CN110228482B - Hybrid power bus station area control method based on intelligent traffic information - Google Patents

Hybrid power bus station area control method based on intelligent traffic information Download PDF

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CN110228482B
CN110228482B CN201910401022.1A CN201910401022A CN110228482B CN 110228482 B CN110228482 B CN 110228482B CN 201910401022 A CN201910401022 A CN 201910401022A CN 110228482 B CN110228482 B CN 110228482B
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bus
degree
distance
speed
bus station
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CN110228482A (en
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付尧
雷雨龙
李兴忠
王林波
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Jilin University
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    • BPERFORMING OPERATIONS; TRANSPORTING
    • B60VEHICLES IN GENERAL
    • B60WCONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W50/00Details of control systems for road vehicle drive control not related to the control of a particular sub-unit, e.g. process diagnostic or vehicle driver interfaces
    • GPHYSICS
    • G08SIGNALLING
    • G08GTRAFFIC CONTROL SYSTEMS
    • G08G1/00Traffic control systems for road vehicles
    • G08G1/09Arrangements for giving variable traffic instructions
    • G08G1/0962Arrangements for giving variable traffic instructions having an indicator mounted inside the vehicle, e.g. giving voice messages
    • G08G1/0967Systems involving transmission of highway information, e.g. weather, speed limits
    • G08G1/096708Systems involving transmission of highway information, e.g. weather, speed limits where the received information might be used to generate an automatic action on the vehicle control
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B60VEHICLES IN GENERAL
    • B60WCONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W50/00Details of control systems for road vehicle drive control not related to the control of a particular sub-unit, e.g. process diagnostic or vehicle driver interfaces
    • B60W2050/0001Details of the control system
    • B60W2050/0002Automatic control, details of type of controller or control system architecture

Abstract

The invention discloses a hybrid power bus stop area control method based on intelligent traffic information, which comprises the following steps of 1: acquiring the speed, the opening degree of an accelerator, the distance from a next bus station and the battery electric quantity information of the bus according to the sampling period; step 2: fuzzifying the speed, the opening degree of an accelerator, the distance from a next bus station and the battery electric quantity information of the bus, and resolving the fuzzification after fuzzy reasoning calculation to obtain a control allowance degree; and step 3: when the control permission degree is { low }, the bus runs according to the original running state; when the control permission degree is { middle, high }, disconnecting a clutch of an engine and a transmission of the public bus, keeping the engine and the transmission in torque-free transmission, and keeping the engine in a closed state; keeping the low gear running of the transmission, allowing downshifting and forbidding upshifting; the driving motor is adopted to drive the bus independently and limit the output power of the bus. The comprehensive energy consumption and the service life of the clutch are improved.

Description

Hybrid power bus station area control method based on intelligent traffic information
Technical Field
The invention relates to the field of adaptive control of a hybrid bus to bus stop areas, in particular to a hybrid bus stop area control method based on intelligent traffic information.
Background
Under the common conditions, the hybrid power bus controls an engine, a driving motor and an automatic transmission assembly according to information such as an accelerator, a brake and a speed, the system performance is better under the conventional driving road condition, but in a bus stop area, the problems of worsening of the whole vehicle energy consumption, the service life of parts of a clutch assembly and riding comfort, such as short-distance starting/stopping of the engine, unnecessary gear shifting and the like, are caused because the conventional control system ignores the driving environment information of the vehicle. Therefore, it is beneficial to introduce Intelligent Transportation (ITS) real-time information and synthesize the information to perform more reasonable control so as to improve the comprehensive performance of the existing system.
In view of the above, the invention provides a hybrid bus station area control method based on Intelligent Transportation (ITS) information, so as to improve the adaptability of a hybrid bus control system to the driving environment.
Disclosure of Invention
The invention designs and develops a hybrid power bus stop area control method based on intelligent traffic information, which can obtain the road condition and the vehicle condition of the bus in real time, effectively reduce the times of starting/stopping an engine, a clutch and gear shifting actions of the hybrid power bus in the area close to the bus stop, and improve the comprehensive energy consumption, the service life of the clutch and the riding comfort of the whole bus.
