CN111645530B - Braking energy rolling optimization control method considering battery life - Google Patents

Braking energy rolling optimization control method considering battery life Download PDF

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CN111645530B
CN111645530B CN202010539196.7A CN202010539196A CN111645530B CN 111645530 B CN111645530 B CN 111645530B CN 202010539196 A CN202010539196 A CN 202010539196A CN 111645530 B CN111645530 B CN 111645530B
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braking
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soc
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CN111645530A (en
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徐薇
陈虹
赵海艳
邓丽飞
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Changchun University of Science and Technology
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60L—PROPULSION OF ELECTRICALLY-PROPELLED VEHICLES; SUPPLYING ELECTRIC POWER FOR AUXILIARY EQUIPMENT OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRODYNAMIC BRAKE SYSTEMS FOR VEHICLES IN GENERAL; MAGNETIC SUSPENSION OR LEVITATION FOR VEHICLES; MONITORING OPERATING VARIABLES OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRIC SAFETY DEVICES FOR ELECTRICALLY-PROPELLED VEHICLES
    • B60L7/00—Electrodynamic brake systems for vehicles in general
    • B60L7/10—Dynamic electric regenerative braking
    • B60L7/18—Controlling the braking effect
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60L—PROPULSION OF ELECTRICALLY-PROPELLED VEHICLES; SUPPLYING ELECTRIC POWER FOR AUXILIARY EQUIPMENT OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRODYNAMIC BRAKE SYSTEMS FOR VEHICLES IN GENERAL; MAGNETIC SUSPENSION OR LEVITATION FOR VEHICLES; MONITORING OPERATING VARIABLES OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRIC SAFETY DEVICES FOR ELECTRICALLY-PROPELLED VEHICLES
    • B60L15/00—Methods, circuits, or devices for controlling the traction-motor speed of electrically-propelled vehicles
    • B60L15/20—Methods, circuits, or devices for controlling the traction-motor speed of electrically-propelled vehicles for control of the vehicle or its driving motor to achieve a desired performance, e.g. speed, torque, programmed variation of speed
    • B60L15/2009—Methods, circuits, or devices for controlling the traction-motor speed of electrically-propelled vehicles for control of the vehicle or its driving motor to achieve a desired performance, e.g. speed, torque, programmed variation of speed for braking
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60L—PROPULSION OF ELECTRICALLY-PROPELLED VEHICLES; SUPPLYING ELECTRIC POWER FOR AUXILIARY EQUIPMENT OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRODYNAMIC BRAKE SYSTEMS FOR VEHICLES IN GENERAL; MAGNETIC SUSPENSION OR LEVITATION FOR VEHICLES; MONITORING OPERATING VARIABLES OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRIC SAFETY DEVICES FOR ELECTRICALLY-PROPELLED VEHICLES
    • B60L7/00—Electrodynamic brake systems for vehicles in general
    • B60L7/24—Electrodynamic brake systems for vehicles in general with additional mechanical or electromagnetic braking
    • B60L7/26—Controlling the braking effect
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T10/00—Road transport of goods or passengers
    • Y02T10/60—Other road transportation technologies with climate change mitigation effect
    • Y02T10/72—Electric energy management in electromobility

Abstract

A rolling optimization control method for braking energy considering battery life belongs to the technical field of vehicle engineering. The invention aims to provide a rolling optimization control method for braking energy, which comprehensively considers the recovery effect of the braking energy and the aging degree of a battery, establishes a unified economic evaluation index, and coordinates and optimizes the economy of a whole vehicle in the braking process and considers the service life of the battery. The method comprises the following steps: and establishing a system model, establishing a braking economy evaluation index, and designing a braking economy optimization controller. The invention aims at the problems of braking energy recovery and battery service life coordination optimization control of the four-wheel hub electric automobile, establishes the unified economic evaluation index of the braking energy recovery and the battery service life coordination optimization control, and provides the braking economic rolling optimization control strategy, which can balance and consider the braking energy loss cost and the battery capacity loss cost, thereby effectively reducing the braking loss cost and improving the overall braking economic efficiency.

