CN115626217A - Tracking control method of wire-controlled steering system - Google Patents

Tracking control method of wire-controlled steering system Download PDF

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Publication number
CN115626217A
CN115626217A CN202211629582.0A CN202211629582A CN115626217A CN 115626217 A CN115626217 A CN 115626217A CN 202211629582 A CN202211629582 A CN 202211629582A CN 115626217 A CN115626217 A CN 115626217A
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steer
wire system
steering
tracking control
sliding mode
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CN115626217B (en
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何舒平
石全刚
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Anhui University
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Anhui University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B62—LAND VEHICLES FOR TRAVELLING OTHERWISE THAN ON RAILS
    • B62D—MOTOR VEHICLES; TRAILERS
    • B62D6/00—Arrangements for automatically controlling steering depending on driving conditions sensed and responded to, e.g. control circuits
    • B62D6/008—Control of feed-back to the steering input member, e.g. simulating road feel in steer-by-wire applications
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B62—LAND VEHICLES FOR TRAVELLING OTHERWISE THAN ON RAILS
    • B62D—MOTOR VEHICLES; TRAILERS
    • B62D5/00—Power-assisted or power-driven steering
    • B62D5/001—Mechanical components or aspects of steer-by-wire systems, not otherwise provided for in this maingroup
    • B62D5/005—Mechanical components or aspects of steer-by-wire systems, not otherwise provided for in this maingroup means for generating torque on steering wheel or input member, e.g. feedback
    • B62D5/006—Mechanical components or aspects of steer-by-wire systems, not otherwise provided for in this maingroup means for generating torque on steering wheel or input member, e.g. feedback power actuated

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  • Engineering & Computer Science (AREA)
  • Chemical & Material Sciences (AREA)
  • Combustion & Propulsion (AREA)
  • Transportation (AREA)
  • Mechanical Engineering (AREA)
  • Steering Control In Accordance With Driving Conditions (AREA)

Abstract

The invention relates to the technical field of automobile steering, in particular to a tracking control method of a steer-by-wire system, which comprises the steps of establishing a steer-by-wire system model, processing equivalent rotary inertia and equivalent damping coefficients of uncertain parameters to obtain lumped uncertainty, setting a target of an extended state observer to be the lumped uncertainty of the estimated steer-by-wire system, designing an extended state observer tracking control algorithm, designing a controller to enable a front wheel steering angle to track a steering wheel command given by a driver, defining a turning angle tracking error and a fractional order sliding mode surface, obtaining the fractional order sliding mode controller based on the extended state observer, and enabling the fractional order sliding mode controller to meet the gradual stable condition of the steer-by-wire system by constructing a Lyapunov function, so that the system can still have good control effect when the system parameters are disturbed or external interference exists.

Description

Tracking control method of wire-controlled steering system
Technical Field
The invention relates to the technical field of automobile steering, in particular to a tracking control method of a wire-controlled steering system.
Background
The automobile steering system is an important component of an automobile, and most of the current steering systems are electric power-assisted steering systems. The electric power steering device directly depends on the motor to provide auxiliary steering power, so that oil consumption is reduced, the power assisting effect is good, driving pressure is relieved for a driver, and driving experience is improved. However, the electric power steering system still does not get rid of the disadvantages of the conventional steering system, i.e., occupies a large space of the automobile, so that a wire-controlled steering system is designed in the prior art, and the mechanical connection between a steering wheel and wheels is eliminated. On one hand, the space of the automobile is saved, and on the other hand, the safety of the automobile is improved.
Many scientific researchers at home and abroad deeply research the tracking problem of the wire-controlled steering system. Such as PID control methods, to allow the front wheel angular displacement to track the input steering wheel signal. The control method can achieve good steering performance to a certain extent. But if the parameters of the system perturb or there is external disturbance, the control effect is reduced. Therefore, a tracking control method with good control effect when the system parameters are perturbed or there is external interference is needed.
Disclosure of Invention
In view of the above, the present invention provides a tracking control method for a steer-by-wire system, so as to solve the problem that the control effect is reduced when the system has a perturbation in parameters or external interference exists.
