A design method of injection law observer for electronic fuel control system based on LQR

Abstract

The purpose of the present invention is to provide a design method for an injection law observer of an electronically controlled fuel system based on LQR, comprising the following steps: establishing a mathematical model of the injection law based on instantaneous common rail pressure, identifying the parameters of the working point model, constructing a state space model, and designing a closed-loop observer of the injection law based on LQR. The present invention establishes a nonlinear model of the injection law based on the instantaneous rail pressure, and performs linearization and model parameter identification at the working point. By selecting three variables, namely, the instantaneous pressure of the common rail pipe, the injection rate, and the rate of change of the injection rate, an observable state space model is established. Based on the established state space model, a real-time observation method of the injection law based on LQR is proposed. The performance of the observer is adjusted by the state error weighting matrix and the output error feedback control weighting matrix to achieve the optimal design of the feedback gain of the closed-loop observer.

Description

Technical Field

[0001] The invention relates to a diesel engine fuel system, in particular to a method for observing the fuel injection law of an electronically controlled fuel system. Background Art

[0002] At present, the fuel injection quantity control of the diesel engine high-pressure common rail system is based on the calibrated MAP map for open-loop control, and the injection process is indirectly adjusted through the rail pressure closed loop and the speed closed loop. However, due to the complex hydraulic influence of the high-pressure common rail system, with the influence of factors such as the working environment, operating conditions, and system structural parameter degradation, this method is difficult to ensure the consistency and reliability of the cyclic injection performance during the operation of the diesel engine.

[0003] In the actual operation of the diesel engine, if the injection information can be monitored in real time, the injection law can be adjusted and corrected in a closed loop, which can greatly improve the accuracy of the injection control. During the injection process, the fuel flows in the pipeline, and the pressure changes caused by the injection propagate in the hydraulic network. The instantaneous fluctuation of the fuel pressure can reflect the information of the injection process. Summary of the invention

[0004] The object of the present invention is to provide a design method for an injection law observer of an electronically controlled fuel system based on LQR, which can realize real-time observation and closed-loop correction of the cyclic injection amount of a high-pressure common rail system.

[0005] The object of the present invention is achieved in that:

[0006] The present invention provides a design method for an electronically controlled fuel system injection law observer based on LQR, which is characterized by:

[0007] (1) Establish a mathematical model of injection law based on instantaneous common rail pressure:

[0008] During the operation of the high-pressure common rail system, the fuel is delivered from the high-pressure oil pump to the common rail pipe, and then distributed to each injector through the high-pressure oil pipe. Part of the fuel entering the injector enters the control chamber for the oil return process, and the other part enters the oil storage chamber for the injection process. Based on the above process, the fuel continuity equation of the common rail pipe is given:

[0009]

[0010] In the formula, Q pump Q is the fuel flow rate supplied by the high pressure fuel pump to the common rail pipe, inj is the injection rate, Q Leak is the fuel leakage rate of the injector, E is the bulk elastic modulus of the fuel, V is the control volume of the common rail pipe, and p is the instantaneous pressure of the common rail pipe, i.e., the rail pressure;

[0011] Ignoring the change in fuel temperature during operation, the fuel elastic modulus E is related to the rail pressure p. The empirical formula of E is expressed as:

[0012] E = 1.2 × 10 4 (1+0.001p)

[0013] Under the action of high-pressure fuel, the common rail control volume V changes with p. Let V be the common rail volume V c And its change ΔV is expressed as:

[0014] V=V c +ΔV(p)

[0015] Where V c is the volume of the common rail pipe, ΔV(p) is the change in the volume of the common rail pipe, and the ΔV(p) caused by the high-pressure fuel is related to p, which is expressed as.

