Active disturbance rejection control method for engine air-fuel ratio delay active adaptation based on control loop reverse design

Abstract

The invention discloses an active disturbance rejection control method for active adaptation of air-fuel ratio delay of an engine based on reverse design of a control loop, which establishes a control-oriented air-fuel ratio system model, has high model precision and small steady-state error, and can accurately reflect the dynamic mixing process and delay process of the air-fuel ratio.

Description

Technical Field

[0001] The present invention relates to the technical field of engine control, and particularly to an active disturbance rejection control method for engine air-fuel ratio delay active adaptation based on reverse design of a control loop. Background Technique

[0002] In modern automotive engines, precise control of the air-fuel ratio is crucial for achieving efficient engine operation, reducing fuel consumption, and minimizing emissions. Traditional air-fuel ratio control methods are typically based on fixed control strategies and are difficult to adapt to the dynamic changes of the engine under different operating conditions. Especially in the presence of delay faults or external disturbances, the control effect will be significantly affected, resulting in large fluctuations in the air-fuel ratio and affecting engine performance and emission indicators.

[0003] Air-fuel ratio control faces many challenges: on the one hand, exhaust delay affects the control quality. There is a delay between the air-fuel ratio value measured by the oxygen sensor and the in-cylinder true value, which limits the bandwidth and adjustment speed of the closed-loop system; on the other hand, there are internal and external disturbances in the air-fuel ratio system, such as the inconsistency between the target fuel injection quantity and the actual fuel injection quantity, the impact of exhaust gas recirculation (EGR) on air-fuel ratio measurement, etc. Traditional control methods such as PID control are difficult to achieve satisfactory dynamic responses under dynamic operating conditions. Although model-based control methods have made certain breakthroughs, they rely highly on model accuracy, involve large amounts of computation, and are not easily implemented in engineering.

[0004] In response to the problems and challenges of the air-fuel ratio system, various solutions have been proposed in the past. The most commonly used method is to regard the air-fuel ratio dynamics as a black box and use a PID controller. The literature (Franceschi E M, Muske K R, Jones J P, et al. An Adaptive Delay-Compensated PID Air Fuel Ratio Controller[J]. Mathematical Analysis, 2007, 1.) uses a PID control algorithm to compensate for the delay caused by the transmission time between the sensor and the actuator. However, a PID controller with fixed gains cannot achieve satisfactory dynamic responses under all operating conditions.

[0005] To solve the problem of system parameter variation under dynamic operating conditions, the literature (Ebrahimi B, Tafreshi R, Masudi H, et al. A parameter-varying filtered PID strategy for air-fuel ratio control of spark ignition engines [J]. Control engineering practice, 2012(8):20.) added a dynamic compensator to the PID control to adapt to the changes in engine operating conditions and improved the control performance.

[0006] Compared with the pure black-box solution, another type of representative method is to regard the air-fuel ratio system as a grey box and use a model-based control method for control. The literature (Liu Xiao-Liang, Wang Sheng-Chang, Li Mao-Yue. Research on air-fuel ratio control and time delay. Highways and Automotive Applications, 2008, (2): 11-14.) studied the time-delay problem in gasoline engine air-fuel ratio control and proposed a method based on a state observer to improve the real-time performance of the control system. The literature (Hou Zhi-Xiang, Wu Yi-Hu, Shen Qun-Tai. Advanced control strategies for engine transient air / fuleratio. Transactions of CSICE, 2003, b21 / b(5): 369-373.) explored the advanced control strategies for the air-fuel ratio under transient conditions of vehicle gasoline engines and improved the control performance by introducing a dynamic compensation mechanism. The literature (Wang S W, Yu D L, Gomm J B, Page G F, Douglas S S. Adaptive neural network model based predictive control for air-fuel ratio of SI engines. Engineering Applications of Artificial Intelligence, 2006, b19 / b(2): 189-200.) used an adaptive neural network model-based predictive control method to achieve precise control of the air-fuel ratio of spark-ignition engines and effectively cope with various disturbances that may exist in the system.The literature (Zhang F, Grigoriadis K M, Franchek M A, Makki I H. Transient lean burn air-fuel ratio control using input shaping method combined with linear parameter-varying control. In: Proceedings of the 2006 American Control Conference. Minnesota, USA: IEEE, 2006. 3290-3295.) proposed a method combining input shaping method with linear parameter-varying control to solve the problem of transient air-fuel ratio control under lean burn conditions, thereby enhancing the anti-disturbance ability of the system.

