Hierarchical energy management method for hybrid electric vehicle based on Tube MPC

Abstract

The invention discloses a Tube MPC-based hybrid electric vehicle layered energy management method. The method comprises the following steps of performing longitudinal dynamic modeling on a hybrid electric vehicle, determining a vehicle demand power formula, constructing an evaluation function of equivalent fuel consumption, and constructing an output power model of a vehicle engine and a battery; carrying out uncertainty analysis on the energy management system, determining uncertain parameters in the vehicle model, quantifying the uncertainty of the uncertain parameters based on probability distribution, and constructing an uncertainty set of the uncertain parameters; on the basis of a dynamic programming algorithm, under the global working condition, the minimum amount of equivalent fuel consumption serves as a target function, an optimal control sequence of the engine is output, and an SOC reference trajectory is generated; and performing tracking solution on the control variables and the state variables in the uncertainty set by applying a Tube model predictive control (Tube MPC) method to obtain an optimal control sequence under uncertain factors, and outputting a first control variable.

Description

Technical Field

[0001] The present invention relates to the field of energy management of hybrid electric vehicles, and particularly to a hierarchical energy management method for hybrid electric vehicles based on Tube MPC. Background Art

[0002] Due to factors such as gasoline shortages, pollution, and global warming, electric vehicles have increasingly attracted the interest of researchers and the industry. Currently, the international automotive industry is attempting to adopt cleaner and safer alternative technologies. Hydrogen fuel cell hybrid electric vehicles are one of the most effective technologies and are receiving continuous attention and development. Optimal energy management is one of the many key aspects of the technological advancement of hybrid electric vehicles.

[0003] Currently, the energy management strategies of hybrid electric vehicles are mainly divided into rule-based and optimization-based energy management strategies. Rule-based energy management strategies mainly design the system operating mode and the energy distribution method of different power sources based on engineering experience and considering the characteristics of each component of the power system. This control strategy does not have specific optimization problems, and the formulated rules mainly come from engineering experience, with strong practicability and good real-time effects, but the energy-saving effect is poor.

[0004] Existing energy management strategies for hybrid electric vehicles optimize the hybrid for the entire operating condition according to the state equation and objective function of the vehicle system, using the optimal control theory to obtain the global optimal solution of the feasible region. In theory, it can achieve the optimal fuel economy, but it requires the global driving condition of the vehicle, and the large amount of calculation is prone to delay, making it difficult to achieve real-time application.

[0005] In order to further improve the energy-saving performance, advanced energy management research combines model predictive control, enabling the energy management strategy to have prior knowledge of the future driving cycle. Thus, when making optimal decisions, it not only focuses on the current state but also considers future situations.

[0006] In addition to requiring the economy of the vehicle to reach optimality, the robustness of the solution is also considered a key performance criterion. Since previous research has focused on the expected optimal performance under a deterministic framework and ignored data ambiguity, changing operating conditions, modeling, and estimation will bring multiple error sources. In practice, ignoring these uncertainties will lead to high operating costs, low overall system efficiency, performance failures, and even an inability to solve problems due to constraint violations.

[0007] Some advanced research on energy management strategies has begun to focus on the uncertainties introduced by real-world random factors. However, if the uncertainties are not properly quantified, the optimization results output by traditional model predictive or stochastic model predictive control may deviate from the optimal control strategy or fail to achieve stable control. In dynamic traffic scenarios, when facing strong random factors, the following three aspects of problems still need to be solved:

[0008] 1) Traditional research focuses on the expected optimal performance under a deterministic framework, ignoring data ambiguity, and the changing operating conditions, modeling, and estimation introduce multiple error sources.

[0009] 2) These uncertainties can lead to high operating costs, low overall system efficiency, performance failures, and even the inability to solve problems due to constraint violations.

[0010] 3) If the uncertainties are not properly quantified, the optimization results output by traditional model predictive or stochastic model predictive control may deviate from the optimal control strategy or fail to achieve stable control.

[0011] A hierarchical energy management system is proposed in a Chinese patent with the patent number CN111516702B, namely, an online real-time hierarchical energy management method and system for a hybrid vehicle. By tracking the state variables of the upper-level system, the stability of energy distribution is improved, but the influence of uncertain factors is not considered. In the present invention, the uncertainties are quantified, and the tube-MPC control model is used to track the state variables of the upper-level system, and the proposed strategy has stronger robustness and generalization ability.

