CN105667520B - A kind of front-wheel side force method of estimation of distributed driving electric car - Google Patents

A kind of front-wheel side force method of estimation of distributed driving electric car Download PDF

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CN105667520B
CN105667520B CN201610108400.3A CN201610108400A CN105667520B CN 105667520 B CN105667520 B CN 105667520B CN 201610108400 A CN201610108400 A CN 201610108400A CN 105667520 B CN105667520 B CN 105667520B
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CN105667520A (en
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丁世宏
张圣道
马莉
江浩斌
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Jiangsu University
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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
    • B60W40/10—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 related to vehicle motion
    • 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
    • B60W2510/00—Input parameters relating to a particular sub-units
    • B60W2510/08—Electric propulsion units
    • B60W2510/083—Torque
    • 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
    • B60W2520/10—Longitudinal speed
    • B60W2520/105—Longitudinal acceleration
    • 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
    • B60W2520/12—Lateral 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
    • B60W2520/12—Lateral speed
    • B60W2520/125—Lateral acceleration
    • 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
    • B60W2520/28—Wheel speed

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  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Mathematical Physics (AREA)
  • Transportation (AREA)
  • Mechanical Engineering (AREA)
  • Steering Control In Accordance With Driving Conditions (AREA)
  • Control Of Driving Devices And Active Controlling Of Vehicle (AREA)
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Abstract

The invention discloses a kind of front-wheel side force method of estimation of distributed driving electric car, mainly comprise the following steps：1, the car status information collected according to various sensors, sliding formwork longitudinal direction force observer is devised based on dynamics of vehicle equation the longitudinal force of tire is estimated in real time；2, each wheel longitudinal force of estimation and longitudinal acceleration signal, lateral acceleration signal, yaw rate signal etc. are transferred to the lateral force observer of sliding formwork, obtain the side force estimate of off-front wheel；3, by filtration module, to the further optimization processing of side force estimated, solve the singular problem occurred in side force estimate, so as to export two final front-wheel side force estimates；Advantages of the present invention：Using Second Order Sliding Mode observer, the real-time of calculating on the one hand ensure that；On the other hand, there is good robustness to the uncertain disturbance that original system is brought to different road surface and tire characteristics, so as to improve crosswise joint effect, keeps the stability of output.

Description

Method for estimating lateral force of front wheel of distributed driving electric vehicle
Technical Field
The invention relates to a method for estimating a lateral force of a tire in vehicle running, in particular to the estimation of the lateral force of a front steering wheel of a distributed drive electric vehicle.
Background
Electric vehicles are becoming an increasingly important part of the automotive industry in the future, against the background of environmental and energy issues. In recent years, an In-wheel motor Electric (IEV) has been receiving widespread attention from researchers. The wheel is driven by a wheel hub motor arranged in a wheel hub or two motors arranged at the position of a differential mechanism, so that power is provided for the whole vehicle. The IEV has the advantages of high corresponding speed, short transmission chain, high transmission efficiency and the like, and is an important development direction in the field of electric automobiles.
Currently, there are still places where improvement is needed for IEV lateral stability control, such as where tire lateral force cannot be accurately estimated under extreme conditions. Notably, tire lateral forces are an important component of lateral dynamics, affecting vehicle ride safety and stability. Therefore, accurate estimation of the tire lateral force will effectively improve the lateral control effect.
Conventional tire lateral force estimation relies on a tire model. Various non-linear tire models have been developed in China and abroad. The Dugoff model establishes expressions representing the relationship among driving (braking) force, cornering force, slip rate, cornering angle and other parameters of the tire according to experimental data; the UniTire model is a semi-empirical tire model proposed by Kuo-Konghui and has the characteristic of meeting high-order theoretical boundary conditions; the Magic Formula model establishes the relationship between the longitudinal force, the lateral force and the aligning moment of the tire and the slip angle, the slip rate, the roll angle and the vertical load by utilizing a sine function. The tire model can estimate the tire force relatively accurately, but the tire lateral force in the tire model is directly related to factors such as a tire slip angle, a vertical load, a longitudinal slip rate and a wheel speed, namely, the related variables are more, a large amount of test data fitting needs to be carried out, the calculated amount is large, and the algorithm of the tire model is complex, so that the requirement of quick response in the application of a real vehicle controller is difficult to meet. Furthermore, with the lateral force estimation method based on a tire model, once the tire characteristics (tire air pressure, wear degree, etc.) or road surface conditions change rapidly, the fitting accuracy will decrease rapidly, so that the tire lateral force estimation is not accurate, resulting in the lateral control effect being affected. It is therefore necessary to propose a lateral force estimation method that is independent of the tire model.