[0016] ΔV=C1(p)·p

[0017] Where: C1(p) is the volume compensation coefficient;

[0018] In addition, Q leak It consists of two parts: the oil return rate of the injector control chamber and the gap leakage rate of the needle valve pair. According to the nozzle flow equation and the annular gap leakage equation, it is obtained:

[0019] Q leak =C leak (p)·Q inj

[0020] Among them, C leak (p) is the fuel leakage coefficient;

[0021] E = 1.2 × 10 4 (1+0.001p) 、 V=V c +ΔV(p) 、 ΔV=C1(p)·p The mathematical model of the fuel flow process is simplified as follows:

[0022]

[0023] make

[0024]

[0025] The mathematical model of injection law based on instantaneous common rail pressure is obtained as follows:

[0026]

[0027] (2) Working point model parameter identification:

[0028] Use a linear model to describe the relationship between fuel flow and pressure change in the common rail pipe

[0029]

[0030] The above formula can be converted to

[0031] dp=K·Q inj ·dt

[0032] dp and Q inj The term is integrated during the injection period to obtain the relationship between the injection amount and the rail pressure change, that is,

[0033] ∫dp=K·∫Q inj dt

[0034] Δp=K·V inj

[0035] Where: Δp is the rail pressure change during injection, V inj is the amount of fuel injected by the injector during the injection period. The injection process corresponds to the rail pressure drop stage. The model parameter K is identified through the rail pressure drop and injection amount information during the injection stage.

[0036] (3) Constructing the state space model:

[0037] Select the instantaneous pressure p and injection rate Q of the common rail pipe inj , the rate of change of injection rate Three variables are used as state variables, namely x1 = p, x2 = Q inj , Considering is approximately a constant, so According to the formula The state space model is obtained as follows:

[0038]

[0039] In the formula, C = [1 00], y is the output of the system;

[0040] Determine the observability of the system, model The observable matrix Ro is calculated as follows:

[0041]

[0042] Ro is full rank, which means that all state variables of the system are observable, and a closed-loop observer can be designed to observe each state variable through the output signal;

[0043] (4) Design of closed-loop observer for injection law based on LQR:

[0044] Closed-loop observer design:

[0045] The state variables of the observer are Let the corresponding observer feedback gain matrix H = [H1, H2, H3] T , then the model of the closed-loop observer is

[0046]

[0047]

[0048] In the formula, is the output of the closed-loop observer model, y is the signal measured by the sensor, here it is the instantaneous rail pressure signal, when the state of the observer When it is not equal to the actual state x of the system, it is reflected in their output The difference between y and y is also not equal. The deviation between the two is used to correct the observed state in real time, and the rolling optimization is performed to form a closed-loop state observer.

[0049] The observation equation of the injection rate is:

[0050]

[0051] Integrate the observed injection rate during the injection phase to obtain the observed value of the injection amount

[0052]

[0053] Where: t0 is the injection start time; t n The moment when fuel injection ends;

[0054] Feedback gain optimization based on LQR:

[0055] The state observation error of the closed-loop observer is defined as

[0056]

[0057] Then the quadratic objective function is

[0058]

[0059] Where: Q is the state error weighting matrix; R is the output error feedback control weighting matrix;

[0060] Q is a semi-positive definite matrix, let Q = diag[q1 q2 q3], q1, q2, q3 are the weight coefficients of the observation errors of the three state variables, R is a positive definite matrix, the only measurable output is the rail pressure p, so R is a 1x1 dimensional matrix, let R = [r];

[0061] By solving the algebraic Riccati equation, we can obtain the positive definite matrix P

[0062] AP+PA T -PC T R -1 CP+Q=0

[0063] Then the optimal error feedback matrix H of the closed-loop observer is

[0064] H T =R -1 CP

[0065] The LQR-based observer adjusts the observation performance of the observer by selecting Q and R.

[0066] The advantages of the present invention are:

[0067] 1. A nonlinear model of fuel injection law based on instantaneous rail pressure was established, and linearization and model parameter identification were performed at the working point. By selecting the instantaneous pressure p of the common rail pipe and the injection rate Q inj , the rate of change of injection rate Three variables are used to establish an observable state space model.