[0007] Although the above methods have achieved breakthroughs at various levels, their control effects highly depend on the accuracy of the control-oriented model. The lack of model accuracy will greatly affect the performance of the controller. At the same time, the improvement of model accuracy will inevitably lead to an increase in the computational workload of such controllers, which will make the controllers not easy to be implemented in engineering. Therefore, in practical applications, it is necessary to balance the relationship between model complexity and computational efficiency to ensure that the designed control system can not only meet the performance requirements but also be implemented in engineering. Summary of the Invention

[0008] The object of the present invention is to provide an active disturbance rejection control method for engine air-fuel ratio delay adaptation based on reverse design of the control loop in view of the technical defects existing in the prior art.

[0009] The technical solution adopted to achieve the object of the present invention is as follows:

[0010] The active disturbance rejection control method for engine air-fuel ratio delay adaptation based on reverse design of the control loop includes the following steps:

[0011] Step 1: According to the engine intake and exhaust processes and the response of sensors during the intake and exhaust processes, establish an air-fuel ratio system model in which a first-order inertial link is connected in series with a pure delay link, and convert the air-fuel ratio system model into a control-oriented air-fuel ratio system model, where the total disturbance f(t) is included in the control-oriented air-fuel ratio system model;

[0012] Step 2: Establish an air-fuel ratio system state space model for a first-order closed-loop system with pure delay, set the control input U1(s) and the system state X1(s), and through Laplace transform, obtain the closed-loop transfer function G(s) of the first-order system, as well as the Laplace form of the delay time between the system output Y1(s) and the system state X1(s) Design the controller of the air-fuel ratio system based on the closed-loop transfer function G(s), and obtain the tracking error E of the controller p (s);

[0013] Step 3, ignoring the total disturbance f(t), establish the closed-loop transfer function G of the first-order system with pure delay XU (s) and set the control input U(s), calculate the system state X(s), set the air-fuel ratio target value R(s), calculate the tracking error E p (s), perform time-domain conversion on it to obtain the tracking error e p (t), based on this, design an extended state observer including the total disturbance and a feedback controller for part of the disturbance, where the extended state observer contains parameters β1 and β2, and the feedback controller contains parameter β2;

[0014] Step 4, perform Laplace transform on the extended state observer in Step 3 to obtain Z2(s), perform Laplace transform on the feedback controller to obtain U2(s), combine the tracking error E p (s) and the air-fuel ratio target value R(s), and configure the parameters β1 and β2, through the closed-loop transfer function G XU (s), obtain the output Y(s) of the air-fuel ratio system, and then calculate the closed-loop transfer function G of the air-fuel ratio system without delay YR (s);

[0015] Step 5, according to the air-fuel ratio system model for control, ignoring the total disturbance f(t), model in the Smith predictor. To estimate the delay time τ2 of the air-fuel ratio system, assume that the actual delay time τ1 of the system is equal to the modeled delay time τ2, and then the Laplace form of the delay time in Step 2 Compensate the closed-loop transfer function G without delay in Step 4 YR (s) for a delay time, combine with the air-fuel ratio target value R(s) to obtain the output Y of the air-fuel ratio system with delay compensation P (s).

[0016] In the above technical solution, in Step 1, the air-fuel ratio system model:

[0017]

[0018] Among them, is the fuel-air equivalence ratio, air-fuel ratio m f is the actual fuel injection quantity of the injector, m air is the fresh air mass, R af is 14.67, represents the fuel-air equivalence ratio in the cylinder, is the sensor measurement value of the fuel-air equivalence ratio, is the fuel-air equivalence ratio after the mixing process without delay, and the time constant is denoted as τ m ; τ d represents the delay time of the exhaust gas transportation process in the exhaust pipe, approximated as a delay link.

[0019] In the above technical solution, in step 1, the control-oriented air-fuel ratio system model is:

[0020]

[0021] where the control input the control system state the control output and respectively represent the estimated values of a and b, and a and b represent two parameters in the control-oriented air-fuel ratio system model.

