determines the opening of the fuel metering valve, controlling the flow of fuel through the injection pump to the common rail. The common rail pressure p serves as the output and feedback of the inner loop. This cycle repeats, forming a cascaded fuel injection control system.

[0094] The following are detailed explanations:

[0095] Step S1: Acquire the pressure signal of the common rail pipe in the high-pressure common rail system;

[0096] Step S2: Using the measured common rail pressure as the input to the Kalman filter, apply the Kalman filtering algorithm to obtain the injection rate. The optimal estimate is obtained. Furthermore, the design method of the Kalman filter is as follows:

[0097] Step S201: Establish a nonlinear mathematical model of the fuel injection law.

[0098] Based on the flow characteristics of fuel in high-pressure fuel lines, the fuel continuity equation for common rail systems is given:

[0099]

[0100] In the formula, Q pump The fuel flow rate supplied to the common rail by the high-pressure fuel pump is 0 during the injection process; Q inj Q represents the fuel injection rate. Leak denoted as the fuel leakage rate of the injector; E is the bulk modulus of fuel elasticity; V is the common rail control volume; and P is the instantaneous pressure of the common rail.

[0101] Ignoring changes in fuel temperature during operation, the fuel elastic modulus E is related to pressure, and E can be expressed by the empirical formula:

[0102] E = 1.2 × 10 4 (1+0.001p) (2)

[0103] Under high-pressure fuel, the common rail control volume V changes with p. Let V be determined by the common rail volume Vp. c Its change ΔV is expressed as:

[0104] V = V c +△V(p) (3)

[0105] The formula ΔV(p) represents the change in the common rail volume. Under the action of high-pressure fuel, ΔV(p) is related to p.

[0106] In equation (1) Q leak It consists of two parts: the return rate of the injector control chamber and the leakage rate of the needle valve assembly clearance. Based on the orifice flow equation and the annular clearance leakage equation, we can obtain:

[0107] Q leak =C leak ·Q inj (4)

[0108] In the formula, C leak The fuel leakage coefficient is relatively small and can be taken as a constant.

[0109] Substituting equations (2) to (4) into equation (1), we obtain the mathematical model of the fuel flow process:

[0110]

[0111] make

[0112]

[0113] The nonlinear mathematical model of the fuel injection law based on instantaneous common rail pressure is obtained as follows:

[0114]

[0115] α(p) has three undetermined parameters: V c , △V(p), C leak It can be identified based on the structural parameters of the common rail pipe and experimental simulation data.

[0116] Step 202: Construct the state-space model for fuel injection estimation and discretize it.

[0117] Select the instantaneous pressure p and injection rate Q of the common rail. inj Rate of change of fuel injection rate As three state variables, namely x1 = p, x2 = Q inj , Considering It is approximately a constant, therefore we have According to equation (7), the nonlinear equation of the system can be obtained:

[0118]

[0119] In the formula, y is the measured output of the system, i.e., the instantaneous pressure p. Equation (14) can be written in state-space form as follows:

[0120]

[0121] Discretize the continuous state-space model (15). Let the sampling step size be Δt, and the state variable x(t) at time t k-1 The derivative at time t can be approximated as:

[0122]

[0123] t k t k-1 Replacing k and k-1, equation (16) can be written as:

[0124] x(k)=x(k-1)+Δt·f(x(k-1)) (11)

[0125] Here vector at this time,

[0126]

[0127] The discrete state-space model can then be expressed as:

[0128]

[0129] Step 203: Optimal Estimation Algorithm Based on Kalman Filtering

[0130] After considering the process noise w(k) and the measurement noise v(k), equation (19) can be written as:

[0131]

[0132] In the formula, w(k) and v(k) are uncorrelated zero-mean Gaussian white noise, and w(k) = [w1(k) w2(k) w3(k)] T v(k) is a scalar. The covariance matrices of the two are defined as Q and R, respectively, where Q is a 3×3 diagonal matrix, Q=diag[q1 q2 q3], and R is a scalar, R=r.

[0133] Let the estimated value of vector x(k) be... According to the Kalman filter algorithm, It is further divided into prior estimates. Posterior estimate

[0134] The optimal estimation method based on Kalman filtering includes two update processes: time update and measurement update. In the time update stage, a nonlinear model is used to calculate the prior state estimate. In the measurement update stage, the error between the measured rail pressure value and the prior estimate is used for feedback correction to calculate the posterior estimate, gradually bringing the posterior estimate closer to the true value. The specific steps are as follows.

[0135] Set initial values and P(0) + The covariance matrices are Q and R, respectively. First, time updates are performed:

[0136] ① Calculate the prior estimate using the nonlinear model (19)

[0137]

[0138] ②In At point A, calculate the Jacobian matrices A(k-1) and M(k-1).

