CN112666833A - Vehicle speed following self-adaptive robust control method for electric automatic driving vehicle - Google Patents

Vehicle speed following self-adaptive robust control method for electric automatic driving vehicle Download PDF

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CN112666833A
CN112666833A CN202011556853.5A CN202011556853A CN112666833A CN 112666833 A CN112666833 A CN 112666833A CN 202011556853 A CN202011556853 A CN 202011556853A CN 112666833 A CN112666833 A CN 112666833A
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vehicle
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vehicle speed
sliding mode
follows
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CN112666833B (en
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赵健
杜金朋
朱冰
陈虹旭
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Jilin University
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Abstract

The invention discloses a vehicle speed following self-adaptive robust control method for an electric automatic driving vehicle, which comprises the following steps: step one, establishing a vehicle second-order longitudinal dynamics model containing uncertain parameters and external interference terms; step two, smoothing the step planning vehicle speed; thirdly, designing the generalized longitudinal force control rate of the vehicle by using a dynamic sliding mode control theory; step four, using RBF neural network to carry out online estimation on the uncertainty item; and step five, designing reasonable bottom-layer actuator switching logic. Has the advantages that: ensuring that the tracking target and its derivative converge to 0 at an exponential rate. The practical application problem of the conventional sliding mode control is relieved to a great extent. The buffeting problem of sliding mode control can be further relieved to a certain extent while the stability of the controller is guaranteed.

Description

Vehicle speed following self-adaptive robust control method for electric automatic driving vehicle
Technical Field
The invention relates to a vehicle speed following self-adaptive robust control method, in particular to a vehicle speed following self-adaptive robust control method for an electric automatic driving vehicle.
Background
Currently, the autonomous vehicle is considered to be capable of greatly alleviating social problems caused by improper operation of a driver due to the advantage that the autonomous vehicle does not need to be operated by the driver, and the autonomous vehicle also has great potential application value in unstructured scenes such as military, agriculture or planetary exploration. The control layer is positioned at the bottom end of the automatic driving vehicle framework, and the vehicle speed tracking module is mainly responsible for accurately tracking the expected vehicle speed, so that the control layer has a very important position in realizing a complex automatic driving task.
The common vehicle speed tracking control algorithm generally uses a desired speed and an acceleration as controller inputs, calculates a proper driving moment or a proper braking pressure to control the vehicle so as to ensure a vehicle speed following effect, and mainly comprises PID control, sliding mode control, model prediction control and the like as shown in Chinese patent publication No. CN112026753A, Chinese patent publication No. CN109991856A and Chinese patent publication No. CN 110780674A.
Since the vehicle itself is a complex time-varying nonlinear system and there are several unknown disturbances in the actual interaction of the vehicle with the environment, these factors will all affect the tracking performance of the vehicle. The PID control robustness of the algorithm is poor, a large amount of setting work is needed for determining a proper PID parameter, a plurality of feedforward calibration quantities are matched to achieve a good control effect, and the debugging workload is large; the conventional sliding mode control has strong interference resistance but has the problem of output buffeting, the method described in the Chinese patent publication No. CN109991856A reduces the buffeting problem by using the fuzzy control principle, but the design of the fuzzy rule and the membership function still needs a large amount of debugging work; the model predictive control described in chinese patent publication No. CN110780674A has high requirements for model accuracy and real-time calculation capability of a processor, and has more limitations in practical application, so it is important to design a practical vehicle speed tracking control algorithm capable of handling factors such as uncertainty of parameters and unavoidable external interference.
Disclosure of Invention
The invention aims to provide a vehicle speed following adaptive robust control method for an electric automatic driving vehicle, which aims to solve the problems that parameters of the electric automatic driving vehicle are uncertain, and the tracking performance of the vehicle is influenced by a plurality of unknown interferences in the actual interaction process with the environment.