[0022] In the above technical solution, in step 1, f(t) represents the sum of disturbances caused by internal and external factors in the system, expressed as:

[0023]

[0024] where Δ a and Δ b respectively represent the modeling errors of a and b, and Δ m is the modeling error of τ m . is caused by the fresh air volume error

[0025] In the above technical solution, in step 2, the air-fuel ratio state space model can be expressed as:

[0026]

[0027] where x1 represents the air-fuel ratio system state, represents the derivative of x1, y1 represents the system output, u1 represents the control input, and τ1 represents the system delay time;

[0028] The result after Laplace transform is:

[0029]

[0030] where G(s) is the transfer function of the system state X1(s) to the control input U1(s).

[0031] In the above technical solution, in step 2, the controller of the air-fuel ratio system:

[0032]

[0033] Among them, U1(s) represents the control input, c1(s) is a supposed polynomial, Y1(s) represents the system output, R(s) represents the target value of the control output, G(s) is the closed-loop transfer function of the system state X1(s) with respect to the control input U1(s), τ1 represents the system delay time,

[0034] In the above technical solution, in step 3, the transfer function

[0035] X(s) = G XU (s)U(s)

[0036]

[0037] In the above technical solution, in step 3, E p (s) = R(s) - X(s), which is converted into the time domain form: e p (t) = r(t) - x(t).

[0038] The extended state observer ESO is expressed as:

[0039]

[0040] Among them, z1 and e p (t) represent the input of the ESO, represents the derivative of z1, and respectively represent the estimated values of a and b, β1 and β2 represent the parameters in the ESO, and the total disturbance f(t) is the sum of β1(e p (t) - z1(t)) and z2, represents the derivative of z2.

[0041] In the above technical solution, in step 3, the feedback controller is:

[0042]

[0043] Among them, u(t) represents the control input, k p represents the parameter in the dynamic error in.

[0044] In the above technical solution, in step 4, the extended state observer is Laplace-transformed to eliminate z1, and we can get:

[0045]

[0046] The feedback controller is Laplace-transformed to get:

[0047]

[0048] Bring the tracking error E p (s)=R(s)-X(s) and the Laplace-transformed extended state observer into the Laplace-transformed feedback controller to obtain the Laplace-transformed control input U(s):

[0049]

[0050] Meanwhile,

[0051]

[0052] The parameter configuration is as follows:

[0053]

[0054] Wherein, represents the bandwidth of the ESO, and ξ represents the damping of the ESO.

[0055] In the above technical solution, in step 4, the closed-loop transfer function of the system is:

[0056]

[0057] Wherein, is the estimated value of the time constant.

[0058] In the above technical solution, in step 5, the closed-loop transfer function of the system is:

[0059]

[0060] In the above technical solution, in step 5, according to the control-oriented air-fuel ratio system model, the Smith predictor is modeled as:

[0061]

[0062] Wherein, x m (t) and y m (t) are the model estimated values of x(t) and y(t) respectively, and τ s is the estimated value of τ d ;

[0063] The air-fuel ratio output value with delay is:

[0064] y p (t)=y(t)-y m (t)+x m (t)

[0065] Wherein, y p (t) is Laplace-transformed to YP (s).

[0066] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0067] 1. The present invention establishes a control-oriented air-fuel ratio system model with high model accuracy and small steady-state error, which can accurately reflect the dynamic mixing process and delay process of the air-fuel ratio.

[0068] 2. The control algorithm of the present invention can effectively handle multi-interference problems inside and outside the system, improve the robustness to delay, and avoid the instability caused by the adjustment of the controller gain.

[0069] 3. The Smith predictor with angular discretization improves the accuracy of the prediction result and improves the dynamic response performance of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 is the effect diagram of the air-fuel ratio model.

[0071] Figure 2 is the structure diagram of the Smith predictor.

[0072] Figure 3 is the system framework diagram of the control method. DETAILED DESCRIPTION OF THE INVENTION

[0073] The present invention will be further described in detail below with reference to specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0074] An active disturbance rejection control algorithm for engine air-fuel ratio delay active adaptation based on control loop reverse design includes the following steps:

[0075] Step 1. According to the engine intake and exhaust processes and the response of sensors during the intake and exhaust processes, establish an air-fuel ratio system model in which a first-order inertial link is connected in series with a pure delay link, and convert the air-fuel ratio system model into a control-oriented air-fuel ratio system model, where the control-oriented air-fuel ratio system model includes total disturbances

[0076] To simplify the control design, the air-fuel ratio λ is converted into the fuel-air equivalence ratio where is the fuel-air equivalence ratio, R af is 14.67, m air is the fresh air mass, m f is the actual fuel injection amount of the injector (the fuel amount participating in combustion), m f is calculated from and is the value of the fuel-air equivalence ratio measured by the oxygen sensor in the engine exhaust pipe.