Disclosure of Invention
In order to solve the problem that the estimation of the lateral force of the tire depends on a tire model too much at present, the invention provides a method for estimating the lateral force of a front steering wheel of a distributed driving electric vehicle, which can estimate the lateral force on the basis of getting rid of the tire model. The method considers the real-time characteristics of the vehicle tire and the change of the road surface condition, and can accurately estimate the lateral force of the tire, thereby improving the transverse control effect of the vehicle. The estimation process is as follows:
1) during the running of the vehicle, the wheel motor controller measures the real-time driving torque T required by each motorijThe wheel speed sensor measures a real-time wheel speed signal omegaij. The driving moment signal and the wheel speed signal are sent to the sliding mode longitudinal force estimation module based on the wheel rotation dynamics, and the sliding mode longitudinal force estimation module obtains the value estimation of the tire longitudinal force according to the real-time collected signals
As described aboveTij、ωijWhere i ═ f, r, f denote front wheels, r denotes rear wheels; j ═ l, r, l denote the left wheel and r denotes the right wheel;
2) the longitudinal acceleration sensor and the lateral acceleration sensor measure real-time longitudinal acceleration signals axAnd a lateral acceleration signal ay(ii) a The longitudinal speed sensor and the lateral speed sensor measure real-time longitudinal speed VxAnd lateral velocity Vy(ii) a Furthermore, the vehicle yaw rate sensor measures a real-time yaw rate signal r and the steering wheel angle sensor measures a steering wheel angle signal δ;
steering wheel angle signal, yaw rate signal, longitudinal acceleration signal, lateral acceleration signal, and longitudinal speed signalSign, lateral velocity signal and estimated longitudinal forceSending the lateral force to a sliding mode lateral force estimation module based on vehicle dynamics, and estimating the lateral force of the front right wheel through calculation by the sliding mode lateral force estimation module
3) And finally, sending the estimated lateral force of the right front wheel and a steering wheel corner signal to the filtering module, aiming at the singular phenomenon appearing in the lateral force estimated value, the filtering module adopts a method of carrying out linearization processing near a singular point so as to output a more accurate lateral force value of the right front wheel, and then further calculating to obtain a lateral force value of the left front wheel, thus obtaining the lateral force estimated values of the two front wheels.
The parameters used in the estimation method process are obtained based on the following measurement parts: the steering wheel angle signal δ is measured by a steering wheel angle sensor, the yaw rate signal r is measured by a yaw rate sensor, and the longitudinal acceleration signal axThe lateral acceleration signal a measured by a longitudinal acceleration sensorySaid longitudinal speed signal V measured by a lateral acceleration sensorxThe lateral speed signal V measured by a longitudinal speed sensoryMeasured by a lateral velocity sensor.
Compared with the prior art, the invention has the beneficial effects that:
1) according to the method, a complex nonlinear tire model is not needed, the tire lateral force is estimated by only applying the second-order sliding-mode observer, the calculation is simple and convenient, and the accuracy and the calculation real-time performance are ensured.
2) The invention can realize accurate estimation of the lateral force of the tire by applying the existing easily-obtained signals in the vehicle state without other expensive sensors, and has lower cost.
3) The invention utilizes a second-order sliding mode observer designed by a Super-spiral algorithm (Super-twist), and the observer has quick convergence and strong robustness to uncertain disturbances such as air resistance, friction coefficient of tires and the like in a vehicle system, namely has strong adaptability to a complex environment.
