CN110550023B - Running stability control method for pure electric multi-section articulated automobile train - Google Patents
Running stability control method for pure electric multi-section articulated automobile train Download PDFInfo
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Abstract
The invention discloses a running stability control method for a pure electric multi-section articulated automobile train, which mainly comprises the following steps: a mathematical state space model of an automobile train to be researched is established, a system matrix A and a control input matrix B1 are obtained, 9 variables of the lateral speed and the yaw speed of an articulated vehicle and the articulation angle, the articulation angular speed and the steering wheel angle of three articulated discs are selected as detection variables, and a sensor outputs real-time signals of the 9 variables and transmits the real-time signals to an ECU. And the ECU predicts the future dynamic change of the tractor through the change of the steering wheel corner and controls the stable operation of the automobile train. The control method can control the motion form of the trailer at the rear part to follow the tractor, ensures the running integrity of the automobile train, effectively avoids the instability phenomena of folding, drifting and snake-shaped existing in the running process of the automobile train, and improves the safe operation performance of the automobile train.
Description
Technical Field
The invention relates to the field of transportation, in particular to a running stability control method for a pure electric multi-section articulated automobile train.
Background
The public transportation field in each city at present mainly provides buses, Bus Rapid Transit (BRT), subways, light rails and taxis, and people can conveniently go out. Because the demand of bus infrastructure is not high, the investment of the whole system is low, and the investment of buses is one of the main means for releasing the pressure of public transport of governments in various regions at present. Although the public transport travel pressure is relieved by increasing the number of bus shifts and the number of bus trains, the problem of large population flow in the large-city traffic cannot be effectively solved due to the limited one-way traffic volume of the buses. Some cities such as mansion doors, zheng zhou and the like vigorously develop lengthened type rapid transit buses connected through hinged disks, although the one-way traffic volume of the passenger cars is increased, the effect of relieving the congestion degree of the public transit is limited, and the construction cost required by specially constructing viaducts or special rapid passages is higher for the operation safety of the rapid transit buses in various places. At present, a plurality of cities in the country use double-layer buses, and although the double-layer buses improve one-way traffic volume, the double-layer buses have higher height compared with the traditional vehicles, have certain requirements on traffic operation environment, and cannot be used in environments with limitation on operation height, such as bridges, culverts and the like. In recent years, rail transportation, such as light rails, subways, and other rails, has been vigorously developed in various places to relieve traffic pressure.
Compared with the traditional transportation means, the rail transportation effectively utilizes the upper space and the underground space existing in the urban space, forms a traffic network system of the rail transportation, does not compete with the traditional ground vehicles in the aspect of road space, and can prolong the length of the vehicle body due to the fact that the vehicle body of the rail transportation is increased, the single transportation efficiency is greatly improved relative to other vehicles, and the rail transportation system plays a great role in relieving traffic flow. But the infrastructure construction cost of the rail transit is higher, and the later maintenance cost is higher when the period is longer. In recent years, a multi-section articulated automobile train is gradually valued by local governments in China as a public transportation solution. The articulated automobile train of multisection connects the carriage through articulated dish, realizes the increase expansion of automobile body, has increased conveying efficiency to do not need the track construction. However, due to the fact that the length of the train body is increased, the operation stability of the train is poor, the phenomenon of instability of movement easily occurs under working conditions of turning, lane changing and the like, and the operation safety of roads is seriously affected.
Chinese document CN 108058726A discloses a "route tracking control method of a full-trailer type train with full-axle steering", and chinese document CN105564447A discloses a "control system of a virtual rail train", the aforementioned patent focuses on the following control of the tracks of the front and rear vehicles of the train, these methods control the rear trailer by using a certain fixed point of the rear trailer body as a variable point and a certain fixed point of the front articulated vehicle as a reference point, and the deviation between the variable point on the rear trailer body and the fixed point of the front tractor is reduced by full-wheel steering, thereby preventing the train from colliding with other transportation vehicles and road facilities on the road, and effectively maintaining the safety of the transportation of the train. However, the research is more focused on track following control at present, and the research on automobile stability control is less, and a large amount of research has shown that the stability control of the automobile train is more important than the track following control under the medium-high speed operation condition and is more significant in the actual transportation.