[0077] At the beginning of the engine cycle, the piston moves downward, and the cylinder inhales a certain amount of fresh air. At the same time, a certain amount of gasoline is injected into the cylinder and mixed with the fresh air to form a mixture. After the compression stroke and the combustion stroke, exhaust gas is formed and discharged from the cylinder through the exhaust pipe. At the same time, it is sensed by the oxygen sensor installed in the exhaust pipe, so as to measure the actual air-fuel ratio. During the engine cycle, the mixing of the exhaust gas in the exhaust pipe can be regarded as a first-order dynamic process, and the time constant is denoted as τ m ; The transport process of the exhaust gas in the exhaust pipe is approximately a time-delay link, and the time delay is τ d . Based on the above mixing and transport processes, in order to provide a theoretical basis for accurately describing the dynamic characteristics of the engine air-fuel ratio and optimizing the design of the engine control system, in this embodiment, the air-fuel ratio is dynamically modeled as a first-order closed-loop system with pure time delay, which is the series combination of a first-order inertial link and a pure time-delay link. Therefore, the air-fuel ratio system model is:

[0078]

[0079] where, represents the fuel-air equivalence ratio in the cylinder, is the measured value of the oxygen sensor for the fuel-air equivalence ratio, is the fuel-air equivalence ratio of the gasoline injected into the cylinder and the air after the mixing process without time delay, is further expressed as:

[0080]

[0081] where, is the expected fuel injection quantity of the injector, Δm f is the expected fuel injection quantity is the deviation between the expected fuel injection quantity f and the actual fuel injection quantity m, which is caused by factors such as the carbon canister and injector error, is the air-fuel ratio error caused by factors such as fresh air mass error and EGR gas.

[0082] Select as the control system state, as the control input u(t), substitute formula (2) into formula (1), and obtain the state-space model:

[0083]

[0084] where, the control input control system state control output equivalent fuel quantity deviation a and b represent two parameters in the state - space model of the control system. By comparing formulas (1), (2) and (3), the expressions for a and b are obtained as follows:

[0085]

[0086] where, Δ m is the modeling error of the time constant τ m , represents the estimated value of the time constant τ m , N is the engine speed, p em , V em and T em are the pressure, volume and temperature of the exhaust pipe respectively, R is the gas constant of the exhaust gas, and the delay time τ d is modeled as:

[0087]

[0088] Substituting for τ m in formula (4), the estimated values of a and b are obtained:

[0089]

[0090] where, Δ a and Δ b represent the modeling errors of a and b respectively, and represent the estimated values of a and b respectively. Substituting formula (7) into formula (3), the air - fuel ratio system model for control is obtained as:

[0091]

[0092] where, f(t) represents the sum of the disturbances caused by internal and external factors in the system, and its form is

[0093]

[0094] In this embodiment, the test data of the engine bench is used to verify the effect of the proposed air - fuel ratio system model, as Figure 1 shown. The fuel quantity is stepped at 1.6 s and 4.8 s respectively. After about 0.2 s, the estimated value and the actual value of the air - fuel ratio system model start to change. It can be seen that the air - fuel ratio system model can accurately reflect the dynamic mixing process and the delay process of the air - fuel ratio. The steady - state error of the air - fuel ratio is about 2.9%, and the accuracy of the air - fuel ratio system model is relatively high, which can be used as the control model in this embodiment.

[0095] Step 2: Establish the air-fuel ratio system state-space model for a first-order closed-loop system with pure time delay. Set the control input U1(s) and the system state X1(s). After Laplace transform, obtain the closed-loop transfer function G(s) of the first-order system, as well as the Laplace form of the delay time between the system output Y1(s) and the system state X1(s). Design the controller of the air-fuel ratio system based on the closed-loop transfer function G(s), and obtain the tracking error E of the controller p (s).