Based on the above object, the present invention provides a tracking control method for a steer-by-wire system, comprising:
establishing a steer-by-wire system model;
processing uncertainty parameters in the model to obtain lumped uncertainty;
designing an extended state observer tracking control algorithm, wherein the target of the extended state observer is to estimate the lumped uncertainty of the steer-by-wire system;
designing a controller to enable a steering angle of a front wheel to track a steering wheel command given by a driver, defining a corner tracking error and a fractional order sliding mode surface, and obtaining a fractional order sliding mode controller based on an extended state observer;
and constructing a Lyapunov function to enable the fractional order sliding mode controller to meet the gradual stable condition of the steer-by-wire system.
The steer-by-wire system model uses a second order dynamic equation to express the dynamic characteristics:
Figure DEST_PATH_IMAGE001
，
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE002
is the equivalent moment of inertia, and is,
Figure DEST_PATH_IMAGE003
is the equivalent damping coefficient of the damping coefficient,
Figure DEST_PATH_IMAGE004
and
Figure DEST_PATH_IMAGE005
respectively a self-aligning moment and a coulomb friction force,
Figure DEST_PATH_IMAGE006
is the steering ratio, u is the motor torque control output,
Figure DEST_PATH_IMAGE007
is the actual angular displacement of the front wheels of the steer-by-wire system,
Figure DEST_PATH_IMAGE008
is the actual angular velocity of the front wheels of the steer-by-wire system,
Figure DEST_PATH_IMAGE009
is the actual angular acceleration of the front wheels of the steer-by-wire system.
Preferably, processing uncertainty parameters in the model, and obtaining the lumped uncertainty comprises:
will have uncertainty parameters
Figure 87874DEST_PATH_IMAGE002
And
Figure 515444DEST_PATH_IMAGE003
the decomposition is as follows:
Figure DEST_PATH_IMAGE010
wherein, the first and the second end of the pipe are connected with each other,
Figure DEST_PATH_IMAGE011
is a nominal part of the equivalent moment of inertia,
Figure DEST_PATH_IMAGE012
is a perturbation part of the equivalent moment of inertia,
Figure DEST_PATH_IMAGE013
is a nominal part of the equivalent damping coefficient,
Figure DEST_PATH_IMAGE014
is the perturbation part of the equivalent damping coefficient;
the state equation of the steer-by-wire system model is as follows:
Figure DEST_PATH_IMAGE015
，
wherein, the first and the second end of the pipe are connected with each other,
Figure DEST_PATH_IMAGE016
respectively, are the state variables of the system,
Figure DEST_PATH_IMAGE017
is the derivative of two state variables of the system,
Figure DEST_PATH_IMAGE018
is the lumped uncertainty.
Preferably, the extended state observer tracking control algorithm is designed to:
Figure DEST_PATH_IMAGE019
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE020
in order to define the auxiliary variable(s),
Figure DEST_PATH_IMAGE021
and
Figure DEST_PATH_IMAGE022
are respectively
Figure DEST_PATH_IMAGE023
And
Figure DEST_PATH_IMAGE024
is determined by the estimated value of (c),
Figure DEST_PATH_IMAGE025
and
Figure DEST_PATH_IMAGE026
are respectively
Figure DEST_PATH_IMAGE027
And
Figure 200110DEST_PATH_IMAGE022
the derivative of (a) is determined,
Figure DEST_PATH_IMAGE028
，
Figure DEST_PATH_IMAGE029
and
Figure DEST_PATH_IMAGE030
is the feedback gain that needs to be designed;
the condition for the estimation error assuming lumped perturbation is
Figure DEST_PATH_IMAGE031
Wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE032
is the upper bound of the estimation error of the lumped perturbation.
Preferably, the steering tracking error is defined as
Figure DEST_PATH_IMAGE033
，
Wherein
Figure DEST_PATH_IMAGE034
Steering wheel commands given to the driver;
the fractional order sliding mode surface is designed as
Figure DEST_PATH_IMAGE035
Wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE036
is composed of
Figure DEST_PATH_IMAGE037
And
Figure DEST_PATH_IMAGE038
respectively, are the coefficients of the associated positive constants,
Figure DEST_PATH_IMAGE039
is the number of the derivation steps,
Figure DEST_PATH_IMAGE040
is to ask for
Figure DEST_PATH_IMAGE041
An operator of the order derivative;
the fractional order sliding mode controller based on the extended state observer is
Figure DEST_PATH_IMAGE042
Wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE043
and
Figure DEST_PATH_IMAGE044
is a positive integer, sign () is a sign function,
Figure DEST_PATH_IMAGE045
is that
Figure DEST_PATH_IMAGE046
The upper bound of (c).
