Energy management method for minimum value principle-dichotomy iteration rapid solution

Abstract

The invention relates to an energy management method for minimum value principle-dichotomy iteration rapid solution. The method comprises the following steps: on the basis of a minimum principle and an ECMS algorithm, introducing a co-state variable about a state SOC (State of Charge) of the hybrid vehicle, establishing a Hamilton function for energy management, simplifying a vehicle key power model by utilizing regression analysis, and simplifying the Hamilton function; the optimal control problem is converted into an optimization process of a co-state variable, a terminal co-state variable function about an initial co-state variable is established according to a mapping relation from the initial co-state variable to the terminal co-state variable, and the optimal initial co-state variable is iteratively solved by adopting a dichotomy; a function dominant solution can be quickly obtained according to the optimal co-state variable sequence and the basic property of a standard quadratic function, Hamilton function values corresponding to feasible gears are sequentially solved and compared, and the dominant solution corresponding to the minimum Hamilton function and the gear are the optimal torque distribution mode and the gear at the current moment. And the fuel economy is improved, and the solving speed and real-time performance of the algorithm are enhanced at the same time.

Description

Technical Field

[0001] The invention belongs to the technical field of energy management of hybrid vehicle, and in particular relates to an energy management method for rapid solution by iterative minimum principle-binary division. Background Art

[0002] Reducing vehicle fuel consumption can not only improve the overall energy efficiency, but also reduce energy consumption from the source. How to effectively reduce energy use, reduce automobile exhaust emissions, and improve energy utilization is still a huge challenge for countries around the world.

[0003] Hybrid vehicles have dual power sources. In order to achieve real-time energy management of HEVs based on optimization, researchers have developed an energy management method based on equivalent minimum fuel consumption. The basic principle of the ECMS method is the Pontryagin minimum principle. The minimum principle was developed based on the classical variational method and is now widely used to solve optimal control problems where control variables are subject to constraints.

[0004] At present, most hybrid vehicle energy management strategies cannot take into account both fuel saving effects and the real-time performance of the entire process, and have the problem of too long calculation time. Considering the limitations of the global optimal method and the rule-based energy management method, it is very necessary to design a method that takes into account both real-time performance and control effects.

[0005] Therefore, this paper proposes an energy management method based on the minimum principle-binary division iteration for fast solution. The ECMS method is derived through the PMP principle, the Hamilton function of energy management is simplified, and the optimal control problem is converted into a co-state variable optimization process. According to the mapping relationship from the initial co-state variables to the terminal co-state variables, the terminal co-state variable function about the initial co-state variables is established, and the binary division iteration is used to solve the optimal initial co-state variables. According to the optimal co-state variable sequence and the basic properties of the standard quadratic function, the explicit solution of the function can be quickly obtained, which improves the fuel economy of energy management and enhances the real-time performance of the algorithm solution. Summary of the invention

[0006] An energy management method based on the minimum principle-dichotomy iterative fast solution. During the predictive cruising process of hybrid electric vehicles, based on the minimum principle, regression analysis is used to simplify the key dynamic model of the vehicle and simplify the Hamilton function of energy management.

[0007] Step S11: Establishment of the minimum equivalent fuel consumption strategy model based on the minimum principle: For the predictive cruise optimization problem in this paper, based on the minimum principle and the ECMS algorithm, combined with the characteristics of the Hamilton function, the optimal control variable is obtained by taking the minimum equivalent fuel consumption; the state quantity of the entire control system is defined as the battery SOC, and the motor output power is used as the control quantity, where the Hamilton function of energy management is defined as follows:

[0008] H(x(t),λ(t),u(t),t)=λ(t)f(x(t)),P bat (t),t)+B e (u(t))…………(1.1)

[0009] Where: State equation battery SOC changes:

[0010]

[0011] Introduce λ(t), which is an n-dimensional co-state variable about the battery SOC state, satisfying the condition:

[0012] Where U oc is the open circuit voltage of the battery, R bat is the internal resistance of the battery, Q bat is the battery capacity, P bat Battery output power, B e is the engine fuel consumption;

[0013] Step S12: According to the minimum principle, the optimal state variable, the optimal control input and the corresponding co-state variable make the Hamilton function achieve the minimum value. In other words, the original minimum value problem is converted into a problem of finding the optimal control variable to make the Hamilton function minimum value.