Disclosure of Invention
In view of the above, it is necessary to provide a method for controlling the running stability of a pure electric multi-section articulated vehicle train, which realizes stable operation of the vehicle train through steering of various axles and wheels.
In order to solve the technical problems, the technical scheme of the invention is as follows: a running stability control method for a pure electric multi-section articulated automobile train comprises a tractor and at least N sections of trailers, wherein N is more than or equal to 2, the tractor and the trailers are articulated sequentially through articulated discs, and the running stability control method is carried out according to the following steps:
s1: installing a speed sensor and an angular velocity sensor on a tractor to acquire the real-time numerical values of the lateral speed and the yaw angular velocity of the tractor, installing an angle sensor and an angular velocity sensor on each hinged disk to respectively acquire the real-time hinged angle and the real-time hinged angular velocity of each hinged disk, installing an angle sensor on a steering wheel of the tractor, and predicting the running form of the tractor according to the angle change;
s2: establishing respective local coordinate systems on a tractor and all trailers, establishing a whole coordinate system on an automobile train, and performing whole stress analysis on the automobile train, wherein a tire stress model adopts a tire magic formula linear region expression;
s3: according to a local coordinate system fixedly connected on the tractor, the tractor is subjected to stress analysis to obtain the mass center lateral acceleration a of the tractoryFront axle tire slip angle alphafAnd rear axle tire sidewall angle alphar；
S4: the N-1 trailers behind the tractor and the tractor are taken as a whole one by one to carry out stress analysis to obtain the N-1 trailer
Center of mass lateral acceleration ay(N-1)Tire slip angle α(N-1)And tire control input steering angle(N-1)The expression of (1);
s5: stress analysis is carried out by taking the tractor and the N-section trailer behind the tractor as a whole to obtain the N-section trailer
Center of mass lateral acceleration ayNFront axle wheel sidewall deviation angle alphaNfAnd rear axle tire sidewall angle alphaNr；
S6: establishing a whole vehicle lateral force balance formula of the automobile train;
s7: establishing a balance equation of yaw moment of the mass center of the tractor;
s8: analyzing the M section to the Nth section of the trailer as a whole to obtain a yaw moment balance expression of the M hinge point; wherein M is from 1 to N;
s9: substituting the lateral acceleration of each mass center of the tractor and the trailer in the steps S3 to S5 and a constraint condition into the steps S6 to S8, simplifying the differential equation established in the steps, and selecting vx、vy、θ1To thetaNAnd the first reciprocal and the second derivative thereof are variables, the simplification ensures that the whole differential equation set only contains the form of the variables, and the constraint condition is as follows:
wherein v isxIs the longitudinal speed, v, of the tractoryAs the lateral speed of the tractor, theta1The articulation angle of the tractor and the first trailer,
θ2for the articulation angle, theta, of the first trailer to the second trailerNThe articulation angle of the N-1 section trailer and the N section trailer, r is the yaw velocity of the tractor, r1Yaw rate, r, of the first trailer2Yaw rate, r, of the second trailerNYaw rate of the nth trailer;
s10: according to the simplification arrangement of step S8, the following are selected:
state variables of the train:
output vector of the automobile train:
the tractor corner input vector is: u is [ ],
all trailer corner control input vectors are U1＝[1,2,…,N]，
The differential equation after the simplification of step S9 is converted into a standard state space equation:
wherein v isy1Is the lateral speed, v, of the first traileryNThe lateral speed of the Nth section of the trailer and the corner of the front wheel of the tractor,1for the first section of the trailer tire corner,2for the second trailer tire corner,Nis the corner of the front axle tire of the Nth trailer, A is the train system matrix, B is the train control matrix, B1The method comprises the following steps of (1) controlling an input matrix for the automobile train, C an output matrix for the automobile train, and D a direct transmission matrix for the automobile train;