Preferably, the Lyapunov function
Figure DEST_PATH_IMAGE047
The formula of (1) is as follows:
Figure DEST_PATH_IMAGE048
the invention has the beneficial effects that: the tracking control method comprises the steps of establishing a steer-by-wire system model, processing equivalent rotary inertia and equivalent damping coefficients of uncertainty parameters to obtain lumped uncertainty, setting a target of an extended state observer as the lumped uncertainty of an estimated steer-by-wire system, designing an extended state observer tracking control algorithm, designing a controller to enable a steering angle of a front wheel to track a steering wheel command given by a driver, defining a corner tracking error and a fractional order sliding mode surface, obtaining the fractional order sliding mode controller based on the extended state observer, and enabling the fractional order sliding mode controller to meet the gradual stable condition of the steer-by-wire system by constructing a Lyapunov function, so that the control method can still have a good control effect when system parameters are perturbed or external interference exists.
Drawings
In order to more clearly illustrate the present invention or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are only the present invention, and those skilled in the art can also obtain other drawings according to the drawings without creative efforts.
FIG. 1 is a schematic structural diagram of a steer-by-wire system in accordance with an embodiment of the present invention;
fig. 2 is a control algorithm schematic diagram of a tracking control method of a steer-by-wire system according to an embodiment of the present invention.
Labeled as:
1. a steering wheel; 2. a steering wheel angle sensor; 3. a road sensing feedback motor; 4. a steering motor; 5. a gear angle sensor; 6. a front wheel; 7. a gear transmission; 8. a tie rod; 9. a main controller; 10. a steering column; 12. a ball head; 13. a knuckle arm; 14. and a steering transmission shaft.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to specific embodiments below.
It is to be noted that technical terms or scientific terms used herein should have the ordinary meaning as understood by those having ordinary skill in the art to which the present invention belongs, unless otherwise defined. The use of "first," "second," and similar terms in the present application do not denote any order, quantity, or importance, but rather the terms are used to distinguish one element from another. The word "comprising" or "comprises", and the like, means that the element or item preceding the word comprises the element or item listed after the word and its equivalent, but does not exclude other elements or items. The terms "connected" or "coupled" and the like are not restricted to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "upper", "lower", "left", "right", and the like are used only to indicate relative positional relationships, and when the absolute position of the object being described is changed, the relative positional relationships may also be changed accordingly.
The embodiment of the specification provides a tracking control method of a steer-by-wire system, which is applied to the steer-by-wire system, for example, the steer-by-wire system comprises an upper layer steering wheel assembly, a lower layer steering execution assembly part and an ECU control panel, as shown in fig. 1, the upper layer steering wheel assembly mainly comprises a steering wheel 1, a steering wheel angle sensor 2, a road feel feedback motor 3 and a steering column 10; the lower steering execution assembly part mainly comprises a steering transmission shaft 14, a steering motor 4, a gear angle sensor 5, a gear transmission device 7, a tie rod 8, a steering knuckle arm 13 and a front wheel 6.
The steering wheel assembly is provided with a steering column 10, the steering wheel 1 is fixed at the upper end of the steering column 10, the steering wheel angle sensor 2 is sleeved on the steering column 10, and the road feel feedback motor 3 is connected to the bottom end of the steering column 10; the steering motor 4 is installed at the top of a steering transmission shaft 14, the gear angle sensor 5 is sleeved in the middle of the steering transmission shaft 14, one end of the gear transmission device 7 is connected with the steering transmission shaft 14, the other end of the gear transmission device is connected with a tie rod 8, two ends of the tie rod 8 are respectively connected with a steering knuckle arm 13 through a ball head 12, and the other end of the steering knuckle arm 13 is connected on a front wheel 6.
Steering wheel angle sensor 2 measures the driver and rotates the angle of steering wheel 1 and gives the signal transmission the inside of main control unit 9, and main control unit 9 sends road surface road conditions information through the form of signal of telecommunication to way sense feedback motor 3, way sense feedback motor 3 drives steering column 10 and rotates then steering wheel 1 also can rotate, and the driver consequently feels the road conditions on road surface.