The invention can limit the output power of the driving motor when the control permission degree is { middle, high }, save the electric quantity, and avoid the starting of the engine due to the low SOC of the battery.
The technical scheme provided by the invention is as follows:
a hybrid power bus station area control method based on intelligent traffic information comprises the following steps:
step 1: acquiring the speed, the opening degree of an accelerator, the distance from a next bus station and the battery electric quantity information of the bus according to the sampling period;
step 2: fuzzifying the speed, the opening degree of an accelerator, the distance from the next bus station and the battery electric quantity information of the bus, and resolving the fuzzification after fuzzy reasoning calculation to obtain a control allowance degree;
the bus comprises a bus body, a bus control system and a bus control system, wherein the bus speed, the accelerator opening, the distance from a next bus station, the battery power and the control permission degree of the bus are divided into three grades; the fuzzy set of the speed, the opening degree of an accelerator and the distance from the bus to the next bus station is { small, medium and large }, and the fuzzy set of the battery capacity and the control permission degree of the bus is { low, medium and high };
and step 3: when the control permission degree is { low }, the bus runs according to the original running state;
when the control permission degree is { middle, high }, disconnecting a clutch of an engine and a transmission of the public bus, keeping the engine and the transmission in torque-free transmission, and keeping the engine in a closed state; keeping the low gear running of the transmission, allowing downshifting and forbidding upshifting; adopt driving motor individual drive public transit passenger train to its output power of control satisfies:
when the control permission degree is { middle }:
Figure BDA0002059775440000021
when the control allowance is { high }:
Figure BDA0002059775440000022
wherein P is the output power of the driving motor, PmaxD is the distance of the bus from the next bus stop, D is the maximum output power of the drive motor0To set the distance, v is the vehicle speed, vminTo minimum vehicle speed, vmaxIn order to be the maximum vehicle speed,
Figure BDA0002059775440000023
η for throttle openingeThe battery charge.
Preferably, in step 2, the information of the speed, the opening degree of the accelerator, the distance to the next bus station and the battery capacity of the bus is fuzzified, the fuzzy domain of the speed of the bus is [0,80], the quantization factor is 1, the fuzzy domain of the distance to the next bus station is [0,150], the quantization factor is 1, the fuzzy domain of the opening degree of the accelerator is [0,100], the quantization factor is 1, the fuzzy domain of the battery capacity is [0,100], the quantization factor is 1, the fuzzy domain of the control allowance is [0,100], and the quantization factor is 1.
Preferably, in step 2, the fuzzy inference calculation uses a Mamdani algorithm to perform the fuzzy inference calculation, and the inference rule is as follows:
IF(Ai)AND(Bi)AND(Ci)AND(Di)THEN(Ei)(i=1,2,…n);
the reasoning result corresponding to the reasoning rule is as follows:
Figure BDA0002059775440000031
wherein the fuzzy inference rule is extracted based on driver manipulation experience, AiTo push at the ith barDistance of bus from bus station ahead in administrative rules, BiFor vehicle speed in the ith inference rule, CiFor the throttle opening value in the ith inference rule, DiFor the battery level in the ith inference rule, EiTo control the degree of permissibility in the ith inference rule,
Figure BDA0002059775440000032
for the inference result in the ith inference rule, ziThe weight occupied by the ith inference rule,
Figure BDA0002059775440000033
the degree that the distance from the bus to the next bus station at the x operating point in the ith inference rule belongs to the corresponding fuzzy domain,
Figure BDA0002059775440000034
the degree that the speed of the bus belongs to the corresponding fuzzy domain at the x working condition point in the ith inference rule,
Figure BDA0002059775440000035
the degree of the throttle opening of the bus at the x operating point in the ith inference rule belonging to the corresponding fuzzy domain,
Figure BDA0002059775440000036
and the battery electric quantity of the bus at the x working condition point in the ith inference rule belongs to the corresponding fuzzy domain degree.
Preferably, in step 2, the obtaining of the control tolerance performs defuzzification processing on the fuzzy inference calculation result by using a weighted average method:
Figure BDA0002059775440000037
in the formula, zdefTo control the degree of permissivity.