Drawings
FIG. 1 is a system diagram of the present invention.
Detailed Description
The invention provides a method for estimating lateral force of a front wheel of a distributed electric vehicle. In order to make the objects, technical solutions and effects of the present invention clearer and clearer, the present invention is further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Fig. 1 is a schematic diagram showing a system relationship of tire lateral force estimation according to the present invention, which includes a wheel side motor controller, a wheel speed sensor, a sliding mode longitudinal force estimation module, a vehicle yaw rate sensor, a vehicle longitudinal acceleration sensor, a vehicle lateral acceleration sensor, a vehicle longitudinal speed sensor, a vehicle lateral speed sensor, a steering wheel rotation angle sensor, a sliding mode lateral force estimation module, and a filter module.
Based on the above system, the method of estimating the tire lateral force of the front wheels (steered wheels) of the vehicle during running according to the present invention is explained below by way of implementation:
the vehicle parameters used are shown in Table 1, and the selected test conditions were 72km/h and serpentine.
TABLE 1 vehicle parameters
Vehicle mass m(kg) 1464
Moment of inertia about z-axis Iz(kg/m2) 2400
Distance from center of mass to front axle a(mm) 1256
Distance from center of mass to rear axle b(mm) 1368
Front wheel base df(mm) 1450
Rear wheel base dr(mm) 1450
Height of center of mass from ground hg(mm) 500
Moment of inertia of wheel Iω(kg/m2) 2.1
Rolling radius of wheel R(mm) 310
1) Wheel rotation dynamics-based sliding mode longitudinal force estimation module acquires tire central speed signal omega in real time according to wheel speed sensorijAnd each tire driving torque signal T acquired by the wheel side controller in real timeijAnd a sliding mode observer is designed by applying a sliding mode observation theory to observe the longitudinal force of the four tires.
The wheel rotational kinetic equation is
Equation (1) can be rewritten as
Wherein x is1＝ωijInput variableRegarded as unknown disturbances and y is the output quantity.
Based on the supercoiling algorithm, the following second-order sliding-mode observer is designed as
According to the finite time convergence theory, there is a time constant T1Is provided with
Further calculating to obtain the longitudinal force of the wheel
Wherein,is x1Is determined by the estimated value of (c),is F1Is estimated andis FxijAn estimate of (d).
2) Based on a seven-degree-of-freedom model of a vehicle, a method for calculating the lateral force of the right front wheel in a sliding-mode lateral force estimation module is as follows
The longitudinal dynamic equation of the vehicle is
m(ax-Vyr)＝(Fxfl+Fxfr)cos-(Fyfl+Fyfr)sinδ+Fxrl+Fxrr. (2)
The lateral dynamic equation of the vehicle is
m(ay+Vxr)＝(Fxfl+Fxfr)sinδ+(Fyfl+Fyfr)cosδ+Fyrl+Fyrr. (3)
The yaw dynamics equation of the vehicle is
Equations (2), (3) can be rewritten as
Substituting equation (5) into equation (4) yields
It is to be noted that the steering wheel angle δ, the yaw rate r, and the vehicle longitudinal acceleration a in equations (5) and (6)xVehicle lateral acceleration ayVehicle longitudinal speed VxAnd lateral velocity VyRespectively, can be measured by the corresponding sensors, and the longitudinal force F thereinxijLongitudinal force estimated by sliding mode longitudinal force estimation moduleInstead. Thus, the right half of equation (6) has only FyfrIs an unknown quantity, and others are known quantities.
Thus, equation (6) can be rewritten as
In the formula,
designing a second-order sliding-mode observer according to the supercoiling algorithm again as
Similarly, when T is more than or equal to T2(T2> 0), the observed value can accurately track the actual value of the device, i.e. the measured value
Thus, an estimated value of the right front wheel lateral force is calculated as
From the equation (7), it is not difficult to find that the denominator contains a sin δ term, and when the steering angle δ is zero, this results in thatBecomes infinite, which is not allowed. In order to solve the problem, the filtering module takes a small interval near the zero point, and then makes a straight line with the head point and the tail point of the interval to replace the change of the original lateral force estimated value in the interval. In other words, the final longitudinal force estimate is in the form of a piecewise function that is a linear equation over the interval taken, with the signal output intact outside the interval.
