CN113978470B - On-line quick estimation method for friction force between tire and road surface - Google Patents

On-line quick estimation method for friction force between tire and road surface Download PDF

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Publication number
CN113978470B
CN113978470B CN202111522483.8A CN202111522483A CN113978470B CN 113978470 B CN113978470 B CN 113978470B CN 202111522483 A CN202111522483 A CN 202111522483A CN 113978470 B CN113978470 B CN 113978470B
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vehicle
calculation
equation
value
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CN113978470A (en
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付志军
郭耀华
何文斌
明五一
赵登峰
殷玉明
周放
姚雷
李家文
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Zhengzhou University of Light Industry
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Zhengzhou University of Light Industry
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W40/00—Estimation or calculation of non-directly measurable driving parameters for road vehicle drive control systems not related to the control of a particular sub unit, e.g. by using mathematical models
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60Q—ARRANGEMENT OF SIGNALLING OR LIGHTING DEVICES, THE MOUNTING OR SUPPORTING THEREOF OR CIRCUITS THEREFOR, FOR VEHICLES IN GENERAL
    • B60Q9/00—Arrangement or adaptation of signal devices not provided for in one of main groups B60Q1/00 - B60Q7/00, e.g. haptic signalling
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W2520/00—Input parameters relating to overall vehicle dynamics
    • B60W2520/10—Longitudinal speed
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W2520/00—Input parameters relating to overall vehicle dynamics
    • B60W2520/26—Wheel slip

Abstract

The invention discloses an online quick estimation method for friction force between a tire and a road surface, wherein a calculation cycle is formed from a first substep to a fifth substep, and a value obtained in the last calculation cycle is used as a value in a formula IV, a formula seven and a formula eight in the next calculation cycle; and repeating the calculation cycle formed by the first sub-step to the fifth sub-step, and performing cyclic recursion calculation so as to perform real-time on-line estimation on the friction between the tire and the road surface in the running process of the motor vehicle. The estimation method has the advantages of small calculated amount, high calculation speed, high error convergence speed in cyclic recursion calculation, accurate result and strong practicability. The invention can calculate the real-time vehicle speed and the real-time wheel slip rate only by relying on the vehicle speed sensor and the ABS system, does not need to additionally increase the accessory cost, and only needs to write the algorithm into the vehicle-mounted ECU, thereby having extremely low realization cost and extremely high popularization and application value.

Description

On-line quick estimation method for friction force between tire and road surface
Technical Field
The invention belongs to the fields of automatic control, information technology and advanced manufacturing, and particularly relates to a method for quickly estimating the friction force of a tire pavement.
Background
The steering behavior of a vehicle on a road is mainly determined by the friction at the tire-road interface. Automobile control systems, particularly active safety control systems such as antilock control systems, traction control systems, and vehicle stability control systems, all require tire-ground friction information to ensure safe and stable vehicle movement.
However, estimating tire-road friction is challenging because tire-road surfaces are highly non-linear and depend on many uncontrolled environmental factors, such as temperature, tire wear, normal forces, tire pressure, road conditions, etc., which are difficult to directly measure. The transient nature of the tire in contact with the road surface, especially under real-time conditions, further increases the complexity of road surface friction estimation.
There are two general methods to estimate the friction between the tire and the road surface, one is based on sensors, such as GPS, optical sensors, etc., however, these sensors are expensive and difficult to apply in practice. The other type of method mainly adopts the estimation methods such as Kalman filtering, least square method and the like, however, the estimation methods are mainly based on a linearization tire model, so that the estimation is inaccurate, meanwhile, the method does not consider parameter error information in the estimation process, and the convergence speed cannot be ensured.
Disclosure of Invention
The invention aims to provide an online quick estimation method for friction force between a tire and a road surface, which realizes online self-adaptive estimation at low cost, ensures that an estimation error is quickly converged to zero and has higher estimation speed.