The invention provides a vehicle speed following self-adaptive robust control method for an electric automatic driving vehicle, which comprises the following steps:
step one, establishing a vehicle second-order longitudinal dynamics model containing uncertain parameters and external interference terms:
differentiation of the model by generalized longitudinal forces
Figure BDA0002858728170000021
As input, with vehicle speed vxAnd longitudinal acceleration
Figure BDA0002858728170000022
The status is as follows:
Figure BDA0002858728170000023
in the formula, x1As the longitudinal speed v of the vehiclex；x2As derivative of longitudinal speed of vehicle
Figure BDA0002858728170000024
Figure BDA0002858728170000025
Wherein C isDThe air resistance coefficient of the vehicle, rho is the air density, and A is the frontal area of the vehicle; u is the generalized longitudinal force F applied to the vehicletDerivative of (2)
Figure BDA0002858728170000026
Figure BDA0002858728170000027
Is an interference item composed of uncertain parameters and external unknown interference together, wherein
Figure BDA0002858728170000028
Is road gradient, F is tire rolling resistance coefficient, FdFor the vehicle to be subjected to external unknown interference, M is the total of the vehicleThe masses include a known vehicle trim mass m and an unknown additional bearing mass Δ m that may vary with the actual use of the vehicle;
step two, smoothing the step planning vehicle speed, which comprises the following specific steps:
smoothing the step planning vehicle speed by using a quadratic function, a linear function and a 2-1-2 spline curve which is connected end to end and can be guided everywhere;
the time function of the actual expected vehicle speed and the longitudinal acceleration is written according to the characteristics of a 2-1-2 spline curve into the following form:
Figure BDA0002858728170000031
in the formula vxdIs the processed desired vehicle speed; v. ofxd1、
Figure BDA0002858728170000032
vxd2、
Figure BDA0002858728170000033
vxd3、
Figure BDA0002858728170000034
The piecewise expected vehicle speed and the longitudinal acceleration are respectively in the form of a quadratic function, a linear function and a quadratic function; a is0、a1、a2、b0、b1、c0、c1、c2Respectively is the coefficient corresponding to each segment of function; t is t0、t1、t2、t3Respectively, start-stop time nodes of each segment function, where t0In order to plan the time point of updating the vehicle speed, other time points need to be set by self, and according to the characteristic that a 2-1-2 spline curve is continuously guided everywhere, the following constraint conditions are obtained:
Figure BDA0002858728170000035
according to the three formulas, the concrete coefficient corresponding to each section of function can be solved, so that a continuously derivable expected vehicle speed curve is obtained;
step three, designing the generalized longitudinal force control rate of the vehicle by utilizing a dynamic sliding mode control theory, which comprises the following steps:
first a tracking error e is defined1＝x1-x1d，x1dIs the system state quantity x1Is desired value, i.e. desired vehicle speed vxdTo ensure that the tracking error can converge to 0, a Lyapunov function V is defined1And derived to obtain
Figure BDA0002858728170000036
As follows:
Figure BDA0002858728170000037
define x according to the above formula2Expected value of
Figure BDA0002858728170000038
Wherein phi1Is a normal number, the above formula is written as
Figure BDA0002858728170000039
Accordingly e1May converge to 0 within a finite time and then define a second tracking error
Figure BDA00028587281700000310
Constructing a sliding mode function sigma according to two defined tracking errors1＝φ2e1+e2Wherein phi2As a normal number, the tracking error e2Is brought into a sliding mode function to obtain
Figure BDA0002858728170000041
Therefore, when the system enters the ideal sliding mode sigma1When 0, tracking error e1And
Figure BDA0002858728170000042
converging the index to 0 to achieve a vehicle speed tracking control target;
designing the control rate of the generalized longitudinal force differential term based on the state space equation of the step one is shown as follows, wherein
Figure BDA0002858728170000043
For an unknown interference term D1Upper bound of, h1、h2Is a normal number:
Figure BDA0002858728170000044
the stability proves that:
defining Lyapunov function V2Derivative it and apply a sliding mode function sigma1The following steps are carried out:
Figure BDA0002858728170000045
two tracking errors e1＝x1-x1d、
Figure BDA0002858728170000046
And substituting the state space equation of the step one into the formula to obtain:
Figure BDA0002858728170000047
finally, the control rate designed in the third step is carried into to obtain the following formula, so as to ensure that
Figure BDA0002858728170000048
In the case of (2), a corroborative sliding mode function σ1Will converge to 0 within a finite time;
Figure BDA0002858728170000049
wherein:
E＝[e1 e2]T；
Figure BDA00028587281700000410
step four, using the RBF neural network to carry out online estimation on the uncertainty item, which comprises the following specific steps:
aiming at uncertain item upper bound under different driving environments
Figure BDA0002858728170000051
The defect which can not be predicted generally is solved by further using an RBF neural network to carry out online estimation on the uncertainty item;
according to the structural characteristics of the RBF neural network, the estimated value of the uncertainty is designed to
Figure BDA0002858728170000052
Wherein omega is the weight matrix of RBF neural network, h (sigma)1) For the intermediate hidden layer neuron output matrix, the neuron output matrix h (σ)1) The concrete form is shown as follows, wherein ciIs the central position of the ith neuron, biWidth for the ith neuron:
Figure BDA0002858728170000053
in defining RBF neural network omega, bi，ciBefore updating rules of three types of parameters, firstly giving adaptive control rate of a generalized longitudinal force differential term:
Figure BDA0002858728170000054
the updating rule of omega is obtained by stability analysis, and the specific steps are as follows:
some parameters are first defined: assume that the best estimate of the uncertainty term is
Figure BDA0002858728170000055
In the formula of omega*The weight is best estimated; error between optimum estimated value of uncertainty and actual value
Figure BDA0002858728170000056
The difference between the network weight of the best estimate of uncertainty and the network weight of the actual estimate is
Figure BDA0002858728170000057
Then defining Lyapunov function V3Derivative it and apply a sliding mode function sigma1Two tracking errors e1、e2The specific form of (1) and the state space equation of step one are taken into:
Figure BDA0002858728170000058
finally, the control rate designed in the step four is substituted to obtain the following formula:
Figure BDA0002858728170000061
let the update rate of the RBF neural network weight be:
Figure BDA0002858728170000062
a similar step two can finally be obtained
Figure BDA0002858728170000063
The form of (A) is as follows:
Figure BDA0002858728170000064
thus ensuring that
Figure BDA0002858728170000065
And
Figure BDA0002858728170000066
in the case of (2), a corroborative sliding mode function σ1Will converge to 0 within a finite time;
biand ciThe updating rule can be realized by a common gradient descent method, and the specific derivation steps are as follows:
firstly, defining a performance index function of the RBF network according to a control target of sliding mode control:
Figure BDA0002858728170000067
calculation of biGradient under performance indicator function E:
Figure BDA0002858728170000068
in the same way, c can be obtainedjGradient under performance indicator function E:
Figure BDA0002858728170000069
the parameter updating rule based on the gradient descent method is finally as follows:
Figure BDA00028587281700000610
in the formula of gammac，γbTo learn the rate, muc，μbIs a momentum factor;
step five, designing a reasonable bottom layer executor switching logic, specifically as follows:
according to the relation between the driving torque, the braking torque and the generalized longitudinal force, the switching rule is designed as follows:
Figure BDA0002858728170000071
in the formula Ft0> 0, represents the drive torque TdOr brake master cylinder pressure PbAn activation threshold of; f. ofd(Ft) And fb(Ft) Formulas for converting the generalized driving force into the driving torque and the master cylinder pressure are respectively expressed as follows:
Figure BDA0002858728170000072
in the formula rwIs the rolling radius of the tire, igTo the transmission ratio of the variator, ifTo distribute the torque of the front axle if0For front axle final drive ratio, ir0Is the transmission ratio of the rear axle main reducer, kbfIs the front wheel braking torque coefficient, kbrIs the rear wheel braking torque coefficient.