s11: according to a modern control theory LQR (quadratic linear control) method, a default R matrix is a diagonal matrix with diagonal elements being only 1, a matrix Q selects different values according to different operating conditions of a steering wheel, and for convenience of control, for example, under the STEP (STEP input) condition of the steering wheel, the Q matrix is taken as a matrix with diagonal elements being 0.4;
s12: the Riccati (Riccati) equation in the regression matrix is written in the ECU: a. theTP+PA+Q-PBR-1BTProgram with P being 0, system matrix A and control input matrix B1The system attribute can be represented, the ECU receives steering wheel corner signals to predict the running state of the tractor, Q, R matrix is selected, A, B, Q, R is directly written into a program, and the ECU solves the control input vector u for each trailer through sensor signal input1(t)＝-KX(t)＝-R-1BTPX(t)And feeding back the control input vector to the real vehicle for control, wherein P is a positive definite matrix, Q is a positive definite (or semi-positive definite) Hermite or real symmetric matrix, R is a positive definite Hermite or real symmetric matrix, K is a feedback gain matrix, and t is time.
Furthermore, in step S1, the interference of non-linear factors such as suspension is ignored, reasonable moderate assumption and neglect are made for modeling the mathematical model of the train, and for the convenience of analyzing the dynamic system of the multi-articulated train, the overall coordinate system and the local coordinate system are defined for the vehicle under study according to the cartesian coordinate system, and the following assumptions are made:
(1) each vehicle unit is rigid, and the left and right structures are completely symmetrical structures;
(2) the influence of longitudinal force on each full-trailer train is ignored, and the running process is constant speed running;
(3) neglecting the roll motion and the pitch motion, each vehicle unit moves in a plane;
(4) taking the turning angle of the front wheel of the tractor as input, and not counting the influence of a steering system;
(5) the tire unit adopts a linear model of a magic formula, considers that the tire cornering property is in a linear range, does not consider the difference of lateral force of a left wheel and a right wheel and the action of tire aligning moment, and ignores the influence of longitudinal force of the tire.
Further, the linear region expression of the tire "magic formula" is as follows: trailer tire cornering force: fN＝kNαN，kNFor tire cornering stiffness of section N trailer, αNIs the tire slip angle of the nth trailer.
Further, in step S2:
tractor barycenter lateral acceleration:
side deflection angle of front axle wheel of tractor:
tractor rear axle wheel side declination:
wherein a represents the longitudinal distance between the front wheel of the tractor and the mass center thereof, b represents the longitudinal distance between the rear wheel of the tractor and the mass center thereof,fthe input turning angle is the front wheel input turning angle of the tractor.
Further, in step S5, the vehicle lateral force balance formula of the train is as follows:
may+m1ay1+m2ay2+…+mNayN＝kfαf+krαr+k1α1+…+k(N-1)α(N-1)+kNfαNf+kNrαNr，
wherein m is the total mass of the tractor, m1To mNRespectively the total vehicle mass of each trailer, ay1To ayNRespectively the mass center lateral acceleration, k, of each trailerfFor the lateral stiffness, k, of the front wheels of the tractorrFor the rear wheel side yaw stiffness, k, of the tractor1To k is(N-1)Respectively the cornering stiffness, k, of each trailerNfThe front wheel cornering stiffness of the nth trailer and the rear wheel cornering stiffness of the nth trailer are kNr.
Compared with the prior art, the invention has the following beneficial effects:
1. the construction of the control method does not need the detection of additional variables, only needs to complete the detection of the self variables of the train, and only needs the variables to complete the solution of the control input variables;
2. the method can effectively improve the single transportation efficiency of the automobile train;
3. the method controls the stable running of the automobile train, and when the parameters of the automobile train change, the parameters are as follows: the structural parameters of the automobile and the train, the quality of the train body and the like are changed, and a good control effect can be still realized by changing the parameter matrix A.