Description

Braking energy rolling optimization control method considering battery life
Technical Field
The invention belongs to the technical field of vehicle engineering.
Background
Factors that limit the development of electric vehicles include not only anxiety in driving range caused by low energy density of batteries and imperfect construction of charging facilities, but also problems of short battery life and high cost. The battery aging phenomenon can occur during the use process of the battery, for example, the battery capacity can be attenuated, the internal resistance can be increased, and the specific energy and the specific power can be reduced, so the problem of the battery aging is directly related to the service life of the battery. The aging mechanism of the battery is complex, and the aging mechanism has direct relation with the external environment of the battery, such as charging and discharging multiplying power, residual capacity of the battery, working temperature and the like. The working principle of the braking energy recovery system is that the motor is used for carrying out feedback braking, so that the kinetic energy of the electric automobile is converted into electric energy to be stored in the battery, and in the process, the aging degree of the battery is influenced by the charging current and the SOC change condition of the battery. Therefore, when the electric automobile brakes, the two indexes of the energy efficiency level and the battery life of the whole automobile are not separated, but are mutually coupled and restricted.
Disclosure of Invention
The invention aims to provide a rolling optimization control method for braking energy, which comprehensively considers the recovery effect of the braking energy and the aging degree of a battery, establishes a unified economic evaluation index, and coordinates and optimizes the economy of a whole vehicle in the braking process and considers the service life of the battery.
The method comprises the following steps:
step one, establishing a system model:
1) establishing an automobile dynamic model:
according to the Newton second law and the moment balance equation, a braking dynamics model is established as follows:
Figure GDA0003682862560000011
Figure GDA0003682862560000012
wherein M represents the whole vehicle mass of the electric vehicle, vxIndicating the braking speed, FxRepresenting the friction between the wheel and the ground, FaRepresenting air resistance, neglecting rolling resistance, JjRepresenting the moment of inertia, omega, of each wheelwjIndicating the rotational speed of the front and rear wheels, ReIndicating the effective rolling radius, T, of the tirebjRepresenting the braking torque acting on the front and rear wheels;
2) establishing a battery model and a battery life loss model:
respectively establishing battery currents IbAnd the battery SOC model is as follows:
Figure GDA0003682862560000013
Figure GDA0003682862560000014
wherein, UocFor open circuit voltage of battery, RinIs the internal resistance of the battery, UocAnd RinAre all functions of the remaining battery capacity SOC and the battery temperature, IbCharging current, P, for the batterybAs battery power, SOC0Is the initial SOC, Q of the batterybatAs battery capacity, 0 and tfRepresenting the initial and terminal moments of the battery charging process;
establishing a control-oriented semi-empirical battery aging model as follows:
Figure GDA0003682862560000021
Figure GDA0003682862560000022
wherein Qloss% is the percentage of battery capacity loss, RgasIs the gas constant, θ is the absolute temperature of the cell, Ah is the total charge throughput of the cell, called Ah throughput, IcTaking the charge-discharge multiplying power of the battery, and taking alpha and beta as model parameters;
important indicators for estimating battery life
Figure GDA0003682862560000023
Where Γ is the nominal life of the battery, γ is the actual life of the battery, EOL represents the end of life of the battery, InomIs the nominal operating current of the battery;
under the assumption that the battery temperature is controllable to the nominal operating temperature, the relationship between the severity factor and the battery operating current and the battery SOC is derived according to the end of life of the battery when the battery capacity loss reaches 20% and equation (5) as follows:
Figure GDA0003682862560000024
the effective ampere-hour throughput of the battery, i.e. the effective life loss, is defined as follows:
Figure GDA0003682862560000025
Aheffrefers to the ampere-hour throughput accumulated by the battery;
step two, establishing a braking economy evaluation index: establishing a braking energy loss cost model and a battery capacity loss cost model 1) calculating the braking energy loss cost
CEloss＝Ce(Emloss+Ealoss+Ebloss+Ehloss)，(10)
Wherein, CElossRepresenting the cost of brake energy loss, CeIndicating the charge per unit energy, including the charge rate and the service rate, Emloss、Ealoss、Ebloss、EhlossRespectively representing the energy loss generated by a hub motor, air resistance, a battery system and a hydraulic system;
2) battery capacity loss cost calculation
Figure GDA0003682862560000026
Wherein, CQlossRepresents the cost of battery capacity loss, CbRepresents the total battery charge, Qloss% is the percentage of battery capacity loss; step three, designing a brake economy optimization controller:
let omegaw＝vx/ReFrom the kinetic equations (1) and (2), and the battery SOC equation (4), the system state space equation is obtained as follows:
Figure GDA0003682862560000031
Figure GDA0003682862560000032
wherein x is [ v ═ vx,SOC]TIs the system state quantity, u ═ Tm,Th]TFor control of quantity, TmAnd ThRespectively a motor braking torque and a hydraulic braking torque;
establishing an optimization control problem:
Figure GDA0003682862560000033
CEloss(k)＝Ce[Pmloss(Tm,ωm)+Paloss(vx)+Pbloss(Tm,ωm)+Phloss(Th,ωm)]Ts，(15)
Figure GDA0003682862560000034
Figure GDA0003682862560000035
equation (17) is a constraint condition of the optimization problem,
Figure GDA0003682862560000036
and
Figure GDA0003682862560000037
is a system state space equation constraint, 4Tm(k)+4Th(k)＝Tref(k) For the equality constraint of the braking torque demand, Tm,max、Th,max、ωm,maxRespectively showing the maximum braking torque of the motor, the maximum braking torque of the hydraulic system and the maximum rotating speed of the motor, and SOCmin≤SOC(k)≤SOCmaxIs a battery optimal operating range constraint;
constrain equation to 4g0Tm(k)+4Th(k)＝Tref(k) Converting into a target function penalty term form, and converting the optimization problem into the following form:
Figure GDA0003682862560000038
Figure GDA0003682862560000039
wherein the content of the first and second substances,
Figure GDA00036828625600000310
in the form of an equality bound penalty term for the objective function, Q1And Q2Respectively corresponding weights of the braking expense loss and the braking demand tracking target;
at sampling time k, according to the state quantity obtained by model prediction, adopting particle swarm optimization to solve independent variable sequence U in all prediction time domainskSo that the objective function J (X (k), U) is predicted in the time domaink) Reaches the minimum, then the first element u thereof is added*(k) Acting on the system, refreshing the optimization problem by using the updated system state information at the next sampling moment, and solving again until the control process is finished, namely:
Figure GDA0003682862560000041
u*(k)＝[Tm *(k),Th *(k)]T＝[1,0,…,0]Uk(k) (21)。
the invention aims at the problems of braking energy recovery and battery service life coordination optimization control of the four-wheel hub electric automobile, establishes the unified economic evaluation index of the braking energy recovery and the battery service life coordination optimization control, and provides the braking economy rolling optimization control strategy which can balance and consider the braking energy loss cost and the battery capacity loss cost, thereby effectively reducing the braking loss cost and improving the overall braking economy.
Drawings
FIG. 1 is a graph of brake speed results for different control strategies;
FIG. 2a is a graph of motor braking torque distribution results for different control strategies;
FIG. 2b is a graph of hydraulic braking torque distribution results for different control strategies;
FIG. 3a is a graph of the variation results of battery SOC for different control strategies;
FIG. 3b is a graph of the results of the change in effective life loss for different control strategies;
FIG. 4 is a graph of brake loss costs results for different control strategies.
