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

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

A kind of front-wheel side force method of estimation of distributed driving electric car
Technical field
Side force of tire method of estimation in being travelled the present invention relates to vehicle, the forward of more particularly to distributed driving electric car Estimate to the side force of wheel.
Background technology
Under the background of environment and energy problem, electric automobile increasingly becomes the pith of future automobile industry.Closely Nian Lai, distributed-driving electric automobile (In-wheel motor Electric, IEV) is by the common concern of researcher.It is logical Cross the wheel hub motor being placed in hub for vehicle wheel or two motors are placed in into differential mechanism position carrys out driving moment, provided to vehicle dynamic Power.IEV has the advantages that corresponding speed is fast, driving-chain is short, transmission is efficient, is an important development side in electric automobile field To.
At present, IEV lateral stability control still suffers from the place for needing to improve, the side force of tire such as under limiting condition Can not accurately it be estimated.It is worth noting that, side force of tire is the important component of horizontal dynamic, vehicle is affected Driving safety and stability.Therefore, the accurate estimation to side force of tire will effectively improve crosswise joint effect.
The estimation of traditional side force of tire depends on tire model.State, inside and outside a variety of non-linear wheels are investigated Loose tool type.Dugoff models are established according to experimental data and represent driving (braking) power, lateral deviation power, slip rate, side drift angle and tire The expression formula of other specification relation；UniTire models are a kind of semiempirical tire models that Guo Konghui academician proposes, have and meet The characteristics of high order theory boundary condition；Magic Formula models establish the longitudinal force of tire, side force using SIN function The relation between aligning torque and side drift angle, slip rate, angle of heel and vertical load.Tire model can carry out phase to tire force Estimate accurate, but side force of tire and slip angle of tire, vertical load, straight skidding rate and wheel speed etc. in tire model Factor is directly related, that is, it is more, it is necessary to carry out substantial amounts of test data fitting to be related to variable, computationally intensive, and tire model Algorithm it is complicated, the needs of so as to be difficult to meet quick response in the application of real vehicle controller.In addition, for based on tire model Side force method of estimation, once tire characteristics (tire pressure and the degree of wear etc.) or surface conditions quickly change, fitting essence Degree will decline rapidly so that side force of tire estimation is inaccurate, causes crosswise joint effect to be affected.So propose a kind of Side force method of estimation independent of tire model is necessary.
The content of the invention
Tire model is depended in order to solve the problems, such as that current side force of tire estimation is excessive, the present invention proposes a kind of point Cloth drives the steering front wheel side force method of estimation of electric car, and it can enter on the basis of tire model is broken away to side force Row estimation.This method considers the real-time characteristic of vehicle tyre and the change of pavement behavior, can estimate the side of tire exactly Xiang Li, so as to improve the crosswise joint effect of vehicle.Estimation procedure is as follows：
1) in vehicle travel process, the wheel motor controller measures the Real Time Drive torque T needed for each motorij, The wheel speed sensors measure real-time wheel speed signal ωij.Driving moment signal and wheel speed signal are sent to and described are based on wheel The sliding formwork longitudinal force estimation module of spin dynamics, sliding formwork longitudinal force estimation module obtain tire and indulged according to real-time collection signal Estimate to the value of power
It is above-mentionedTij、ωijIn, i=f, r, f represent front-wheel, and r represents trailing wheel；J=l, r, l represent revolver, and r represents right Wheel；
2) longitudinal acceleration sensor and lateral acceleration sensor measure real-time longitudinal acceleration signal axWith Lateral acceleration signal ay；The longitudinal speed sensor and lateral acceleration sensor measure real-time longitudinal velocity VxWith it is lateral Speed Vy；In addition, the yaw rate sensor measures real-time yaw rate signal r, and the steering wheel Rotary angle transmitter measures steering wheel angle signal δ；
By steering wheel angle signal, yaw rate signal, longitudinal acceleration signal, lateral acceleration signal, longitudinal direction speed Spend signal, side velocity signal and the longitudinal force estimatedIt is sent to the sliding formwork side force estimation mould based on dynamics of vehicle Block, sliding formwork side force estimation module estimate the side force of off-front wheel by computing
3) the off-front wheel side force of estimation and steering wheel angle signal finally, are sent to the filtration module, for The unusual appearance occurred in side force estimate, filtration module take the method that linearization process is carried out near singular point, from And the lateral force value of accurate off-front wheel is exported, front left wheel side is further calculated to force value, thus obtains two front-wheels Side force estimate.
Parameter during method of estimation of the present invention is to be based on obtaining with lower part measurement：The steering wheel angle signal δ is measured by steering wheel angle sensor, the yaw rate signal r is measured by yaw-rate sensor, the longitudinal direction adds Rate signal axMeasured by longitudinal acceleration sensor, the lateral acceleration signal ayMeasured by lateral acceleration sensor, institute State longitudinal speed signal VxMeasured by longitudinal speed sensor, the side velocity signal VyMeasured by lateral acceleration sensor.