[0139] ③ Calculate the covariance matrix P(k) of the prior estimates. - :

[0140] P(k) - =A(k-1)P(k-1) + A(k-1) T +M(k-1)·Q·M(k-1) T (16)

[0141] Measurement update phase:

[0142] ④ Kalman filter gain

[0143] K(k)=P(k) - C(k) T [C(k)P(k) - C(k) T +R] -1 (17)

[0144] ⑤ At time k, the measured value y(k) and the prior estimate The difference is used as feedback to correct the optimal estimation system and obtain the posterior estimate.

[0145]

[0146] ⑥ Calculate the posterior estimation error covariance matrix P(k) + :

[0147] P(k) + =(IK(k)C(k))P(k) - (IK(k)C(k)) T +K(k)·R·K(k) T (19)

[0148] It should be noted that at each time k, the posterior estimate is obtained according to equation (25). In The optimal estimate of the fuel injection rate is:

[0149]

[0150] Step S3, the real-time estimated fuel injection rate The summation is performed during the fuel injection phase to obtain the observed fuel injection quantity.

[0151]

[0152] Where k1 is the start time of fuel injection, k2 is the end time of fuel injection, and k2-k1 is the duration of fuel injection.

[0153] To verify the Kalman filtering method, simulation data was obtained under the conditions of rail pressure 100MPa / injection pulse width 1.0ms. White noise was added to the data, and the optimal estimation of the injection pattern was performed using the Kalman filter designed in this invention. Figures 3 to 5 The estimated results for common rail pressure, injection rate, and injection quantity are shown under the condition of 100 MPa / 1.0 ms. It can be seen that the Kalman filter proposed in this paper can achieve rapid tracking of rail pressure and injection rate. Comparing the estimated injection quantity for a single injection with the actual values, the maximum error is 5.92%, the minimum error is 0.07%, and the average error is 1.99%.

[0154] Step S4, with the estimated fuel injection quantity This feedback loop forms a closed loop for the fuel injection quantity, which is the target fuel injection quantity V. obj Compared with the estimated fuel injection quantity The difference is subtracted, and the resulting fuel injection quantity error ΔV is input into controller 1 (i.e., the fuel injection quantity closed-loop controller). The output of controller 1 is the change in target rail pressure ΔP. obj .

[0155] Furthermore, the fuel injection quantity controller 1 mentioned in step S4 is a PI controller, and the implementation method is as follows:

[0156] In each injection cycle, according to the target injection quantity Vobj Compared with the estimated fuel injection quantity To calculate the error of fuel injection quantity

[0157]

[0158] Controller 1 uses a PI controller, and the controller output is the change in target rail pressure ΔP. obj

[0159] △P obj =k p ·△V+k i ·∫△Vdt (23)

[0160] In the formula, k p k is the proportionality coefficient. i This is the integral coefficient. In each injection cycle, based on ΔP... obj Adjust the target value P of the rail pressure obj This allows for the adjustment of the fuel injection quantity.

[0161] Step S5, the change in target rail pressure ΔP obj Adding the initial rail pressure P0, we obtain the current target rail pressure P. obj The input is fed into the inner loop of the rail pressure control. The output of the rail pressure controller is the opening degree of the fuel metering valve, which controls the fuel to pass through the injection pump and then to the common rail. The common rail pressure p is the output and feedback of the inner loop.

[0162] The cycle repeats to form a cascade control system for fuel injection quantity.

[0163] A simulation model was established based on the cascade closed-loop control principle of fuel injection quantity in a high-pressure common rail system. At 120 MPa, the target fuel injection quantity is 64.5 mm. 3 (Corresponding to a 1.2ms pulse width), design a PI controller with parameters k. p =1.86, k i =0.8. At t=50ms, an interference ΔV was added. inj =-2mm 3 , Figure 6 This refers to the fuel injection quantity output response of the closed-loop control system. Figure 7 This is the output response of the fuel injection quantity controller. Figure 6 , 7 It can be seen that the fuel injection quantity suddenly decreases at t=50ms. After passing through the fuel injection quantity controller, the change in target rail pressure ΔP is output. obj ΔP obj The injection quantity is increased by increasing the set rail pressure. After several injection cycles, the injection quantity adjustment process is completed, and the target injection quantity matches the actual injection quantity. From Figure 6 and Figure 7It can be seen that the cascade control method proposed in this invention can accurately achieve closed-loop control of the fuel injection quantity.