[0014] minH(x(t),λ(t),u(t),t)

[0015] Step S13: Establishment of regression model of key components of hybrid vehicle: This paper replaces the state quantity change equation in the complex Hamilton function with the regression model of engine power and fuel consumption and the regression model of battery current with respect to SOC and motor mechanical power to reduce the calculation complexity of the function;

[0016] Among them, the regression model of engine power and fuel consumption is as follows:

[0017]

[0018] The current, motor mechanical power, and battery SOC are subjected to regression analysis, and the battery current quadratic polynomial regression model is established as follows:

[0019]

[0020] Incorporate the regression model analysis results into the Hamilton function of formula 1.1, as follows:

[0021]

[0022] The initial optimal control problem is transformed into the optimization process of co-state variables. The co-state variables have a mapping relationship over time, and then the whole problem is transformed into the optimization problem of the initial co-state variables.

[0023] Step S21: derive the mapping relationship from the initial co-state variable λ(0) to the terminal co-state variable λ(t) at time t:

[0024]

[0025] Step S22: Determine the optimal initial co-state variable value so that the co-state variable value at the terminal time t obtained under the drive of the optimal control criterion satisfies the terminal necessity condition. The terminal co-state variable necessity condition at the time t is defined as the terminal co-state variable function in the following form:

[0026] F(λ(0))=λ(t)-κ(SOC(t)-SOC ref )…………(2.2)

[0027] In the formula, λ(0) is the initial co-state variable, λ(t) is the co-state variable at the terminal time t, SOC ref is the reference SOC value;

[0028] Step S23: the co-state variable is a scalar, and the optimal condition at time 0-t is F(λ(0))=0. The optimal initial co-state variable value is obtained by rooting the terminal co-state variable, that is, solving F(λ(0))=0;

[0029] Step S24: This paper applies the bisection method to iteratively solve the root of the terminal co-state variable: First, determine the upper and lower boundaries of the co-state variable at the initial moment: λ(0)∈[λ MIN (0),λ MAX (0)], and from the conditional relationship satisfied by the covariate boundary, λ MIN (0)<0,λ MAX (0)≥0; According to the initial iteration time, the relationship between the terminal co-state variables corresponding to the upper and lower boundaries of the initial co-state variables should be F(λ MIN (0))*F(λ MAX (0))<0, use the bisection method to iteratively solve the optimal initial co-state variable λ(0), and then obtain the optimal co-state variable of the sequence with respect to time;

[0030] The original function is converted into a standard quadratic function form. Combined with the obtained optimal co-state variable sequence, the basic properties of the quadratic function can be used to quickly obtain the function analytical solution and derive the optimal gear and torque distribution method at the current moment.

[0031] Step 31: To facilitate calculation, the Hamilton function in Equation 1.6 is further organized into a standard quadratic function form containing control variables and co-state variables:

[0032]

[0033] In the formula, the parameters of the quadratic function are as follows:

[0034] A1(t)=λ(t)p 20

[0035] B1(t)=λ(t)(p 10 +p 11 P m (t))

[0036]

[0037] A2(t)=a2+λ(t)p 02

[0038] B2(t)=(-a1-2a2P req (t))+λ(t)(p 01 +p 11 SOC(t))

[0039]

[0040] Step 32: When the car is cruising, the motor torque is a continuous variable, the gear is a discrete variable, and the vehicle has three gear shifting instructions to choose from. The three gear shifting instructions (downshift, hold and upshift) correspond to three Hamilton functions. To achieve the optimal solution, the minimum values ​​of the three Hamilton functions are solved at the same time, and three independent Hamilton functions are defined as follows:

[0041]

[0042] Among them, -1, 0, and 1 represent downshift, hold, and upshift respectively. At the same time, the gear is subject to the constraints of vehicle speed and engine speed, so the three Hamilton functions of downshift, hold, and upshift are not necessarily meaningful. If downshift or upshift exceeds the gear constraint, the gear selection is held;

[0043] Step 33: After obtaining the quadratic function form of the Hamilton function in equation 3.1, it can be seen that the Hamilton function is a quadratic equation about the motor torque. By giving the battery SOC and gear at the current moment, the value and explicit solution of the quadratic equation can be obtained. The Hamilton function values ​​corresponding to the feasible gears are solved and compared in turn. The explicit solution and gear corresponding to the minimum Hamilton function are the optimal control variable values: The explicit solution of the Hamilton function is:

[0044]

[0045] Where P m,min (t) and P m,max (t) are the minimum and maximum mechanical power of the motor at the current moment, P m,opt (t) is the optimal motor output power at the current moment.

[0046] Based on the optimal motor output power and gear obtained above, the optimal output power of the engine is obtained, and the optimal output torque of the engine is indirectly calculated based on information such as vehicle speed, and the optimal gear and torque distribution at the current time t are derived.

[0047] Compared with the prior art, the present invention has the following beneficial effects:

[0048] 1. The energy management method described in this patent is based on the minimum principle-binary division iterative fast solution, which replaces the complex state quantity change equation with the vehicle regression model, reduces the difficulty of solution, and improves the calculation speed of the controller.

[0049] 2. The energy management method described in this patent is based on the minimum principle-binary division iterative fast solution. On the basis of the minimum principle and the ECMS algorithm, it uses a fast solution method to optimize the initial co-state variables, and solves the optimal initial co-state variables through binary division iterative solution to obtain the optimal co-state variable sequence and state sequence, and updates the co-state variable sequence in real time, which further simplifies the problem, reduces fuel consumption, and increases the calculation speed.

[0050] 3. This method quickly obtains the analytical solution of the Hamilton function through mathematical derivation, reduces discrete and iterative operations, improves the fuel economy of energy management, and enhances the real-time performance of the algorithm solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] The following description of the embodiments will become easier to understand with reference to the accompanying drawings, in which:

[0052] Figure 1 A control flow chart of an energy management method based on the minimum principle-binary division iterative fast solution according to an embodiment of the present invention;

[0053] Figure 2 A real-time solution flow chart of an energy management method based on the minimum principle-binary division iterative fast solution according to an embodiment of the present invention;

[0054] Figure 3 This is a simplified structural diagram of a P2 coaxial parallel hybrid vehicle applicable to an example of the present invention.

[0055] Figure 4 A simplified diagram for explaining the present invention in detail DETAILED DESCRIPTION

[0056] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be understood as limiting the present invention.

[0057] Reference Figure 1-4 An energy management method and solution process for a hybrid vehicle based on the minimum principle binary division iterative rapid solution will be described, but the present invention is not limited to these embodiments.

[0058] An energy management method based on the minimum principle-dichotomy iterative fast solution. During the predictive cruising process of hybrid electric vehicles, based on the minimum principle, regression analysis is used to simplify the key dynamic model of the vehicle and simplify the Hamilton function of energy management.

[0059] Step S11: Establishment of the minimum equivalent fuel consumption strategy model based on the minimum principle: For the predictive cruise optimization problem in this paper, based on the minimum principle and the ECMS algorithm, combined with the characteristics of the Hamilton function, the optimal control variable is obtained by taking the minimum equivalent fuel consumption; the state quantity of the entire control system is defined as the battery SOC, and the motor output power is used as the control quantity, where the Hamilton function of energy management is defined as follows:

[0060] H(x(t),λ(t),u(t),t)=λ(t)f(x(t)),P bat (t),t)+B e (u(t))…………(1.1)

