CN113050653A - Steer-by-wire system modeling control method for processing state inequality constraint - Google Patents

Steer-by-wire system modeling control method for processing state inequality constraint Download PDF

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CN113050653A
CN113050653A CN202110324005.XA CN202110324005A CN113050653A CN 113050653 A CN113050653 A CN 113050653A CN 202110324005 A CN202110324005 A CN 202110324005A CN 113050653 A CN113050653 A CN 113050653A
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steer
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state
wire system
steering
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CN113050653B (en
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孙浩
杨路文
朱梓诚
屠鲁川
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Hefei University of Technology
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0221—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving a learning process
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0276—Control of position or course in two dimensions specially adapted to land vehicles using signals provided by a source external to the vehicle

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Abstract

The invention discloses a modeling control method of a steer-by-wire system capable of processing state inequality constraint, belonging to the technical field of control methods of steer-by-wire systems, and comprising the following operation steps: constructing a dynamic model of the steer-by-wire system; constructing a one-to-one mapping conversion function based on the limitation of state inequality constraint borne by the system in the actual working process; converting a state variable constrained by a state inequality in a system into a new 'free' state variable by using a conversion function to obtain a kinetic equation after variable conversion; aiming at the converted kinetic equation and performance constraint, establishing a controller based on the Udwadia-Kalaba theory to control the operation of the system; the control method of the steer-by-wire system considering the state inequality constraint can lead the system to quickly, stably and accurately track the given tracking performance requirement under the condition of simultaneously meeting the requirements of the performance constraint and the state inequality constraint, and opens up a new way for the modeling control of a mechanical system containing the state inequality constraint.

Description

Steer-by-wire system modeling control method for processing state inequality constraint
Technical Field
The invention relates to the technical field of control methods of steer-by-wire systems, in particular to a modeling control method of a steer-by-wire system capable of processing state inequality constraints.
Background
With the continuous progress of science and technology, an assistant driving system and an unmanned automobile become a new hot research field, and the intelligent steering of the automobile becomes a necessary trend. The performance of the automobile steering system directly influences the operation stability of the automobile, and plays an important role in ensuring the safe driving of the automobile, reducing traffic accidents and protecting the personal safety of drivers. Although the traditional mechanical steering system improves the transfer characteristic of the steering force of the automobile to a certain extent, the fixed transmission ratio of the mechanical connection between the steering wheel and the steering wheel causes the defect that the steering characteristic of the automobile changes along with the speed of the automobile. The steer-by-wire system directly drives the steering wheel through the steering motor, replaces the traditional mechanical or hydraulic connection, realizes the active steering, thereby improving the operation stability and the active safety of the vehicle. In the actual operation process of the steer-by-wire system, the system state quantity is often limited in a certain constraint range, and the steer-by-wire system is a typical mechanical system with state inequality constraint.
Researchers at home and abroad do a lot of research work aiming at the problem of active steering control of a steer-by-wire system, and the steering angle of the vehicle is accurately controlled by feeding back state information in the running process of the vehicle and applying classical control theories such as PID control, LQR control, sliding mode control, robust control and the like. These control strategies all achieve certain effects, but it is difficult to ensure that the system state quantity does not exceed a given boundary in the whole control process. The state inequality constraint generated by the structure or the working environment of the steer-by-wire system must be strictly ensured, and once the constraint is exceeded, the problems of deviation of steering control, reduction of the stability of the automobile and the like can be caused.
Therefore, it is desirable to provide a control method capable of simultaneously handling the state inequality constraint and the tracking trajectory problem.
Disclosure of Invention
The invention provides a steer-by-wire system modeling control method capable of processing state inequality constraints for solving the problems, and solves the technical problem that the steer-by-wire system control method in the prior art is difficult to simultaneously process the state inequality constraints and track.
In order to achieve the purpose, the invention adopts the following technical scheme:
a modeling control method of a steer-by-wire system capable of processing state inequality constraint comprises the following operation steps:
s1, establishing a steer-by-wire system dynamic model;
s2, constructing a one-to-one mapping conversion function based on the limitation of state inequality constraint borne by the system in the actual working process;
s3, converting the state variables in the system constrained by the state inequality into new 'free' state variables by using a conversion function to obtain a kinetic equation after variable conversion;
and S4, establishing a controller based on Udwadia-Kalaba theory to control the operation of the system according to the converted kinetic equation and the performance constraint.