Preferably, the method further comprises the steps between the step 1 and the step 2, the effectiveness judgment is carried out on the collected speed, the opening degree of an accelerator, the distance from a next bus station and the battery electric quantity information of the bus, if the effectiveness judgment is carried out, the next step is carried out, and if the effectiveness judgment is invalid, the resampling is carried out;
and when the acquired speed, the accelerator opening, the distance from the next bus station and the battery power of the bus are in the corresponding fuzzy theory domain, the bus is valid, otherwise, the bus is invalid.
Preferably, before the validity judgment, the collected speed, the accelerator opening, the distance from the next bus station and the battery power information of the bus are subjected to first-order low-pass filtering.
Preferably, in step 1, the sampling period is 5 ms.
Preferably, n is 3.
The invention has the following beneficial effects:
(1) according to the method for controlling the bus stop area of the hybrid bus based on the ITS (intelligent transportation) information, the state information of the bus is integrated, the real-time position information of the bus, the real-time distance information of the front bus stop and the like are obtained by the intelligent transportation system, and the hybrid bus close to the bus stop is controlled, so that the starting/stopping of an engine, the clutch and the gear shifting action times of the hybrid bus in the bus stop area can be effectively reduced, and the integrated energy consumption of the system, the service life of the clutch and the riding comfort of the whole bus are improved to a certain extent. The invention can limit the output power of the driving motor when the control permission degree is { middle, high }, save the electric quantity, and avoid the starting of the engine due to the low SOC of the battery.
(2) The method for controlling the bus stop area of the hybrid power bus based on the ITS information is realized on the software level without adding extra hardware configuration, and has the characteristics of low cost and good reusability.
(3) The method for controlling the bus stop area of the hybrid power bus based on the ITS information adopts a fuzzy reasoning mode, fully utilizes and refers to the operation experience of people, and has certain intelligent level.
(4) The ITS information-based hybrid power bus station area control method has universality and portability, and can be applied to other various types of buses with hybrid and automatic speed change systems.
Drawings
FIG. 1 is a schematic diagram of a hybrid system architecture applied to a hybrid bus station area control method based on intelligent traffic information.
FIG. 2 is a functional module schematic diagram of a hybrid power bus stop area control method based on intelligent traffic information.
FIG. 3 is a flow chart of the process of the method for controlling the bus stop area of the hybrid bus based on intelligent transportation information.
FIG. 4 is a flow chart of fuzzy reasoning in the intelligent transportation information-based hybrid bus station area control method.
Detailed Description
The present invention is further described in detail below with reference to the attached drawings so that those skilled in the art can implement the invention by referring to the description text.
This invention may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein, but rather as being provided for the purpose of illustration and description. In the drawings, the size and relative sizes of structures and regions may be exaggerated for clarity.
As shown in fig. 1, the diagram is a schematic diagram of a hybrid bus system on which the method for controlling the bus stop area of the hybrid bus based on ITS information is implemented, and a program for implementing the method for controlling the bus stop area of the hybrid bus based on ITS information is installed and operated in a VCU (vehicle control unit). The hybrid system is composed of an engine, a clutch, a driving motor, an AMT transmission, a power energy storage device, a high-voltage electric steering mechanism, a drive axle, wheels, and the like, and is a common structure of the existing hybrid vehicle, and therefore, the specific structure and connection mode thereof are not described herein.
The VCU of the vehicle controller interacts with all assembly controllers through a controller local area network, receives key switch signals, accelerator pedal signals, braking signals, vehicle speed, handle signals, current gear signals, motor batteries and other assembly information, recognizes driver intention, judges current vehicle state and working condition, coordinates and controls motor, battery, clutch, AMT and other power assembly components to realize the functions of the hybrid power system of the whole vehicle (including engine idle speed start-stop, pure electric, engine single drive, combined drive, braking energy recovery and the like).
As shown in fig. 2, the diagram is a schematic diagram of functional modules of a bus stop area control method of a hybrid electric bus based on ITS information, and the functions of the modules are as follows:
1. and the input signal processing module is used for processing signals of the input system such as vehicle speed, accelerator opening, real-time distance from the next bus station, battery electric quantity and the like, and filtering out interference and wild points of the signals by adopting a first-order low-pass filtering mode.
