METHOD FOR ESTIMATING A VALUE OF A FRICTION FORCE EXERTED ON A PART OF A POWER STEERING SYSTEM BY MEANS OF A MATHEMATICAL MODEL

Abstract

A method for estimating a value of a friction force exerted on a part of a power steering system of a vehicle, the part of the power steering system including at least one motor exerting a motor torque, the value of the friction force making it possible to modify the motor torque, by means of a mathematical model.

Claims

1. A method of estimating a value of a frictional force exerted on a portion of a power steering system of a vehicle, said portion of the power steering system comprising at least one motor exerting a motor torque, said value of the frictional force making it possible to modify the motor torque, wherein it comprises the following steps: determining a portion of a model power steering system corresponding to a mathematical model virtually representing the portion of the power steering system, measuring, on the portion of the power steering system, a value of at least one input variable, calculating at least one output parameter by means of the mathematical model and the at least one input variable, measuring, on the portion of the power steering system, a value of at least one output variable representing a physical quantity similar to the at least one output parameter, calculating at least one deviation between the at least one output parameter and the at least one output variable, correcting a value of at least one internal parameter of said mathematical model as a function of the deviation and of an internal coefficient, determining the value of the frictional force from the at least one corrected internal parameter.

2. The estimation method according to claim 1, wherein the mathematical model is a 1-order mathematical model, comprising a model mass, equivalent to a set of the inertias of the portion of the model power steering system, which is subjected to at least one force exerted on the portion of the model power steering system.

3. The estimation method according to claim 1, wherein the frictional force of the mathematical model is determined by a LuGre model.

4. The estimation method according to claim 1, wherein the at least one internal coefficient enabling the correction of the at least one internal parameter is determined by an application of Lyapunov's theorem.

5. The estimation method according to claim 1, wherein the at least one input variable is selected from: the motor torque, a steering wheel torque, a lateral acceleration of the vehicle or a force on the tie rods.

6. The estimation method according to claim 1, wherein the output parameter and the output variable correspond to a rotational speed of the motor.

Description

[0075] The invention will be better understood, thanks to the description hereinafter, which relates to an embodiment according to the present invention, given as a non-limiting example and explained with reference to the appended schematic drawings, in which:

[0076] FIG. 1 is a schematic representation of a mechanical-type power steering system of a vehicle

[0077] FIG. 2 is a simplified representation of the power steering system of FIG. 1.

[0078] The invention concerns a method for estimating a value of a frictional force exerted on at least one portion of a power steering system 1 of a vehicle 2, and more particularly for a motor vehicle 2 intended for transporting passengers.

[0079] The power steering system 1 described below is of the mechanical type.

[0080] In a manner known per se, and as shown in FIG. 1, said power steering system 1 comprises a steering wheel 3 which allows a driver to maneuver said power steering system 1 by exerting a force, called “steering wheel torque” T3, on said steering wheel 3.

[0081] Said steering wheel 3 is preferably mounted on a steering column 4, guided in rotation on the vehicle 2, and which meshes, by means of a steering pinion 5, on a rack 6, which is itself guided in translation in a steering casing 7 fastened to said vehicle 2.

[0082] Preferably, each of the ends of said rack 6 is connected to a steering tie rod 8, 9 attached to the steering knuckle of a steered wheel 10, 11 (respectively a left wheel 10 and a right wheel 11), such that the longitudinal translational movement of the rack 6 makes it possible to modify the turning angle (yaw angle) of the steered wheels.

[0083] Moreover, the steered wheels 10, 11 can preferably also be driving wheels.

[0084] The power steering system 1 also comprises a control motor 12 intended to output a control torque T12, to assist the maneuvering of said power steering system 1.

[0085] The control motor 12 will preferably be an electric motor, with two operating directions, and preferably a rotary electric motor, of the brushless type.

[0086] The control motor 12 can engage, where appropriate via a reducer of the gear reducer type, either on the steering column 4 itself, to form a so-called “single pinion” mechanism, or directly on the rack 6, for example by means of a second pinion 13 separate from the steering pinion 5 which enables the steering column 4 to mesh with the rack 6, so as to form a so-called “double pinion” mechanism, as illustrated in FIG. 1, or else by means of a ball screw which cooperates with a corresponding thread of said rack 6, at a distance from said steering pinion 5.