[0012] A plug-in hybrid vehicle variable-time-domain model predictive energy management method in a Chinese patent with the patent number CN111731262A adopts a model predictive control framework, with fuel consumption as the optimization target, and solves for the optimal control variables in the prediction time domain to improve fuel economy, but the robustness of the system is not considered. In the present invention, the optimal control variables are solved by the DP algorithm to ensure fuel economy, and the Tube-MPC is used to track the SOC reference trajectory under uncertain factors, while ensuring the economy and robustness of the strategy.

[0013] The present invention takes a hybrid vehicle as the research object, abandons the traditional optimization of the vehicle's economy under a deterministic framework, considers the influence of uncertain factors, and at the same time takes into account the economy and robustness of the hybrid vehicle. A hierarchical energy management method based on tube model predictive control (Tube MPC) is proposed. This method includes a deterministic framework and an uncertainty framework. Under the deterministic framework, through the dynamic programming algorithm, the minimum equivalent fuel consumption under the global working conditions is solved, the optimal engine control sequence is generated, and a reference trajectory is constructed. Under the uncertainty framework, considering the influence of uncertain factors, based on the optimal engine control sequence and the reference trajectory, the engine is controlled to track the reference trajectory based on the tube model predictive control (Tube MPC) algorithm, and the control operation under the uncertainty framework is output to solve the technical problems of low system efficiency, deviation of the output result from the optimal control strategy, and inability to achieve stable control in the face of random factors in the energy management strategy under the deterministic framework. Summary of the Invention

[0014] The technical solution of the present invention is as follows:

[0015] A hierarchical energy management method for a hybrid vehicle based on tube MPC, comprising the following steps:

[0016] Step 1, perform longitudinal dynamics modeling on the hybrid vehicle, determine the vehicle demand power formula, construct an evaluation function for equivalent fuel consumption, and construct an output power model of the vehicle engine and battery;

[0017] Step 2, perform uncertainty analysis on the energy management system, determine the uncertain parameters in the vehicle model, estimate the uncertainty of the uncertain parameters based on the probability distribution, and construct an uncertainty set of the uncertain parameters;

[0018] Step 3, based on the dynamic programming algorithm, under the global working conditions, take the minimum equivalent fuel consumption as the objective function, output the optimal engine control sequence, and generate the SOC reference trajectory;

[0019] Step 4, apply the tube model predictive control (Tube MPC) method, according to the optimal engine control sequence and the reference trajectory, track and solve the control variables and state variables within the uncertainty set, obtain the optimal control sequence under uncertain factors, and output the first control variable.

[0020] Before performing longitudinal dynamics modeling on the hybrid vehicle and uncertainty analysis on the energy management system, vehicle parameters are obtained, and the vehicle parameters include: vehicle parameters, engine parameters, motor parameters, and power battery parameters;

[0021] The vehicle parameters include: vehicle mass, frontal area, rolling resistance coefficient, air resistance coefficient, tire radius, and main reducer ratio;

[0022] The engine parameters include: the maximum engine speed and the maximum engine output power;

[0023] The motor parameters include: the maximum motor speed and the maximum motor torque;

[0024] The power battery parameters include: the battery capacity and the SOC range.

[0025] In the first step, the vehicle demand power formula is:

[0026] P veh =(Fr + F w + F i + F j )u a ,

[0027] where P veh is the demand power, F r is the rolling resistance, F w is the air resistance, F i is the gradient resistance, F i is the acceleration resistance, and u a is the driving speed;

[0028] The longitudinal dynamic model of the vehicle is specifically:

[0029]

[0030] where m is the vehicle mass, g is the acceleration due to gravity, C r is the rolling resistance coefficient, i is the road gradient, C d is the air resistance coefficient, A is the frontal area, ρ is the air density, u a is the driving speed, is the driving acceleration.

[0031] In the first step, building the output power model of the vehicle engine and battery includes:

[0032] The demand power model of the vehicle engine and motor is:

[0033] P veh =(P eng + P mot )η,

[0034] where P veh is the demand power, P eng is the engine power, P mot is the motor power, and η is the mechanical transmission efficiency;

[0035] The engine model is established by numerical modeling, and the fuel consumption rate is obtained by interpolation. The engine fuel consumption model is specifically:

[0036]

[0037] Among them, is the instantaneous fuel consumption of the engine at time t, and P eng (t) is the power of the engine at time t, and η eng (t) is the working efficiency of the engine at time t, and Q lhv is the lower heating value of gasoline fuel;

[0038] The electricity consumption is equivalently reduced to the current actual fuel consumption. The equivalent fuel consumption of the vehicle at any moment is specifically:

[0039]

[0040] Among them, is the instantaneous fuel consumption of the vehicle at time t, is the equivalent fuel consumption of the battery at time t, and specifically:

[0041]

[0042] Among them, s(t) is the oil-electric conversion equivalent factor; P bat (t) is the battery power; the battery model is simplified to an equivalent internal resistance model, and specifically:

[0043]

[0044] Among them, P bat is the battery power, U oc is the open-circuit voltage, R0 is the battery internal resistance, I(t) is the battery current, and Q bat is the battery capacity, and SOC0 is the initial state SOC of the battery.