2. The fuzzy inference module firstly fuzzifies input signals such as vehicle speed, accelerator opening, real-time distance from a next bus station, electromagnetic electric quantity and the like, then carries out fuzzy inference calculation according to an experience-based fuzzy rule base (extracted based on the operation experience of a driver), carries out defuzzification on inference obtained results, and finally obtains control permission information.
3. And the hybrid power comprehensive control module judges the control permission information input into the system, executes a comprehensive control function only when the control permission information is greater than a predefined threshold value requirement and the current vehicle and working condition information meet the control requirement, and coordinates control units such as a TCU (transmission control unit), an MCU (microprogrammed control unit), an ECU (electronic control unit) and the like to cooperatively complete control of the clutch, the driving motor, the engine and the transmission.
As shown in fig. 3, the method for controlling the bus stop area of the hybrid bus based on the intelligent transportation information provided by the invention comprises the following steps:
step 1: and acquiring the speed, the opening of an accelerator, the distance from the next bus station and the battery power information of the bus according to a sampling period (5ms), and filtering out the interference and the wild points of the signals by adopting a first-order low-pass filtering mode.
Step 2: carrying out validity judgment on the collected speed, the opening of an accelerator, the distance from a next bus station and the battery electric quantity information of the bus, if the collected speed, the opening of the accelerator and the distance from the next bus station are valid, carrying out the next step, and if the collected distance is invalid, re-sampling;
and when the acquired speed, the accelerator opening, the distance from the next bus station and the battery power of the bus are in the corresponding fuzzy theory domain, the bus is valid, otherwise, the bus is invalid.
And step 3: and fuzzifying the speed, the opening degree of the accelerator, the distance from the next bus station and the battery electric quantity information of the bus.
Considering the real-time calculation and problem solving of the system, the membership function is in a trigonometric function form, the membership function is used for converting an accurate value of a physical quantity into a linguistic variable value which is easy to understand, and fuzzy linguistic variables of real-time distance, vehicle speed, accelerator opening and control allowance of a front bus station and a domain of discourse of the fuzzy linguistic variable are respectively given.
The fuzzy domain of the speed of the bus is [0,80], the quantization factor of the fuzzy domain is 1, the fuzzy domain of the distance from the next bus station is [0,150], the quantization factor of the fuzzy domain is 1, the fuzzy domain of the opening degree of the accelerator is [0,100], the quantization factor of the fuzzy domain of the battery capacity is 1, and the speed of the bus, the opening degree of the accelerator, the distance from the next bus station and the battery capacity are divided into three grades; the fuzzy set of the speed, the opening degree of the accelerator and the distance from the next bus station of the bus is { small, medium and large }, and the fuzzy set of the battery capacity of the bus is { low, medium and high }.
And 4, step 4: fuzzy reasoning calculation is carried out on the speed, the opening degree of an accelerator, the distance from a next bus station and the battery power of the fuzzified bus, a Mamdani algorithm is specifically adopted for carrying out the fuzzy reasoning calculation, and the reasoning rule is as follows:
IF(Ai)AND(Bi)AND(Ci)AND(Di)THEN(Ei)(i=1,2,…n);
the reasoning result corresponding to the reasoning rule is as follows:
Figure BDA0002059775440000071
obtaining a total inference result muE(z):
Figure BDA0002059775440000072
Wherein the fuzzy inference rule is extracted based on driver manipulation experience, AiDistance of bus from front bus station in the ith inference rule, BiFor vehicle speed in the ith inference rule, CiFor the throttle opening value in the ith inference rule, DiFor the battery level in the ith inference rule, EiTo control the degree of permissibility in the ith inference rule,
Figure BDA0002059775440000073
for the inference result in the ith inference rule, ziThe weight occupied by the ith inference rule,
Figure BDA0002059775440000074
the degree that the distance from the bus to the next bus station at the x operating point in the ith inference rule belongs to the corresponding fuzzy domain,
Figure BDA0002059775440000075
the degree that the speed of the bus belongs to the corresponding fuzzy domain at the x working condition point in the ith inference rule,
Figure BDA0002059775440000076
the degree of the throttle opening of the bus at the x operating point in the ith inference rule belonging to the corresponding fuzzy domain,
Figure BDA0002059775440000077
the battery electric quantity of the bus at the x working condition point in the ith inference rule is slavedTo the extent that it corresponds to a domain of ambiguity, in this embodiment, n is 3.