In the formula (8), T is a time constant, and when T ═ T, the steering angle δ is zero; Δ is the neighborhood radius centered at point T;the lateral force estimates for the right front wheel and the left front wheel, respectively.
While the invention has been described in terms of various specific embodiments, those skilled in the art will recognize that the invention can be practiced with modification within the spirit and scope of the claims.

Claims (4)

1. A method for estimating the lateral force of a front wheel of a distributed driving electric vehicle is characterized by comprising the following steps:
1) in the running process of the vehicle, the torque T required by each motor and measured by the wheel motor controllerijAnd a wheel speed signal omega detected by a wheel speed sensorijSending the signals to a sliding mode longitudinal force estimation module, and calculating the longitudinal force estimation value of the tire by the sliding mode longitudinal force estimation module according to the signals acquired in real time
Estimation of tire longitudinal forceThe specific calculation of (a) is as follows:
1-1) establishing a wheel rotation dynamic equation as follows:
<mrow> <msub> <mi>I</mi> <mi>&amp;omega;</mi> </msub> <msub> <mover> <mi>&amp;omega;</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>T</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>RF</mi> <mrow> <mi>x</mi> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
rewriting equation (1) to
<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mfrac> <mrow> <msub> <mi>dx</mi> <mn>1</mn> </msub> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <msub> <mi>u</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>F</mi> <mn>1</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>y</mi> <mo>=</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced>
Wherein x is1＝ωijInput variableAs unknown disturbance, y is the output quantity;
1-2) designing a second-order sliding-mode observer based on a supercoiling algorithm:
<mrow> <mtable> <mtr> <mtd> <mrow> <mfrac> <mrow> <mi>d</mi> <mover> <mi>x</mi> <mo>^</mo> </mover> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <msub> <mi>u</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>=</mo> <mo>-</mo> <msub> <mi>&amp;lambda;</mi> <mn>1</mn> </msub> <msup> <mrow> <mo>|</mo> <mrow> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> </mrow> <mo>|</mo> </mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </msup> <mi>s</mi> <mi>i</mi> <mi>g</mi> <mi>n</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>z</mi> <mn>2</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mtable> <mtr> <mtd> <mrow> <mfrac> <mrow> <msub> <mi>dz</mi> <mn>2</mn> </msub> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <mo>-</mo> <msub> <mi>&amp;lambda;</mi> <mn>0</mn> </msub> <mi>s</mi> <mi>i</mi> <mi>g</mi> <mi>n</mi> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mo>(</mo> <msub> <mi>&amp;lambda;</mi> <mn>0</mn> </msub> <mo>&gt;</mo> <mn>0</mn> <mo>,</mo> <msub> <mi>&amp;lambda;</mi> <mn>1</mn> </msub> <mo>&gt;</mo> <mn>0</mn> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mtd> </mtr> </mtable> <mo>;</mo> </mrow>
1-3) according to the finite time convergence theory, there is a certain constant T1(T1> 0) so that
Thus, the estimated value of the wheel longitudinal force is:
<mrow> <msub> <mover> <mi>F</mi> <mo>^</mo> </mover> <mrow> <mi>x</mi> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mo>-</mo> <mfrac> <msub> <mi>I</mi> <mi>&amp;omega;</mi> </msub> <mi>R</mi> </mfrac> <msub> <mover> <mi>F</mi> <mo>^</mo> </mover> <mn>1</mn> </msub> </mrow>
wherein,is x1Is determined by the estimated value of (c),is F1Is estimated andis FxijAn estimated value of (d);
wherein i ═ f, r, f denote front wheels, r denotes rear wheels; j ═ l, r, l denote the left wheel and r denotes the right wheel;
2) a steering wheel angle signal delta, a yaw rate signal r and a longitudinal acceleration signal axLateral acceleration signal ayLongitudinal velocity signal VxLateral velocity signal VyAnd the longitudinal force estimated by the sliding mode longitudinal force estimation moduleTransmitted to a sliding mode lateral force estimation module based on vehicle dynamics, which estimates the lateral force of the front right wheel
3) Sending the lateral force of the right front wheel estimated by the sliding mode lateral force estimation module and a steering wheel corner signal delta to the filtering module; the filtering module carries out linearization processing on the estimated right front wheel lateral force near the moment when the steering wheel corner signal delta is zero, outputs an accurate right front wheel lateral force estimated value, and obtains a left front wheel lateral force estimated value through simple calculation, thereby obtaining a final two front wheel lateral force estimated value.