Detailed Description
Firstly, establishing a system model; secondly, establishing a unified braking economy evaluation index, namely establishing a braking energy loss cost model and a battery capacity loss cost model; and finally, designing a braking economy rolling optimization controller based on a model prediction control method.
The method comprises the following specific steps:
step one, establishing a system model:
1) establishing an automobile dynamic model:
according to the Newton second law and the moment balance equation, a braking dynamics model is established as follows:
Figure GDA0003682862560000042
Figure GDA0003682862560000043
wherein M represents the whole vehicle mass of the electric vehicle, vxIndicating the braking speed, FxRepresenting the friction between the wheel and the ground, FaIndicating air resistanceHere, the rolling resistance is neglected. J. the design is a squarejRepresenting the moment of inertia, ω, of each wheelwjIndicating the rotational speed of the front and rear wheels, ReIndicating the effective rolling radius of the tire. T isbjRepresenting the braking torque acting on the front and rear wheels.
2) Establishing a battery model and a battery life loss model:
respectively establishing battery currents IbAnd the battery SOC model is as follows:
Figure GDA0003682862560000051
Figure GDA0003682862560000052
wherein, UocIs the open circuit voltage of the battery, RinIs the internal resistance of the battery, UocAnd RinAre both functions of the battery remaining capacity SOC and the battery temperature. I.C. AbCharging current for battery, PbIs the battery power, SOC0Is the initial SOC, Q of the batterybatAs battery capacity, 0 and tfIndicating the initial and terminal moments of the battery charging process. It is to be noted that the battery temperature is also an important state quantity of the battery model, and it is assumed here that the battery system has an independent battery temperature control system and is capable of accurately controlling the battery temperature.
Establishing a control-oriented semi-empirical battery aging model as follows:
Figure GDA0003682862560000053
Figure GDA0003682862560000054
wherein Q isloss% is the percentage of the loss of battery capacity, RgasIs the gas constant, and θ is the cell absolute temperature. Ah is aIs the total charge throughput of the battery, referred to as Ah throughput. I iscAlpha and beta are model parameters for the charge and discharge rate of the battery.
Typically, the end of battery life is considered when the loss of capacity of the battery reaches 20% of the nominal capacity. Battery life is defined as the total ampere-hour throughput at which the battery reaches end of life, and the ratio of the nominal life to the actual life of the battery is defined as a severity factor that quantifies the degree of aging of the battery relative to nominal operating conditions, and is also an important indicator for estimating battery life.
Figure GDA0003682862560000055
Where Γ is the nominal life of the battery and γ is the actual life of the battery, which is a function of the operating current, operating temperature and SOC of the battery. EOL denotes the end of life of the battery, InomIs the nominal operating current of the battery. When the battery is operated at a greater duty cycle, the severity factor will be greater than 1, which will increase the aging of the battery and decrease its life.
Under the assumption that the battery temperature is controllable to the nominal operating temperature, the relationship between the severity factor and the battery operating current and the battery SOC is derived from the end of life of the battery when the battery capacity loss reaches 20% and equation (5) as follows:
Figure GDA0003682862560000056
to accurately characterize the age of a battery, the effective ampere-hour throughput of the battery is defined, i.e., the effective life loss is as follows:
Figure GDA0003682862560000061
Aheffrefers to the cumulative ampere-hour throughput of the battery, i.e., the effective battery life loss, when the same aging effect is achieved under nominal conditionsAnd (5) consuming.
Step two, establishing a braking economy evaluation index:
in order to unify the brake recovery energy and the battery life economy evaluation index, a brake energy loss cost model and a battery capacity loss cost model are respectively established below.