[0096] For a first-order closed-loop system with pure time delay, if errors and disturbances are not considered, its air-fuel ratio system state-space model can be expressed as follows:

[0097]

[0098] Among them, x1 represents the air-fuel ratio system state, represents the derivative of x1, y1 represents the system output, u1 represents the control input, τ1 represents the system delay time, A and B represent model parameters. Perform Laplace transform on formula (10) to convert the time domain to the complex frequency domain, and the result is:

[0099]

[0100] Among them, s represents the variable in the complex frequency domain, the complex frequency of Laplace transform, G(s) is the first-order system closed-loop transfer function of the system state X1(s) to the control input U1(s), and Y1(s) represents the system output. For a first-order closed-loop system with pure time delay, assume the controller of the air-fuel ratio system (initial form, the same as the following air-fuel ratio extended state observer) is in the following form:

[0101]

[0102] Among them, R(s) represents the air-fuel ratio target value of the control output, and c1(s) and c2(s) are assumed polynomials. Substitute formula (12) into formula (11) and organize to obtain:

[0103]

[0104] To improve the robustness to time delay, it is desired that there is no term, then there must be

[0105]

[0106] Among them, Δ1(s) is the polynomial to be determined, then the closed-loop transfer function of the system is:

[0107]

[0108] To make the closed-loop transfer function of formula (15) stable and have a certain stability margin, the simplest way is as follows:

[0109]

[0110] Then we can get:

[0111]

[0112] Substitute formula (17) into formula (12) and after arrangement, we get:

[0113]

[0114] Formula (18) is the form that the controller should have under normal circumstances. Note that in the above derivation, c1(s) only needs to satisfy being a rational fraction polynomial and being stable, and there is no need to restrict its form. Therefore, c1(s) can be designed to obtain different controllers.

[0115] Step 3: Ignore the total disturbance, establish the closed-loop transfer function G XU (s) of the first-order system with pure delay, set the control input U(s), calculate the system state X(s), set the air-fuel ratio target value R(s), calculate the tracking error E p (s), perform time-domain conversion on it to obtain the tracking error e p (t). Based on this, design an extended state observer and a feedback controller including the total disturbance, where the extended state observer contains parameters β1 and β2;

[0116] For the air-fuel ratio system model formula (8), since it is difficult to obtain the true value of f(t), in this embodiment, an estimation mechanism is introduced to obtain an approximate value of f(t), and then it is compensated in the control law, so as to effectively suppress the disturbance of the air-fuel ratio system. To simplify the algorithm design of this embodiment and capture the main dynamic changes of the air-fuel ratio system, when calculating the transfer function G XU (s) of the air-fuel ratio system state x(t) with respect to the control input u(t), this term is omitted, then:

[0117]

[0118] If we want to use the active disturbance rejection algorithm to control the air-fuel ratio system model (8), the control input must be equivalently written in the form of formula (18), that is, the variable entering the extended state observer ESO must be Let the tracking error E p (s) between the target value and the system state value be:

[0119]

[0120] Substituting equations (20) and (21) into equation (22), we get:

[0121] E p (s) = R(s) - X(s) (23)

[0122] Converting equation (23) into the time domain form, we have:

[0123] e p (t) = r(t) - x(t) (24)

[0124] where r(t) is the target value, and e p (t) is the predicted tracking error, then we have:

[0125]

[0126] For equation (25), considering equivalent to the total disturbance, the air-fuel ratio extended state observer (ESO) can be designed as:

[0127]

[0128] where z1 and e p (t) represent the inputs of the air-fuel ratio extended state observer, represents the derivative of z1, β1 and β2 represent the parameters in the air-fuel ratio extended state observer (ESO), and z2 represents the amount of compensated disturbance in the air-fuel ratio system (a part of the compensated total disturbance), represents the derivative of z2.

[0129] Furthermore, according to the design method of the extended state observer (ESO), the feedback controller can be designed as:

[0130]

[0131] where u(t) represents the control input, and k p represents the parameter in the dynamic error .

[0132] Substituting equation (27) into equation (25), the total disturbance is compensated by the -z2 part in , and the same part in is compensated by , then the predicted tracking error e p (t) can be transformed into the dynamic error:

[0133]

[0134] At this time, it is easy to obtain k p must be negative, and e p (t) can exponentially converge to 0, otherwise it will exponentially diverge.