[0045] In the second step, the uncertain parameters include the rolling resistance coefficient C r , the air resistance coefficient C d and the slope i. C r , C d and i depend on multiple variables.

[0046] In the second step: During the optimization process, consider the uncertainty interval and introduce the uncertain values and

[0047] Under the uncertain optimization framework, the uncertain parameters are represented by their nominal values and uncertainty values:

[0048]

[0049] is the vector of parameter uncertainty values, P un is the vector of parameter nominal values, and α represents the vector containing the uncertainty associated with each parameter, specifically:

[0050]

[0051] P un = [C d , C r , i],

[0052]

[0053] where α sup (i) is the maximum possible value that the uncertainty α(i) can take, and the uncertain parameter takes values according to a symmetric distribution with a mean equal to the nominal value P un (i), and the uncertainty set of the uncertain parameter is:

[0054]

[0055] In the third step, the dynamic programming algorithm includes the following steps: The global working condition is divided into N sub - stages at 1 - s intervals, and the optimization is carried out from the initial stage x(1) to the end - stage x(N - 1), and finally a set of optimal engine power output sequences is obtained to minimize the total cost of the vehicle;

[0056] Take the SOC of the battery as the state variable:

[0057] x(k)= SOC(k),

[0058] Take the output torque and speed of the engine as the control variables, then the control variables of the vehicle at the k - th stage are:

[0059] u(k)= [T eng (k), n eng (k)] T ,

[0060] The expression of the vehicle state - transfer equation is:

[0061] x k+1 = f(x k , u k ),

[0062] According to the global working - condition information, calculate the required torque and speed of the vehicle; and construct an objective function for minimizing the fuel consumption of the vehicle, and the global objective function for minimizing the total equivalent fuel - consumption cost of the whole vehicle is specifically:

[0063]

[0064] To ensure that the vehicle meets the actual driving conditions, the following constraints are defined:

[0065]

[0066] Among them, P eng,min and P eng,max are the minimum output power and maximum output power of the engine respectively; P bat,min and P bat,max are the maximum charging power and maximum discharging power of the power battery respectively; SOC min and SOC max are the minimum value and maximum value of the state of charge respectively, and SOC end is the SOC at the end of the driving condition; δ represents the allowable error of the SOC of the vehicle at the end of the condition.

[0067] In the fourth step described above, the application of the model predictive control method includes the following steps:

[0068] Linearize the nonlinear system of the hybrid vehicle to obtain a linear time-varying system;

[0069] Discretize the linear time-varying system to obtain a discrete linear time-varying system;

[0070] Use the trajectory and control sequence obtained by the dynamic programming algorithm to linearize the system for each finite time horizon and formulate the terminal cost;

[0071] Construct a Tube MPC optimization problem, solve to obtain the optimal control sequence within the uncertainty set, and output the first control variable of the optimal control sequence.

[0072] The Tube MPC optimization problem is:

[0073]

[0074] Among them, N P is the prediction horizon; N c is the control horizon, P is the weight matrix of the state variables, and Q is the weight matrix of the control variables.

[0075] Apply the first control variable to the hybrid vehicle to control the engine speed and torque of the vehicle, and realize the hierarchical energy management of the hybrid vehicle.

[0076] The beneficial effects of the present invention are:

[0077] Since traditional research focuses on the expected optimal performance under a deterministic framework while ignoring data ambiguity, changing operating conditions, modeling, and estimation introduce multiple sources of error. In practice, ignoring these uncertainties can lead to high operating costs, low overall system efficiency, performance failures, and even the inability to solve problems due to constraint violations. Moreover, if uncertainties are not properly quantified, the optimized results output by traditional model prediction or stochastic model prediction may deviate from the optimal control strategy or fail to achieve stable control.