The invention has the beneficial effects that:
1. based on the thought of a back-stepping method, the invention redesigns the vehicle speed tracking sliding mode function and ensures that the tracking target and the derivative thereof can be converged to 0 at an exponential speed.
2. The method utilizes a dynamic sliding mode control principle, incorporates actual control input into a sliding mode function, transfers the buffeting defect of the conventional sliding mode control into a differential term by designing the control rate of the actual control input differential term, and finally performs buffeting inhibition through an integrator, thereby greatly relieving the practical application problem of the conventional sliding mode control.
3. The invention solves the problem that the uncertain interference upper bound of the longitudinal vehicle speed tracking is not suitable for obtaining by using the self-adaptive principle and the RBF neural network self-adaptive algorithm, thereby not only ensuring the stability of the controller, but also further relieving the buffeting problem of the sliding mode control to a certain extent.
Drawings
Fig. 1 is a schematic diagram of a general architecture of the trajectory tracking control of the electric autonomous vehicle according to the present invention.
FIG. 2 is a schematic diagram of a vehicle speed adaptive robust control architecture of an electric autopilot vehicle according to the present invention.
Detailed Description
Please refer to fig. 1 to 2:
the invention provides a strong-robustness vehicle speed following control method of an electric four-wheel-drive automatic driving vehicle, which specifically comprises the following steps of:
step one, establishing a vehicle second-order longitudinal dynamics model containing uncertain parameters and external interference terms.
In general, the longitudinal dynamics model of the vehicle ignores the influence of air resistance, ramp resistance and the like, but the method of the invention mainly researches the vehicle speed tracking control under the conditions that the parameters are uncertain and certain external interference is generated, and the two items cannot be ignored. Thus, a complete longitudinal dynamics model was used, as shown in the following formula:
Figure BDA0002858728170000081
wherein M is the total mass of the vehicle including the known vehicle service mass M and the unknown additional bearing mass Δ M that may vary with the actual use of the vehicle; v. ofxIs the vehicle longitudinal speed; the longitudinal acceleration of the vehicle can be expressed as the derivative of the longitudinal speed of the vehicle, irrespective of the influence of the yaw rate and the lateral speed when the vehicle is turning
Figure BDA0002858728170000082
FtLongitudinal forces generated by the interaction of the vehicle tire with the ground; fslopeThe vehicle is subjected to ramp resistance; g is the acceleration of gravity;
Figure BDA0002858728170000083
is the road grade; ffThe rolling resistance of the vehicle; f is the tire rolling resistance coefficient; fwindIs the air resistance borne by the vehicle; cDIs the vehicle air resistance coefficient; ρ is the air density; a is the frontal area of the vehicle; fdThe vehicle is subjected to external unknown interference.
Deriving said longitudinal dynamics model to obtain a differential with a generalized longitudinal force
Figure BDA0002858728170000084
As input, with vehicle speed vxAnd longitudinal acceleration
Figure BDA0002858728170000085
A second order model of the state, as shown in detail below:
Figure BDA0002858728170000091
in the formula, x1As the longitudinal speed v of the vehiclex；x2As derivative of longitudinal speed of vehicle
Figure BDA0002858728170000092
Figure BDA0002858728170000093
u is the generalized longitudinal force F applied to the vehicletA derivative of (a);
Figure BDA0002858728170000094
the interference item is composed of uncertain parameters and external unknown interference.
And step two, smoothing the step planning vehicle speed in order to improve the control effect of the controller.
In order to improve the control effect of the controller and ensure the riding comfort of the vehicle, a quadratic function, a linear function and a 2-1-2 spline curve which is connected end to end and can be guided everywhere are adopted to carry out smoothing treatment on the step planning vehicle speed.