In order to make the aforementioned and other objects, features and advantages of the invention comprehensible, preferred embodiments accompanied with figures are described in detail below.
Drawings
FIG. 1 is an overall flow diagram of an embodiment of the present invention.
Fig. 2 is a schematic structural view of a full-axle steering four-section six-axle hinged pure electric vehicle train in an embodiment of the invention.
Fig. 3 is an overall stress analysis diagram of the controlled train according to the embodiment of the present invention.
FIG. 4 is a diagram illustrating the effect of the steering wheel before control under a specific condition of step input according to an embodiment of the present invention.
FIG. 5 is a diagram illustrating the effect of the steering wheel after control under a specific condition of step input according to the embodiment of the present invention.
In the figure: 1-a tractor, 11-a tractor front axle tire, 12-a tractor rear axle tire, 2-a first trailer, 3-a second trailer, 4-a third trailer, 41-a third trailer front axle tire, and 42-a third trailer rear axle tire.
Detailed Description
To further illustrate the technical means and effects of the present invention adopted to achieve the predetermined objects, the following detailed description of the embodiments, structures, features and effects according to the present invention will be made with reference to the accompanying drawings and preferred embodiments.
As shown in fig. 1-5, a method for controlling the running stability of a pure electric multi-section articulated automobile train comprises a tractor 1 and three-section trailers (a first trailer 2, a second trailer 3, and a third trailer 4), the tractor and the trailers are articulated sequentially through articulated discs, and six shafts of the automobile train are distributed as follows: the tractor 1 and the third section trailer 4 respectively have a root axle around each, first section trailer 2 and second section trailer 3 respectively, carry out according to following step:
s1: establishing respective local coordinate systems on the tractor 1 and all the trailers, establishing a global coordinate system on the train, performing global stress analysis on the train, neglecting the interference of nonlinear factors such as suspension and the like, reasonably and moderately assuming and neglecting the mathematical model modeling of the train, performing vehicle dynamics system analysis on the multi-articulated train, defining the global coordinate system and the local coordinate system of the researched vehicle according to the specification of a Cartesian coordinate system, and making the following assumptions:
(1) each vehicle unit is rigid, and the left and right structures are completely symmetrical structures;
(2) the influence of longitudinal force on each full-trailer train is ignored, and the running process is constant speed running;
(3) neglecting the roll motion and the pitch motion, each vehicle unit moves in a plane;
(4) taking the turning angle of the front wheel of the tractor as input, and not counting the influence of a steering system;
(5) the tire unit adopts a linear model of a magic formula, considers that the tire cornering property is in a linear range, does not consider the difference of lateral force of a left wheel and a right wheel and the action of tire aligning moment, and ignores the influence of longitudinal force of the tire.
Wherein, the tire stress model adopts a tire 'magic formula' linear region expression: trailer tire cornering force: fN＝kNαN。kNFor tire cornering stiffness of section N trailer, αNIs the tire slip angle of the nth trailer.
S2: according to a local coordinate system fixedly connected on the tractor 1, carrying out stress analysis on the tractor 1 to obtain the mass center lateral acceleration of the tractor 1
Slip angle of front axle tire 11
S3: constructing an integral coordinate system by taking the tractor 1 and the first trailer 2 as a whole and carrying out stress analysis to obtain the first trailer
Mass center lateral acceleration:
tire slip angle:
tire control input steering angle1The expression of (c) is also obtained.