In order to achieve the above purpose, the invention provides an online rapid estimation method for friction force between a tire and a road surface, which is used for a motor vehicle, wherein the vehicle is provided with a vehicle-mounted ECU, a vehicle speed sensor connected with the vehicle-mounted ECU, an ABS system and a driving system, and the ABS system provides real-time wheel slip rate s for the vehicle-mounted ECU during running of the vehicle; vehicle during runningECU-mounted driving force F obtained by a driving system d Driving force F d The unit of (2) is N;
the ECU stores the vehicle mass data determined by the vehicle manufacturer, the wind resistance coefficient of the vehicle, and the estimated value of the friction force identification parameter thetaIs a new value of (1) and vehicle speed estimation parameter>Initial value of (1), estimated gain K, on-line adaptive estimated law constant eta 3 The filter constant eta obtained by trial and error 1 And eta 2 ；
The invention is carried out according to the following steps:
the first step is to construct a basic equation and store the basic equation in the vehicle-mounted ECU;
the basic equation includes formulas one to ten;
the formula one is a vehicle driving dynamics equation:
in the formula I, m is the vehicle mass and is obtained by an on-board ECU, the unit is kg, v is the vehicle speed and is obtained by a vehicle speed sensor, F d F for driving force obtained by the drive system of the vehicle for the in-vehicle ECU f The tire road surface friction force obtained by the calculation of the formula ten is F a ＝C a v 2 C is wind resistance a The wind resistance coefficient is obtained by a vehicle-mounted ECU; alpha is a gradient angle, the unit is degree, and sin alpha is a sine function value of the gradient angle; g is the acceleration of gravity in meters per second squared;
the second formula is a continuous micro friction model:
F f ＝b 1 tanh(b 2 s)-b 3 tanh(b 4 s)+b 5 tanh(b 6 s)+b 7 s；
wherein F is f Is the friction between the tyre and the groundThe method comprises the steps of carrying out a first treatment on the surface of the The second formula is a continuous micro friction model, b 1 ,b 2 ,b 3 ,b 4 ,b 5 ，b 6 And b 7 S is the tire slip rate, and tanh is a mathematical tangent function;
in the formula II, b 2 ,b 4 ,b 6 The method is obtained by curve fitting through a magic formula;
b 1 ,b 3 ,b 5 ,b 7 the method is obtained through calculation of a formula III, the formula III is obtained by substituting the formula II into the formula I, and the formula III is an online estimation law:
in the formula III, s is the slip ratio of the wheel and is obtained by an ABS system;
transforming equation three to equation four:
in the fourth formula, θ is a friction force identification parameter, +.>
And θ obtains its estimated value from formula nine;
in formula four, ψ= [ -tanh (b 2 s),tanh(b 4 s),-tanh(b 6 s),-s,-g]The method comprises the steps of carrying out a first treatment on the surface of the g is the acceleration of gravity in meters per second squared;
the fifth formula is a first filtering variable formula:
in the fifth formula, η 1 The filter constant obtained for trial and error is stored in the vehicle-mounted ECU, v f A filter variable of v; psi phi type f A filter variable of ψ; v is the vehicle speed and is sensed by the vehicle speedObtaining by a device; by solving the first equation in equation fiveObtain v f The method comprises the steps of carrying out a first treatment on the surface of the By solving the second equation in equation five +.>Resulting in the parameter ψ used in equation seven f ；
Equation six is the second filter variable equation:
in the formula six, eta 2 And eta 1 All are filter constants obtained through trial and error and are stored in the vehicle-mounted ECU in advance, v f The method comprises the steps of obtaining by solving a first equation in a formula five; psi is expressed by the expression psi= [ -tanh (b) in formula four 2 s),tanh(b 4 s),-tanh(b 6 s),-s,-g]Calculating to obtain; g and H are auxiliary filtering variables, and the values of G and H are obtained through calculation according to a formula six;
the formula seven is:in the seventh formula, W is an online adaptive estimation law auxiliary variable;
is the estimated value of the friction force identification parameter theta, and the parameter is +.>Acquiring an initial value by the vehicle-mounted ECU; in the recursive calculation after the first calculation, the parameter in equation seven +.>The value of (2) is calculated by a formula nine in the previous calculation cycle;
the formula eight is:
in the formula eight, K is the estimated gain obtained by trial and error and is prestored in the vehicle-mounted ECU; e is the error of the estimation and,when the vehicle-mounted ECU is turned on and the first calculation formula eight is calculated after the vehicle runs,/>Taking an initial value stored in the vehicle-mounted ECU; in the recursive calculation after the first calculation, +.>Taking the +.sub.f calculated by equation eight in the previous calculation cycle>A value; when the vehicle-mounted ECU is turned on and the vehicle is first calculated after running, the parameters +.>Acquiring an initial value by the vehicle-mounted ECU; in the recursive calculation after the first calculation, the parameter in equation eight +.>The value of (2) is calculated by a formula nine in the previous calculation cycle;
the formula nine is:
in formula nine, eta 3 Obtaining and storing in advance in a vehicle-mounted ECU (electronic control unit) through a trial-and-error method for online self-adaptive estimation law constant;
by calculation ofObtaining b 1 ,b 3 ,b 5 ,b 7 Estimate of +.>Use b 1 ,b 3 ,b 5 ,b 7 Estimate of (2)Instead of b in equation 2 1 ,b 3 ,b 5 ,b 7 Then the formula ten is obtained;
the formula ten is:F f is the friction force between the tire and the road surface;
and a second step of:
during running of the vehicle, the vehicle-mounted ECU estimates the friction force F between the tire and the road surface on line according to the following substeps f A value;
the first substep is:
the vehicle-mounted ECU first calculates a value psi by a formula IV to serve as a calculation basis of a formula VI; v is calculated by the formula five f Value sum psi f The value is used as the calculation basis of a formula six;
the second substep is: the vehicle-mounted ECU calculates the values of the auxiliary filtering variables G and H through a formula six and takes the values as a calculation basis of a formula seven;
the third substep is: the vehicle-mounted ECU calculates the value of W through a formula seven and serves as a calculation basis of a formula nine;
the fourth substep is: the vehicle-mounted ECU calculates and obtains the estimated value of the friction force identification parameter through a formula nineFurther calculate b 1 ,b 3 ,b 5 ,b 7 Estimate of +.>And is used as a calculation basis of a formula ten;
fifth sonThe method comprises the following steps: the friction force F between the tire and the road surface under the current calculation cycle is obtained through the ten calculation of the formula f ；
The first sub-step to the fifth sub-step form a calculation cycle, and the calculation cycle is obtainedIs used as +.f in equation four, equation seven and equation eight in the next calculation cycle>Is a value of (2); and repeating the calculation cycle formed by the first sub-step to the fifth sub-step, and performing cyclic recursion calculation so as to perform real-time on-line estimation on the friction between the tire and the road surface in the running process of the motor vehicle.
In each calculation cycle of the cyclic recursion calculation, it is calculated by the formula eightAnd is calculated with formula nine>Comparing, let formula eight calculate +.>Is calculated from the value of (2) and the formula nine>The difference in the values of +.>If after more than 20 cyclic recursions +.>The vehicle ECU issues an error alert.
The invention has the following advantages:
the estimation method has the advantages of small calculated amount, high calculation speed, high error convergence speed in cyclic recursion calculation, accurate result and strong practicability.
The invention can calculate the real-time vehicle speed and the real-time wheel slip rate only by relying on the vehicle speed sensor and the ABS system, and the vehicle speed sensor and the ABS system are basically necessary components of the vehicle, so that the invention can realize the on-line quick estimation of the friction force between the tire and the road surface only by writing an algorithm into the vehicle-mounted ECU without additionally increasing the cost of accessories, thereby having extremely low realization cost and very high popularization and application value.
The invention checks the calculation process through the formula eight, ensures that the error can be quickly converged to the vicinity of the zero value under various conditions, and gives an alarm if the error can not be quickly converged to the vicinity of the zero value, and the designer adjusts the initial values of all the parameters and then tests the parameters again. The calculation formulas can ensure the convergence speed of errors in the cyclic recursion calculation, and the formula eight plays roles of verification and warning. Meanwhile, the error can be converged rapidly, which also shows the effectiveness of the estimation method of the invention.
Drawings
FIG. 1 is a schematic diagram of equation one;
fig. 2 is a graph of experimental results of the present invention applied to a passenger car.
In the second graph, the actual friction force is shown by a solid line, and the estimated value is shown by a broken line.