1) Braking energy loss cost calculation
The energy recovered in the braking process is the energy obtained by subtracting the braking loss from the initial braking energy, the braking energy loss cost is defined as the charging cost required by the lost energy, and the braking energy loss cost is calculated as follows:
CEloss＝Ce(Emloss+Ealoss+Ebloss+Ehloss)， (10)
wherein, CElossRepresenting the cost of brake energy loss, CeThe charge rate required per unit energy is expressed, including charge electricity rate and service rate. Emloss、Ealoss、Ebloss、EhlossRespectively representing the energy loss generated by the hub motor, the air resistance, the battery system and the hydraulic system.
2) Battery capacity loss cost calculation
From the end of battery life when the battery capacity loss reaches 20% of nominal capacity, the cost of battery capacity loss during braking can be calculated as follows:
Figure GDA0003682862560000062
wherein, CQlossRepresents the cost of battery capacity loss, CbRepresents the total battery cost, Qloss% is the percentage of battery capacity loss.
Step three, designing a brake economy optimization controller:
under the general braking running condition, the ground can provide enough friction force for the tire, and omega is set for simplifying the design of a controllerw＝vx/ReObtaining the system shape according to the dynamic equations (1) and (2) and the battery SOC equation (4)The state space equation is as follows:
Figure GDA0003682862560000063
Figure GDA0003682862560000064
wherein x is [ v ═ vx,SOC]TIs a system state quantity, u ═ Tm,Th]TFor control of quantity, TmAnd ThRespectively a motor braking torque and a hydraulic braking torque. The problem of the coordinated optimization control of the braking energy and the service life of the battery is a multivariable multi-target control process, the system is more in constraint, and a model prediction control method is adopted to design a controller. Discretizing the optimization problem according to a forward Euler method, wherein the sampling time is Ts。
According to the model predictive control principle and the established objective function, the following optimization control problem is established:
Figure GDA0003682862560000071
CEloss(k)＝Ce[Pmloss(Tm,ωm)+Paloss(vx)+Pbloss(Tm,ωm)+Phloss(Th,ωm)]Ts，(15)
Figure GDA0003682862560000072
Figure GDA0003682862560000073
equation (17) is a constraint condition of the optimization problem,
Figure GDA0003682862560000074
and
Figure GDA0003682862560000075
is a system state space equation constraint, 4Tm(k)+4Th(k)＝Tref(k) For the constraint of the braking torque demand equality, Tm,max、Th,max、ωm,maxRespectively represents the maximum braking torque of the motor, the maximum braking torque of a hydraulic system, the maximum rotating speed of the motor and the SOCmin≤SOC(k)≤SOCmaxIs a battery optimal operating range constraint.
In order to facilitate the real-time realization of the controller, a particle swarm algorithm is adopted for solving, and an equality is constrained by 4g0Tm(k)+4Th(k)＝Tref(k) Converting into an objective function penalty term form, and converting an optimization problem into the following forms:
Figure GDA0003682862560000076
Figure GDA0003682862560000077
wherein the content of the first and second substances,
Figure GDA0003682862560000078
is the form of an equality constrained objective function penalty term, Q1And Q2The weights are respectively corresponding to the braking expense loss and the braking demand tracking target.
At a sampling time k, solving independent variable sequences U in all prediction time domains by adopting a particle swarm optimization according to the state quantity obtained by model predictionkSo that the objective function J (X (k), U) is predicted in the time domaink) Reach minimum, then first element u*(k) And acting on the system, refreshing the optimization problem by using the updated system state information at the next sampling moment, and solving again until the control process is finished. Namely:
Figure GDA0003682862560000079
u*(k)＝[Tm *(k),Th *(k)]T＝[1,0,…,0]Uk(k).(21)。
and (3) verification:
in order to verify the optimization effect of the designed brake economy controller, simulation analysis is carried out on an AMESim and Matlab/Simulink combined simulation platform, and economy comparison is carried out on the AMESim and Matlab/Simulink combined simulation platform and an energy recovery maximization strategy and a battery life loss minimization strategy. The braking distribution mode adopted by the energy recovery maximization strategy is electro-hydraulic series braking, when the braking requirement of the motor cannot be met, the braking mode is compensated by hydraulic braking, and the braking mode adopted by the battery life loss minimization strategy is pure hydraulic braking. The initial vehicle speed of the simulation working condition is 30m/s, the expected deceleration is-3 m/s2, the initial SOC of the battery is 50%, and the initial effective service life loss of the battery is 0. The relevant parameters of the controller are shown in table 1.