The steering motor 4 receives a steering signal sent by the autonomous controller 9 to make corresponding action, the steering motor 4 drives the steering transmission shaft 14 to rotate, the steering transmission shaft 14 drives the gear transmission device 7 to operate, the gear transmission device 7 drives the tie rod 8 to move left and right, the tie rod 8 drives the knuckle arm 13 to operate through the ball head 12, and the knuckle arm 13 drives the front wheel 6 to steer. The gear angle sensor 5 measures the steering angle of the gear and transmits the steering angle to the main controller 9, so that a closed loop is formed.
In the steer-by-wire system, a driver input interface (a steering wheel) and an actuating mechanism (a steering wheel) are connected through a steer-by-wire (electronic signal), and then an electric signal command is sent to a steering motor, so that the steering system is controlled. The structure of design like this not only provides more sufficient space for arranging of other spare parts in the cabin, and the steering column has improved the security to driver's injury when avoiding the vehicle collision moreover. And replace traditional mechanical connection with the mode of electric connection, the front wheel steering action reaction is faster, and is more direct, more slim and graceful than mechanical transmission.
And the steer-by-wire system, because there is not hard connection between steering wheel and steering actuating assembly, so the ground vibrations are only transmitted to the steering wheel rarely, the comfortableness is strong, meanwhile the maneuverability of the driver is strengthened, the steering ratio of the system can be adjusted at will, because there is not hard connection between the wheel rotation angle and the steering wheel, so the wheel rotation angle and the steering wheel rotation angle can be controlled by the system completely.
The tracking control method provided by the embodiment of the specification comprises the following steps:
step 1: model definition and algorithm parameter definition;
the general steer-by-wire system uses a second order dynamic equation to express its dynamic characteristics as follows:
Figure 730798DEST_PATH_IMAGE001
in the formula (I), the compound is shown in the specification,
Figure 612167DEST_PATH_IMAGE002
is the equivalent moment of inertia and is,
Figure 109007DEST_PATH_IMAGE003
is the equivalent damping coefficient of the damping coefficient,
Figure 244585DEST_PATH_IMAGE004
and
Figure 903099DEST_PATH_IMAGE005
respectively, self-righting moment and coulomb friction.
Figure 271763DEST_PATH_IMAGE006
Is the turn ratio. u is the motor torque control output;
Figure 555983DEST_PATH_IMAGE007
is the actual angular displacement of the front wheels of the steer-by-wire system,
Figure 326493DEST_PATH_IMAGE008
is the actual angular velocity of the front wheels of the steer-by-wire system,
Figure 155909DEST_PATH_IMAGE009
is the actual angular acceleration of the front wheels of the steer-by-wire system.
With uncertainty parameter
Figure 11869DEST_PATH_IMAGE002
And
Figure 332736DEST_PATH_IMAGE003
the decomposition is as follows:
Figure 692173DEST_PATH_IMAGE010
wherein, the first and the second end of the pipe are connected with each other,
Figure 692490DEST_PATH_IMAGE011
is a nominal part of the equivalent moment of inertia,
Figure 19435DEST_PATH_IMAGE012
is the perturbation part of the equivalent moment of inertia.
Figure 661769DEST_PATH_IMAGE013
Is a nominal part of the equivalent damping coefficient,
Figure 141292DEST_PATH_IMAGE014
is the perturbation part of the equivalent damping coefficient.
The model state equation is as follows:
Figure 578089DEST_PATH_IMAGE015
。
wherein the content of the first and second substances,
Figure 893795DEST_PATH_IMAGE016
respectively, are state variables of the system.
Figure 808662DEST_PATH_IMAGE017
Is the derivative of two state variables of the system.
Figure 142691DEST_PATH_IMAGE018
Is the lumped uncertainty.
And 2, step: and designing a tracking control algorithm of the extended state observer.
Step 2.1 the objective of the extended state observer is: the lumped uncertainty of the steer-by-wire system is estimated. Defining auxiliary variables
Figure 750390DEST_PATH_IMAGE020
The extended state observer is designed as follows:
Figure DEST_PATH_IMAGE049
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE050
and
Figure DEST_PATH_IMAGE051
are respectively
Figure DEST_PATH_IMAGE052
And
Figure 409517DEST_PATH_IMAGE053
an estimate of (d).
Figure DEST_PATH_IMAGE054
And
Figure 596916DEST_PATH_IMAGE055
are respectively
Figure 34719DEST_PATH_IMAGE050
And
Figure 813319DEST_PATH_IMAGE022
the derivative of (c).