[0068] 2. Based on the established state space model, a real-time observation method of injection law based on LQR is proposed. The performance of the observer is adjusted through the state error weighting matrix and the output error feedback control weighting matrix to achieve the optimal design of the closed-loop observer feedback gain. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 It is a block diagram of the closed-loop observer of the fuel injection law of the present invention;

[0070] Figure 2 This is a comparison chart between the observed value and the actual value of the injection law;

[0071] Figure 3 It is a comparison chart between the observed value and the actual value of the common rail pressure;

[0072] Figure 4 This is a comparison chart between the observed value and the actual value of the injection rate;

[0073] Figure 5 This is a comparison chart between the observed and actual values ​​of the injection amount. DETAILED DESCRIPTION

[0074] The present invention is described in more detail below with reference to the accompanying drawings:

[0075] Combination Figure 1-5 , the present invention specifically comprises the following steps:

[0076] Step 1. Establish a mathematical model of injection law based on instantaneous common rail pressure

[0077] During the operation of the high-pressure common rail system, the fuel is delivered from the high-pressure oil pump to the common rail pipe, and then distributed to each injector through the high-pressure oil pipe. Part of the fuel entering the injector enters the control chamber for the oil return process, and the other part enters the oil storage chamber for the injection process. Based on the above physical process, the fuel continuity equation of the common rail pipe is given:

[0078]

[0079] In the formula, Q pump Q is the fuel flow rate supplied by the high-pressure fuel pump to the common rail pipe, and its value is 0 during the injection process; inj is the injection rate; Q Leak is the fuel leakage rate of the injector; E is the bulk elastic modulus of the fuel; V is the control volume of the common rail pipe; p is the instantaneous pressure of the common rail pipe, that is, the rail pressure.

[0080] Ignoring the change in fuel temperature during operation, the fuel elastic modulus E is related to the rail pressure p. The empirical formula of E is expressed as:

[0081] E = 1.2 × 10 4 (1+0.001p) (2)

[0082] Under the action of high-pressure fuel, the common rail control volume V changes with p. Let V be the common rail volume V c And its change ΔV is expressed as:

[0083] V=V c +ΔV(p) (3)

[0084] Where V c is the volume of the common rail pipe; ΔV(p) is the change in the volume of the common rail pipe. The ΔV(p) caused by high-pressure fuel is related to p and can be expressed as.

[0085] ΔV=C1(p)·p (4)

[0086] Where: C1(p) is the volume compensation coefficient.

[0087] In addition, Q in formula (1) leak It consists of two parts: the oil return rate of the injector control chamber and the gap leakage rate of the needle valve pair. According to the nozzle flow equation and the annular gap leakage equation, it can be obtained:

[0088] Q leak =C leak (p)·Q inj (4)

[0089] Among them, C leak(p) is the fuel leakage coefficient, which changes with the rail pressure.

[0090] Substituting equations (2) to (4) into equation (1), the mathematical model of the fuel flow process is simplified as follows:

[0091]

[0092] make

[0093]

[0094] The mathematical model of injection law based on instantaneous common rail pressure is obtained as follows:

[0095]

[0096] In the formula, K(p) changes with the rail pressure p, and the model is a nonlinear differential equation.

[0097] Step 2. Identification of operating point model parameters

[0098] During the injection process of the common rail system, the outflow of high-pressure fuel causes the rail pressure to change. Due to the pressure accumulation of the common rail pipe, the rail pressure fluctuation caused by fuel injection is about 5%, and the change in K value caused by this is small. Therefore, under a certain set rail pressure, K can be approximated as a constant, and a linear model can be used to describe the relationship between fuel flow and pressure change in the common rail pipe.

[0099]

[0100] At this time, there is an undetermined coefficient K in the model. Formula (8) can be converted to

[0101] dp=K·Q inj ·dt (9)

[0102] dp and Q inj The term is integrated during the injection period to obtain the relationship between the injection amount and the rail pressure change, that is,

[0103] ∫dp=K·∫Q inj dt (10)

[0104] Δp=K·V inj (11)

[0105] Where: Δp is the rail pressure change during injection, V inj is the amount of fuel injected by the injector during the injection period. Since the injection process corresponds to the rail pressure drop stage, the model parameter K can be identified through the rail pressure drop and injection amount information during the injection stage.

[0106] A high-pressure common rail system simulation model was built based on AMESim. The simulation was carried out at a rail pressure of 160 MPa, with the injection pulse width ranging from 0.8 ms to 1.8 ms and an interval of 0.1 ms. The injection amount and rail pressure drop under different pulse widths were obtained. The parameter K value was identified based on this data, as shown in Table 1.