[0061] Where: State equation battery SOC changes:

[0062]

[0063] Introduce λ(t), which is an n-dimensional co-state variable about the battery SOC state, satisfying the condition:

[0064] Where U oc is the open circuit voltage of the battery, R bat is the internal resistance of the battery, Q bat is the battery capacity, P bat Battery output power, B e is the engine fuel consumption;

[0065] Step S12: According to the minimum principle, the optimal state variable, the optimal control input and the corresponding co-state variable make the Hamilton function achieve the minimum value. In other words, the original minimum value problem is converted into a problem of finding the optimal control variable to make the Hamilton function minimum value.

[0066] minH(x(t),λ(t),u(t),t)

[0067] Step S13: Establishment of regression model of key components of hybrid vehicle: This paper replaces the state quantity change equation in the complex Hamilton function with the regression model of engine power and fuel consumption and the regression model of battery current with respect to SOC and motor mechanical power to reduce the calculation complexity of the function;

[0068] Among them, the regression model of engine power and fuel consumption is as follows:

[0069]

[0070] The current, motor mechanical power, and battery SOC are subjected to regression analysis, and the battery current quadratic polynomial regression model is established as follows:

[0071]

[0072] Incorporate the regression model analysis results into the Hamilton function of formula 1.1, as follows:

[0073]

[0074] The initial optimal control problem is transformed into the optimization process of co-state variables. The co-state variables have a mapping relationship over time, and then the whole problem is transformed into the optimization problem of the initial co-state variables.

[0075] Step S21: derive the mapping relationship from the initial co-state variable λ(0) to the terminal co-state variable λ(t) at time t:

[0076]

[0077] Step S22: Determine the optimal initial co-state variable value so that the co-state variable value at the terminal time t obtained under the drive of the optimal control criterion satisfies the terminal necessity condition. The terminal co-state variable necessity condition at the time t is defined as the terminal co-state variable function in the following form:

[0078] F(λ(0))=λ(t)-κ(SOC(t)-SOC ref )…………(2.2)

[0079] In the formula, λ(0) is the initial co-state variable, λ(t) is the co-state variable at the terminal time t, SOC ref is the reference SOC value;

[0080] Step S23: the co-state variable is a scalar, and the optimal condition at time 0-t is F(λ(0))=0. The optimal initial co-state variable value is obtained by rooting the terminal co-state variable, that is, solving F(λ(0))=0;

[0081] Step S24: This paper applies the bisection method to iteratively solve the root of the terminal co-state variable: First, determine the upper and lower boundaries of the co-state variable at the initial moment: λ(0)∈[λ MIN (0),λ MAX (0)], and from the conditional relationship satisfied by the covariate boundary, λ MIN (0)<0,λ MAX (0)≥0; According to the initial iteration time, the relationship between the terminal co-state variables corresponding to the upper and lower boundaries of the initial co-state variables should be F(λ MIN (0))*F(λ MAX (0))<0, use the bisection method to iteratively solve the optimal initial co-state variable λ(0), and then obtain the optimal co-state variable of the sequence with respect to time;

[0082] The original function is converted into a standard quadratic function form. Combined with the obtained optimal co-state variable sequence, the basic properties of the quadratic function can be used to quickly obtain the function analytical solution and derive the optimal gear and torque distribution method at the current moment.

[0083] Step 31: To facilitate calculation, the Hamilton function in Equation 1.6 is further organized into a standard quadratic function form containing control variables and co-state variables:

[0084]

[0085] In the formula, the parameters of the quadratic function are as follows:

[0086] A1(t)=λ(t)p 20

[0087] B1(t)=λ(t)(p 10 +p11 P m (t))

[0088]

[0089] A2(t)=a2+λ(t)p 02

[0090] B2(t)=(-a1-2a2P req (t))+λ(t)(p 01 +p 11 SOC(t))

[0091]