2. The method of estimating lateral force of front wheel of a distributed-drive electric vehicle according to claim 1, wherein said steering wheel angle signal δ is measured by a steering wheel angle sensor, said yaw rate signal r is measured by a yaw rate sensor, and said longitudinal acceleration signal axThe lateral acceleration signal a measured by a longitudinal acceleration sensorySaid longitudinal speed signal V measured by a lateral acceleration sensorxThe lateral speed signal V measured by a longitudinal speed sensoryMeasured by a lateral velocity sensor.
3. The front wheel lateral force estimation method of a distributed-drive electric vehicle according to claim 1, wherein in the step 2), the right front lateral force estimation is estimated in a sliding mode lateral force estimation moduleWheel side forceThe method comprises the following steps:
2-1) establishing a longitudinal kinetic equation of
m(ax-Vyr)＝(Fxfl+Fxfr)cosδ-(Fyfl+Fyfr)sinδ+Fxrl+Fxrr(2)
The lateral kinetic equation is
m(ay+Vxr)＝(Fxfl+Fxfr)sinδ+(Fyfl+Fyfr)cosδ+Fyrl+Fyrr(3)
The yaw kinetic equation is
<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>I</mi> <mi>Z</mi> </msub> <mover> <mi>r</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mi>a</mi> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <msub> <mi>F</mi> <mrow> <mi>x</mi> <mi>f</mi> <mi>l</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>F</mi> <mrow> <mi>x</mi> <mi>f</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>sin</mi> <mi>&amp;delta;</mi> <mo>+</mo> <mrow> <mo>(</mo> <msub> <mi>F</mi> <mrow> <mi>y</mi> <mi>f</mi> <mi>l</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>F</mi> <mrow> <mi>y</mi> <mi>f</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>cos</mi> <mi>&amp;delta;</mi> <mo>&amp;rsqb;</mo> <mo>-</mo> <mi>b</mi> <mrow> <mo>(</mo> <msub> <mi>F</mi> <mrow> <mi>y</mi> <mi>r</mi> <mi>l</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>F</mi> <mrow> <mi>y</mi> <mi>r</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <mfrac> <msub> <mi>d</mi> <mi>f</mi> </msub> <mn>2</mn> </mfrac> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <msub> <mi>F</mi> <mrow> <mi>x</mi> <mi>f</mi> <mi>r</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>F</mi> <mrow> <mi>x</mi> <mi>f</mi> <mi>l</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>cos</mi> <mi>&amp;delta;</mi> <mo>+</mo> <mrow> <mo>(</mo> <msub> <mi>F</mi> <mrow> <mi>y</mi> <mi>f</mi> <mi>l</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>F</mi> <mrow> <mi>y</mi> <mi>f</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>sin</mi> <mi>&amp;delta;</mi> <mo>&amp;rsqb;</mo> <mo>+</mo> <mfrac> <msub> <mi>d</mi> <mi>r</mi> </msub> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <msub> <mi>F</mi> <mrow> <mi>x</mi> <mi>r</mi> <mi>r</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>F</mi> <mrow> <mi>x</mi> <mi>r</mi> <mi>l</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
2-2) rewriting equations (2), (3) to
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>F</mi> <mrow> <mi>y</mi> <mo>,</mo> <mi>f</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>F</mi> <mrow> <mi>y</mi> <mi>f</mi> <mi>l</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>F</mi> <mrow> <mi>y</mi> <mi>f</mi> <mi>r</mi> </mrow> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mo>-</mo> <mi>m</mi> <mo>(</mo> <mrow> <msub> <mi>a</mi> <mi>x</mi> </msub> <mo>-</mo> <msub> <mi>V</mi> <mi>y</mi> </msub> <mi>r</mi> </mrow> <mo>)</mo> <mo>+</mo> <mo>(</mo> <mrow> <msub> <mi>F</