[0107] Table 1 Injection stage related parameters and identification parameters

[0108]

[0109] It can be seen from Table 1 that the K value does not change much under different injection pulse widths. Therefore, under the rail pressure of 160 MPa, the identified average value of K is taken, which is -0.112.

[0110] Step 3. Construct the state-space model.

[0111] Select the instantaneous pressure p and injection rate Q of the common rail pipe inj , the rate of change of injection rate Three variables are used as state variables, namely x1 = p, x2 = Q inj , Considering is approximately a constant, so According to formula (8), the state space model is as follows:

[0112]

[0113] In the formula, C=[1 0 0], y is the output of the system.

[0114] Then determine the observability of the system. The observability matrix Ro of model (12) is calculated as follows:

[0115]

[0116] Ro is full rank, which means that all state variables of the system are observable, and a closed-loop observer can be designed to observe each state variable through the output signal.

[0117] Step 4. Design of closed-loop observer for injection pattern based on LQR

[0118] Step 4.1 Closed-loop observer design

[0119] The state variables of the observer are Let the corresponding observer feedback gain matrix H = [H1, H2, H3] T , then the model of the closed-loop observer is

[0120]

[0121] In the formula, is the output of the closed-loop observer model, and y is the signal measured by the sensor, which is the instantaneous rail pressure signal. The structure of the closed-loop observer of the injection quantity proposed by the present invention is as follows: Figure 1 shown.

[0122] The observation equation of the injection rate is:

[0123]

[0124] The observed injection rate is integrated during the injection phase to obtain the injection amount.

[0125]

[0126] Where: t0 is the injection start time; t n The injection end time.

[0127] 4.2 Feedback gain optimization based on LQR

[0128] The state observation error of the closed-loop observer is defined as

[0129]

[0130] Then the quadratic objective function is

[0131]

[0132] Where: Q is the state error weighting matrix; R is the output error feedback control weighting matrix.

[0133] Q is a semi-positive definite matrix, let Q = diag[q1 q2 q3], q1, q2, q3 are the weight coefficients of the observation errors of the three state variables. R is a positive definite matrix, since the only measurable output is the rail pressure p, R is a 1x1 dimensional matrix, let R = [r].

[0134] By solving the algebraic Riccati equation, we can obtain the positive definite matrix P

[0135] AP+PA T -PC T R -1 CP+Q=0 (19)

[0136] Then the optimal error feedback matrix H of the closed-loop observer is

[0137] H T =R -1 CP (20)

[0138] LQR control adjusts the observer performance by selecting Q and R.

[0139] Under the condition of rail pressure of 160Mpa and injection pulse width of 1.2ms, the method proposed in the present invention is applied to conduct simulation research. The initial state values ​​of the three state variables of the state observer are set to x0 = [1600; 0; 0], at this time, Q = diag

[11501] , R = [0.001], at this time, the feedback gain matrix H = [3556.45-387.32-31.62] T, and the pole is located at [-0.0816, -1778.2 + 1778.0i, -1778.2-1778.0i].

[0140] Figures 2 to 5 This is the result of observation of fuel injection law. Figure 2 , 3 4, it can be seen that under the condition of 1.2ms injection pulse width, the rail pressure and injection rate observation values ​​are highly consistent with the simulation data. Figure 5 As shown, there are 50 consecutive injections, and the maximum error between the observed value and the actual value of each injection amount is 6.39%, the minimum error is 1.47%, and the average error is 4.46%.

