CN111391916B - Steer-by-wire system assist control strategy taking into account driver steering characteristics - Google Patents

Steer-by-wire system assist control strategy taking into account driver steering characteristics Download PDF

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CN111391916B
CN111391916B CN202010230524.5A CN202010230524A CN111391916B CN 111391916 B CN111391916 B CN 111391916B CN 202010230524 A CN202010230524 A CN 202010230524A CN 111391916 B CN111391916 B CN 111391916B
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vehicle
driver
steering
follows
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CN111391916A (en
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王安
赵万忠
陈莉娟
冯健
匡登明
张子俊
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Nanjing University of Aeronautics and Astronautics
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B62—LAND VEHICLES FOR TRAVELLING OTHERWISE THAN ON RAILS
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Abstract

The invention provides a steer-by-wire system auxiliary control strategy considering the steering characteristics of drivers based on a steer-by-wire double-motor system, which can carry out individualized auxiliary driving on three types of drivers and keep the steering styles of the drivers in the steering process. And acquiring steering characteristic parameters of the driver based on the driver model parameter identification for designing the personalized auxiliary strategy. On one hand, the method can assist the driver to carry out path tracking experiments in a personalized mode, improve the tracking precision and reduce the tracking error, and on the other hand, the physiological and psychological burdens of the driver can be relieved through auxiliary control, so that the best performance of a man-vehicle system is realized. The personalized auxiliary control strategy fully exerts the potential of the steer-by-wire system as an intelligent driving platform, greatly improves the safety of the system, improves the driving feeling of a driver, embodies the driving style of the driver, and has wide development prospect and application value.

Description

Steer-by-wire system assist control strategy taking into account driver steering characteristics
Technical Field
The invention relates to the field of auxiliary driving systems, in particular to a steer-by-wire system auxiliary control strategy considering the steering characteristics of a driver.
Background
The steer-by-wire system is used as an important platform for future intelligent driving, and the important position of the steer-by-wire system is increasingly highlighted. Today's research on steer-by-wire systems is mainly focused on improving the performance of the system, and little attention is paid to the driving state of the driver during steering of the vehicle, mainly including physiological and psychological burdens. The method comprehensively considers the steering performance of the vehicle and the physiological and psychological states of the driver, fully utilizes the control advantages of the mu robust control algorithm in external interference and model uncertainty, and develops the personalized auxiliary controllers for different drivers, thereby realizing the best overall performance of the human-vehicle, not only improving the path tracking precision of the vehicle in the steering process, but also reducing the physiological and psychological burdens of the driver, and having wide development prospect and application value.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides an auxiliary control strategy of the steer-by-wire system considering the steering characteristics of the driver, fully exerts the potential of the steer-by-wire system as an intelligent driving platform, greatly improves the safety of the system, improves the driving feeling of the driver, reflects the driving style of the driver, and has wide development prospect and application value.
The invention comprises the following steps:
1) aiming the driver model:
Figure BDA0002429139580000011
wherein the content of the first and second substances,
Figure BDA0002429139580000012
represents the ideal lateral displacement of the preview point; tau ispIs the preview time; y(s) and φ(s) are the current lateral displacement and yaw angle of the vehicle; l is the driver's pre-aim distance; thetasw(s) is the driver's steering wheel angle; ghIs the steering proportional gain; tau isLIs the differential time constant; tau isd1Is the pure delay time; tau isd2Is the delay time for the driver to react;
let the steering gear ratio of the by-wire system be RgThen thetafd＝θsw/RgIs the steering angle applied to the front wheels by the driver, and is available at zero initial conditions:
Figure BDA0002429139580000021
2) establishing a vehicle and line control system model:
2.1) setting the position of the gravity center of the vehicle on the ground as (X, Y), and deducing the kinematic and dynamic relations of the vehicle by a two-degree-of-freedom model according to the kinematic relation of the vehicle and the dynamic relation of the vehicle as follows:
Figure BDA0002429139580000022
wherein: x0,Y0,φ0Is the position and state of the vehicle at the initial time; phi is the yaw angle of the vehicle; β is the centroid slip angle of the vehicle; omegarIs the yaw rate of the vehicle; v is the actual speed of the vehicle; vxIs the lateral velocity of the vehicle; vyIs the longitudinal speed of the vehicle; m is the mass of the vehicle, k1Is the stiffness of the front wheel, k2Is the rear wheel stiffness, IzIs the moment of inertia of the vehicle, a is the front axle length, b is the rear axle base, δfCorner of front wheel of automobile, d1And d2Representing model errors;
2.2) assuming that the two front wheel turning angles of the vehicle are the same, the dynamic model of the steering subsystem is as follows:
Figure BDA0002429139580000023
wherein theta issIs the total pinion angle, BRIs the equivalent damping coefficient, JREquivalent moment of inertia, G2Is the reduction ratio of the angle of rotation of the pinion to the wheel, T is the total motor output torque, G1Is the reduction ratio of the motor output to the pinion, eta is the efficiency of the reducer, drIs a road surface disturbance, tauRIs the aligning moment of the tire, tp,tmIs the drag distance, X, of the tirerIs the displacement of the rack or rack,r pis the radius of the pinion;
2.3) people-vehicleThe system model is written in the form of a state space, and the state variables of the system are defined as
Figure BDA0002429139580000031
Driver and controller of the design share steering ownership: deltaf＝δfd+δfcWherein δfcIs the front wheel steering angle input by the controller. w ═ YPIs the reference path, u is the designed auxiliary current, ktIs the torque coefficient of the motor;
2.4) designing an individualized auxiliary controller, wherein a human-vehicle system model is represented as follows:
Figure BDA0002429139580000032
Figure BDA0002429139580000033
Figure BDA0002429139580000034
d＝[0 0 d1 d2 0 d3 d4 d5]T； (11)
the following evaluation functions are defined in consideration of the path tracking error of the vehicle, the physiological and psychological burden of the driver, and the output of the controller, in combination:
Figure BDA0002429139580000035
wherein:
Figure BDA0002429139580000036
Q＝diag(q1,q2,q3)；q1，q2，q3r is a weighting factor;
2.5) define the output of the controller as follows:
Z＝CZx+DZw+RZu (13)
wherein:
Figure BDA0002429139580000037
2.6) converting the optimization problem into | | Z | | non-woven phosphor2Is optimized
J＝||Z||2； (14)
3) Representation and processing system uncertainty:
the vehicle dynamics model can also be described by a transfer matrix in the laplace domain:
Figure BDA0002429139580000041
the uncertainty region is expressed as the multiplicative uncertainty:
Gp(s)＝G(s)(1+WIΔI(s)) (16)
the multiplicative weight function of a by-wire system needs to satisfy the following requirements:
Figure BDA0002429139580000042
front wheel stiffness k1The uncertain range of the rigidity of (1) is 15%, and the rigidity k of the rear wheel2Is 10% and the uncertainty range of vehicle speed is 10%, according to equation (17), for Gfβ(s),Gfr(s) solving of multiplicative weighting function, WpIs a performance weighting function, and therefore, the weighting function matrix is chosen to be:
Figure BDA0002429139580000043
4) design and solution of μ controller:
according to μ control theory, the N matrix can be partitioned:
Figure BDA0002429139580000044
the uncertainty of the transfer function from ω to z and containing the N Δ structure can be expressed as follows:
F(N,Δ)＝N22+N21Δ(I-N11Δ)-1N12 (20)
according to equation (20), Δ (I-N)11Δ)-1The stability of the system will be affected, the structural singular value μ is described as a function of the singular value and the spectral radius, and for a diagonal standard perturbation, the structural singular value μ can be expressed as:
Figure BDA0002429139580000045
based on the mu control theory, the essential conditions of the robust stability of the closed loop system are as follows:
det(I-M(jω)Δ(jω))≠0 (22)
assuming that the nominal system M and the disturbance Δ are both stable, the essential conditions for system stability are therefore:
Figure BDA0002429139580000054
in consideration of the robust performance of the closed-loop system, the essential conditions for the system stability represented by the structural singular values are as follows:
Figure BDA0002429139580000055
therefore, the boundaries of the structure singular values under complex perturbations are defined by the spectral radii and the singular values:
ρ(N(jω))≤μ(N(jω))≤σ(N(jω)) (25)
d is a matrix that can be slowed down by Δ, so
Figure BDA0002429139580000051
Consideration of H using an indirect D-K iterative algorithm∞And mu analyzing the introduced region to solve the controller to obtain a min which can be minimized in frequency domainK||DND-1||∞The controllers K, D and K of the upper boundary can be freely selected; first, fix D(s) to solve for minK||DND-1||∞N is then fixed to solve for d(s), thereby obtaining the minimum of the respective frequency domains.