Further, the building of the steer-by-wire system dynamics model in the step (1) is as follows:
Figure BDA0002993877380000021
wherein, JeqRepresenting the equivalent moment of inertia of the system, BeqThe equivalent viscous friction coefficient of the system is shown,
Figure BDA0002993877380000022
indicating the Coulomb friction of the steering system, FsDenotes the Coulomb friction coefficient, τeRepresenting the steering aligning moment of the front wheels, r representing a conversion parameter, N1And N2Indicating the number of teeth, r, of the rack and gear box, respectivelygIndicating the connection ratio, tau, of the steering motordisThe total ripple interference is represented by the sum of,
Figure BDA0002993877380000031
indicating the control input of the rotational torque, delta, driving the steering motorfWhich indicates the steering angle of the front wheels,
Figure BDA0002993877380000032
represents deltafThe first derivative of (a) is,
Figure BDA0002993877380000033
represents deltafThe second derivative of (a);
equivalent moment of inertia J of systemeqBy the moment of inertia J of the steering motorfwAnd moment of inertia J of steered front wheelssmEquivalence is obtained, and the specific equivalence relation is as follows:
Figure BDA0002993877380000034
coefficient of friction B of equivalent viscosity of systemeqCoefficient of viscous friction B by steering motorfwAnd coefficient of viscous friction B of steered front wheelssmEquivalence is obtained, and the specific equivalence relation is as follows:
Figure BDA0002993877380000035
the total impulse disturbance of the system is mainly composed of the sixth torque harmonic tausm6And the twelfth torque harmonic τsm12The formula is as follows:
Figure BDA0002993877380000036
front wheel steering return torque taueIs a function expression of the geometric parameters of the automobile steering when the automobile tire side inclination angle alphafLess than 5 °, the expression can be simplified as follows:
τe＝-(lc+lp)Cfαf (5)
wherein lcIndicating the mechanical drag of the front wheel,/pIndicates the track of the front wheel, CfIndicating front wheel tire sidewall deflection stiffness.
Further, in S2, the actual operation process of the steer-by-wire system is based on the front wheel steering angle δfThe state inequality constraint is applied to limit, a one-to-one mapping conversion function is constructed, and the steering angle of the front wheel is subjected to bilateral inequality constraint such asShown below:
δfmin＜δf＜δfmax (6)
based on the functional properties of the tangent function, a conversion function I of the following general form is established:
y＝tan(k0δf+k1)+k2 (7)
three parameters k in the transfer function I0、k1And k2The actual state of the front wheel steering angle is bound by two boundaries delta of an inequality constraint formula (6)fminAnd deltafmaxDetermining
Figure BDA0002993877380000041
Figure BDA0002993877380000042
tan(k0*0+k1)+k2＝0 (10)
In conjunction with equations (8), (9) and (10), the values of the three parameters are solved:
Figure BDA0002993877380000043
Figure BDA0002993877380000044
k2＝-tan k1 (13)
combining equations (7), (11), (12) and (13), the final sorted transfer function II is:
Figure BDA0002993877380000045
further, in S3, converting the state variables in the system constrained by the state inequality into new "free" state variables based on the conversion function, and obtaining the kinetic equation after the variable conversion includes:
the new variable y is used to describe the bilaterally constrained front wheel steering angle delta according to the transfer function II (14)fAs follows:
Figure BDA0002993877380000046
after differentiating the time t, we get:
Figure BDA0002993877380000047
after time derivation in equation (16), we obtain:
Figure BDA0002993877380000051
combining the formulas (15), (16) and (17) and the steer-by-wire system prime dynamic model (1), obtaining a converted dynamic equation:
Figure BDA0002993877380000052
further, establishing a controller based on the Udwadia-Kalaba theory to control the operation of the system based on the transformed kinetic equation and the performance constraint in S4 includes:
the converted steer-by-wire system kinetic equation is written into the form of Uwadia-Kalaba kinetic equation:
Figure BDA0002993877380000053
wherein:
Figure BDA0002993877380000054
Figure BDA0002993877380000055
Figure BDA0002993877380000056
q＝y
the expression equation of the constraint moment of the system is obtained as follows:
Figure BDA0002993877380000057
wherein: tau represents a performance constraint moment, and when the steer-by-wire system needs to run along a preset track under the constraint of a state inequality, tau represents a rotation moment which is required to be generated by a steering motor; b represents an array in a second order constraint; q represents an intermediate vector with respect to y;
Figure BDA0002993877380000058
respectively representing the first derivative and the second derivative of q; t represents the operating time of the steer-by-wire system;
the rotating torque required by the steering motor is obtained through the operation, the expected steering angle is compared with the actual steering angle, closed loop feedback is formed, and the drive-by-wire steering system can accurately track the given tracking performance requirement.