Claims

1. A design method for an injection law observer of an electronically controlled fuel system based on LQR, characterized by: (1) Establish a mathematical model of injection law based on instantaneous common rail pressure: During the operation of the high-pressure common rail system, the fuel is delivered from the high-pressure oil pump to the common rail pipe, and then distributed to each injector through the high-pressure oil pipe. Part of the fuel entering the injector enters the control chamber for the oil return process, and the other part enters the oil storage chamber for the injection process. Based on the above process, the fuel continuity equation of the common rail pipe is given: In the formula, Q pump Q is the fuel flow rate supplied by the high pressure fuel pump to the common rail pipe, inj is the injection rate, Q Leak is the fuel leakage rate of the injector, E is the bulk elastic modulus of the fuel, V is the control volume of the common rail pipe, and p is the instantaneous pressure of the common rail pipe, i.e., the rail pressure; Ignoring the change in fuel temperature during operation, the fuel elastic modulus E is related to the rail pressure p. The empirical formula of E is expressed as: E=1.2×10 4 (1+0.001p) Under the action of high-pressure fuel, the common rail control volume V changes with p. Let V be the common rail volume V c And its change ΔV is expressed as: V=V c +ΔV(p) Where V c is the volume of the common rail pipe, ΔV(p) is the change in the volume of the common rail pipe, and the ΔV(p) caused by the high-pressure fuel is related to p, which can be expressed as: ΔV=C1(p)·p Where: C1(p) is the volume compensation coefficient; In addition, Q leak It consists of two parts: the oil return rate of the injector control chamber and the gap leakage rate of the needle valve pair. According to the nozzle flow equation and the annular gap leakage equation, it is obtained: Q leak =C leak (p)·Q inj Among them, C leak (p) is the fuel leakage coefficient; E = 1.2 × 10 4 (1+0.001p), V=V c +ΔV(p),ΔV=C1(p·p) The mathematical model of the fuel flow process is simplified as follows: make The mathematical model of injection law based on instantaneous common rail pressure is obtained as follows: (2) Working point model parameter identification: Use a linear model to describe the relationship between fuel flow and pressure change in the common rail pipe The above formula can be converted to dp=K·Q inj ·dt dp and Q inj The term is integrated during the injection period to obtain the relationship between the injection amount and the rail pressure change, that is, ∫dp=K·∫Q inj dt Δp=K·V inj Where: Δp is the rail pressure change during injection, V inj is the amount of fuel injected by the injector during the injection period. The injection process corresponds to the rail pressure drop stage. The model parameter K is identified through the rail pressure drop and injection amount information during the injection stage. (3) Constructing the state space model: Select the instantaneous pressure p and injection rate Q of the common rail pipe inj , the rate of change of injection rate Three variables are used as state variables, namely x1 = p, x2 = Q inj , Considering is approximately a constant, so According to the formula The state space model is obtained as follows: y=Cx In the formula, C = [1 0 0], y is the output of the system; Determine the observability of the system, model The observable matrix Ro is calculated as follows: Ro is full rank, which means that all state variables of the system are observable, and a closed-loop observer can be designed to observe each state variable through the output signal; (4) Design of closed-loop observer for injection law based on LQR: Closed-loop observer design: The state variables of the observer are Let the corresponding observer feedback gain matrix H = [H1, H2, H3] T , then the model of the closed-loop observer is In the formula, is the output of the closed-loop observer model, y is the signal measured by the sensor, here it is the instantaneous rail pressure signal, when the state of the observer When it is not equal to the actual state x of the system, it is reflected in their output The difference between y and y is also not equal. The deviation between the two is used to correct the observed state in real time, and the rolling optimization is performed to form a closed-loop state observer. The observation equation of the injection rate is: Integrate the observed injection rate during the injection phase to obtain the observed value of the injection amount Where: t0 is the injection start time; t n The moment when fuel injection ends; Feedback gain optimization based on LQR: The state observation error of the closed-loop observer is defined as Then the quadratic objective function is Where: Q is the state error weighting matrix; R is the output error feedback control weighting matrix; Q is a semi-positive definite matrix, let Q = diag[q1 q2 q3], q1, q2, q3 are the weight coefficients of the observation errors of the three state variables, R is a positive definite matrix, the only measurable output is the rail pressure p, so R is a 1x1 dimensional matrix, let R = [r]; By solving the algebraic Riccati equation, we can obtain the positive definite matrix P AP+PA T -PC T R -1 CP+Q=0 Then the optimal error feedback matrix H of the closed-loop observer is H T =R -1 CP The LQR-based observer adjusts the observation performance of the observer by selecting Q and R.

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