[0078] The present invention provides a novel hierarchical energy management method for hybrid electric vehicles based on Tube MPC. Based on the dynamic programming (DP) algorithm, with the minimum equivalent fuel consumption as the objective function, the optimal control sequence of the engine is output to generate a reference trajectory. Considering the uncertainties of uncertain parameters, according to the optimal control sequence of the engine and the reference trajectory, the tube model predictive control algorithm (Tube MPC) is applied to track and solve the control variables and state variables to obtain the optimal control sequence. Finally, the first control variable is applied to the hybrid electric vehicle, and it has the following advantages:

[0079] Introduce an uncertainty handling mechanism: By constructing an uncertainty set for uncertain parameters and explicitly considering these uncertainties during the optimization process, it is ensured that the system can still maintain robustness in complex and changing actual driving environments.

[0080] Hierarchical energy management framework: Combining the deterministic framework and the uncertainty framework, it realizes the organic combination of global optimal control and local optimal control. The deterministic framework is responsible for global optimization to ensure the minimum equivalent fuel consumption; the uncertainty framework, through the tube model predictive control, ensures that the system state can track the reference trajectory in the future time period even in the presence of uncertainties.

[0081] Significantly improve fuel economy: Through the combination of the dynamic programming algorithm and the tube model predictive control, the present invention can achieve minimized equivalent fuel consumption globally, significantly improving the fuel economy of the vehicle. Experimental results show that compared with traditional methods, the fuel economy of the strategy proposed by the present invention has increased by 11.65%, and it maintains stable performance in complex and changing actual driving environments.

[0082] Enhance system robustness: By introducing an uncertainty handling mechanism, the present invention can ensure the stability and robustness of the system when facing complex and changing actual driving environments. Experimental verification shows that the present invention exhibits good control effects in the simulation results of various working conditions, avoiding the performance degradation or failure problems that may occur in traditional methods in these situations. Description of the Drawings

[0083] Figure 1 It is a schematic diagram of the dynamic programming algorithm;

[0084] Figure 2 Schematic diagram for uncertainty integration;

[0085] Figure 3 Schematic diagram of the principle of Tube MPC algorithm;

[0086] Figure 4 Schematic diagram of the hierarchical energy management framework. Specific implementation manners

[0087] The present invention will be further described below with reference to the accompanying drawings.

[0088] A hierarchical energy management method for a hybrid electric vehicle based on Tube MPC of the present invention mainly includes the following steps:

[0089] Step 1, vehicle longitudinal dynamics modeling

[0090] Perform longitudinal dynamics modeling on the hybrid electric vehicle, determine the vehicle demand power formula, construct an evaluation function for equivalent fuel consumption, and construct an output power model of the vehicle engine and battery.

[0091] First, obtain vehicle parameters, which include: vehicle parameters, engine parameters, motor parameters, and power battery parameters;

[0092] The vehicle parameters include: vehicle mass, frontal area, rolling resistance coefficient, air resistance coefficient, tire radius, and main reducer ratio;

[0093] The engine parameters include: maximum engine speed and maximum engine output power;

[0094] The motor parameters include: maximum motor speed and maximum motor torque;

[0095] The power battery parameters include: battery capacity and SOC range.

[0096] Through longitudinal dynamics analysis of the hybrid electric vehicle, model the vehicle components. The vehicle demand power model is specifically:

[0097] P veh =(Fr + F w + F i + F j )u a (1)

[0098] Wherein, P veh is the demand power, F r is the rolling resistance, F w is the air resistance, F i is the gradient resistance, F j is the acceleration resistance, and u ais the driving speed.

[0099] The resistance model of the vehicle is specifically:

[0100]

[0101] where m is the vehicle mass, g is the acceleration due to gravity, C r is the rolling resistance coefficient, i is the road gradient, C d is the air resistance coefficient, A is the frontal area, ρ is the air density, u a is the driving speed, is the driving acceleration.

[0102] In this embodiment, the power of the hybrid truck comes from the engine and the motor, and the demand power model is specifically:

[0103] P veh =(P eng +P mot )η (3)

[0104] where P veh is the demand power, P eng is the engine power, P mot is the motor power, and η is the mechanical transmission efficiency.

[0105] The engine model is established by numerical modeling, and the fuel consumption rate is obtained by interpolation. Specifically, the engine fuel consumption model is specifically:

[0106]

[0107] where, is the instantaneous fuel consumption of the engine at time t, P eng (t) is the power of the engine at time t, η eng (t) is the working efficiency of the engine at time t, Q lhv is the lower calorific value of gasoline.