Figure DEST_PATH_IMAGE056
，
Figure 821727DEST_PATH_IMAGE057
And
Figure DEST_PATH_IMAGE058
is the feedback gain that needs to be designed.
The estimation error of the lumped perturbation is assumed to have the following condition:
Figure 563549DEST_PATH_IMAGE031
，
wherein, the first and the second end of the pipe are connected with each other,
Figure 606591DEST_PATH_IMAGE032
is the upper bound of the estimation error of the lumped disturbance, which is a very small value.
Step 2.2 design controller to make front wheel steering angle follow steering wheel command given by driver
Figure 805360DEST_PATH_IMAGE034
The corner tracking error is defined as follows:
Figure 566643DEST_PATH_IMAGE033
。
the fractional order slip form design is as follows:
Figure 892582DEST_PATH_IMAGE059
wherein, the first and the second end of the pipe are connected with each other,
Figure 55710DEST_PATH_IMAGE037
and
Figure 923916DEST_PATH_IMAGE038
respectively, are the coefficients of the associated positive constants,
Figure 438073DEST_PATH_IMAGE039
is the derivative order (which may be a decimal number).
Figure DEST_PATH_IMAGE060
Is to ask for
Figure 770966DEST_PATH_IMAGE041
Operator of the second derivative.
The design of the fractional order sliding mode controller based on the extended state observer is as follows:
Figure 37868DEST_PATH_IMAGE042
in the formula (I), the compound is shown in the specification,
Figure 594751DEST_PATH_IMAGE043
and
Figure 65047DEST_PATH_IMAGE061
is a positive integer, sign () is a sign function,
Figure 732789DEST_PATH_IMAGE045
is that
Figure 355662DEST_PATH_IMAGE046
The upper bound of (c) can be expressed by a mathematical expression as:
Figure DEST_PATH_IMAGE062
。
constructing a Lyapunov function
Figure 286709DEST_PATH_IMAGE047
And the gradual stable condition is met, as shown in the formula:
Figure 759147DEST_PATH_IMAGE063
the above formula shows that the compound has the advantages of,
Figure DEST_PATH_IMAGE064
is negative. Therefore, the controller is designed to ensure system stability.
Those of ordinary skill in the art will understand that: the discussion of any embodiment above is meant to be exemplary only, and is not intended to intimate that the scope of the disclosure, including the claims, is limited to those examples; within the idea of the invention, also features in the above embodiments or in different embodiments may be combined, steps may be implemented in any order, and there are many other variations of the different aspects of the invention as described above, which are not provided in detail for the sake of brevity.
The present invention is intended to embrace all such alternatives, modifications and variances which fall within the broad scope of the appended claims. Therefore, any omissions, modifications, substitutions, improvements and the like that may be made without departing from the spirit and principles of the invention are intended to be included within the scope of the invention.

Claims (5)

1. A tracking control method for a steer-by-wire system, comprising:
establishing a steer-by-wire system model;
processing uncertainty parameters in the model to obtain lumped uncertainty;
designing an extended state observer tracking control algorithm, wherein the target of the extended state observer is to estimate the lumped uncertainty of the steer-by-wire system;
designing a controller to enable a steering angle of a front wheel to track a steering wheel command given by a driver, defining a corner tracking error and a fractional order sliding mode surface, and obtaining a fractional order sliding mode controller based on an extended state observer;
constructing a Lyapunov function to enable the fractional order sliding mode controller to meet the gradual stable condition of the steer-by-wire system;
the steer-by-wire system model uses a second order dynamic equation to express the dynamic characteristics:
Figure 190258DEST_PATH_IMAGE002
，
in the formula (I), the compound is shown in the specification,
Figure 576240DEST_PATH_IMAGE004
is the equivalent moment of inertia, and is,
Figure 90398DEST_PATH_IMAGE006
is the equivalent damping coefficient of the damping device,
Figure 688870DEST_PATH_IMAGE008
and
Figure 719886DEST_PATH_IMAGE010
respectively a self-aligning moment and a coulomb friction force,
Figure 11190DEST_PATH_IMAGE012
is the steering ratio, u is the motor torque control output,
Figure 747065DEST_PATH_IMAGE014
is the actual angular displacement of the front wheels of the steer-by-wire system,
Figure 414807DEST_PATH_IMAGE016
is the actual angular velocity of the front wheels of the steer-by-wire system,
Figure 801795DEST_PATH_IMAGE018
is the actual angular acceleration of the front wheels of the steer-by-wire system.