Compared with the prior art, the invention provides a steer-by-wire system modeling control method capable of processing state inequality constraints, which has the following beneficial effects:
1. in the modeling control method of the steer-by-wire system capable of processing the state inequality constraint, the steering system from a steering actuator to a steering front wheel is modeled into a steering motor to drive a load steering wheel through a gear-rack gearbox, and a more accurate dynamic model of the steer-by-wire system is constructed.
2. In the problem of state inequality constraint, a method for constructing a conversion function for converting a double-edge bounded state quantity into an unbounded state quantity is provided. By this state transformation a transformed system is obtained which is free from the state inequality constraints.
3. And designing a constraint moment expression equation of the steer-by-wire system based on solving the Uwadia-Kalaba kinetic equation of the converted system and the performance constraint of the system. The simulation result carried out by Matlab shows that the motion of the steer-by-wire system meets the requirement and the tracking track is accurate and perfect.
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FIG. 1 is a flow chart of a control method according to an embodiment of the present invention;
FIG. 2 is a schematic structural diagram of a steer-by-wire system according to an embodiment of the present invention;
FIG. 3 is a flow chart of the overall structure of the controller according to the embodiment of the present invention;
FIG. 4 is a diagram illustrating a state inequality constraint variable transformation mapping relationship according to an embodiment of the present invention;
FIG. 5 is a schematic diagram of a system stability sinusoid tracking simulation according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments.
In the description of the present invention, it is to be understood that the terms "upper", "lower", "front", "rear", "left", "right", "top", "bottom", "inner", "outer", and the like, indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, are merely for convenience in describing the present invention and simplifying the description, and do not indicate or imply that the device or element being referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus, should not be construed as limiting the present invention.
Example 1:
as shown in fig. 1, the present embodiment provides a steer-by-wire system modeling control method capable of processing state inequality constraints, the operation steps are as follows:
s1, establishing a steer-by-wire system dynamic model;
s2, constructing a one-to-one mapping conversion function based on the limitation of state inequality constraint borne by the system in the actual working process;
s3, converting the state variables in the system constrained by the state inequality into new 'free' state variables by using a conversion function to obtain a kinetic equation after variable conversion;
and S4, establishing a controller based on Udwadia-Kalaba theory to control the operation of the system according to the converted kinetic equation and the performance constraint.
Further, the building of the steer-by-wire system dynamics model in S1 is:
Figure BDA0002993877380000071
wherein, JeqRepresenting the equivalent moment of inertia of the system, BeqThe equivalent viscous friction coefficient of the system is shown,
Figure BDA0002993877380000081
indicating the Coulomb friction of the steering system, FsDenotes the Coulomb friction coefficient, τeRepresenting the steering aligning moment of the front wheels, r representing a conversion parameter, N1And N2Indicating the number of teeth, r, of the rack and gear box, respectivelygIndicating the connection ratio, tau, of the steering motordisThe total ripple interference is represented by the sum of,
Figure BDA0002993877380000082
indicating the control input of the rotational torque, delta, driving the steering motorfWhich indicates the steering angle of the front wheels,
Figure BDA0002993877380000083
represents deltafThe first derivative of (a) is,
Figure BDA0002993877380000084
represents deltafThe second derivative of (a);
equivalent moment of inertia J of systemeqBy the moment of inertia J of the steering motorfwAnd moment of inertia J of steered front wheelssmEquivalence is obtained, and the specific equivalence relation is as follows:
Figure BDA0002993877380000085
coefficient of friction B of equivalent viscosity of systemeqCoefficient of viscous friction B by steering motorfwAnd coefficient of viscous friction B of steered front wheelssmEquivalence is obtained, and the specific equivalence relation is as follows:
Figure BDA0002993877380000086
the total impulse disturbance of the system is mainly composed of the sixth torque harmonic tausm6And the twelfth torque harmonic τsm12The formula is as follows:
Figure BDA0002993877380000087
front wheel steering return torque taueIs a function expression of the geometric parameters of the automobile steering when the automobile tire side inclination angle alphafLess than 5 °, the expression can be simplified as follows:
τe＝-(lc+lp)Cfαf (5)
wherein lcIndicating the mechanical drag of the front wheel,/pIndicates the track of the front wheel, CfIndicating front wheel tire sidewall deflection stiffness.