[0108] The electric energy consumption can be equivalently reduced to the current actual fuel consumption. The instantaneous equivalent fuel consumption of the vehicle is specifically:

[0109]

[0110] where, is the instantaneous fuel consumption of the vehicle at time t, is the equivalent fuel consumption of the battery at time t, specifically:

[0111]

[0112] where \(s(t)\) is the equivalent factor of oil-electricity conversion; \(P\) bat (t) is the battery power. The battery model is simplified to an equivalent internal resistance model, specifically:

[0113]

[0114] where \(P\) bat is the battery power, \(U_{o}\) c is the open-circuit voltage, \(R_{0}\) is the battery internal resistance, \(I(t)\) is the battery current, \(Q\) bat is the battery capacity, and \(SOC_{0}\) is the initial state of charge (SOC) of the battery.

[0115] Step 2: Uncertainty analysis

[0116] Perform uncertainty analysis on the energy management system, determine the uncertain parameters in the vehicle model, estimate the uncertainty of the uncertain parameters based on probability distributions, and construct the uncertainty sets of the uncertain parameters. This step ensures that the subsequent control strategies can maintain robustness in an uncertain environment.

[0117] To estimate the required power \(P\) veh of the vehicle, when calculating the rolling resistance \(F\) r and the air resistance \(F\) w , the rolling resistance coefficient \(C\) r , the air resistance coefficient \(C\) d and the slope \(i\) are considered fixed, but \(C\) r , \(C\) d and \(i\) depend on many variables, such as vehicle speed, tire pressure, and road surface conditions, and it may deviate from its nominal value when the operating conditions change. Therefore, the uncertain parameters include the rolling resistance coefficient \(C\) r , the air resistance coefficient \(C\) d and the slope \(i\). The uncertainty intervals are considered in the optimization process, and the uncertain values and

[0118] Different from other methods that require probability assignment, in the uncertain optimization framework, uncertainty is modeled according to bounded intervals called uncertainty sets, where uncertainty can take any random value. The uncertain parameters are represented by their nominal values and uncertainty values:

[0119]

[0120] is the vector of parameter uncertainty values, \(P\) un is the vector of parameter nominal values, and \(\alpha\) represents the vector containing the uncertainty associated with each parameter, specifically:

[0121]

[0122] P un = [C d , C r , i](10)

[0123]

[0124] where α sup (i) is the maximum possible value that the uncertainty α(i) can take, and the uncertain parameter takes values according to a symmetric distribution with a mean equal to the nominal value P un (i). The uncertainty set of the uncertain parameter is:

[0125]

[0126] Step 3, deterministic optimization strategy

[0127] Based on the dynamic programming (DP) algorithm, an optimal control strategy under the deterministic framework is constructed. In the case of the global operating conditions, with the minimum equivalent fuel consumption as the objective function, the optimal engine control sequence is output to generate a reference trajectory.

[0128] Under the deterministic framework, the dynamic programming algorithm is a numerical method for seeking the global optimal solution through backward calculation and forward optimization operations, as Figure 1 shown. The global optimization problem of the vehicle can be formulated as: dividing the global operating conditions into N sub-stages at 1 s intervals, optimizing from the initial stage x(1) to the end stage x(N - 1), and finally obtaining a set of optimal engine power output sequences to minimize the total cost of the vehicle. Determining the sequence of engine power values also determines a sequence of battery SOC values. Therefore, through the dynamic programming algorithm, the present invention can obtain the optimal engine control sequence of the vehicle under the global operating conditions and the reference trajectory of the SOC change.

[0129] As an important parameter, the SOC can affect the control strategy to a great extent. Therefore, the SOC of the battery is used as the state variable:

[0130] x(k) = SOC(k) (14)

[0131] Taking the output torque and speed of the engine as the control variables, the control variables of the vehicle in the k-th stage are:

[0132] u(k) = [T eng (k), n eng (k)] T (15)

[0133] The expression of the state transition equation of the vehicle is:

[0134] x k+1 = f(xk , u k ) (16)

[0135] According to the global operating conditions information, calculate the required torque and speed of the vehicle; and construct an objective function with the minimum fuel consumption of the vehicle based on the required torque and speed of the vehicle. Specifically, the global objective function for minimizing the total equivalent fuel consumption cost of the whole vehicle is specifically as follows:

[0136]

[0137] To ensure that the vehicle meets the actual driving conditions, not only the state variables and control variables need to be within a reasonable range, but also the components of the vehicle's powertrain need to be physically constrained. The constraint conditions are as follows:

[0138]

[0139] Among them, P eng,min , P eng,max are the minimum output power and the maximum output power of the engine respectively; P bat,min , P bat,max are the maximum charging power and the maximum discharging power of the power battery respectively; SOC min , SOC max are the minimum value and the maximum value of the state of charge respectively, and SOC end is the SOC at the end of the driving condition; δ represents the allowable error of the SOC of the vehicle at the end of the condition.