2. The tracking control method of a steer-by-wire system according to claim 1, wherein said processing uncertainty parameters in the model to obtain a lumped uncertainty comprises:
will have uncertainty parameters
Figure 264000DEST_PATH_IMAGE004
And
Figure 221592DEST_PATH_IMAGE006
the decomposition is as follows:
Figure 178178DEST_PATH_IMAGE020
wherein the content of the first and second substances,
Figure 170404DEST_PATH_IMAGE022
is a nominal part of the equivalent moment of inertia,
Figure 69090DEST_PATH_IMAGE024
is a perturbation part of the equivalent moment of inertia,
Figure 513978DEST_PATH_IMAGE026
is a nominal part of the equivalent damping coefficient,
Figure 507211DEST_PATH_IMAGE028
is the perturbation part of the equivalent damping coefficient;
the state equation of the steer-by-wire system model is:
Figure 619523DEST_PATH_IMAGE030
，
wherein the content of the first and second substances,
Figure 423531DEST_PATH_IMAGE032
respectively, are the state variables of the system,
Figure 621294DEST_PATH_IMAGE034
is the derivative of two state variables of the system,
Figure 651174DEST_PATH_IMAGE036
is the lumped uncertainty.
3. The tracking control method of a steer-by-wire system according to claim 2,
the tracking control algorithm of the extended state observer is designed as follows:
Figure 617993DEST_PATH_IMAGE038
wherein, the first and the second end of the pipe are connected with each other,
Figure 858481DEST_PATH_IMAGE040
in order to define the auxiliary variable(s),
Figure 261650DEST_PATH_IMAGE042
and
Figure 878576DEST_PATH_IMAGE044
are respectively
Figure 434322DEST_PATH_IMAGE046
And
Figure 845712DEST_PATH_IMAGE048
is determined by the estimated value of (c),
Figure 503220DEST_PATH_IMAGE050
and
Figure 392679DEST_PATH_IMAGE052
are respectively
Figure DEST_PATH_IMAGE053
And
Figure 786620DEST_PATH_IMAGE044
the derivative of (a) of (b),
Figure DEST_PATH_IMAGE055
，
Figure DEST_PATH_IMAGE057
and
Figure DEST_PATH_IMAGE059
is the feedback gain that needs to be designed;
assuming lumped perturbation estimation error conditions are
Figure DEST_PATH_IMAGE061
Wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE063
is an upper bound on the estimation error of the lumped perturbation.
4. The tracking control method of a steer-by-wire system according to claim 3, wherein a steering tracking error is defined as
Figure DEST_PATH_IMAGE065
，
Wherein
Figure DEST_PATH_IMAGE067
Steering wheel commands given to the driver;
the fractional order sliding mode surface is designed as
Figure DEST_PATH_IMAGE069
Wherein, the first and the second end of the pipe are connected with each other,
Figure DEST_PATH_IMAGE071
is composed of
Figure DEST_PATH_IMAGE073
And
Figure DEST_PATH_IMAGE075
respectively, are the coefficients of the associated positive constants,
Figure DEST_PATH_IMAGE077
is the number of the derivation steps,
Figure DEST_PATH_IMAGE079
is to ask for
Figure DEST_PATH_IMAGE081
An operator of the order derivative;
the fractional order sliding mode controller based on the extended state observer is
Figure DEST_PATH_IMAGE083
Wherein, the first and the second end of the pipe are connected with each other,
Figure DEST_PATH_IMAGE085
and
Figure DEST_PATH_IMAGE087
is a positive integer, sign () is a sign function,
Figure DEST_PATH_IMAGE089
is that
Figure DEST_PATH_IMAGE091
The upper bound of (c).
5. The tracking control method of a steer-by-wire system according to claim 4, characterized in that the Lyapunov function
Figure DEST_PATH_IMAGE093
The formula of (1) is as follows:
Figure 428298DEST_PATH_IMAGE094
。
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CN113183950A (en) * 2021-05-11 2021-07-30 江苏大学 Self-adaptive control method for steering of active front wheel of electric automobile

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CN103576710A (en) * 2012-08-07 2014-02-12 株式会社电装 Control system and vehicle steering control system
CN104015728A (en) * 2013-02-28 2014-09-03 福特全球技术公司 Vehicle
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