The time function of the actual desired vehicle speed and longitudinal acceleration can be written in the following form according to the characteristics of the '2-1-2' spline curve:
Figure BDA0002858728170000095
in the formula vxdIs the processed desired vehicle speed; v. ofxd1、
Figure BDA0002858728170000096
vxd2、
Figure BDA0002858728170000097
vxd3、
Figure BDA0002858728170000098
The piecewise expected vehicle speed and the longitudinal acceleration are respectively in the form of a quadratic function, a linear function and a quadratic function; a is0、a1、a2、b0、b1、c0、c1、c2Respectively is the coefficient corresponding to each segment of function; t is t0、t1、t2、t3Respectively, start-stop time nodes of each segment function, where t0In order to plan the time point of updating the vehicle speed, other time points need to be set by self. According to the characteristic of continuous guidance everywhere of the 2-1-2 spline curve, the following constraint conditions can be written:
Figure BDA0002858728170000099
writing the constraint in the form of a matrix:
Vxp＝TC
in the formula VxpIs t0The vehicle speed information vector at the moment, T is a matrix formed by time information of each section of the spline curve, and C is a coefficient vector of each section of the spline curve, and the concrete form is as follows:
Figure BDA0002858728170000101
C＝[a0 a1 a2 b0 b1 c0 c1 c2]T
in the above matrix, VxpAll of them beingAs is known, the time point information in T can be artificially defined, so that the coefficient vector C can be directly solved, and finally a smooth expected speed curve is obtained.
And step three, designing the generalized longitudinal force control rate of the vehicle by utilizing a dynamic sliding mode control theory based on the thought of a backstepping method.
First a tracking error e is defined1＝x1-x1d，x1dIs the system state quantity x1Is desired value, i.e. desired vehicle speed vxd. To ensure that the tracking error can converge to 0, a Lyapunov function V is defined1And derived to obtain
Figure BDA0002858728170000102
As follows:
Figure BDA0002858728170000103
define x according to the above formula2Expected value of
Figure BDA0002858728170000104
Wherein phi1Is a normal number, the above formula can be written as
Figure BDA0002858728170000105
Accordingly e1Can converge to 0 within a limited time. Then defining a second tracking error
Figure BDA0002858728170000106
Constructing a sliding mode function sigma according to two defined tracking errors1＝φ2e1+e2Wherein phi2As a normal number, the tracking error e2Is brought into a sliding mode function to obtain
Figure BDA0002858728170000107
Therefore, when the system enters the ideal sliding mode sigma1When 0, tracking error e1And
Figure BDA0002858728170000108
and converging the index to 0 to achieve the vehicle speed tracking control target.
Designing the control rate of the generalized longitudinal force differential term based on the state space equation of the step one is shown as follows, wherein
Figure BDA0002858728170000109
For an unknown interference term D1Upper bound of, h1、h2Is a normal number:
Figure BDA00028587281700001010
the stability proves that:
defining Lyapunov function V2Derivative it and apply a sliding mode function sigma1＝φ2e1+e2The following steps are carried out:
Figure BDA0002858728170000111
two tracking errors e1＝x1-x1d、
Figure BDA0002858728170000112
And substituting the state space equation of the step one into the formula to obtain:
Figure BDA0002858728170000113
finally, the control rate designed in the step three is substituted to obtain the following formula,
Figure BDA0002858728170000114
wherein:
E＝[e1 e2]T；
Figure BDA0002858728170000115
under the assumption of phi1，φ2If it is determined that h can be set1Such that Q is a positive definite matrix, can be made
Figure BDA0002858728170000116
And the zero point is always smaller than zero in the interval of removing the zero point, so that the system is ensured to enter a sliding mode within limited time, and the control target is finally realized.