Compared with prior art, the beneficial effect that shows of the present invention is：
1) present invention is only carried out without complicated non-linear tire model using Second Order Sliding Mode observer to side force of tire Estimation, calculate real-time that is easy and ensure that accuracy and calculate.
2) present invention applies the existing signal easily obtained in vehicle-state, it is not necessary to which other expensive sensors just can be real Now side force of tire is accurately estimated, cost is relatively low.
3) the Second Order Sliding Mode observer that the present invention designs with super-twisting algorithm (Super-twist), the observer have The uncertain disturbance such as fast convergence and the air drag to occurring in Vehicular system, the coefficient of friction of tire has very strong Robustness, i.e., there is stronger adaptability to complex environment.
Brief description of the drawings
Fig. 1 is the phylogenetic relationship schematic diagram of the present invention.
Embodiment
The invention provides a kind of front-wheel side force method of estimation of distributed electrical motor-car.To make the purpose of the present invention, skill Art scheme and effect are clearer, clear and definite, and the present invention is described in more detail for the embodiment that develops simultaneously referring to the drawings.It should manage Solution, specific embodiment described herein only to explain the present invention, are not intended to limit the present invention.
Be shown in Fig. 1 the present invention side force of tire estimation phylogenetic relationship schematic diagram, it include wheel motor controller, Wheel speed sensors, sliding formwork longitudinal force estimation module, yaw rate sensor, longitudinal direction of car acceleration transducer, vehicle Lateral acceleration sensor, vehicular longitudinal velocity sensor, vehicle lateral acceleration sensor, steering wheel angle sensor, sliding formwork Side force estimation module, filtration module.
Based on said system, explain the present invention to the vehicle front-wheel (deflecting roller) during traveling below by specific implementation Side force of tire method of estimation：
The vehicle parameter of use is as shown in table 1, and the operating condition of test of selection is 72km/h, snakelike.
The vehicle parameter of table 1
Vehicle mass m(kg) 1464
Around z-axis rotary inertia Iz(kg/m2) 2400
Barycenter is to front axle distance a(mm) 1256
Barycenter is to rear axle distance b(mm) 1368
Front axle away from df(mm) 1450
Hind axle away from dr(mm) 1450
Barycenter is away from ground level hg(mm) 500
Vehicle wheel rotation inertia Iω(kg/m2) 2.1
Vehicle wheel roll radius R(mm) 310
1) the sliding formwork longitudinal force estimation module based on wheel spin dynamics collects in real time according to the wheel speed sensors Tire centerline rate signal ωijEach tire driving torque signal T collected in real time with the wheel side controllerij, with cunning Mould Observation Theory devises sliding mode observer and the longitudinal force of four tires is observed.
Wheel spin dynamics equation is
Equation (1) is rewritable to be
Wherein, x1=ωij, input variableRegard unknown disturbance as, y is output quantity.
Designing following Second Order Sliding Mode observer based on super-twisting algorithm is
Theoretical, the existence time constant T according to finite time convergence control1, have
Wheel longitudinal force, which is further calculated, is
Wherein,It is x1Estimate,It is F1Estimate andIt is FxijEstimate.
2) vehicle seven freedom model is based on, the method for off-front wheel side force is calculated such as in sliding formwork side force estimation module Under
Longitudinal direction of car kinetics equation is
m(ax-VyR)=(Fxfl+Fxfr)cos-(Fyfl+Fyfr)sinδ+Fxrl+Fxrr. (2)
The lateral kinetics equation of vehicle is
m(ay+VxR)=(Fxfl+Fxfr)sinδ+(Fyfl+Fyfr)cosδ+Fyrl+Fyrr. (3)
Vehicular yaw kinetics equation is
Equation (2), (3) it is rewritable into
Equation (5) is substituted into equation (4), can be obtained
It is worth noting that, steering wheel angle δ, yaw velocity r, longitudinal direction of car acceleration a in equation (5) and (6)x、 Vehicle side acceleration ay, vehicular longitudinal velocity VxAnd side velocity VyIt can be measured respectively by above-mentioned corresponding sensor, this Outside, longitudinal force F thereinxijThe longitudinal force estimated by sliding formwork longitudinal force estimation moduleInstead of.Therefore, right the half of equation (6) There was only F in portionyfrFor unknown quantity, other is all known quantity.