And 5: and (3) performing defuzzification processing on the result by adopting a weighted average method (adopting a gravity center method) aiming at the inference result to obtain the final control permission:
Figure BDA0002059775440000078
in the formula, zdefTo control the degree of permissivity;
the ambiguity domain of the control allowance is [0,100], the quantization factor is 1, the control allowance is divided into three levels, the ambiguity set is { low, medium, high }, and steps 3-5 are shown in FIG. 4.
Step 6: when the control permission degree is { low }, the bus runs according to the original running state;
when the control permission degree is { middle, high }, disconnecting a clutch of an engine and a transmission of the public bus, keeping the engine and the transmission in torque-free transmission, and keeping the engine in a closed state; keeping the low gear running of the transmission, allowing downshifting and forbidding upshifting; adopt driving motor individual drive public transit passenger train to its output power of control satisfies:
when the control permission degree is { middle }:
Figure BDA0002059775440000081
when the control allowance is { high }:
Figure BDA0002059775440000082
wherein P is the output power of the driving motor, PmaxD is the distance of the bus from the next bus stop, D is the maximum output power of the drive motor0To set the distance, v is the vehicle speed, vminTo minimum vehicle speed, vmaxIn order to be the maximum vehicle speed,
Figure BDA0002059775440000083
η for throttle openingeThe battery charge.
As shown in table 1, it is a control rule table in the bus stop area control method of the hybrid electric bus based on ITS information. The control rule considers the control permission degrees of the real-time distance from the bus station, the vehicle speed and the accelerator opening degree in different values. Inference rules are a summary of human inference experiences, each rule corresponding to a respective operating condition.
Table 1 control rules table
Figure BDA0002059775440000084
Figure BDA0002059775440000091
Figure BDA0002059775440000101
Figure BDA0002059775440000111
According to the method for controlling the bus stop area of the hybrid bus based on the ITS (intelligent transportation) information, the state information of the bus is integrated, the real-time position information of the bus, the real-time distance information of the front bus stop and the like are obtained by the intelligent transportation system, and the hybrid bus close to the bus stop is controlled, so that the starting/stopping of an engine, the clutch and the gear shifting action times of the hybrid bus in the bus stop area can be effectively reduced, and the integrated energy consumption of the system, the service life of the clutch and the riding comfort of the whole bus are improved to a certain extent. The invention can limit the output power of the driving motor when the control permission degree is { middle, high }, save the electric quantity, and avoid the starting of the engine due to the low SOC of the battery.
While embodiments of the invention have been described above, it is not limited to the applications set forth in the description and the embodiments, which are fully applicable in various fields of endeavor to which the invention pertains, and further modifications may readily be made by those skilled in the art, it being understood that the invention is not limited to the details shown and described herein without departing from the general concept defined by the appended claims and their equivalents.

Claims (8)

1. A hybrid power bus station area control method based on intelligent traffic information is characterized by comprising the following steps:
step 1: acquiring the speed, the opening degree of an accelerator, the distance from a next bus station and the battery electric quantity information of the bus according to the sampling period;
step 2: fuzzifying the speed, the opening degree of an accelerator, the distance from the next bus station and the battery electric quantity information of the bus, and resolving the fuzzification after fuzzy reasoning calculation to obtain a control allowance degree;
the bus comprises a bus body, a bus control system and a bus control system, wherein the bus speed, the accelerator opening, the distance from a next bus station, the battery power and the control permission degree of the bus are divided into three grades; the fuzzy set of the speed, the opening degree of an accelerator and the distance from the bus to the next bus station is { small, medium and large }, and the fuzzy set of the battery capacity and the control permission degree of the bus is { low, medium and high };
and step 3: when the control permission degree is { low }, the bus runs according to the original running state;
when the control permission degree is { middle, high }, disconnecting a clutch of an engine and a transmission of the public bus, keeping the engine and the transmission in torque-free transmission, and keeping the engine in a closed state; keeping the low gear running of the transmission, allowing downshifting and forbidding upshifting; adopt driving motor individual drive public transit passenger train to its output power of control satisfies:
when the control permission degree is { middle }:
Figure FDA0002481467680000011
when the control allowance is { high }:
Figure FDA0002481467680000012
wherein P is the output power of the driving motor, PmaxD is the distance of the bus from the next bus stop, D is the maximum output power of the drive motor0To set the distance, v is the vehicle speed, vminTo minimum vehicle speed, vmaxIn order to be the maximum vehicle speed,
Figure FDA0002481467680000013
η for throttle openingeThe battery charge.