[0135] Step 4: Take the Laplace transform of the extended state observer in Step 3 to obtain Z2(s), and take the Laplace transform of the feedback controller to obtain U2(s). Combine the tracking error E p (s) and the air-fuel ratio target value R(s), and configure the parameters β1 and β2. Through the closed-loop transfer function G XU (s), obtain the air-fuel ratio system output Y(s), and then calculate the air-fuel ratio system closed-loop transfer function G without delay YR (s).

[0136] Taking the Laplace transform of formula (26) and eliminating z1, we can get:

[0137]

[0138] Taking the Laplace transform of formula (27), we can obtain the control input:

[0139]

[0140] Substitute formulas (23) and (29) into formula (30) and make appropriate arrangements to obtain the control input:

[0141]

[0142] Let U2(s) = F(s)(R(s) - X(s)), where F(s) is a rational polynomial, and also Therefore:

[0143]

[0144] Further arranging, we can get:

[0145]

[0146] Observing formula (33), it can be seen that it is the transfer function of the closed-loop system and there is no delay link in the feedback loop, thus achieving the purpose of eliminating the influence of delay on the control effect.

[0147] In order to eliminate G XU (s) to simplify the transfer function, F(s) needs to have zeros Then substitute into the numerator polynomial of F(s), and we have:

[0148]

[0149] It can be sorted out as follows:

[0150]

[0151] The above formula is the relationship that should be satisfied between β1 and β2. In order to keep the air-fuel ratio expansion state observer ESO itself stable, both β1 and β2 need to satisfy being greater than zero. Therefore, we can take:

[0152]

[0153] Let ω 2 = t - 1, 2ξω = t, then formula (36) can be rewritten as:

[0154]

[0155] Formula (37) is the configuration method of β1 and β2. β1 and β2 are parameters in the air-fuel ratio expansion state observer ESO, is the bandwidth of the air-fuel ratio expansion state observer ESO, and ξ is the damping of the air-fuel ratio expansion state observer ESO.

[0156] Substitute formula (35) into the expression of F(s), we get:

[0157]

[0158] At this time, the closed-loop transfer function is:

[0159]

[0160] When s → 0, G XU (s) → 1, the low-frequency gain of the closed-loop transfer function is 1. Therefore, k p can be designed as any negative number. In particular, at this time, if we let k p = -β1, then another pair of zero-poles can be cancelled. At this time, the closed-loop transfer function of the stable and delay-free system becomes:

[0161]

[0162] At this time, the closed-loop transfer function is surely stable, and it is easy to obtain that it is equivalent to a first-order PI control, that is,

[0163] Step 5: According to the air-fuel ratio system model oriented to control, ignoring the total disturbance f(t), model the Smith predictor to estimate the delay time τ2 of the air-fuel ratio system. Assume that the actual delay time τ1 of the system is equal to the modeled delay time τ2, and then the Laplace form of the delay time in step 2 Compensate the delay-free closed-loop transfer function G YR(s) A delay time, combined with the air-fuel ratio target value R(s), gives the output Y of the air-fuel ratio system with delay compensation P (s).

[0164] The result of the Smith predictor is as Figure 2 shown, G m (s) is the transfer function of the ideal model of the air-fuel ratio system dynamics, τ1 is the actual delay time of the system, τ2 is the delay time obtained by modeling, and Y p (s) is the output of the Smith predictor. Ideally, the modeling is accurate enough, i.e., G m (s) = G p (s) (the general transfer function of the actual air-fuel ratio system), τ1 = τ2, C(s) is the general form of the controller of the actual air-fuel ratio system, and Y act (s) is the output of the actual system. Then the closed-loop transfer function of the system is:

[0165]

[0166] Therefore, according to formulas (40) and (41), G m (s) = G YR (s).

[0167] The result of the system at this time is as Figure 2 shown. Through compensation, the delay link is no longer included in the feedback loop, which is equivalent to predicting the feedback signal in advance, thus eliminating the influence of the delay link on the system stability and improving the control effect of the system.