Further improvement, the method for deducing the preview driver model in the step 1) is as follows:
the lateral displacement deviation from the predicted position to the preview point may be expressed as follows:
Figure BDA0002429139580000056
the first order driver preview model may be represented as follows:
Figure BDA0002429139580000052
according to the Taylor formula:
Figure BDA0002429139580000053
a driver model can be derived.
In a further improvement, the motion relationship of the whole vehicle in the step 2) is represented as follows:
Figure BDA0002429139580000061
the dynamics of the vehicle can be represented as follows in a two-degree-of-freedom model:
Figure BDA0002429139580000062
the invention has the beneficial effects that:
the strategy can be used for carrying out personalized auxiliary driving on three types of drivers, namely a young novice driver A, a young skilled driver B and an old driver C, and keeping the steering style of the drivers in the steering process. And acquiring steering characteristic parameters of the driver based on the driver model parameter identification for designing the personalized auxiliary strategy. The provided strategy can assist a driver to perform a path tracking experiment in a personalized manner, improve the tracking precision and reduce the tracking error, and can reduce the physiological and psychological burdens of the driver through auxiliary control, so that the best performance of a man-vehicle system is realized. The personalized auxiliary control strategy fully exerts the potential of the steer-by-wire system as an intelligent driving platform, greatly improves the safety of the system, improves the driving feeling of a driver, embodies the driving style of the driver, and has wide development prospect and application value.
Drawings
Fig. 1 is a schematic view of a preview driver model.
FIG. 2 is a vehicle model in a global coordinate system.
FIG. 3 is a schematic view of a steering actuator module.
FIG. 4 is a weight function Gfβ(s)
FIG. 5 is a weight function Gfr(s)。
Fig. 6 is a block diagram of a design of a mu controller of the drive-by-wire system.
FIG. 7 is a D-K iterative algorithm iteration block diagram.
Fig. 8(a) is a simulation result of the lateral displacement of the driver without the assist control.
Fig. 8(b) is a simulation result of the lateral displacement of the driver under the assist control.
Fig. 8(c) is a simulation result of the driver state under the assist control.
Fig. 8(d) is a simulation result of the driver style and the compensation control under the assist control.
Fig. 8(e) is a simulation result of a process of proposing driver compensation under assist control.
FIG. 9(a) is a comparison graph of the simulation results of lateral displacement under different algorithms.
Fig. 9(b) is a comparison graph of the state simulation results of the drivers under different algorithms.
Fig. 9(c) is a comparison graph of the results of the simulation of the yaw rate and the centroid slip angle of the vehicle under different algorithms.
FIG. 9(d) is a comparison graph of the side displacement simulation results of different algorithms.
Fig. 9(e) is a comparison graph of simulation results of the steering wheel angle and the vehicle state under different algorithms.
Detailed Description
The invention will be further explained with reference to the drawings.
1.1 preview driver model:
the driver can steer the steering wheel angle to track the reference path. Steering is a dynamic behavior that can be represented by a driver model. Fig. 1 shows a schematic diagram of a predictive driver model that can simulate the actual steering behavior of the driver.
The lateral displacement deviation from the predicted position to the predicted aiming point can be expressed as follows
Figure BDA0002429139580000071
Wherein
Figure BDA0002429139580000072
Represents the ideal lateral displacement of the preview point; tau ispIs the preview time; y(s) and φ(s) are the current lateral displacement and yaw angle of the vehicle; l is the driver's pre-aim distance.
The first order driver preview model can be expressed as follows
Figure BDA0002429139580000073
Wherein theta issw(s) is the driver's steering wheel angle; ghIs the steering proportional gain; tau isLIs the differential time constant; tau isd1Is the pure delay time; tau isd2Is the delay time for the driver to react.