To make Q a positive definite matrix only guarantees the following:
Figure BDA0002858728170000117
step four, using RBF neural network to carry out online estimation on the uncertainty item;
aiming at uncertain item upper bound under different driving environments
Figure BDA0002858728170000118
The disadvantage that can not be predicted in general is solved by the step of performing online estimation on the uncertainty term by using an RBF neural network.
According to the structural characteristics of the RBF neural network, the estimated value of the uncertainty is designed to
Figure BDA0002858728170000121
Wherein omega is the weight matrix of RBF neural network, h (sigma)1) The matrix is output for the intermediate hidden layer neurons. Neuron output matrix h (σ)1) A concrete form can be represented as follows, wherein ciIs the central position of the ith neuron, biWidth for the ith neuron:
Figure BDA0002858728170000122
in defining RBF neural network omega, bi，ciBefore updating the rules of the three parameters, the generalized longitudinal force is given firstlyDifferential term adaptive control rate:
Figure BDA0002858728170000123
the updating rule of omega is obtained by stability analysis, and the specific steps are as follows:
some parameters are first defined: assume that the best estimate of the uncertainty term is
Figure BDA0002858728170000124
In the formula of omega*The weight is best estimated; error between optimum estimated value of uncertainty and actual value
Figure BDA0002858728170000125
The difference between the network weight of the best estimate of uncertainty and the network weight of the actual estimate is
Figure BDA0002858728170000126
Then defining Lyapunov function V3Derivative it and apply a sliding mode function sigma1Two tracking errors e1、e2The specific form of (1) and the state space equation of step one are taken into:
Figure BDA0002858728170000127
finally, the control rate designed in the step four is substituted to obtain the following formula:
Figure BDA0002858728170000128
let the update rate of the RBF neural network weight be:
Figure BDA0002858728170000131
then a similarity can be obtainedIn the second step
Figure BDA0002858728170000132
The form of (A) is as follows:
Figure BDA0002858728170000133
thus ensuring that
Figure BDA0002858728170000134
And
Figure BDA0002858728170000135
in the case of (2), a corroborative sliding mode function σ1Will converge to 0 within a finite time.
biAnd ciThe updating rule can be realized by a common gradient descent method, and the specific derivation steps are as follows:
firstly, defining a performance index function of the RBF network according to a control target of sliding mode control:
Figure BDA0002858728170000136
calculation of biGradient under performance indicator function E:
Figure BDA0002858728170000137
in the same way, c can be obtainedjGradient under performance indicator function E:
Figure BDA0002858728170000138
the parameter updating rule based on the gradient descent method is finally as follows:
Figure BDA0002858728170000139
in the formula of gammac，γbTo learn the rate, muc，μbIs a momentum factor.
Fifthly, reasonably designing bottom-layer actuator switching logic;
in general, the driving actuator and the braking actuator cannot act on the vehicle at the same time, so that a reasonably designed bottom-layer actuator switching logic is needed to ensure that only one actuator acts at the same time.
According to the relation between the driving torque, the braking torque and the generalized longitudinal force, the switching rule is designed as follows:
Figure BDA0002858728170000141
in the formula Ft0> 0, represents the drive torque TdOr brake master cylinder pressure PbAn activation threshold of; f. ofd(Ft) And fb(Ft) Formulas for converting the generalized driving force into the driving torque and the master cylinder pressure are respectively expressed as follows:
Figure BDA0002858728170000142
in the formula rwIs the rolling radius of the tire, igTo the transmission ratio of the variator, ifTo distribute the torque of the front axle if0For front axle final drive ratio, ir0Is the transmission ratio of the rear axle main reducer, kbfIs the front wheel braking torque coefficient, kbrIs the rear wheel braking torque coefficient.