[0140] Step 4, Uncertainty optimization strategy

[0141] A hybrid electric vehicle is a nonlinear system. The method of tube model predictive control (Tube MPC) is applied in the present invention to solve the control variables during the driving process. First, the global operating conditions of the vehicle are globally optimized by using the dynamic programming algorithm to obtain the optimal control sequence u ref (k) = [T eng (k), n eng (k)] T of the engine of the vehicle under the global operating conditions, and the reference trajectory x ref (k) = SOC(k) of the SOC change is integrated with the uncertainty set of the uncertain parameters. As shown in Figure 2 , the tube model predictive control (Tube MPC) algorithm is applied to optimize and solve the control variables within [k, k + n]. As shown in Figure 3 , the optimal control sequence within [k, k + n] is obtained. Finally, the first control variable is applied to the hybrid electric vehicle. The hierarchical energy management control process proposed by the present invention is as shown in Figure 4As shown. Tube Model Predictive Control (Tube MPC) ensures that the nominal system state can track the reference trajectory within a future time period by constructing a Robust Positive Invariant (RPI) set, even in the presence of uncertainties. This method not only improves the system's robustness but also ensures that the energy utilization efficiency of the vehicle remains at an optimal level in a complex and changing real driving environment.

[0142] The application of the model predictive control method includes the following steps: linearize the nonlinear system of the hybrid electric vehicle to obtain a linear time-varying system; discretize the linear time-varying system to obtain a discrete linear time-varying system; use the trajectory and control sequence obtained by the dynamic programming algorithm to linearize the system for each finite time horizon and formulate the terminal cost; construct the Tube MPC optimization problem, solve to obtain the optimal control sequence within the uncertainty set, and output the first control variable of the optimal control sequence.

[0143] Considering the influence of actual bounded uncertain disturbances, the system model of the controlled vehicle can be described as:

[0144]

[0145] Where, is the system state variable SOC, is the system control variable, is the bounded uncertainty.

[0146] The nonlinear system dynamics equation is linearized around the SOC reference trajectory x obtained from the DP algorithm ref and the corresponding control sequence u ref to obtain the following linear time-varying system using Taylor series expansion, specifically:

[0147]

[0148] To apply MPC, the obtained linear time-varying system is discretized to obtain the linear discrete model of the actual system as:

[0149]

[0150]

[0151] Where, is the state variable of the actual system, is the control variable of the actual system, T is the discrete time step, and I is the identity matrix.

[0152] Separate the influence of the bounded disturbance on the system and define the following nominal system:

[0153]

[0154] Where, is the nominal system state variable, is the control variable of the nominal system. The state error between the actual system and the nominal system is:

[0155]

[0156] The control objective is to compensate for the error between the actual state and the nominal system state without violating the constraints, so that the nominal system state is as close as possible to the reference. Thus, the control input of the actual system is defined as:

[0157]

[0158] where K is the control coefficient of the state feedback gain, which can be solved by directly configuring the system poles.

[0159] The dynamic equation of the error system is:

[0160] e(k + 1) = x(k + 1) - z(k + 1) (27)

[0161] e(k + 1) = (A + BK)e(k) + ω(k) (28)

[0162] Define S(k) as the robust positive invariant set (RPI) of the error system. The error at any time is bounded by e(k) ∈ S(k). S(k) can be calculated in the following way, specifically:

[0163]

[0164] where, represents the Minkowski sum operation between sets. For two given sets M and N, the Minkowski sum is defined as:

[0165]

[0166] To satisfy the state and control constraints in the discrete linear time-varying system equation, the nominal system needs to satisfy and where represents the Pontryagin difference operation between sets. For two given sets M and N, the Pontryagin difference is defined as:

[0167]

[0168] The optimization problem of Tube MPC for the hierarchical energy management strategy of hybrid electric vehicles is constructed as follows, specifically:

[0169]

[0170] Its constraints are as follows:

[0171]

[0172] Among them, Np is the prediction horizon; Nc is the control horizon, P is the weight matrix of state variables, and Q is the weight matrix of control variables.

[0173] Apply the first control variable to the hybrid vehicle to control the engine speed and torque of the vehicle, and achieve hierarchical energy management of the hybrid vehicle.

[0174] To verify the fuel economy of the proposed hierarchical energy management strategy under multiple uncertainty factors, its fuel consumption is compared with the theoretically optimal global dynamic programming strategy and the widely used rule-based strategy in practical applications. The initial SOC(0) is selected as 0.6. DP solves the entire driving cycle through the backward recursion method. From the last state, the optimal control variable of the engine and the lowest fuel consumption at each state are obtained forward. Then, through forward recursion, the optimal control sequence under the entire driving cycle is obtained according to the solved optimal control variable of the engine. DP evenly distributes the power output of the engine from the perspective of the whole process. Therefore, theoretically, DP is the optimal solution and is used as a comparison benchmark with the other two strategies here.