mi> <mrow> <mi>x</mi> <mi>f</mi> <mi>l</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>F</mi> <mrow> <mi>x</mi> <mi>f</mi> <mi>r</mi> </mrow> </msub> </mrow> <mo>)</mo> <mi>cos</mi> <mi>&amp;delta;</mi> <mo>+</mo> <msub> <mi>F</mi> <mrow> <mi>x</mi> <mi>r</mi> <mi>l</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>F</mi> <mrow> <mi>x</mi> <mi>r</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>/</mo> <mi>sin</mi> <mi>&amp;delta;</mi> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>F</mi> <mrow> <mi>y</mi> <mo>,</mo> <mi>r</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>F</mi> <mrow> <mi>y</mi> <mi>r</mi> <mi>l</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>F</mi> <mrow> <mi>y</mi> <mi>r</mi> <mi>r</mi> </mrow> </msub> <mo>=</mo> <mi>m</mi> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mi>y</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>x</mi> </msub> <mi>r</mi> <mo>)</mo> </mrow> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>F</mi> <mrow> <mi>x</mi> <mi>f</mi> <mi>l</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>F</mi> <mrow> <mi>x</mi> <mi>f</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>sin</mi> <mi>&amp;delta;</mi> <mo>-</mo> <msub> <mi>F</mi> <mrow> <mi>y</mi> <mo>,</mo> <mi>f</mi> </mrow> </msub> <mi>cos</mi> <mi>&amp;delta;</mi> <mo>.</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
2-3) substituting equation (5) into (4) to obtain
<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>I</mi> <mi>Z</mi> </msub> <mover> <mi>r</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mi>a</mi> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <msub> <mi>F</mi> <mrow> <mi>x</mi> <mi>f</mi> <mi>l</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>F</mi> <mrow> <mi>x</mi> <mi>f</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>&amp;delta;</mi> <mo>+</mo> <msub> <mi>F</mi> <mrow> <mi>y</mi> <mo>,</mo> <mi>f</mi> </mrow> </msub> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;delta;</mi> <mo>&amp;rsqb;</mo> <mo>-</mo> <msub> <mi>bF</mi> <mrow> <mi>y</mi> <mo>,</mo> <mi>r</mi> </mrow> </msub> <mo>+</mo> <mfrac> <msub> <mi>d</mi> <mi>f</mi> </msub> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <msub> <mi>F</mi> <mrow> <mi>x</mi> <mi>f</mi> <mi>r</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>F</mi> <mrow> <mi>x</mi> <mi>f</mi> <mi>l</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>cos</mi> <mi>&amp;delta;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <mfrac> <msub> <mi>d</mi> <mi>f</mi> </msub> <mn>2</mn> </mfrac> <msub> <mi>F</mi> <mrow> <mi>y</mi> <mo>,</mo> <mi>f</mi> </mrow> </msub> <mi>sin</mi> <mi>&amp;delta;</mi> <mo>-</mo> <msub> <mi>d</mi> <mi>f</mi> </msub> <msub> <mi>F</mi> <mrow> <mi>y</mi> <mi>f</mi> <mi>r</mi> </mrow> </msub> <mi>sin</mi> <mi>&amp;delta;</mi> <mo>+</mo> <mfrac> <msub> <mi>d</mi> <mi>r</mi> </msub> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <msub> <mi>F</mi> <mrow> <mi>x</mi> <mi>r</mi> <mi>r</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>F</mi> <mrow> <mi>x</mi> <mi>r</mi> <mi>l</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>.</mo> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
2-4) equation (6) is rewritten as
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mover> <mi>r</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <msub> <mi>u</mi> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>F</mi> <mn>2</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>y</mi> <mn>2</mn> </msub> <mo>=</mo> <mi>r</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>