Further, in the step (2), the steering angle δ is based on the front wheel steering angle in the actual working process of the steer-by-wire systemfThe state inequality constraint is applied to limit, a one-to-one mapping conversion function is constructed, and the bilateral inequality constraint applied to the steering angle of the front wheel is as follows:
δfmin＜δf＜δfmax (6)
based on the functional properties of the tangent function, a conversion function I of the following general form is established:
y＝tan(k0δf+k1)+k2 (7)
three parameters k in the transfer function I0、k1And k2The actual state of the front wheel steering angle is bound by two boundaries delta of an inequality constraint formula (6)fminAnd deltafmaxDetermining
Figure BDA0002993877380000091
Figure BDA0002993877380000092
tan(k0*0+k1)+k2＝0 (10)
In conjunction with equations (8), (9) and (10), the values of the three parameters are solved:
Figure BDA0002993877380000093
Figure BDA0002993877380000094
k2＝-tan k1 (13)
combining equations (7), (11), (12) and (13), the final sorted transfer function II is:
Figure BDA0002993877380000095
further, in the step (3), the state variables in the system constrained by the state inequality are converted into new "free" state variables based on the conversion function, and the obtained kinetic equation after variable conversion includes:
describing the bilaterally constrained predecessors with a new variable y according to the transfer function II (14)Wheel steering angle deltafAs follows:
Figure BDA0002993877380000096
after differentiating the time t, we get:
Figure BDA0002993877380000101
after time derivation in equation (16), we obtain:
Figure BDA0002993877380000102
combining the formulas (15), (16) and (17) and the steer-by-wire system prime dynamic model (1), obtaining a converted dynamic equation:
Figure BDA0002993877380000103
further, in the step (4), establishing a controller based on the Udwadia-Kalaba theory to control the operation of the system based on the converted kinetic equation and the performance constraint includes:
the converted steer-by-wire system kinetic equation is written into the form of Uwadia-Kalaba kinetic equation:
Figure BDA0002993877380000104
wherein:
Figure BDA0002993877380000105
Figure BDA0002993877380000106
Figure BDA0002993877380000107
q＝y
the expression equation of the constraint moment of the system is obtained as follows:
Figure BDA0002993877380000111
wherein: tau represents a performance constraint moment, and when the steer-by-wire system needs to run along a preset track under the constraint of a state inequality, tau represents a rotation moment which is required to be generated by a steering motor; b represents an array in a second order constraint; q represents an intermediate vector with respect to y;
Figure BDA0002993877380000112
respectively representing the first derivative and the second derivative of q; t denotes the operating time of the steer-by-wire system.
The rotating torque required by the steering motor is obtained through the operation, the expected steering angle is compared with the actual steering angle, closed loop feedback is formed, and the drive-by-wire steering system can accurately track the given tracking performance requirement.
And then judging and adjusting related parameters of the controller of the steer-by-wire system according to a comparison result of the expected value and the actual value of the steering angle of the front wheels of the steer-by-wire system. When a front wheel steering angle is given by the steer-by-wire system, an actual value of the front wheel steering angle of the steer-by-wire system is measured and recorded by an angle sensor, due to the existence of assembly errors, the rotational inertia value of the front wheel to be steered has certain deviation, and the steering angle may have deviation, so that the rotational inertia value of the front wheel to be steered is adjusted through a comparison result, the actual value of the front wheel steering angle is close to an expected value, an optimal value meeting the precision requirement is found through multiple experiments, and the performance of the controller can be better verified.