So as to which equation (6) is rewritable to be
In formula,
It is again depending on super-twisting algorithm design Second Order Sliding Mode observer
Similarly, as t >=T2(T2＞ 0) when, observation can accurate its actual value of tracker, i.e.,
So as to which the estimate for calculating off-front wheel side force is
From formula (7), it is seen that denominator contains sin δ items, when steering angle sigma is zero, necessarily result inBecome unlimited Greatly, this is not permitted.In view of the above-mentioned problems, the filtration module is in zero crossings by taking one section of small section, then Change of the former side force estimate on the section is replaced as straight line with the first and last end points in the section.In other words, finally Longitudinal force estimate be a piecewise function form, it is linear equation in taken section, in section external signal as former state it is defeated Go out.
In formula (8), T is time constant, and in t=T, steering angle sigma zero；Δ is the radius of neighbourhood centered on T points；The respectively side force estimate of off-front wheel, the near front wheel.
Although the present invention is described according to various embodiments, it will be appreciated by persons skilled in the art that this hair It is bright to be implemented with modification in the scope of claims.

Claims (4)

1. a kind of front-wheel side force method of estimation of distributed driving electric car, it is characterised in that comprise the following steps：
1) in vehicle travel process, the torque T needed for each motor that wheel motor controller is measuredijSurveyed with wheel speed sensors The wheel speed signal ω obtainedijSliding formwork longitudinal force estimation module is sent to, sliding formwork longitudinal force estimation module is according to the letter collected in real time Number, calculate the longitudinal force estimate of tire
The estimate of longitudinal force of tireSpecific be calculated as follows：
1-1) establishing wheel spin dynamics equation is：
<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>
Equation (1) is rewritten into
<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, x1=ωij, input variableRegard unknown disturbance as, y is output quantity；
1-2) design the Second Order Sliding Mode observer based on super-twisting 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>
It is 1-3) theoretical according to finite time convergence control, a certain constant T be present1(T1＞ 0) so that
So as to which the estimate of 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,It is x1Estimate,It is F1Estimate andIt is FxijEstimate；
Wherein, i=f, r, f represent front-wheel, and r represents trailing wheel；J=l, r, l represent revolver, and r represents right wheel；
2) by steering wheel angle signal δ, yaw rate signal r, longitudinal acceleration signal ax, lateral acceleration signal ay, longitudinal direction Rate signal Vx, side velocity signal VyThe longitudinal force estimated with sliding formwork longitudinal force estimation moduleIt is transferred to and is moved based on vehicle The sliding formwork side force estimation module of mechanics, sliding formwork side force estimation module estimate the side force of off-front wheel
3) side force for the off-front wheel for estimating sliding formwork side force estimation module, and steering wheel angle signal δ are sent to filter Ripple module；The filtration module by the off-front wheel side force estimated at the time of steering wheel angle signal δ is zero near carry out Linearization process, accurate off-front wheel side force estimate is exported, and by being simply calculated the near front wheel side force estimate, So as to obtain two final front-wheel side force estimates.
2. the front-wheel side force method of estimation of distributed driving electric car according to claim 1, it is characterised in that described Steering wheel angle signal δ is measured by steering wheel angle sensor, the yaw rate signal r is surveyed by yaw-rate sensor Obtain, the longitudinal acceleration signal axMeasured by longitudinal acceleration sensor, the lateral acceleration signal ayBy side acceleration Sensor measures, the longitudinal speed signal VxMeasured by longitudinal speed sensor, the side velocity signal VyBy side velocity Sensor measures.
3. the front-wheel side force method of estimation of distributed driving electric car according to claim 1, it is characterised in that in institute State in step 2), off-front wheel side force is estimated in sliding formwork side force estimation moduleMethod it is as follows：
2-1) establishing longitudinal dynamics equation is
m(ax-VyR)=(Fxfl+Fxfr)cosδ-(Fyfl+Fyfr)sinδ+Fxrl+Fxrr (2)
Lateral dynamics equation is
m(ay+VxR)=(Fxfl+Fxfr)sinδ+(Fyfl+Fyfr)cosδ+Fyrl+Fyrr (3)
Yaw kinetics 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) equation (2), (3) are rewritten as
<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>
Equation (5) 2-3) is substituted into (4), obtained
<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 into
<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>
Super-twisting algorithm 2-5) is used, design Second Order Sliding Mode observer is
<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,T2During ＞ 0, observer can accurately track its actual value, i.e.,
And then the estimate for calculating off-front wheel side force is：
4. the front-wheel side force method of estimation of distributed driving electric car according to claim 1, it is characterised in that in institute State in step 3), filtration module is to the side force that estimatesThe process for optimizing processing is as follows：
Set direction disk angular signal δ is T at the time of being zero, takes a closed neighborhood centered on T, Δ is the radius of neighbourhood, at this When in neighborhood, original function is replaced with straight line, when outside neighborhood, then exports as former state, obtains the piecewise function of side 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,For off-front wheel side force estimate,For the near front wheel side force estimate.
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