Detailed Description
The invention provides an online quick estimation method for friction force between a tire and a road surface, which is used for a motor vehicle, wherein the vehicle is provided with a vehicle-mounted ECU, a vehicle speed sensor connected with the vehicle-mounted ECU, an ABS system and a driving system, and the ABS system provides real-time wheel slip rate s for the vehicle-mounted ECU in the running process of the vehicle; the vehicle-mounted ECU obtains the driving force F by the driving system during the running process of the vehicle d Driving force F d Is in units of N (cattle);
the ECU stores the vehicle mass data determined by the vehicle manufacturer, the wind resistance coefficient of the vehicle, and the estimated value of the friction force identification parameter thetaIs>Initial value of (+)>And->The initial values of (2) are positive constants approaching 0, and are all smaller than 0.01, and are determined by a designer; the algorithm in the invention obtains the numerical pair ++of the friction force between the tire and the road surface through recursive calculation>And->Insensitive to initial values),%>Initial value of (1), estimated gain K, on-line adaptive estimated law constant eta 3 The filter constant eta obtained by trial and error 1 And eta 2 ；
The on-line rapid estimation method of the friction force between the tire and the road surface comprises the following steps:
the first step is to construct a basic equation and store the basic equation in the vehicle-mounted ECU;
the basic equation includes formulas one to ten;
the formula one is a vehicle driving dynamics equation:
in the formula I, m is the vehicle mass and is obtained by an on-board ECU, the unit is kg, v is the vehicle speed and is obtained by a vehicle speed sensor, F d F for driving force obtained by the drive system of the vehicle for the in-vehicle ECU f Calculated for the formula tenTire road surface friction force, F a ＝C a v 2 C is wind resistance a The wind resistance coefficient is obtained by a vehicle-mounted ECU; alpha is a gradient angle, the unit is degree, and sin alpha is a sine function value of the gradient angle; the gradient angle alpha is obtained by an inclination angle sensor connected with the vehicle-mounted ECU and arranged on the vehicle body, can be obtained by a GPS module connected with the vehicle-mounted ECU, can be obtained by an observer algorithm, and is obtained by a conventional technology and is not described in detail. g is the acceleration of gravity in meters per second squared;
the second formula is a continuous micro friction model:
F f ＝b 1 tanh(b 2 s)-b 3 tanh(b 4 s)+b 5 tanh(b 6 s)+b 7 s；
wherein F is f Is the friction between the tire and the ground; f (F) f It is difficult to directly measure through the sensor, the common practice is to calculate the friction through the magic formula that is commonly used, but because the relevant parameter value in the magic formula can only be obtained through off-line experimental data, the on-line update can not be realized along with the driving working condition, and therefore, the on-line real-time friction estimation can not be realized. Therefore, the invention provides a new continuous micro friction model as shown in a formula II; the formula II is a continuous micro friction model, b1, b2, b3, b4, b5, b6 and b7 are constant coefficients in the continuous micro friction model, s is the tire slip rate, and tanh is a mathematical tangent function;
in the formula II, b 2 ,b 4 ,b 6 The method is obtained by curve fitting through a magic formula; the magic formula is a well-known formula and is not described in detail.
b 1 ,b 3 ,b 5 ,b 7 The method is obtained through calculation of a formula III, the formula III is obtained by substituting the formula II into the formula I, and the formula III is an online estimation law:
in the formula III, s is the slip ratio of the wheel and is obtained by an ABS system;
transforming equation three to equation four:
in the fourth formula, θ is a friction force identification parameter, +.>
And θ obtains its estimated value from formula nine;
in formula four, ψ= [ -tanh (b 2 s),tanh(b 4 s),-tanh(b 6 s),-s,-g]The method comprises the steps of carrying out a first treatment on the surface of the g is the acceleration of gravity in meters per second squared;
the fifth formula is a first filtering variable formula:
in the fifth formula, η 1 The filter constant obtained for trial and error is stored in the vehicle-mounted ECU, v f A filter variable of v; psi phi type f A filter variable of ψ; v is the vehicle speed and is acquired by a vehicle speed sensor; by solving the first equation in equation fiveObtain v f The method comprises the steps of carrying out a first treatment on the surface of the By solving the second equation in equation five +.>Resulting in the parameter ψ used in equation seven f ；
Equation six is the second filter variable equation:
in the formula six, eta 2 And eta 1 All are filter constants obtained through trial and error and are stored in the vehicle-mounted ECU in advance, v f Obtained by solving the first equation in equation fiveThe method comprises the steps of carrying out a first treatment on the surface of the Psi is expressed by the expression psi= [ -tanh (b) in formula four 2 s),tanh(b 4 s),-tanh(b 6 s),-s,-g]Calculating to obtain; g and H are auxiliary filtering variables, and the values of G and H are obtained through calculation according to a formula six;
the formula seven is:in the seventh formula, W is an online adaptive estimation law auxiliary variable;
is the estimated value of the friction force identification parameter theta, and the parameter is +.>Acquiring an initial value by the vehicle-mounted ECU; in the recursive calculation after the first calculation, the parameter in equation seven +.>The value of (2) is calculated by a formula nine in the previous calculation cycle;
the formula eight is:
in the formula eight, K is the estimated gain obtained by trial and error and is prestored in the vehicle-mounted ECU; e is the error of the estimation and,when the vehicle-mounted ECU is turned on and the first calculation formula eight is calculated after the vehicle runs,/>Taking an initial value stored in the vehicle-mounted ECU; in the recursive calculation after the first calculation, +.>Taking the +.sub.f calculated by equation eight in the previous calculation cycle>A value; when the vehicle-mounted ECU is turned on and the vehicle is first calculated after running, the parameters +.>Acquiring an initial value by the vehicle-mounted ECU; in the recursive calculation after the first calculation, the parameter in equation eight +.>The value of (2) is calculated by a formula nine in the previous calculation cycle;
the formula nine is:
in formula nine, eta 3 Obtaining and storing in advance in a vehicle-mounted ECU (electronic control unit) through a trial-and-error method for online self-adaptive estimation law constant;
by calculation ofObtaining b 1 ,b 3 ,b 5 ,b 7 Estimate of +.>Use b 1 ,b 3 ,b 5 ,b 7 Estimate of (2)Instead of b in equation 2 1 ,b 3 ,b 5 ,b 7 Then the formula ten is obtained;
the formula ten is:F f is the friction force between the tire and the road surface;
and a second step of:
during running of the vehicle, the vehicle-mounted ECU estimates the friction force F between the tire and the road surface on line according to the following substeps f A value;
the first substep is:
the vehicle-mounted ECU first calculates a value psi by a formula IV to serve as a calculation basis of a formula VI; v is calculated by the formula five f Value sum psi f The value is used as the calculation basis of a formula six;
the second substep is: the vehicle-mounted ECU calculates the values of the auxiliary filtering variables G and H through a formula six and takes the values as a calculation basis of a formula seven;
the third substep is: the vehicle-mounted ECU calculates the value of W through a formula seven and serves as a calculation basis of a formula nine;
the fourth substep is: the vehicle-mounted ECU calculates and obtains the estimated value of the friction force identification parameter through a formula nineFurther calculate b 1 ,b 3 ,b 5 ,b 7 Estimate of +.>And is used as a calculation basis of a formula ten;
the fifth substep is: the friction force F between the tire and the road surface under the current calculation cycle is obtained through the ten calculation of the formula f ；
The first sub-step to the fifth sub-step form a calculation cycle, and the calculation cycle is obtainedIs used as +.f in equation four, equation seven and equation eight in the next calculation cycle>Is a value of (2); and repeating the calculation cycle formed by the first sub-step to the fifth sub-step, and performing cyclic recursion calculation so as to perform real-time on-line estimation on the friction between the tire and the road surface in the running process of the motor vehicle.
The estimation method has the advantages of small calculated amount, high calculation speed, high error convergence speed in cyclic recursion calculation, accurate result and strong practicability.
The invention can calculate the real-time vehicle speed and the real-time wheel slip rate only by relying on the vehicle speed sensor and the ABS system, and the vehicle speed sensor and the ABS system are basically necessary components of the vehicle, so that the invention can realize the on-line quick estimation of the friction force between the tire and the road surface only by writing an algorithm into the vehicle-mounted ECU without additionally increasing the cost of accessories, thereby having extremely low realization cost and very high popularization and application value.
In each calculation cycle of the cyclic recursion calculation, it is calculated by the formula eightAnd is calculated with formula nine>Comparing, let formula eight calculate +.>Is calculated from the value of (2) and the formula nine>The difference in the values of +.>If after more than 20 cyclic recursions +.>The vehicle ECU issues an error alert.