Wherein,
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>u</mi> <mn>2</mn> </msub> <mo>=</mo> <mo>&amp;lsqb;</mo> <mi>a</mi> <mrow> <mo>(</mo> <msub> <mi>F</mi> <mrow> <mi>x</mi> <mi>f</mi> <mi>l</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>F</mi> <mrow> <mi>x</mi> <mi>f</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>sin</mi> <mi>&amp;delta;</mi> <mo>+</mo> <msub> <mi>aF</mi> <mrow> <mi>y</mi> <mo>,</mo> <mi>f</mi> </mrow> </msub> <mi>cos</mi> <mi>&amp;delta;</mi> <mo>-</mo> <msub> <mi>bF</mi> <mrow> <mi>y</mi> <mo>,</mo> <mi>r</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <mfrac> <msub> <mi>d</mi> <mi>f</mi> </msub> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <msub> <mi>F</mi> <mrow> <mi>x</mi> <mi>f</mi> <mi>r</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>F</mi> <mrow> <mi>x</mi> <mi>f</mi> <mi>l</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>cos</mi> <mi>&amp;delta;</mi> <mo>+</mo> <mfrac> <msub> <mi>d</mi> <mi>f</mi> </msub> <mn>2</mn> </mfrac> <msub> <mi>F</mi> <mrow> <mi>f</mi> <mo>,</mo> <mi>y</mi> </mrow> </msub> <mi>sin</mi> <mi>&amp;delta;</mi> <mo>+</mo> <mfrac> <msub> <mi>d</mi> <mi>r</mi> </msub> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <msub> <mi>F</mi> <mrow> <mi>x</mi> <mi>r</mi> <mi>r</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>F</mi> <mrow> <mi>x</mi> <mi>r</mi> <mi>l</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>/</mo> <msub> <mi>I</mi> <mi>Z</mi> </msub> <mo>,</mo> </mrow> </mtd> </mtr> </mtable> </mfenced>
<mrow> <msub> <mi>F</mi> <mn>2</mn> </msub> <mo>=</mo> <mo>-</mo> <mfrac> <mrow> <msub> <mi>d</mi> <mi>f</mi> </msub> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>&amp;delta;</mi> </mrow> <msub> <mi>I</mi> <mi>Z</mi> </msub> </mfrac> <msub> <mi>F</mi> <mrow> <mi>y</mi> <mi>f</mi> <mi>r</mi> </mrow> </msub> <mo>.</mo> </mrow>
2-5) designing a second-order sliding-mode observer by applying a supercoiling algorithm
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mfrac> <mrow> <mi>d</mi> <mover> <mi>r</mi> <mo>^</mo> </mover> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <msub> <mi>u</mi> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>z</mi> <mn>3</mn> </msub> <mo>,</mo> <msub> <mi>z</mi> <mn>3</mn> </msub> <mo>=</mo> <mo>-</mo> <msub> <mi>&amp;lambda;</mi> <mn>3</mn> </msub> <msup> <mrow> <mo>|</mo> <mrow> <mover> <mi>r</mi> <mo>^</mo> </mover> <mo>-</mo> <mi>r</mi> </mrow> <mo>|</mo> </mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </msup> <mi>s</mi> <mi>i</mi> <mi>g</mi> <mi>n</mi> <mrow> <mo>(</mo> <mover> <mi>r</mi> <mo>^</mo> </mover> <mo>-</mo> <mi>r</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>z</mi> <mn>4</mn> </msub> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mtable> <mtr> <mtd> <mrow> <mfrac> <mrow> <msub> <mi>dz</mi> <mn>4</mn> </msub> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <mo>-</mo> <msub> <mi>&amp;lambda;</mi> <mn>4</mn> </msub> <mi>s</mi> <mi>i</mi> <mi>g</mi> <mi>n</mi> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mn>4</mn> </msub> <mo>-</mo> <msub> <mi>z</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mo>(</mo> <msub> <mi>&amp;lambda;</mi> <mn>3</mn> </msub> <mo>&gt;</mo> <mn>0</mn> <mo>,</mo> <msub> <mi>&amp;lambda;</mi> <mn>4</mn> </msub> <mo>&gt;</mo> <mn>0</mn> <mo>)</mo> <mo>.</mo> </mrow> </mtd> </mtr> </mtable> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>
t≥T2,T2When > 0, the observer is able to accurately track its actual value, i.e.