Example 2: based on example 1, but with the following differences:
the steer-by-wire system shown in fig. 2 is the object of the modeling and control of the present invention. As shown in fig. 2, the system can be divided into two parts: the upper half part comprises a steering wheel, a steering wheel angle sensor and a feedback motor; the lower half part comprises a steering motor, a pinion angle sensor, a gear rack gearbox and a steering front wheel. The steering wheel feedback motor simulates the interaction between the front wheels of the vehicle and the road surface in the driving process, so as to provide real road feel for the driver; the front wheel steering motor provides actual steering torque for the two front wheels through the gear-rack gearbox and the steering arm; the angle sensor collects steering angle information for closed loop control.
Example 3: based on examples 1 and 2, but with the difference:
the input quantity of the controller shown in fig. 3 is the steering angle of the steer-by-wire system and the inequality constraint of a given state, the control moment required by the front wheel steering motor is obtained through calculation of the steer-by-wire system controller, the actual steering angle measured by the angle sensor is subjected to closed-loop control adjustment through a negative feedback controller, and finally the steering angle of the front wheel of the steer-by-wire system accurately reaches the expected steering angle and does not exceed a given boundary.
Example 4: based on examples 1, 2 and 3, but with the difference:
fig. 4 shows a mapping relationship of one-to-one state transition. The steering angle of the front wheels being limited to δ in the upper boundfmaxLower bound of δfminIn the bilateral constraint, a tangent function is selected as a state conversion function, the unique function characteristic of the tangent function is utilized, the front wheel steering angle is input as an independent variable, and a new state quantity y which is not constrained by a boundary is obtained. Similarly, the state quantity y can also be converted into a corresponding front wheel steering angle in a similar manner, and the monotonicity of the tangent function ensures the one-to-one correspondence of the mapping.
Example 5: based on examples 1, 2, 3 and 4, but with the difference:
fig. 5 is a simulation diagram showing that after the parameters of the steer-by-wire system controller are adjusted, a sinusoidal track and a bilateral state inequality constraint are given, and the steering angle of the front wheel of the steer-by-wire system follows the expected required track. In the figure, a dotted line represents a preset target motion given track of the steer-by-wire system, and a solid line represents an actual motion track of a front wheel steering angle of the steer-by-wire system, so that under the action of the controller, the actual motion track does not exceed a given boundary along with the preset target motion given track, the effect is good, and the design method is proved to be effective.
Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art will readily appreciate that many modifications, substitutions, and improvements, which are within the spirit and scope of the invention, are intended to be included within the scope of the invention.

Claims (5)

1. A modeling control method of a steer-by-wire system capable of processing state inequality constraints is characterized by comprising the following steps:
s1, establishing a steer-by-wire system dynamic model;
s2, constructing a one-to-one mapping conversion function based on the limitation of state inequality constraint borne by the system in the actual working process;
s3, converting the state variables in the system constrained by the state inequality into new 'free' state variables by using a conversion function to obtain a kinetic equation after variable conversion;
and S4, establishing a controller based on Udwadia-Kalaba theory to control the operation of the system according to the converted kinetic equation and the performance constraint.