The invention checks the calculation process through the formula eight, ensures that the error can be quickly converged to the vicinity of the zero value under various conditions, and gives an alarm if the error can not be quickly converged to the vicinity of the zero value, and the designer adjusts the initial values of all the parameters and then tests the parameters again. The calculation formulas can ensure the convergence speed of errors in the cyclic recursion calculation, and the formula eight plays roles of verification and warning. Meanwhile, the error can be converged rapidly, which also shows the effectiveness of the estimation method of the invention.
The invention is adopted to test and verify a certain passenger car. The result of friction estimation of the driving wheel under the straight running condition of the vehicle speed of 20Km/h (Km/h) is shown in fig. 2.
The control result shows that the method provided by the invention can accurately and rapidly realize the online rapid estimation of the friction force between the tire and the road surface.
The above embodiments are only for illustrating the technical solution of the present invention, and it should be understood by those skilled in the art that although the present invention has been described in detail with reference to the above embodiments: modifications and equivalents may be made thereto without departing from the spirit and scope of the invention, which is intended to be encompassed by the claims.

Claims (2)

1. The on-line quick estimation method of the friction force between the tire and the road surface is used for motor vehicles, the vehicle is provided with a vehicle-mounted ECU, a vehicle speed sensor, an ABS system and a driving system, wherein the vehicle speed sensor, the ABS system and the driving system are connected with the vehicle-mounted ECU, and the ABS system provides real-time wheel slip rate s for the vehicle-mounted ECU in the running process of the vehicle; the vehicle-mounted ECU obtains the driving force F by the driving system during the running process of the vehicle d Driving force F d The unit of (2) is N;
the ECU stores the vehicle mass data determined by the vehicle manufacturer, the wind resistance coefficient of the vehicle, and the estimated value of the friction force identification parameter thetaIs a new value of (1) and vehicle speed estimation parameter>Initial value of (1), estimated gain K, on-line adaptive estimated law constant eta 3 The filter constant eta obtained by trial and error 1 And eta 2 ；
The method is characterized by comprising the following steps of:
the first step is to construct a basic equation and store the basic equation in the vehicle-mounted ECU;
the basic equation includes formulas one to ten;
the formula one is a vehicle driving dynamics equation:
in the formula I, m is the vehicle mass and is obtained by an on-board ECU, the unit is kg, v is the vehicle speed and is obtained by a vehicle speed sensor, F d F for driving force obtained by the drive system of the vehicle for the in-vehicle ECU f The tire road surface friction force obtained by the calculation of the formula ten is F a ＝C a v 2 C is wind resistance a The wind resistance coefficient is obtained by a vehicle-mounted ECU; alpha is a gradient angle, the unit is degree, and sin alpha is a sine function value of the gradient angle; g is the acceleration of gravity in meters per second squared;
the second formula is a continuous micro friction model:
F f ＝b 1 tanh(b 2 s)-b 3 tanh(b 4 s)+b 5 tanh(b 6 s)+b 7 s；
wherein F is f Is the friction between the tire and the ground; the second formula is a continuous micro friction model, b 1 ,b 2 ,b 3 ,b 4 ,b 5 ，b 6 And b 7 S is the tire slip rate, and tanh is a mathematical tangent function;
in the formula II, b 2 ,b 4 ,b 6 The method is obtained by curve fitting through a magic formula;
b 1 ,b 3 ,b 5 ,b 7 the method is obtained through calculation of a formula III, the formula III is obtained by substituting the formula II into the formula I, and the formula III is an online estimation law:
in the formula III, s is the slip ratio of the wheel and is obtained by an ABS system;
transforming equation three to equation four:
in the fourth formula, θ is a friction force identification parameter, +.>
And θ obtains its estimated value from formula nine;
in formula four, ψ= [ -tanh (b 2 s),tanh(b 4 s),-tanh(b 6 s),-s,-g]The method comprises the steps of carrying out a first treatment on the surface of the g is the acceleration of gravity in meters per second squared;
the fifth formula is a first filtering variable formula:
in the fifth formula, η 1 The filter constant obtained for trial and error is stored in the vehicle-mounted ECU, v f A filter variable of v; psi phi type f A filter variable of ψ; v is the vehicle speed and is acquired by a vehicle speed sensor; by solving the first equation in equation fiveObtain v f The method comprises the steps of carrying out a first treatment on the surface of the By solving the second equation in equation five +.>Resulting in the parameter ψ used in equation seven f ；
Equation six is the second filter variable equation:
in the formula six, eta 2 And eta 1 All are filters obtained by trial and errorConstant and prestore in vehicle-mounted ECU, v f The method comprises the steps of obtaining by solving a first equation in a formula five; psi is expressed by the expression psi= [ -tanh (b) in formula four 2 s),tanh(b 4 s),-tanh(b 6 s),-s,-g]Calculating to obtain; g and H are auxiliary filtering variables, and the values of G and H are obtained through calculation according to a formula six;
the formula seven is:in the seventh formula, W is an online adaptive estimation law auxiliary variable;
is the estimated value of the friction force identification parameter theta, and the parameter is +.>Acquiring an initial value by the vehicle-mounted ECU; in the recursive calculation after the first calculation, the parameter in equation seven +.>The value of (2) is calculated by a formula nine in the previous calculation cycle;
the formula eight is:
in the formula eight, K is the estimated gain obtained by trial and error and is prestored in the vehicle-mounted ECU; e is the error of the estimation and,when the vehicle-mounted ECU is turned on and the first calculation formula eight is calculated after the vehicle runs,/>Taking an initial value stored in the vehicle-mounted ECU; in the recursive calculation after the first calculation, +.>Taking the +.sub.f calculated by equation eight in the previous calculation cycle>A value; when the vehicle-mounted ECU is turned on and the vehicle is first calculated after running, the parameters +.>Acquiring an initial value by the vehicle-mounted ECU; in the recursive calculation after the first calculation, the parameter in equation eight +.>The value of (2) is calculated by a formula nine in the previous calculation cycle;
the formula nine is:
in formula nine, eta 3 Obtaining and storing in advance in a vehicle-mounted ECU (electronic control unit) through a trial-and-error method for online self-adaptive estimation law constant;
by calculation ofObtaining b 1 ,b 3 ,b 5 ,b 7 Estimate of +.>Use b 1 ,b 3 ,b 5 ,b 7 Estimate of (2)Instead of b in equation 2 1 ,b 3 ,b 5 ,b 7 Then the formula ten is obtained;
the formula ten is:F f is the friction force between the tire and the road surface;
and a second step of:
during running of the vehicle, the vehicle-mounted ECU estimates the friction force F between the tire and the road surface on line according to the following substeps f A value;
the first substep is:
the vehicle-mounted ECU first calculates a value psi by a formula IV to serve as a calculation basis of a formula VI; v is calculated by the formula five f Value sum psi f The value is used as the calculation basis of a formula six;
the second substep is: the vehicle-mounted ECU calculates the values of the auxiliary filtering variables G and H through a formula six and takes the values as a calculation basis of a formula seven;
the third substep is: the vehicle-mounted ECU calculates the value of W through a formula seven and serves as a calculation basis of a formula nine;
the fourth substep is: the vehicle-mounted ECU calculates and obtains the estimated value of the friction force identification parameter through a formula nineFurther calculate b 1 ,b 3 ,b 5 ,b 7 Estimate of +.>And is used as a calculation basis of a formula ten;
the fifth substep is: the friction force F between the tire and the road surface under the current calculation cycle is obtained through the ten calculation of the formula f ；
The first sub-step to the fifth sub-step form a calculation cycle, and the calculation cycle is obtainedIs used as +.f in equation four, equation seven and equation eight in the next calculation cycle>Is a value of (2); heavy weightAnd carrying out calculation circulation formed by the first sub-step to the fifth sub-step, and carrying out circulation recursion calculation, so that the friction force between the tire and the road surface is estimated on line in real time in the running process of the motor vehicle.
2. The method for online rapid estimation of friction between a tire and a road surface according to claim 1, wherein:
in each calculation cycle of the cyclic recursion calculation, it is calculated by the formula eightAnd calculated with equation nineComparing, let formula eight calculate +.>Is calculated from the value of (2) and the formula nine>The difference in the values of +.>If after more than 20 cyclic recursions +.>The vehicle ECU issues an error alert.
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