[0168] For the air-fuel ratio system model (8), its essence is a first-order inertial link in series with a pure delay link. Since f(t) represents the "total disturbance" caused by various internal and external factors and it is difficult to obtain the true value, it is ignored in the modeling of the Smith predictor. Then there is:

[0169]

[0170] where, x m (t) and y m (t) are the estimated values of the air-fuel ratio system model of x(t) and y(t) respectively, τ s is the estimated value of τ d , and the output of the Smith predictor is:

[0171] y p (t) = y(t) - y m (t) + x m (t) (43)

[0172] where, y p(t) is the air-fuel ratio without delay estimated by the Smith predictor, denoted as y p (t) to estimate x(t) (y p (t) is Laplace-transformed to Y P (s)), and then e p (t) can be calculated as follows:

[0173] e p (t) = r(t) - x(t) = r(t) - y p (t) = r(t) - y(t) + y m (t) - x m (t) (44)

[0174] When applied to engine control, models in the forms of formulas (42) and (44) cannot be directly run on the ECU (Electronic Control Unit). Discretization is required. Considering the engine's ignition cycle, the Smith predictor is discretized, that is, formula (44) is discretized to obtain:

[0175] e p (k + 1) = r(k + 1) - y(k + 1) + y m (k + 1) - x m (k + 1) (45)

[0176] Among them, y(k + 1) is the sensor measurement value, and r(k + 1) is the given target value. Then, what needs to be solved are y m (k + 1) and x m (k + 1).

[0177] Taking the discretization of y m (k + 1) as an example. First, the delay time τ measured in seconds s and the time constant are converted to be measured in crankshaft angles, and we have:

[0178]

[0179] Among them, L is the delay time measured in crankshaft angles, T is the time constant measured in crankshaft angles, and N is the engine speed. For formula (42), substituting τ s and with L and T respectively and performing Laplace transformation, we get:

[0180]

[0181] Among them, The bilinear transformation is used to convert D(s) into discrete form, and the formula for bilinear transformation is:

[0182]

[0183] Among them, θ is the discrete step length, which is selected as the ignition interval between cylinders. For a 4-cylinder engine,

[0184] Substitute formula (49) into e -Ls Convert it to z -L / θ , and the discrete form of D(s) can be obtained:

[0185]

[0186] Then there is Y m (z) = D(z)U(z). Substitute D(z) and convert it to the difference form to get:

[0187]

[0188] To prevent The result of is not an integer. Perform linear interpolation on And :

[0189]

[0190] Among them, l is the integer part of , and α is the decimal part of . Substitute formula (52) into formula (51) to obtain the final discrete form of y m :

[0191]

[0192] Similarly, according to the above derivation method, the discrete form of x m can be obtained:

[0193]

[0194] Substitute formulas (53) and (54) into (45) to obtain the calculation formula of e p (k + 1).

[0195] The above is only the preferred embodiment of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. An active disturbance rejection control method for engine air-fuel ratio delay active adaptation based on reverse design of control loop, characterized in that Including the following steps: Step 1: According to the engine intake and exhaust processes and the sensor response during the intake and exhaust processes, establish an air-fuel ratio system model in which a first-order inertial link is connected in series with a pure delay link, and transform the air-fuel ratio system model into an air-fuel ratio system model oriented to control. The air-fuel ratio system model oriented to control includes a total disturbance f(t); Step 2: Establish an air-fuel ratio system state-space model for a first-order closed-loop system with pure time delay. Set the control input U1(s) and the system state X1(s). After Laplace transformation, obtain the closed-loop transfer function G(s) of the first-order system, as well as the Laplace form of the delay time between the system output Y1(s) and the system state X1(s). Design a controller for the air-fuel ratio system based on the closed-loop transfer function G(s) to obtain the tracking error E p (s); Step 3, ignoring the total disturbance f(t), establish the closed-loop transfer function G of the pure time-delay first-order system XU (s) and set the control input U(s), calculate the system state X(s), set the air-fuel ratio target value R(s), and calculate the tracking error E p (s), perform time-domain conversion on it to obtain the tracking error e p (t). Based on this, design an extended state observer including the total disturbance and a feedback controller for part of the disturbance, where the extended state observer contains built-in defined parameters β1 and β2, and the parameters β1 and β2 are used in the derivation of the feedback controller; Step 4: After performing Laplace transform on the extended state observer in Step 3, we obtain Z2(s). After performing Laplace transform on the feedback controller, we obtain U2(s). Combine the tracking error E p (s) and the air-fuel ratio target value R(s), and configure the parameters β1 and β2. Through the closed-loop transfer function G XU (s), we obtain the air-fuel ratio system output Y(s). Then calculate the air-fuel ratio system closed-loop transfer function G YR (s) without delay; Step 5, based on the control-oriented air-fuel ratio system model, ignoring the total disturbance f(t), model the Smith predictor to estimate the delay time τ2 of the air-fuel ratio system. Assume that the actual delay time τ1 of the system is equal to the modeled delay time τ2, and then the Laplace form of the delay time in Step 2 Compensate the delay-free closed-loop transfer function G YR (s) with a delay time, combined with the air-fuel ratio target value R(s), to obtain the output Y P (s) of the delay-compensated air-fuel ratio system.