2. The modeling control method of the steer-by-wire system capable of dealing with the state inequality constraint according to claim 1, characterized in that: the building of the steer-by-wire system dynamics model in S1 is:
Figure FDA0002993877370000011
wherein, JeqRepresenting the equivalent moment of inertia of the system, BeqThe equivalent viscous friction coefficient of the system is shown,
Figure FDA0002993877370000012
indicating the Coulomb friction of the steering system, FsDenotes the Coulomb friction coefficient, τeRepresenting the steering aligning moment of the front wheels, r representing a conversion parameter, N1And N2Indicating the number of teeth, r, of the rack and gear box, respectivelygIndicating the connection ratio, tau, of the steering motordisThe total ripple interference is represented by the sum of,
Figure FDA0002993877370000013
indicating the control input of the rotational torque, delta, driving the steering motorfWhich indicates the steering angle of the front wheels,
Figure FDA0002993877370000014
represents deltafThe first derivative of (a) is,
Figure FDA0002993877370000015
represents deltafThe second derivative of (a);
equivalent moment of inertia J of systemeqBy the moment of inertia J of the steering motorfwAnd moment of inertia J of steered front wheelssmEquivalence is obtained, and the specific equivalence relation is as follows:
Figure FDA0002993877370000016
coefficient of friction B of equivalent viscosity of systemeqCoefficient of viscous friction B by steering motorfwAnd coefficient of viscous friction B of steered front wheelssmEquivalence is obtained, and the specific equivalence relation is as follows:
Figure FDA0002993877370000021
the total impulse disturbance of the system is mainly composed of the sixth torque harmonic tausm6And the twelfth torque harmonic τsm12The formula is as follows:
Figure FDA0002993877370000022
front wheel steering return torque taueIs a function expression of the geometric parameters of the automobile steering when the automobile tire side inclination angle alphafLess than 5 °, the expression can be simplified as follows:
τe＝-(lc+lp)Cfαf (5)
wherein lcIndicating the mechanical drag of the front wheel,/pIndicates the track of the front wheel, CfIndicating front wheel tire sidewall deflection stiffness.
3. The modeling control method of a steer-by-wire system capable of dealing with the state inequality constraint according to claim 1, wherein in S2, the front wheel steering angle δ is based on the actual working process of the steer-by-wire systemfAnd (3) constructing a one-to-one mapping conversion function under the constraint of the state inequality:
δfmin＜δf＜δfmax (6)
based on the functional properties of the tangent function, a conversion function I of the following general form is established:
y＝tan(k0δf+k1)+k2 (7)
three parameters k in the transfer function I0、k1And k2The actual state of the front wheel steering angle is bound by two boundaries delta of an inequality constraint formula (6)fminAnd deltafmaxDetermining
Figure FDA0002993877370000023
Figure FDA0002993877370000024
tan(k0*0+k1)+k2＝0 (10)
In conjunction with equations (8), (9) and (10), the values of the three parameters are solved:
Figure FDA0002993877370000031
Figure FDA0002993877370000032
k2＝-tan k1 (13)
combining equations (7), (11), (12) and (13), the final sorted transfer function II is:
Figure FDA0002993877370000033
4. the modeling control method for steer-by-wire system capable of handling state inequality constraints according to claim 1, wherein the step S3 of converting the state variables in the system constrained by the state inequality into new "free" state variables based on the conversion function, and obtaining the variable-converted kinetic equation comprises:
the new variable y is used to describe the bilaterally constrained front wheel steering angle delta according to the transfer function II (14)fAs follows:
Figure FDA0002993877370000034
after differentiating the time t, we get:
Figure FDA0002993877370000035
after time derivation in equation (16), we obtain:
Figure FDA0002993877370000036
combining the formulas (15), (16) and (17) and the steer-by-wire system prime dynamic model (1), obtaining a converted dynamic equation:
Figure FDA0002993877370000041
5. the modeling control method of a steer-by-wire system capable of handling state inequality constraints as recited in claim 1, wherein said step of establishing a controller based on Udwadia-Kalaba theory to control the operation of the system based on transformed kinetic equations and performance constraints in S4 comprises:
the converted steer-by-wire system kinetic equation is written into the form of Uwadia-Kalaba kinetic equation:
Figure FDA0002993877370000042
wherein:
Figure FDA0002993877370000043
Figure FDA0002993877370000044
Figure FDA0002993877370000045
q＝y
the expression equation of the constraint moment of the system is obtained as follows:
Figure FDA0002993877370000046
wherein: tau represents a performance constraint moment, and when the steer-by-wire system needs to run along a preset track under the constraint of a state inequality, tau represents a rotation moment which is required to be generated by a steering motor; b represents an array in a second order constraint; q represents an intermediate vector with respect to y;
Figure FDA0002993877370000047
respectively representing the first derivative and the second derivative of q; t represents the operating time of the steer-by-wire system;
the rotating torque required by the steering motor is obtained through the operation, the expected steering angle is compared with the actual steering angle, closed loop feedback is formed, and the drive-by-wire steering system can accurately track the given tracking performance requirement.
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