Claims (1)

1. A vehicle speed following adaptive robust control method for an electric autonomous vehicle, characterized by: the method comprises the following steps:
step one, establishing a vehicle second-order longitudinal dynamics model containing uncertain parameters and external interference terms:
the model is based on generalized longitudinal forceDifferential of (2)
Figure FDA0002858728160000011
As input, with vehicle speed vxAnd longitudinal acceleration
Figure FDA0002858728160000012
The status is as follows:
Figure FDA0002858728160000013
in the formula, x1As the longitudinal speed v of the vehiclex；x2As derivative of longitudinal speed of vehicle
Figure FDA0002858728160000014
Figure FDA0002858728160000015
Wherein C isDThe air resistance coefficient of the vehicle, rho is the air density, and A is the frontal area of the vehicle; u is the generalized longitudinal force F applied to the vehicletDerivative of (2)
Figure FDA0002858728160000016
Figure FDA0002858728160000017
Is an interference item composed of uncertain parameters and external unknown interference together, wherein
Figure FDA00028587281600000112
Is road gradient, F is tire rolling resistance coefficient, FdThe total mass of the vehicle comprises known vehicle servicing mass M and unknown additional bearing mass Deltam which can change along with the actual use process of the vehicle;
step two, smoothing the step planning vehicle speed, which comprises the following specific steps:
smoothing the step planning vehicle speed by using a quadratic function, a linear function and a 2-1-2 spline curve which is connected end to end and can be guided everywhere;
the time function of the actual expected vehicle speed and the longitudinal acceleration is written according to the characteristics of a 2-1-2 spline curve into the following form:
Figure FDA0002858728160000018
in the formula vxdIs the processed desired vehicle speed; v. ofxd1、
Figure FDA0002858728160000019
vxd2、
Figure FDA00028587281600000110
vxd3、
Figure FDA00028587281600000111
The piecewise expected vehicle speed and the longitudinal acceleration are respectively in the form of a quadratic function, a linear function and a quadratic function; a is0、a1、a2、b0、b1、c0、c1、c2Respectively is the coefficient corresponding to each segment of function; t is t0、t1、t2、t3Respectively, start-stop time nodes of each segment function, where t0In order to plan the time point of updating the vehicle speed, other time points need to be set by self, and according to the characteristic that a 2-1-2 spline curve is continuously guided everywhere, the following constraint conditions are obtained:
Figure FDA0002858728160000021
according to the three formulas, the concrete coefficient corresponding to each section of function can be solved, so that a continuously derivable expected vehicle speed curve is obtained;
step three, designing the generalized longitudinal force control rate of the vehicle by utilizing a dynamic sliding mode control theory, which comprises the following steps:
first a tracking error e is defined1＝x1-x1d，x1dIs the system state quantity x1Is desired value, i.e. desired vehicle speed vxdTo ensure that the tracking error can converge to 0, a Lyapunov function V is defined1And derived to obtain
Figure FDA0002858728160000022
As follows:
Figure FDA0002858728160000023
define x according to the above formula2Expected value of
Figure FDA0002858728160000024
Wherein phi1Is a normal number, the above formula is written as
Figure FDA0002858728160000025
Accordingly e1May converge to 0 within a finite time and then define a second tracking error
Figure FDA0002858728160000026
Constructing a sliding mode function sigma according to two defined tracking errors1＝φ2e1+e2Wherein phi2As a normal number, the tracking error e2Is brought into a sliding mode function to obtain
Figure FDA0002858728160000027
Therefore, when the system enters the ideal sliding mode sigma1When 0, tracking error e1And
Figure FDA0002858728160000028
converging the index to 0 to achieve a vehicle speed tracking control target;
designing the control rate of the generalized longitudinal force differential term based on the state space equation of the step one is shown as follows, wherein
Figure FDA0002858728160000029
For an unknown interference term D1Upper bound of, h1、h2Is a normal number:
Figure FDA00028587281600000210
the stability proves that:
defining Lyapunov function V2Derivative it and apply a sliding mode function sigma1The following steps are carried out:
Figure FDA0002858728160000031