2. The control method according to claim 1, characterized in that In the said Step 1, the air-fuel ratio system model: Among them, is the fuel-air equivalence ratio, is the air-fuel ratio m f is the actual fuel injection quantity of the fuel injector, m air is the fresh air mass, R af is 14.67, represents the fuel-air equivalence ratio in the cylinder, is the sensor measurement value of the fuel-air equivalence ratio, is the fuel-air equivalence ratio after the mixing process but without delay, and the time constant is denoted as τ m ; τ d represents the delay time when the transport process of the exhaust gas in the exhaust pipe is approximated as a delay link.

3. The control method according to claim 1, wherein In the said Step 1, the air-fuel ratio system model oriented to control is: Among them, the control input Control system state Control output and respectively represent the estimated values of a and b, where a and b are two parameters in the control-oriented air-fuel ratio system model.

4. The control method according to claim 1, wherein In the said Step 1, f(t) represents the sum of the disturbances caused by internal and external factors in the system, expressed as: Among them, Δ a and Δ b respectively represent the modeling errors of a and b, and Δ m is the modeling error of τ m . is caused by the fresh air volume error.

5. The control method according to claim 1, characterized in that, In the said Step 2, the air-fuel ratio state space model can be expressed as: where x1 represents the air-fuel ratio system state, represents the derivative of x1, y1 represents the system output, u1 represents the control input, and τ1 represents the system delay time; The result after Laplace transform is: Among them, G(s) is the transfer function of the system state X1(s) to the control input U1(s).

6. The control method according to claim 1, wherein In the said Step 2, the controller of the air-fuel ratio system: Among them, U1(s) represents the control input, c1(s) is the assumed polynomial, Y1(s) represents the system output, R(s) represents the target value of the control output, G(s) is the closed-loop transfer function of the system state X1(s) with respect to the control input U1(s), and τ1 represents the system delay time.

7. The control method according to claim 1, wherein In the said Step 3, in the said Step 3, The transfer function X(s) = G XU (s)U(s) E p (s) = R(s) - X(s), converted to the time domain form: e p (t) = r(t) - x(t). The extended state observer ESO is expressed as: where, z1 and e p (t) represents the input of the ESO, represents the derivative of z1, and represent the estimated values of a and b respectively, β1 and β2 represent the parameters in the ESO, and the total disturbance f(t) is the sum of β1(e p (t) - z1(t)) and z2, represents the derivative of z2. The feedback controller is: Among them, u(t) represents the control input, and k p represents the dynamic error parameter in.

8. The control method according to claim 1, characterized in that In the said Step 4, perform Laplace transform on the extended state observer and eliminate z1, and the result is: Perform Laplace transform on the feedback controller, and the result is: Bring the tracking error E p (s) = R(s) - X(s) and the Laplace-transformed extended state observer into the Laplace-transformed feedback controller to obtain the Laplace-transformed control input U2(s): Meanwhile, The parameter configuration is: Among them, represents the bandwidth of the ESO, and ξ represents the damping of the ESO.

9. The control method according to claim 1, wherein In the said Step 4, the closed-loop transfer function of the system is: Among them, is the estimated value of the time constant.

10. The control method according to claim 1, wherein In the said Step 5, the closed-loop transfer function of the system is: According to the air-fuel ratio system model oriented to control, model the Smith predictor as: where x m (t) and y m (t) are the model estimates of x(t) and y(t), respectively, and τ s is the estimate of τ d ; The air-fuel ratio output value without delay is: y p y(t) = y(t) - y m + x m (t) Among them, y p (t) is Laplace-transformed to Y P (s).

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