Claims

1. A cascade closed-loop control method for estimating fuel injection quantity in a high-pressure common rail system based on Kalman filtering, characterized in that, This method consists of a fuel injection quantity closed loop and a rail pressure closed loop. Step S1: Acquire the pressure signal of the common rail pipe in the high-pressure common rail system; Step S2: Using the common rail pressure p output from the rail pressure closed loop as the input to the Kalman filter, the method of estimating the injection quantity of the high-pressure common rail system based on Kalman filtering is applied to obtain the observed value of the injection quantity. Step S3, with the estimated fuel injection quantity This feedback loop forms a closed loop for the fuel injection quantity, which is the target fuel injection quantity V. obj Compared with the estimated fuel injection quantity The difference is subtracted, and the resulting fuel injection quantity error ΔV is input into the fuel injection quantity closed-loop controller. The output of the fuel injection quantity closed-loop controller is the change in target rail pressure ΔP. obj ; Step S4, the change in target rail pressure ΔP obj Adding the initial rail pressure P0, we obtain the current target rail pressure P. obj ; Step S5, target rail pressure P obj The difference between the common rail pressure p and the feedback is input to the rail pressure controller. The output of the rail pressure controller is the opening degree of the fuel metering valve, which controls the fuel to pass through the fuel injection pump and then to the common rail. The common rail pressure p is the output and feedback of the rail pressure closed loop. In step S2, the specific steps of the method for estimating the injection quantity of the high-pressure common rail system based on Kalman filtering are as follows: 1) Based on the fuel system flow process, establish a nonlinear mathematical model of the fuel injection law based on instantaneous common rail pressure: The nonlinear mathematical model of the fuel injection law based on instantaneous common rail pressure is as follows: In equation (1), p is the instantaneous pressure of the common rail, and Q inj This refers to the fuel injection rate; In equation (2), C leak V is the fuel leakage coefficient, taken as a constant; c ΔV(p) represents the common rail volume; ΔV(p) represents the change in common rail volume, which is related to the instantaneous pressure p of the common rail. 2) Constructing the state-space model: Select common rail pressure p and injection rate Q inj Rate of change of fuel injection rate The three variables are used as state variables, namely x1 = p, x2 = Q. inj , It is approximately a constant, therefore we have According to equation (1), the nonlinear equation of the system can be obtained: In equation (3), y is the measured output of the system, i.e., the instantaneous pressure p; Equation (3) can be written in state-space form as follows: 3) Discretize the continuous state-space model (4): Let the sampling step size be Δt, and the state variable x at time t k-1 The derivative at time t can be approximated as: t k t k-1 Replacing k and k-1, equation (5) can be written as: x(k)=x(k-1)+Δt·f(x(k-1)) (6) Here vector at this time, The discrete state-space model can then be expressed as: 4) Considering process noise w(k) and measurement noise v(k) in the model, equation (8) can be written as: In equation (9), w(k) and v(k) are uncorrelated zero-mean Gaussian white noise, and w(k) = [w1(k)w2(k)w3(k)] T Let v(k) be a scalar; define the covariance matrices of w(k) and v(k) as Q and R, respectively, where Q is a 3×3 diagonal matrix, Q = diag[q1q2 q3], and R is a scalar, R = r; let the estimated value of x(k) be... According to the Kalman filter algorithm, 5) Linearize the nonlinear model: At sampling time k, let the estimated value of x(k) be... According to the Kalman filter algorithm, Divided into prior estimates and posterior estimate The posterior estimate of the state variable x(k) at time k-1 Therefore in At w(k-1)0=0, performing a Taylor series expansion on x(k)=g(x(k-1),w(k-1)), omitting terms of second order and above, yields an approximately linearized expression of the state equation: In equation (10), A(k-1) and M(k-1) are the values ​​of x(k) in the equation. The Jacobian matrix at that point, i.e.: Substituting equation (7) into equation (11), we get M(k-1) is a constant: 6) Optimal estimation of fuel injection quantity for high-pressure common rail system based on Kalman filtering: Set initial values and P(0) + The covariance matrices are Q and R, respectively. First, time updates are performed starting from time k=1: ① Calculate the prior estimate using the discrete state-space model (8) ②In At point A, calculate the Jacobian matrices A(k-1) and M(k-1); ③ Calculate the covariance matrix P(k) of the prior estimates. - : P(k) - =A(k-1)P(k-1) + A(k-1) T +M(k-1)·Q·M(k-1) T (15) ④ Calculate the Kalman filter gain K(k)=P(k) - C(k) T [C(k)P(k) - C(k) T +R] -1 (16) ⑤ At time k, the measured value y(k) and the prior estimate The difference is used as feedback to correct the optimal estimation system and obtain the posterior estimate. Equation (17) yields the posterior estimate at time k. In That is, the optimal estimate of the fuel injection rate: ⑥ Calculate the posterior estimation error covariance matrix P(k) + : P(k) + =(I-K(k)C(k))P(k) - (I-K(k)C(k)) T +K(k)·R·K(k) T (19) The posterior estimate is continuously updated by iterating through equations (14) to (19). And the posterior estimation error covariance matrix P(k) + ; 7) Real-time online estimation of fuel injection quantity: Based on the estimated fuel injection rate The estimated amount of fuel injected is obtained by summing the values ​​during the fuel injection phase. Where k1 is the start time of fuel injection, k2 is the end time of fuel injection, and Δt = k2 - k1 is the duration of fuel injection.

2. The cascade closed-loop control method for estimating the injection quantity of a high-pressure common rail system based on Kalman filtering according to claim 1, characterized in that, The fuel injection quantity closed-loop controller mentioned in step S3 is a PI controller, and the controller outputs the change in target rail pressure ΔP. obj The method is as follows: △P obj =k p ·△V+k i ·∫△Vdt (21) In the formula, k p k is the proportionality coefficient. i is the integral coefficient.

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