TABLE 1 brake economy optimization controller related parameters
Figure GDA0003682862560000081
The results of brake speed and electro-hydraulic brake torque distribution for three different brake control strategies are shown in fig. 1 and 2, respectively. The results show that the actual brake speed under the three control strategies is able to track the upper brake demand. The energy recovery maximization control strategy mainly adopts motor braking, the insufficient part is compensated by hydraulic braking before 1.8s due to the fact that the braking requirement exceeds the motor braking working range, and the motor braking is completely carried out after 1.8 s. Conversely, the battery life loss minimization control strategy is fully braked by the hydraulic system to achieve a minimum battery life loss. In the braking economy optimization control, the motor braking and the hydraulic braking jointly provide braking torque requirements, and the braking cost loss minimization is realized through the coordination optimization of the motor braking and the hydraulic braking.
Fig. 3 and 4 show the results of battery SOC versus battery life loss and braking loss costs for different braking control strategies. The results show that in this set of braking conditions, the final battery SOC for the braking energy recovery maximization control strategy is the highest, about 50.25%, the battery life loss minimization control strategy has a battery effective life loss of 0.018, and the braking cost loss for the braking economy optimization control strategy is 0.063 yuan.
And corresponding data of simulation results under different control strategies are shown in the table 2. According to the simulation result, the brake loss cost of the brake control strategy only considering the service life of the battery is the largest, and the results of the other two control strategies are relatively close. Through calculation, compared with an energy recovery maximization strategy, the braking economy control strategy has the advantages that the SOC increment of the battery is reduced by 25.81%, the effective service life loss of the battery is reduced by 35%, the braking loss cost is reduced by 5.97%, and the designed braking economy controller has a certain braking economy optimization effect. It should be noted that the effectiveness of brake economy optimization is directly related to battery capacity, cost, and battery charging cost.
TABLE 2 Battery SOC, effective life loss and brake loss cost results for different strategies
Figure GDA0003682862560000091

Claims (1)

1. A rolling optimization control method for braking energy considering battery life is characterized in that: the method comprises the following steps:
step one, establishing a system model:
1) establishing an automobile dynamic model:
according to the Newton second law and the moment balance equation, a braking dynamics model is established as follows:
Figure FDA0002538268160000011
Figure FDA0002538268160000012
wherein M represents the whole vehicle mass of the electric vehicle, vxIndicating the braking speed, FxRepresenting the friction between the wheel and the ground, FaDenotes air resistance, neglecting rolling resistance, JjRepresenting the moment of inertia, omega, of each wheelwjIndicating the rotational speed of the front and rear wheels, ReIndicating the effective rolling radius, T, of the tirebjRepresenting the braking torque acting on the front and rear wheels;
2) establishing a battery model and a battery life loss model:
respectively establishing battery currents IbAnd the battery SOC model is as follows:
Figure FDA0002538268160000013
Figure FDA0002538268160000014
wherein, UocFor open circuit voltage of battery, RinIs the internal resistance of the battery, UocAnd RinAre all functions of the remaining battery SOC and the battery temperature, IbCharging current, P, for the batterybAs battery power, SOC0Is the initial SOC, Q of the batterybatAs battery capacity, 0 and tfRepresenting the initial time and the termination time of the battery charging process;
establishing a control-oriented semi-empirical battery aging model as follows:
Figure FDA0002538268160000015
Figure FDA0002538268160000016