S4: constructing a global coordinate system by taking the tractor 1, the first trailer 2 and the second trailer 3 as a whole and carrying out stress analysis to obtain the second trailer 3
Mass center lateral acceleration:
tire slip angle:
s5: constructing an integral coordinate system by taking the tractor 1, the first trailer 2, the second trailer 3 and the third trailer 4 as a whole and carrying out stress analysis to obtain the third trailer 4
Mass center lateral acceleration:
s6: establishing a whole vehicle lateral force balance formula of the automobile train:
may+m1ay1+m2ay2+m3ay3＝kfαf+krαr+k1α1+k2α2+k3α3+k4α4。
s7: establishing a balance equation of the mass center yaw moment of the tractor:
s8: and analyzing the three trailers as a whole to obtain a yaw moment balance expression of the first hinge point:
s9: and taking the second trailer 3 and the third trailer 4 as a whole to obtain a yaw moment balance expression of a second hinge point:
s10: the yaw moment balance expression of the third articulated point of the third articulated vehicle 4 is analyzed separately:
s11: substituting the lateral acceleration of each mass center of the tractor and the trailer in the steps S2 to S5 and a constraint condition into the steps S6 to S10, simplifying the differential equation established in the steps, and selecting vx、vy、θ1To thetaNAnd the first reciprocal and the second derivative thereof are variables, the simplification ensures that the whole differential equation set only contains the form of the variables, and the constraint condition is as follows:
s12: according to the simplification arrangement of step S11, the following are selected:
state variables of the train:
output vector of the automobile train:
the tractor corner input vector is: u is [ ],
all hangersThe vehicle turning angle control input vector is U1＝[1,2,…,N]，
The differential equation after the simplification of step S11 is converted into a standard state space equation:
wherein, A is a train system matrix, B is a train control input matrix, B1 is a train control matrix, C is a train output matrix, and D is a train direct transmission matrix;
s10: installing a speed sensor and an angular velocity sensor on a tractor to acquire the real-time numerical values of the lateral speed and the yaw angular velocity of the tractor, installing an angle sensor and an angular velocity sensor on each hinged disk to respectively acquire the real-time hinged angle and the real-time hinged angular velocity of each hinged disk, installing an angle sensor on a steering wheel of the tractor, and predicting the running form of the tractor according to the angle change;
s11: according to a modern control theory LQR (quadratic linear control) method, a default R matrix is a diagonal matrix with diagonal elements being only 1, a matrix Q selects different values according to different operating conditions of a steering wheel, and for convenience of control, for example, under the STEP (STEP input) condition of the steering wheel, the Q matrix is taken as a matrix with diagonal elements being 0.4;
s12: the Riccati (Riccati) equation in the regression matrix is written in the ECU: a. theTP+PA+Q-PBR-1BTThe system matrix A and the control input matrix B are determined by the system attributes, the ECU receives steering wheel angle signals to predict the running state of the tractor, Q, R matrix is selected, A, B, Q, R is directly written into the program, and the ECU solves the control input vector u for each trailer through sensor signal input1(t)＝-KX(t)＝-R-1BTPX(t)And feeding back the control input vector to the real vehicle for control, wherein P is a positive definite matrix, Q is a positive definite (or semi-positive definite) Hermite or real symmetric matrix, R is a positive definite Hermite or real symmetric matrix, K is a feedback gain matrix, and t is time.
The meanings of the characters in FIG. 3 and the above formula are shown in the following table:
the method obtains a system matrix A and a control input matrix B by establishing a mathematical state space model of the train needing to be researched1The lateral speed and the yaw rate of the articulated vehicle and the total 9 variables of the articulation angle, the articulation angular speed and the steering wheel angle of the three articulated disks are selected as detection variables, and 8 variables except the steering wheel angle can be obtained by installing sensors on the vehicle body and the articulated disks. The sensor outputs real-time signals of 9 variables, and the real-time signals are transmitted to the ECU. The ECU predicts the future dynamic change of the tractor through the change of the steering wheel angle, determines the values of a matrix Q and R, signals 8 variables except the steering wheel angle into a matrix X, solves the Riccati (Riccati) equation in a degraded matrix according to the values of A, B1 and Q, R in the ECU and the LQR principle to obtain the control input vector of the front wheel tires of the first to the third section of the trailer, feeds back the control input vector to the steering of the tires of the trailer, and controls the stable operation of the train. The control method can control the motion form of the trailer at the rear part to follow the tractor, ensures the running integrity of the automobile train, effectively avoids the instability phenomena of folding, drifting and snake-shaped existing in the running process of the automobile train, and improves the safe operation performance of the automobile train.