And further calculating an estimated value of the right front wheel lateral force as follows:
4. a distributed drive electric as claimed in claim 1Method for estimating the lateral force of the front wheels of a motor car, characterized in that in step 3), a filter module is used for estimating the lateral forceThe optimization process is carried out as follows:
setting the moment when the steering wheel corner signal delta is zero as T, taking a closed neighborhood taking T as a center, and taking delta as a neighborhood radius, when the delta is in the neighborhood, replacing the original function by a straight line, and when the delta is out of the neighborhood, outputting the original function to obtain a piecewise function of the lateral force:
<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mover> <mi>F</mi> <mo>^</mo> </mover> <mrow> <mi>y</mi> <mi>f</mi> <mi>r</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mo>(</mo> <mfrac> <mrow> <msubsup> <mover> <mi>F</mi> <mo>^</mo> </mover> <mrow> <mi>y</mi> <mi>f</mi> <mi>r</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <mi>T</mi> <mo>+</mo> <mi>&amp;Delta;</mi> <mo>)</mo> </mrow> <mo>-</mo> <msubsup> <mover> <mi>F</mi> <mo>^</mo> </mover> <mrow> <mi>y</mi> <mi>f</mi> <mi>r</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <mi>T</mi> <mo>-</mo> <mi>&amp;Delta;</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mn>2</mn> <mi>&amp;Delta;</mi> </mrow> </mfrac> <mo>)</mo> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mi>T</mi> <mo>+</mo> <mi>&amp;Delta;</mi> <mo>)</mo> <mo>+</mo> <msubsup> <mover> <mi>F</mi> <mo>^</mo> </mover> <mrow> <mi>y</mi> <mi>f</mi> <mi>r</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>(</mo> <mi>T</mi> <mo>-</mo> <mi>&amp;Delta;</mi> <mo>)</mo> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>t</mi> <mo>&amp;Element;</mo> <mo>&amp;lsqb;</mo> <mi>T</mi> <mo>-</mo> <mi>&amp;Delta;</mi> <mo>,</mo> <mi>T</mi> <mo>+</mo> <mi>&amp;Delta;</mi> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mfrac> <msub> <mi>I</mi> <mi>Z</mi> </msub> <mrow> <msub> <mi>d</mi> <mi>f</mi> </msub> <mi>sin</mi> <mi>&amp;delta;</mi> </mrow> </mfrac> <msub> <mover> <mi>F</mi> <mo>^</mo> </mover> <mn>2</mn> </msub> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>t</mi> <mo>&amp;NotElement;</mo> <mo>&amp;lsqb;</mo> <mi>T</mi> <mo>-</mo> <mi>&amp;Delta;</mi> <mo>,</mo> <mi>T</mi> <mo>+</mo> <mi>&amp;Delta;</mi> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>F</mi> <mo>^</mo> </mover> <mrow> <mi>y</mi> <mi>f</mi> <mi>l</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>F</mi> <mrow> <mi>y</mi> <mo>,</mo> <mi>f</mi> </mrow> </msub> <mo>-</mo> <msub> <mover> <mi>F</mi> <mo>^</mo> </mover> <mrow> <mi>y</mi> <mi>f</mi> <mi>r</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced>
wherein,is an estimate of the right front wheel lateral force,left front wheel lateral force estimate.
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