According to the Taylor formula:
Figure BDA0002429139580000074
from equations (1-3), the driver model can be derived as follows
Figure BDA0002429139580000075
Let the steering gear ratio of the by-wire system be RgThen thetafd＝θsw/RgAvailable at the zero initial condition, equation (5) may be described as follows:
Figure BDA0002429139580000081
1.2 vehicle and by-wire system model:
fig. 2 shows a vehicle model in a global coordinate system. Setting the position of the center of gravity of the vehicle on the ground to (X, Y), the kinematic relationship of the entire vehicle can be expressed by equation (6) as follows:
Figure BDA0002429139580000082
wherein: x0,Y0,φ0Is the position and state of the vehicle at the initial time; phi is the yaw angle of the vehicle; β is the centroid slip angle of the vehicle; omegarIs the yaw rate of the vehicle; v is the actual speed of the vehicle; vxIs the lateral velocity of the vehicle; vyIs the longitudinal speed of the vehicle.
The dynamics of the vehicle can be represented as follows in a two-degree-of-freedom model:
Figure BDA0002429139580000083
where m is the mass of the vehicle and k1Is the stiffness of the front wheel, k2Is the rear wheel stiffness, IzIs the moment of inertia of the vehicle, a is the front axle length, b is the rear axle base, δfCorner of front wheel of automobile, d1And d2Representing the model error.
According to the equations (6-7), the kinematic and dynamic relationships of the vehicle can be derived as follows:
Figure BDA0002429139580000084
as shown in the steering actuator module of fig. 3, steering torque is transmitted from the steering dual motors to the front wheel corners. The process comprises two direct current motors, two reducers, two clutches, two steering columns, two pinions and a rack mechanism. Assuming that the two front wheels are at the same angle, the dynamic model of the steering subsystem is as follows:
Figure BDA0002429139580000091
wherein theta issIs the total pinion angle, BRIs the equivalent damping coefficient, JREquivalent moment of inertia, G2Is the reduction ratio of the angle of rotation of the pinion to the wheel, T is the total motor output torque, G1Is the reduction ratio of the motor output to the pinion, eta is the efficiency of the reducer, drIs a road surface disturbance, tauRIs the aligning moment of the tire, tp,tmIs the drag distance, X, of the tirerIs the displacement of the rack or rack,r pis the radius of the pinion.
To facilitate the design of the controller, the human-vehicle system model may be written in the form of a state space. The state variables of the system are defined as
Figure BDA0002429139580000092
Driver and controller of the design share steering ownership: deltaf＝δfd+δfcWherein δfcIs the front wheel steering angle input by the controller. w ═ YPIs the reference path, u is the designed auxiliary current, ktIs the torque coefficient of the motor.
In the personalized assist controller design, the human-vehicle system model may be represented as follows:
Figure BDA0002429139580000093
Figure BDA0002429139580000094
Figure BDA0002429139580000101
d＝[0 0 d1 d2 0 d3 d4 d5]T (11)
in combination with the path tracking error of the vehicle, the driver's physiological and psychological burden, and the output of the controller, we define the following evaluation function.
Figure BDA0002429139580000102
Wherein:
Figure BDA0002429139580000103
Q＝diag(q1,q2,q3)；q1，q2，q3and R is a weighting factor.
The output of the controller is defined as follows:
Z＝CZx+DZw+RZu (13)
wherein:
Figure BDA0002429139580000104
therefore, the optimization problem can be converted into | | Z | | non-woven phosphor2Is optimized
J＝||Z||2 (14)
3.1 System uncertainty representation and handling:
by-wire systems suffer from non-linearities of the front and rear wheel tires, which can be treated as parameter uncertainties. At the same time, there is uncertainty in the vehicle speed during the turn. It is therefore necessary to first deal with the uncertainties present in the system accordingly.
The vehicle dynamics model can also be illustrated by a transfer matrix in the laplace domain.
Figure BDA0002429139580000105
The uncertainty region may be expressed as a multiplicative uncertainty.
Gp(s)＝G(s)(1+WIΔI(s)) (16)
The multiplicative weight function of a by-wire system needs to meet the following requirements.