According to the control method, the rear trailers of the four-section six-shaft automobile train can follow the front tractor to finish specific actions under different working conditions by controlling the steering of the tires of the trailers, if a driver inputs a corner under the working condition of single wire shifting through a steering wheel, the steering wheel of the tractor finishes the working condition of single wire shifting, the control method can realize that the rear three-section trailers can follow the tractor to finish the working condition of single wire shifting, and the running stability of the vehicle is ensured. Theoretically, the method not only can realize the running stability control of the four-section six-shaft vehicle, but also can complete longer running stability control of the automobile train.
Although the present invention has been described with reference to the preferred embodiments, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (5)
1. A running stability control method for a pure electric multi-section articulated automobile train comprises a tractor and at least N trailers, wherein N is more than or equal to 2, the tractor and the trailers are articulated sequentially through articulated discs, and the method is characterized by comprising the following steps:
s1: the method comprises the steps that a speed sensor and an angular velocity sensor are mounted on a tractor to obtain real-time numerical values of lateral speed and yaw angular velocity of the tractor, an angle sensor and an angular velocity sensor are mounted on each hinged disk to respectively obtain real-time hinged angles and hinged angular velocities of the hinged disks, and an angle sensor is mounted on a steering wheel of the tractor;
s2: establishing respective local coordinate systems on a tractor and all trailers, establishing a whole coordinate system on an automobile train, and performing whole stress analysis on the automobile train, wherein a tire stress model adopts a tire magic formula linear region expression;
s3: according to a local coordinate system fixedly connected on the tractor, the tractor is subjected to stress analysis to obtain the mass center lateral acceleration a of the tractoryFront axle tire slip angle alphafAnd rear axle tire sidewall angle alphar；
S4: the tractor and the N-1 trailers behind the tractor are taken as a whole one by one to carry out stress analysis to obtain the mass center lateral acceleration a of the N-1 trailery(N-1)Tire slip angle α(N-1)And tire control input steering angle(N-1)The expression of (1);
s5: carrying out stress analysis by taking the tractor and the N-section trailer behind the tractor as a whole to obtain the mass center lateral acceleration a of the N-section traileryNFront axle wheel sidewall deviation angle alphaNfAnd rear axle tire sidewall angle alphaNr；
S6: establishing a whole vehicle lateral force balance formula of the automobile train;
s7: establishing a balance equation of yaw moment of the mass center of the tractor;
s8: analyzing the M section to the Nth section of the trailer as a whole to obtain a yaw moment balance expression of the M hinge point; wherein M is from 1 to N;
s9: substituting the lateral acceleration of each mass center of the tractor and the trailer in the steps S3 to S5 and a constraint condition into the steps S6 to S8, simplifying the differential equation established in the steps, and selecting vx、vy、θ1To thetaNAnd the first reciprocal and the second derivative thereof are variables, the simplification ensures that the whole differential equation set only contains the form of the variables, and the constraint condition is as follows:
wherein v isxIs the longitudinal speed, v, of the tractoryAs the lateral speed of the tractor, theta1Is the angle of articulation, theta, of the tractor with the first trailer2For the articulation angle, theta, of the first trailer to the second trailerNThe articulation angle of the N-1 section trailer and the N section trailer, r is the yaw velocity of the tractor, r1Yaw rate, r, of the first trailer2Yaw rate, r, of the second trailerNYaw rate of the nth trailer;
s10: according to the simplification arrangement of step S9, the following are selected:
state variables of the train:
output vector of the automobile train:
the tractor corner input vector is: u is [ ],