[0175] The fuel consumption is shown in Table 1. Since the DP strategy optimizes from a global perspective and ensures that the engine operating point is at the optimal efficiency point, the fuel economy is the highest; the rule-based energy management strategy is simple to calculate and convenient to use, but its threshold parameters are determined in advance and cannot ensure that it operates in the optimal efficiency range of the engine at each operating point, so the fuel economy is relatively poor; while the proposed energy management strategy (PEMS) is also achieved through optimization, but because it is a short-term planning optimization and cannot search globally, the fuel economy is slightly lower than the DP strategy, but the final SOC value is closer to the initial value, and it can maintain the stability of SOC compared with the DP strategy. At the same time, the fuel economy of the proposed strategy is 11.65% higher than that of the rule-based strategy, the fuel consumption is 4.641 L / 100 km, and the fuel economy reaches 92.67%. It can be seen that the energy management strategy proposed by the present invention has good fuel economy.

[0176] Table 1 Comparison of fuel consumption

[0177]

[0178] The driving conditions of a vehicle are of great significance for evaluating the control effect of the overall vehicle energy management strategy. When simulating and testing the energy management strategy of a hybrid vehicle, standard driving cycles are mostly used, such as WLTC, FTP75, CHTC, etc. However, it is difficult for standard driving cycles to reflect the actual driving situation. In order to accurately reflect the control effect of the energy management strategy under the actual driving conditions of the driver, in this embodiment, the road driving conditions in Nanning are collected and tested to obtain the real driving conditions that conform to the driver's daily driving route as the test conditions.

[0179] The state variable (SOC) generated by the DP algorithm is used as the reference state of the Tube-MPC to achieve the tracking of the SOC reference trajectory. To verify the robustness of this strategy, comparative experiments on SOC reference trajectory tracking are carried out under the test conditions (TEST) and the standard driving cycles WLTC, FTP75, and CLTC, respectively. The experimental results are shown in Table 2. Under all driving conditions, the relative error of SOC reference trajectory tracking is controlled within 2%. Since the test conditions are trained and learned in advance, the accuracy of speed prediction is higher, so the smallest average relative error is obtained under the test conditions. The experimental results show that considering the influence of uncertain factors, the control model constructed based on Tube-MPC follows the SOC reference trajectory well and has strong robustness and generalization ability.

[0180] Table 2 Comparison of SOC tracking under different driving conditions

[0181]

Claims

1. A hierarchical energy management method for hybrid electric vehicles based on Tube MPC, characterized in that, It includes the following steps: Step 1: Conduct longitudinal dynamics modeling on a hybrid vehicle, determine the vehicle demand power formula, construct an evaluation function for equivalent fuel consumption, and construct an output power model for the vehicle engine and battery; Step 2: Conduct uncertainty analysis on the energy management system, determine the uncertain parameters in the vehicle model, estimate the uncertainty of the uncertain parameters based on probability distribution, and construct an uncertainty set for the uncertain parameters; Step 3: Based on the dynamic programming algorithm, under global driving conditions, with the minimum equivalent fuel consumption as the objective function, output the optimal engine control sequence and generate the SOC reference trajectory; Step 4: Apply the tube model predictive control method. According to the optimal engine control sequence and the reference trajectory, track and solve the control variables and state variables within the uncertainty set to obtain the optimal control sequence under uncertain factors, and output the first control variable.

2. The method according to claim 1, wherein Before conducting longitudinal dynamics modeling on the hybrid vehicle and uncertainty analysis on the energy management system, obtain vehicle parameters, and the vehicle parameters include: vehicle parameters, engine parameters, motor parameters, and power battery parameters; The vehicle parameters include: vehicle mass, frontal area, rolling resistance coefficient, air resistance coefficient, tire radius, and main reduction ratio; The engine parameters include: maximum engine speed and maximum engine output power; The motor parameters include: maximum motor speed and maximum motor torque; The power battery parameters include: battery capacity and SOC range.

3. The method according to claim 1, characterized in that, In the said Step 1, the vehicle demand power formula is: P veh = (F r + F w + F i + F j ) u a , Among them, P veh is the required power, F r is the rolling resistance, F w is the air resistance, F i is the gradient resistance, F j is the acceleration resistance, u a is the driving speed; The specific longitudinal dynamics model of the vehicle is: Among them, m is the vehicle mass, g is the acceleration due to gravity, C r is the rolling resistance coefficient, i is the road gradient, C d is the air resistance coefficient, A is the frontal area, ρ is the air density, u a is the driving speed, is the driving acceleration.