[0092] Step 32: When the car is cruising, the motor torque is a continuous variable, the gear is a discrete variable, and the vehicle has three gear shifting instructions to choose from. The three gear shifting instructions (downshift, hold and upshift) correspond to three Hamilton functions. To achieve the optimal solution, the minimum values ​​of the three Hamilton functions are solved at the same time, and three independent Hamilton functions are defined as follows:

[0093]

[0094] Among them, -1, 0, and 1 represent downshift, hold, and upshift respectively. At the same time, the gear is subject to the constraints of vehicle speed and engine speed, so the three Hamilton functions of downshift, hold, and upshift are not necessarily meaningful. If downshift or upshift exceeds the gear constraint, the gear selection is held;

[0095] Step 33: After obtaining the quadratic function form of the Hamilton function in equation 3.1, it can be seen that the Hamilton function is a quadratic equation about the motor torque. By giving the battery SOC and gear at the current moment, the value and explicit solution of the quadratic equation can be obtained. The Hamilton function values ​​corresponding to the feasible gears are solved and compared in turn. The explicit solution and gear corresponding to the minimum Hamilton function are the optimal control variable values: The explicit solution of the Hamilton function is:

[0096]

[0097] Where P m,min (t) and P m,max (t) are the minimum and maximum mechanical power of the motor at the current moment, P m,opt (t) is the optimal motor output power at the current moment.

[0098] Based on the optimal motor output power and gear obtained above, the optimal output power of the engine is obtained, and the optimal output torque of the engine is indirectly calculated based on information such as vehicle speed, and the optimal gear and torque distribution at the current time t are derived.

[0099] The present invention uses more terms such as SOC, but does not exclude the possibility of using other terms. These terms are used only to more conveniently describe and explain the essence of the present invention; interpreting them as any additional restrictions is contrary to the spirit of the present invention.

[0100] Although the embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the claims and their equivalents.

Claims

1. An energy management method based on the minimum principle-binary division iterative fast solution, characterized by: During the predictive cruising process, the hybrid vehicle uses regression analysis to simplify the key dynamic model of the vehicle based on the minimum principle and ECMS algorithm, and simplifies the Hamilton function of energy management; Step S11: Establishment of the minimum equivalent fuel consumption strategy model based on the minimum principle: For the predictive cruise optimization problem in this paper, based on the minimum principle and the ECMS algorithm, combined with the characteristics of the Hamilton function, the optimal control variable is obtained by taking the minimum equivalent fuel consumption; the state quantity of the entire control system is defined as the battery SOC, and the motor output power is used as the control quantity, where the Hamilton function of energy management is defined as follows: H(x(t),λ(t),u(t),t)=λ(t)f(x(t)),P bat (t),t)+B e (u(t))………(1.1) Where: State equation battery SOC changes: Introduce λ(t), which is an n-dimensional co-state variable about the battery SOC state, satisfying the condition: Where U oc is the open circuit voltage of the battery, R bat is the internal resistance of the battery, Q bat is the battery capacity, P bat Battery output power, B e is the engine fuel consumption; Step S12: According to the minimum principle, the optimal state variable, the optimal control input and the corresponding co-state variable make the Hamilton function achieve the minimum value. In other words, the original minimum value problem is converted into a problem of finding the optimal control variable to make the Hamilton function minimum value. minH(x(t),λ(t),u(t),t) Step S13: Establishment of regression model of key components of hybrid vehicle: This paper replaces the state quantity change equation in the complex Hamilton function with the regression model of engine power and fuel consumption and the regression model of battery current with respect to SOC and motor mechanical power to reduce the calculation complexity of the function; Among them, the regression model of engine power and fuel consumption is as follows: The current, motor mechanical power, and battery SOC are subjected to regression analysis, and the battery current quadratic polynomial regression model is established as follows: Incorporate the regression model analysis results into the Hamilton function of formula 1.1, as follows:

2. The energy management method of the minimum principle-binary division iterative fast solution according to claim 1 is characterized by: The initial optimal control problem is transformed into the optimization process of co-state variables. The co-state variables have a mapping relationship over time, and then the whole problem is transformed into the optimization problem of the initial co-state variables. Step S21: derive the mapping relationship from the initial co-state variable λ(0) to the terminal co-state variable λ(t) at time t: Step S22: Determine the optimal initial co-state variable value so that the co-state variable value at the terminal time t obtained under the drive of the optimal control criterion satisfies the terminal necessity condition. The terminal co-state variable necessity condition at the time t is defined as the terminal co-state variable function in the following form: F(λ(0))=λ(t)-κ(SOC(t)-SOC ref )………(2.2) In the formula, λ(0) is the initial co-state variable, λ(t) is the co-state variable at the terminal time t, SOC ref is the reference SOC value; Step S23: the co-state variable is a scalar, and the optimal condition at time 0-t is F(λ(0))=0. The optimal initial co-state variable value is obtained by rooting the terminal co-state variable, that is, solving F(λ(0))=0; Step S24: This paper applies the bisection method to iteratively solve the root of the terminal co-state variable: First, determine the upper and lower boundaries of the co-state variable at the initial moment: λ(0)∈[λ MIN (0),λ MAX (0)], and from the conditional relationship satisfied by the covariate boundary, λ MIN (0)<0,λ MAX (0)≥0; According to the initial iteration time, the relationship between the terminal co-state variables corresponding to the upper and lower boundaries of the initial co-state variables should be F(λ MIN (0))*F(λ MAX (0))<0, the optimal initial comorphic variable λ(0) is solved iteratively by the bisection method, and then the optimal comorphic variable of the sequence with respect to time is obtained.

3. The energy management method of the minimum principle-binary division iterative fast solution according to claim 1 is characterized by: The original function is converted into a standard quadratic function form, combined with the optimal co-state variable sequence obtained in claim 2, and the basic properties of the quadratic function can be used to quickly obtain the function analytical solution, and derive the optimal gear position and torque distribution method at the current moment; Step 31: To facilitate calculation, the Hamilton function in Equation 1.6 is further organized into a standard quadratic function form containing control variables and co-state variables: In the formula, the parameters of the quadratic function are as follows: A1(t)=λ(t)p 20 B1(t)=λ(t)(p 10 +p 11 P m (t)) A2(t)=a2+λ(t)p 02 B2(t)=(-a1-2a2P req (t))+λ(t)(p 01 +p 11 SOC(t)) Step 32: When the car is cruising, the motor torque is a continuous variable, the gear is a discrete variable, and the vehicle has three gear shifting instructions to choose from. The three gear shifting instructions (downshift, hold and upshift) correspond to three Hamilton functions. To achieve the optimal solution, the minimum values ​​of the three Hamilton functions are solved at the same time, and three independent Hamilton functions are defined as follows: Among them, -1, 0, and 1 represent downshift, hold, and upshift respectively. At the same time, the gear is constrained by the vehicle speed and engine speed. Therefore, the three Hamilton functions of downshift, hold, and upshift are not necessarily meaningful. If downshift or upshift exceeds the gear constraint, the gear selection is held. Step 33: After obtaining the quadratic function form of the Hamilton function in equation 3.1, it can be seen that the Hamilton function is a quadratic equation about the motor torque. By giving the battery SOC and gear at the current moment, the value and explicit solution of the quadratic equation can be obtained. The Hamilton function values ​​corresponding to the feasible gears are solved and compared in turn. The explicit solution and gear corresponding to the minimum Hamilton function are the optimal control variable values: The explicit solution of the Hamilton function is: Where P m,min (t) and P m,max (t) are the minimum and maximum mechanical power of the motor at the current moment, P m,opt (t) is the optimal motor output power at the current moment; Based on the optimal motor output power and gear obtained above, the optimal output power of the engine is obtained, and the optimal output torque of the engine is indirectly calculated based on information such as vehicle speed, and the optimal gear and torque distribution at the current time t are derived.

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