all trailer corner control input vectors are U1＝[1,2,…,N]，
The differential equation after the simplification of step S9 is converted into a standard state space equation:
wherein v isy1Is the lateral speed, v, of the first traileryNThe lateral speed of the Nth section of the trailer and the corner of the front wheel of the tractor,1for the first section of the trailer tire corner,2for the second trailer tire corner,Nis the corner of the front axle tire of the Nth trailer, A is the train system matrix, B is the train control matrix, B1The method comprises the following steps of (1) controlling an input matrix for the automobile train, C an output matrix for the automobile train, and D a direct transmission matrix for the automobile train;
s11: the Riccati (Riccati) equation in the regression matrix is written in the ECU: a. theTP+PA+Q-PBR-1BTProgram with P being 0, system matrix A and control input matrix B1The system attribute can be represented, the ECU receives steering wheel corner signals to predict the running state of the tractor, Q, R matrix is selected, A, B, Q, R is directly written into a program, and the ECU solves the control input vector u for each trailer through sensor signal input1(t)＝-KX(t)＝-R-1BTPX(t)And feeding back the control input vector to the real vehicle for control, wherein P is a positive definite matrix, Q is a positive definite (or semi-positive definite) Hermite or real symmetric matrix, R is a positive definite Hermite or real symmetric matrix, K is a feedback gain matrix, and t is time.
2. The method for controlling the running stability of the pure electric multi-section articulated vehicle train according to claim 1, wherein the method comprises the following steps: the interference of the non-linear factors should be ignored in step S2.
3. The method for controlling the running stability of the pure electric multi-section articulated vehicle train according to claim 1, wherein the method comprises the following steps: the expression of the linear region of the magic formula of the tire is as follows: trailer tire cornering force: fN＝kNαN，kNFor tire cornering stiffness of section N trailer, αNIs the tire slip angle of the nth trailer.
4. The method for controlling the running stability of the pure electric multi-section articulated vehicle train according to claim 1, wherein the method comprises the following steps: in step S3:
tractor barycenter lateral acceleration:
side deflection angle of front axle wheel of tractor:
tractor rear axle wheel side declination:
wherein a represents the longitudinal distance between the front wheel of the tractor and the mass center thereof, b represents the longitudinal distance between the rear wheel of the tractor and the mass center thereof,fthe input turning angle is the front wheel input turning angle of the tractor.
5. The method for controlling the running stability of the pure electric multi-section articulated vehicle train according to claim 1, wherein the method comprises the following steps: step S6 the balance formula of the lateral force of the whole automobile of the automobile and the train is as follows:
may+m1ay1+m2ay2+…+mNayN＝kfαf+krαr+k1α1+…+k(N-1)α(N-1)+kNfαNf+kNrαNr，
wherein m is the total mass of the tractor, m1To mNRespectively the total vehicle mass of each trailer, ay1To ayNRespectively the mass center lateral acceleration, k, of each trailerfFor the lateral stiffness, k, of the front wheels of the tractorrFor the rear wheel side yaw stiffness, k, of the tractor1To k is(N-1)Respectively the cornering stiffness, k, of each trailerNfThe front wheel cornering stiffness of the nth trailer and the rear wheel cornering stiffness of the nth trailer are kNr.
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| CN113548058A (en) * | 2021-09-22 | 2021-10-26 | 天津所托瑞安汽车科技有限公司 | Semi-trailer train folding angle prediction method, equipment and storage medium |
| WO2023234271A1 (en) * | 2022-05-31 | 2023-12-07 | 先進モビリティ株式会社 | Automated driving method executed by articulated vehicle |
| JP7469424B1 (en) | 2022-10-03 | 2024-04-16 | 先進モビリティ株式会社 | Method for automatic driving of articulated vehicles |
| CN115817199B (en) * | 2022-11-30 | 2023-09-26 | 同济大学 | Traction guiding cooperative control method and system for virtual rail train |
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