Figure BDA0002429139580000111
Front wheel stiffness k1The uncertain range of the rigidity of (1) is 15%, and the rigidity k of the rear wheel2Is 10% and the uncertainty range of vehicle speed is 10%. According to equation 17. Gfβ(s),GfrThe solution of the(s) multiplicative weighting function is shown in fig. 5. WpIs a performance weighting function. Thus, the weighting function matrix is chosen as:
Figure BDA0002429139580000112
3.2 design and solution of μ controller:
fig. 6 is a block diagram of a μ controller design.
According to μ control theory, the N matrix can be partitioned:
Figure BDA0002429139580000113
the uncertainty of the transfer function from ω to z and containing the N Δ structure can be expressed as follows:
F(N,Δ)＝N22+N21Δ(I-N11Δ)-1N12 (20)
according to equation (20), Δ (I-N)11Δ)-1The structural singular values μ are described as a function of the singular values and the spectral radii. For the diagonal standard perturbation, the structural singular value μ can be expressed as:
Figure BDA0002429139580000114
based on the mu control theory, the essential condition of the robust stability of the closed loop system is
det(I-M(jω)Δ(jω))≠0 (22)
It is assumed that both the nominal system M and the disturbance Δ are stable. Therefore, the essential conditions for the system stability are:
Figure BDA0002429139580000115
in consideration of the robust performance of the closed-loop system, the essential conditions for the system stability represented by the structural singular values are as follows:
Figure BDA0002429139580000122
therefore, the boundaries of the structure singular values under complex perturbations can be defined by the spectral radii and the singular values.
ρ(N(jω))≤μ(N(jω))≤σ(N(jω)) (25)
D can be exchanged with delta, so
Figure BDA0002429139580000121
The structural singular value μ is an important tool for analyzing the robustness of the system. The design of the μ controller is to minimize the μ value within given conditions. But no direct mu-controlled solution exists. So the indirect D-K iterative algorithm considers H∞And μ analysis is introduced to solve the problem. The relevant principle is shown in the corresponding iterative block diagram of equation (26) shown in fig. 7.
The purpose of solving the controller is to obtain a min that can be minimized in the frequency domainK||DND-1||∞The upper bound controller K. D and K can be freely selected. First, fix D(s) to solve for minK||DND-1||∞N is then fixed to solve for d(s), thereby obtaining the minimum of the respective frequency domains.
4.1 personalized secondary controller verification:
4.11 different drivers compare as follows:
this section mainly compares the steering behavior of the three drivers before and after the use of the auxiliary controller. Besides, the states of the vehicle and the burden difference of the driver under the two working conditions are further analyzed. As shown in fig. 8(a), it is difficult for the driver a to perform a good path tracking experiment due to the lack of driving experience. Driver C is an older driver who has greater muscle and reaction delay and less steering proportional gain than other drivers. Thus, driver C is accustomed to steering slowly and tends to be conservative in the steering process. In contrast, driver C is an experienced young driver, and exhibits better path tracking, e.g., less tracking error.
The personalized auxiliary controller designed by the method can assist drivers to track paths under the conditions of road surface interference, side wind interference and uncertainty of a system model, and is shown in step 8 (b). The controller can reduce 80% of the path tracking error of the driver A, 70% of the path tracking error of the driver B and 71% of the path tracking error of the driver C, and the controller can greatly reduce the physiological burden of the driver and is particularly embodied in that the steering wheel angle is less than 90%. At the same time, this controller can not only provide individualized assist control for three drivers but also retain their steering styles see fig. 8 (d). Taking driver a as an example, fig. 8(e) shows a specific process of the human-vehicle sharing control. The front wheel steering angle in the vehicle steering process is controlled by the input front wheel steering angle of a driver and the front wheel steering angle compensated by the controller together, so that the function of auxiliary control is realized.
4.12 comparison of different control algorithms
Taking a driver A and a driver B as an example, the method carries out comparative analysis on a mu control algorithm and a pid control algorithm under the conditions of uncertain system and external interference.