two tracking errors e1＝x1-x1d、
Figure FDA0002858728160000032
And substituting the state space equation of the step one into the formula to obtain:
Figure FDA0002858728160000033
finally, the control rate designed in the third step is carried into to obtain the following formula, so as to ensure that
Figure FDA0002858728160000034
In the case of (2), a corroborative sliding mode function σ1Will converge to 0 within a finite time;
Figure FDA0002858728160000035
wherein:
E＝[e1 e2]T；
Figure FDA0002858728160000036
step four, using the RBF neural network to carry out online estimation on the uncertainty item, which comprises the following specific steps:
aiming at uncertain item upper bound under different driving environments
Figure FDA0002858728160000038
The defect which can not be predicted generally is solved by further using an RBF neural network to carry out online estimation on the uncertainty item;
according to the structural characteristics of the RBF neural network, the estimated value of the uncertainty is designed to
Figure FDA0002858728160000037
Wherein omega is the weight matrix of RBF neural network, h (sigma)1) For the intermediate hidden layer neuron output matrix, the neuron output matrix h (σ)1) The concrete form is shown as follows, wherein ciIs the central position of the ith neuron, biWidth for the ith neuron:
Figure FDA0002858728160000041
in defining RBF neural network omega, bi，ciBefore updating rules of three types of parameters, firstly giving adaptive control rate of a generalized longitudinal force differential term:
Figure FDA0002858728160000042
the updating rule of omega is obtained by stability analysis, and the specific steps are as follows:
some parameters are first defined: assume that the best estimate of the uncertainty term is
Figure FDA0002858728160000043
In the formula of omega*The weight is best estimated; error between optimum estimated value of uncertainty and actual value
Figure FDA0002858728160000044
The difference between the network weight of the best estimate of uncertainty and the network weight of the actual estimate is
Figure FDA0002858728160000045
Then defining Lyapunov function V3Derivative it and apply a sliding mode function sigma1Two tracking errors e1、e2The specific form of (1) and the state space equation of step one are taken into:
Figure FDA0002858728160000046
finally, the control rate designed in the step four is substituted to obtain the following formula:
Figure FDA0002858728160000047
let the update rate of the RBF neural network weight be:
Figure FDA0002858728160000048
a similar step two can finally be obtained
Figure FDA0002858728160000049
The form of (A) is as follows:
Figure FDA0002858728160000051
thus ensuring that
Figure FDA0002858728160000052
And
Figure FDA0002858728160000053
in the case of (2), a corroborative sliding mode function σ1Will converge to 0 within a finite time;
biand ciThe updating rule can be realized by a common gradient descent method, and the specific derivation steps are as follows:
firstly, defining a performance index function of the RBF network according to a control target of sliding mode control:
Figure FDA0002858728160000054
calculation of biGradient under performance indicator function E:
Figure FDA0002858728160000055
in the same way, c can be obtainedjGradient under performance indicator function E:
Figure FDA0002858728160000056
the parameter updating rule based on the gradient descent method is finally as follows:
Figure FDA0002858728160000057
in the formula of gammac，γbTo learn the rate, muc，μbIs a momentum factor;
step five, designing a reasonable bottom layer executor switching logic, specifically as follows:
according to the relation between the driving torque, the braking torque and the generalized longitudinal force, the switching rule is designed as follows:
Figure FDA0002858728160000058
in the formula Ft0> 0, represents the drive torque TdOr brake master cylinder pressure PbAn activation threshold of; f. ofd(Ft) And fb(Ft) Formulas for converting the generalized driving force into the driving torque and the master cylinder pressure are respectively expressed as follows:
Figure FDA0002858728160000061
in the formula rwIs the rolling radius of the tire, igTo the transmission ratio of the variator, ifTo distribute the torque of the front axle if0For front axle final drive ratio, ir0Is the transmission ratio of the rear axle main reducer, kbfIs the front wheel braking torque coefficient, kbrIs the rear wheel braking torque coefficient.
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