4. The method according to claim 1, wherein In the said Step 1, constructing the output power model for the vehicle engine and battery includes: The demand power model for the vehicle engine and motor is: P veh = (P eng + P mot ) η, Among them, P veh is the required power, P eng is the engine power, P mot is the motor power, and η is the mechanical transmission efficiency; The engine model is established by numerical modeling, and the fuel consumption rate is obtained by interpolation. The specific engine fuel consumption model is: Wherein, is the instantaneous fuel consumption of the engine at time t, P eng (t) is the power of the engine at time t, η eng (t) is the working efficiency of the engine at time t, Q lhv is the low calorific value of gasoline fuel; The electric energy consumption is equivalently reduced to the current actual fuel consumption, and the specific equivalent fuel consumption of the vehicle at an instant is: Among them, is the instantaneous fuel consumption of the vehicle at time t, is the equivalent fuel consumption of the battery at time t, specifically: where s(t) is the oil-electric conversion equivalent factor; P bat (t) is the battery power; the battery model is simplified to an equivalent internal resistance model, specifically: Among them, P bat is the battery power, U oc is the open-circuit voltage, R0 is the battery internal resistance, I(t) is the battery current, Q bat is the battery capacity, and SOC0 is the initial state SOC of the battery.

5. The method according to claim 1, wherein In the second step, the uncertain parameters include the rolling resistance coefficient C r , the air resistance coefficient C d and the slope i.

6. The method according to claim 1, wherein In the said Step 2: Considering the uncertainty interval during the optimization process and introducing uncertain values and Under the uncertainty optimization framework, the uncertain parameters are represented by their nominal values and uncertainty values: is the vector of uncertain parameter values, P un is the vector of nominal parameter values, and α represents the vector containing the uncertainty associated with each parameter, specifically: P un = [C d , C r , i], where α sup (i) is the maximum possible value that the uncertainty a(i) can take, and the uncertain parameter takes values according to a symmetric distribution with a mean equal to the nominal value P un (i), and the uncertainty set of the uncertain parameter is:

7. The method according to claim 1, wherein In the said Step 3, the dynamic programming algorithm includes the following steps: Divide the global driving conditions into N sub-stages at 1s intervals, optimize from the initial stage x(1) to the end stage x(N - 1), and finally obtain a set of optimal engine power output sequences to minimize the total cost of the vehicle; Take the SOC of the battery as the state variable: x(k) = SOC(k), With the output torque and speed of the engine as the control variables, the control variables of the vehicle at the k-th stage are: u(k) = [T eng (k), n eng (k)] T , The expression of the vehicle state transition equation is: x k+1 = f(x k , u k ), According to the global driving condition information, calculate the demand torque and speed of the vehicle; and construct an objective function for minimizing the vehicle fuel consumption based on the demand torque and speed of the vehicle. The specific global objective function for minimizing the total cost of the vehicle's equivalent fuel consumption is: To ensure that the vehicle meets the actual driving situation, define the following constraint conditions: Among them, P eng,min , P eng,max are respectively the minimum output power and the maximum output power of the engine; P bat,min , P bat,max are respectively the maximum charging power and the maximum discharging power of the power battery; SOC min , SOC max are respectively the minimum value and the maximum value of the state of charge, and SOC end is the SOC at the end of the driving condition; δ represents the allowable error of the SOC of the vehicle at the end of the condition.

8. The method according to claim 1, wherein In the said Step 4, applying the model predictive control method includes the following steps: Linearize the nonlinear system of the hybrid vehicle to obtain a linear time-varying system; Discretize the linear time-varying system to obtain a discrete linear time-varying system; The trajectory and control sequence obtained by using the dynamic programming algorithm are used to linearize the system for each finite time horizon and formulate the terminal cost; Construct a Tube MPC optimization problem, solve to obtain the optimal control sequence within the uncertainty set, and output the first control variable of the optimal control sequence.

9. The method according to claim 8, wherein The Tube MPC optimization problem is as follows: Among them, N p is the prediction time domain; N c is the control time domain, P is the weight matrix of the state variables, and Q is the weight matrix of the control variables.

10. The method according to claim 1, characterized in that, Apply the first control variable to the hybrid vehicle to control the engine speed and torque of the vehicle, and achieve hierarchical energy management of the hybrid vehicle.

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