Fig. 9(a) shows that both controllers can perform steering assist control for the driver a, while the path tracking effect of the vehicle is improved to some extent. Compared with pid control, the proposed controller reduces path tracking error by 75%, exhibiting better path tracking capability. Fig. 9(b) shows that both controllers can reduce the physiological burden on driver a, particularly in response to a reduction in the steering wheel angle. However, since the pid control algorithm is generally robust against external disturbances, the psychological burden on the driver a is still not reduced, which means that the differential of the steering wheel angle is still large. Therefore, the novice driver at this time is still in a highly stressed state. In contrast, the driver a assisted by the μ control algorithm can well compensate for the lack of the driving experience, and has a small burden on itself. It will be appreciated that novices prefer to use the mu-control algorithm as an auxiliary control. Fig. 9(c) illustrates the yaw rate and the centroid slip angle of the vehicle under three conditions, while also illustrating the advantage of the noted control algorithm in maintaining vehicle stability. Overall, driver a can achieve better system performance and driving conditions under the proposed control.
The assistance effect of the Pid controller is small and at this time the physiological burden on the driver B is increased on the contrary as shown in fig. 9(d) and fig. 9 (e). In other words, a skilled driver would prefer to perform steering operation on his own independently because of the general effect of pid control. The performance of the human-vehicle system can still be improved when driver B is assisted by the designed controller. It can be concluded that the proposed controller is still suitable for drivers with driving experience.
While the invention has been described in terms of its preferred embodiments, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention.

Claims (3)

1. A steer-by-wire system assist control strategy that takes into account driver steering characteristics, characterized by the steps of:
1) aiming the driver model:
Figure FDA0003010217050000011
wherein the content of the first and second substances,
Figure FDA0003010217050000012
represents the ideal lateral displacement of the preview point; tau ispIs the preview time; y(s) and φ(s) are the current lateral displacement and yaw angle of the vehicle; l is the driver's pre-aim distance; thetasw(s) is the driver's steering wheel angle; ghIs the steering proportional gain; tau isLIs the differential time constant; tau isd1Is the pure delay time; tau isd2Is the delay time for the driver to react; vxIs the lateral velocity of the vehicle; d1(s) is an external disturbance;
let the steering gear ratio of the by-wire system be RgThen thetafd＝θsw/RgIs the steering angle applied to the front wheels by the driver, and is available at zero initial conditions:
Figure FDA0003010217050000013
2) establishing a vehicle and line control system model:
2.1) setting the position of the gravity center of the vehicle on the ground as (X, Y), and deducing the kinematic and dynamic relations of the vehicle according to the two-degree-of-freedom model of the kinematic relation and the dynamic relation of the vehicle as follows:
Figure FDA0003010217050000014
wherein: x0,Y0,φ0Is the position and state of the vehicle at the initial time; phi is the yaw angle of the vehicle; β is the centroid slip angle of the vehicle; omegarIs the yaw rate of the vehicle; v is the actual speed of the vehicle; vxIs the lateral velocity of the vehicle; vyIs the longitudinal speed of the vehicle; m is the mass of the vehicle, k1Is the stiffness of the front wheel, k2Is the rear wheel stiffness, IzIs the moment of inertia of the vehicle, a is the front axle length, b is the rear axle base, δfCorner of front wheel of automobile, d1And d2Representing model error, d3Is an external disturbance;
2.2) assuming that the two front wheel turning angles of the vehicle are the same, the dynamic model of the steering subsystem is as follows:
Figure FDA0003010217050000021
wherein theta issIs the total pinion angle, BRIs the equivalent damping coefficient, JREquivalent moment of inertia, G2Is the reduction ratio of the angle of rotation of the pinion to the wheel, T is the total motor output torque, G1Is the reduction ratio of the motor output to the pinion, eta is the efficiency of the reducer, drIs a road surfaceInterference, τRIs the aligning moment of the tire, tp,tmIs the drag distance, X, of the tirerIs the displacement of the rack, rpIs the radius of the pinion; β is the centroid slip angle of the vehicle; omegarIs the yaw rate of the vehicle;
2.3) writing the human-vehicle system model into the form of state space, and defining the state variables of the system as