2. The intelligent transportation information-based hybrid bus station area control method according to claim 1, wherein in step 2, the speed, the accelerator opening, the distance to the next bus station, and the battery power information of the bus are fuzzified, the ambiguity domain of the speed of the bus is [0,80], the quantization factor is 1, the ambiguity domain of the distance to the next bus station is [0,150], the quantization factor is 1, the ambiguity domain of the accelerator opening is [0,100], the quantization factor is 1, the ambiguity domain of the battery power is [0,100], the quantization factor is 1, the ambiguity domain of the control allowance is [0,100], and the quantization factor is 1.
3. The intelligent transportation information-based hybrid electric bus station area control method as claimed in claim 2, wherein in step 2, the fuzzy inference calculation adopts a Mamdani algorithm to perform fuzzy inference calculation, and the inference rule is as follows:
IF(Ai)AND(Bi)AND(Ci)AND(Di)THEN(Ei)(i=1,2,…n);
the reasoning result corresponding to the reasoning rule is as follows:
Figure FDA0002481467680000021
wherein the fuzzy inference rule is extracted based on driver manipulation experience, AiDistance of bus from front bus station in the ith inference rule, BiFor vehicle speed in the ith inference rule, CiFor the throttle opening value in the ith inference rule, DiFor the battery level in the ith inference rule, EiTo control the degree of permissibility in the ith inference rule,
Figure FDA0002481467680000022
for the inference result in the ith inference rule, ziThe weight occupied by the ith inference rule,
Figure FDA0002481467680000023
the degree that the distance from the bus to the next bus station at the x operating point in the ith inference rule belongs to the corresponding fuzzy domain,
Figure FDA0002481467680000024
the degree that the speed of the bus belongs to the corresponding fuzzy domain at the x working condition point in the ith inference rule,
Figure FDA0002481467680000025
the degree of the throttle opening of the bus at the x operating point in the ith inference rule belonging to the corresponding fuzzy domain,
Figure FDA0002481467680000026
and the battery electric quantity of the bus at the x working condition point in the ith inference rule belongs to the corresponding fuzzy domain degree.
4. The intelligent transportation information-based hybrid bus station area control method as claimed in claim 3, wherein in step 2, the control permission degree is obtained by performing defuzzification processing on the fuzzy inference calculation result by adopting a weighted average method:
Figure FDA0002481467680000027
in the formula, zdefTo control the degree of permissivity.
5. The intelligent transportation information-based hybrid bus station area control method as claimed in claim 2 or 3, wherein between step 1 and step 2, the method further comprises the steps of judging the validity of the collected speed, the opening degree of an accelerator, the distance from the next bus station and the battery power information of the bus, if valid, performing the next step, and if invalid, re-sampling;
and when the acquired speed, the accelerator opening, the distance from the next bus station and the battery power of the bus are in the corresponding fuzzy theory domain, the bus is valid, otherwise, the bus is invalid.
6. The intelligent transportation information-based hybrid bus station area control method as claimed in claim 5, wherein the collected information of the speed, the opening degree of an accelerator, the distance from the next bus station and the battery power of the bus is subjected to first-order low-pass filtering before the validity judgment is performed.
7. The intelligent transportation information-based hybrid bus station area control method as claimed in claim 1, wherein in step 1, the sampling period is 5 ms.
8. The intelligent transportation information-based hybrid bus station area control method as claimed in claim 3, wherein n is 3.
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