wherein Qloss% is the percentage of battery capacity loss, RgasIs the gas constant, θ is the absolute temperature of the cell, Ah is the total charge throughput of the cell, called Ah throughput, IcTaking the charge-discharge multiplying power of the battery, and taking alpha and beta as model parameters;
important indicators for estimating battery life
Figure FDA0002538268160000017
Wherein gamma is the nominal life of the battery, gamma is the actual life of the battery, EOL represents the end time of the life of the battery, InomA nominal operating current for the battery;
under the assumption that the battery temperature is controllable to the nominal operating temperature, the relationship between the severity factor and the battery operating current and the battery SOC is derived from the end of life of the battery when the battery capacity loss reaches 20% and equation (5) as follows:
Figure FDA0002538268160000021
the effective ampere-hour throughput of the battery, i.e., the effective life loss, is defined as follows:
Figure FDA0002538268160000022
Aheffrefers to the ampere-hour throughput accumulated by the battery;
step two, establishing a braking economy evaluation index: establishing a braking energy loss cost model and a battery capacity loss cost model 1) calculating the braking energy loss cost
CEloss＝Ce(Emloss+Ealoss+Ebloss+Ehloss)， (10)
Wherein, CElossRepresenting the cost of brake energy loss, CeUnit of expressionThe charge rate required for energy, including the charge rate of electricity and the service rate, Emloss、Ealoss、Ebloss、EhlossRespectively representing energy losses generated by a hub motor, air resistance, a battery system and a hydraulic system;
2) battery capacity loss cost calculation
Figure FDA0002538268160000023
Wherein, CQlossRepresenting the cost of loss of battery capacity, CbRepresents the total battery charge, Qloss% is the percentage of battery capacity loss; step three, designing a brake economy optimizing controller:
let omegaw＝vx/ReFrom the kinetic equations (1) and (2), and the battery SOC equation (4), the system state space equation is obtained as follows:
Figure FDA0002538268160000024
Figure FDA0002538268160000025
wherein x ═ vx,SOC]TIs a system state quantity, u ═ Tm,Th]TFor control of quantity, TmAnd ThRespectively a motor braking torque and a hydraulic braking torque;
establishing an optimization control problem:
Figure FDA0002538268160000026
CEloss(k)＝Ce[Pmloss(Tm,ωm)+Paloss(vx)+Pbloss(Tm,ωm)+Phloss(Th,ωm)]Ts， (15)
Figure FDA0002538268160000031
Figure FDA0002538268160000032
equation (17) is a constraint condition for the optimization problem,
Figure FDA0002538268160000033
and
Figure FDA0002538268160000034
is a system state space equation constraint, 4Tm(k)+4Th(k)＝Tref(k) For the constraint of the braking torque demand equality, Tm,max、Th,max、ωm,maxRespectively represents the maximum braking torque of the motor, the maximum braking torque of a hydraulic system, the maximum rotating speed of the motor and the SOCmin≤SOC(k)≤SOCmaxIs a battery optimal operating range constraint;
constrain equation to 4g0Tm(k)+4Th(k)＝Tref(k) Converting into a target function penalty term form, and converting the optimization problem into the following form:
Figure FDA0002538268160000035
Figure FDA0002538268160000036
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0002538268160000037
is an equality constrained objective function penalty term form，Q1And Q2Respectively corresponding weights of the braking expense loss and the braking demand tracking target;
at sampling time k, according to the state quantity obtained by model prediction, adopting particle swarm optimization to solve independent variable sequence U in all prediction time domainskSo that the objective function J (X (k), U) is predicted in the time domaink) Reaches the minimum, then the first element u thereof is added*(k) Acting on the system, refreshing the optimization problem by using the updated system state information at the next sampling moment, and solving again until the control process is finished, namely:
Figure FDA0002538268160000038
u*(k)＝[Tm *(k),Th *(k)]T＝[1,0,…,0]Uk(k) (21)。
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