Figure FDA0003010217050000022
Driver and controller of the design share steering ownership: deltaf＝δfd+δfcWherein δfcIs the front wheel turning angle input by the controller; w ═ YPIs the reference path, u is the designed auxiliary current, ktIs the torque coefficient of the motor;
2.4) designing an individualized auxiliary controller, wherein a human-vehicle system model is represented as follows:
Figure FDA0003010217050000023
A,B1，B2is an equation of state
Figure FDA0003010217050000024
D is the interference amount;
Figure FDA0003010217050000025
Figure FDA0003010217050000026
d＝[0 0 d1 d2 0 d3 d4 d5]T； (11)
ktis the torque coefficient of the motor, JREquivalent moment of inertia, Jm2 being an electric machineRotational inertia of d1、d2、d3、d4、d5Is an external disturbance;
the following evaluation functions are defined in consideration of the path tracking error of the vehicle, the physiological and psychological burden of the driver, and the output of the controller, in combination:
Figure FDA0003010217050000031
wherein:
Figure FDA0003010217050000032
Q＝diag(q1,q2,q3)；q1，q2，q3，Ris a weight factor;
2.5) define the output of the controller as follows:
Z＝CZx+DZw+RZu (13)
wherein:
Figure FDA0003010217050000033
2.6) converting the optimization problem into | | Z | | non-woven phosphor2Is optimized
J＝||Z||2； (14)
3) Representation and processing system uncertainty:
the vehicle dynamics model is illustrated by a transfer matrix in the laplace domain:
Figure FDA0003010217050000034
the uncertainty region is expressed as the multiplicative uncertainty:
Gp(s)＝G(s)(1+WIΔI(s)) (16)
the multiplicative weight function of a by-wire system needs to satisfy the following requirements:
Figure FDA0003010217050000035
front wheel stiffness k1The uncertain range of the rigidity of (1) is 15%, and the rigidity k of the rear wheel2Is 10% and the uncertainty range of vehicle speed is 10%, according to equation (17), for Gfβ(s),Gfr(s) solving of multiplicative weighting function, WpIs a performance weighting function, and therefore, the weighting function matrix is chosen to be:
Figure FDA0003010217050000041
4) design and solution of μ controller:
according to the mu control theory, the N matrix is partitioned:
Figure FDA0003010217050000042
the uncertainty of the transfer function from ω to z and including the N Δ structure is represented as follows:
F(N,Δ)＝N22+N21Δ(I-N11Δ)-1N12 (20)
according to equation (20), Δ (I-N)11Δ)-1The stability of the system will be affected, the structural singular value μ is described as a function of the singular value and the spectral radius, and for the diagonal standard perturbation, the structural singular value μ is expressed as:
Figure FDA0003010217050000043
based on the mu control theory, the essential conditions of the robust stability of the closed loop system are as follows:
det(I-M(jω)Δ(jω))≠0 (22)
assuming that the nominal system M and the disturbance Δ are both stable, the essential conditions for system stability are therefore:
Figure FDA0003010217050000044
in consideration of the robust performance of the closed-loop system, the essential conditions for the system stability represented by the structural singular values are as follows:
Figure FDA0003010217050000045
therefore, the boundaries of the structure singular values under complex perturbations are defined by the spectral radii and the singular values:
ρ(N(jω))≤μ(N(jω))≤σ(N(jω)) (25)
d is a sum-delta switching matrix, so
Figure FDA0003010217050000051
Consideration of H using an indirect D-K iterative algorithm∞And mu analyzing the introduced region to solve the controller to obtain a min minimized in frequency domainK||DND-1||∞The controllers K, D and K of the upper boundary are freely selected; first, fix D(s) to solve for minK||DND-1||∞N is then fixed to solve for d(s), thereby obtaining the minimum of the respective frequency domains.
2. The steer-by-wire system assist control strategy taking into account driver steering characteristics of claim 1, wherein: the method for deducing the preview driver model in the step 1) comprises the following steps:
the lateral displacement deviation from the predicted position to the preview point is expressed as follows:
Figure FDA0003010217050000052
the first order driver preview model is represented as follows:
Figure FDA0003010217050000053
according to the Taylor formula:
Figure 1
a driver model is derived.
3. The steer-by-wire system assist control strategy taking into account driver steering characteristics of claim 1, wherein: the motion relationship of the whole vehicle described in step 2) is expressed as follows:
Figure FDA0003010217050000055
the two-degree-of-freedom model of the vehicle dynamics is expressed as follows:
Figure FDA0003010217050000056
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