[0087] The method of estimating the value of the frictional force according to the invention is exerted on a portion of the power steering system 1. In the case explained below, the portion of the power steering system corresponds to the entire power steering system 1 as represented in FIG. 1 and downstream of a torque sensor 23 measuring the steering wheel torque T3, that is to say the steering system comprising the rack 6 up to the torque sensor 23.

[0088] The method comprises a step of determining a portion of a model power steering system corresponding to a mathematical model representing the power steering system 1. The portion of the model power steering system 1′ used in the invention is a simplified representation of the power steering system 1 as represented in FIG. 2. In the example depicted in FIGS. 1 and 2, the portion of the model power steering system 1′ will be referred to as the model power steering system 1′.

[0089] To simplify a software implementation and reduce a resource consumption of a computer of the power steering system 1, said power steering system 1 is represented in the method according to the invention by the mathematical model which is a simplified virtual representation of the actual studied steering system 1.

[0090] The mathematical model is a 1-order system.

[0091] More specifically, the mathematical model, corresponding to the model power steering system 1′, comprises a model rack 6′ on which a model steering pinion 5′ is exerted and a model control motor 12′ engaging the model rack 6′ by means of a second model pinion 13′.

[0092] The mathematical model comprises one single model mass M, corresponding to a set of the inertias of the model power steering system 1′.

[0093] The model mass M is written according to the formula:

M=m.sub.RA+n.sub.1.sup.2.Math.J.sub.MO+n.sub.2.sup.2.Math.J.sub.DRP  [Math 5]

[0094] with:

[0095] m.sub.RA: mass of the model rack 6′

[0096] J.sub.MO: inertia of the model control motor 12′

[0097] J.sub.DRP: inertia of the model steering pinion 5′

[0098] n.sub.1: reduction ratio of the reducer+second model pinion 13′ set

[0099] n.sub.2: reduction ratio of the model steering pinion 5′

[0100] It is determined that the model mass M is subjected to at least one force exerted on the model power steering system 1′. In the example, the model mass M is subjected to 4 forces: [0101] a model motor force T.sub.MO which is equivalent to the control torque T12 of the control motor 12 in the actual power steering system 1, [0102] a model driver force T.sub.TB which is substantially equivalent to the steering wheel torque T3 measured by a torque sensor 23 in the actual power steering system 1, except for the frictional values at the level of the steering column 4, [0103] a model tie rod force F.sub.TR-RA which is equivalent to a force applied by the steering tie rods 8, 9 on the rack 6. This force is not measured directly, it is estimated from a lateral acceleration γ of the vehicle according to the following linear relationship:

F.sub.TR-RA=−Ĝ.Math.γ  [Math 6]

[0104] With Ĝ: an internal parameter representing a coefficient of proportionality between a transverse force and a lateral acceleration of the vehicle, in a domain of linear behavior of the tires, [0105] a model frictional force F.sub.Friction which is equivalent to a frictional force F.sub.Friction exerted on the actual power steering system 1.

[0106] It is also determined that the model frictional force {circumflex over (F)}.sub.Friction is modeled by a LuGre model according to the following expressions:

[00002]$\begin{array}{cc}{\hat{F}}_{\mathrm{friction}}={\hat{\sigma }}_0+\hat{z}+{\sigma }_1.Math.h\left(v\right).Math.\hat{z}+{\hat{\sigma }}_2.Math.v& \left[\mathrm{Math}7\right]\\ \hat{z}=v-{\hat{\sigma }}_0.Math.\frac{.Math.v.Math.}{g\left(v\right)}.Math.\hat{z}& \left[\mathrm{Math}8\right]\\ g\left(v\right)=F_c+\left(F_s-F_c\right).Math.\exp \exp \left(-{\left(\frac{v}{v_s}\right)}^2\right)& \left[\mathrm{Math}9\right]\\ h\left(v\right)=\frac{v_d}{v_d+.Math.v.Math.}& \left[\mathrm{Math}10\right]\end{array}$

[0107] with:

[0108] {circumflex over (σ)}.sub.0{circumflex over (σ)}.sub.1, {circumflex over (σ)}.sub.2: internal parameters of the mathematical model, representing respectively a bonding stiffness, an internal damping, and a viscous coefficient of friction according to a LuGre model,

[0109] {circumflex over (z)}: an internal state of the LuGre model

[0110] v: rotational speed of the control motor 12 corresponding to the speed of the model mass M

[0111] v.sub.s: “Stribeck speed”, that is to say a parameter of the LuGre model controlling a shape of the Stribeck curve which describes the transition between static and dynamic frictions

[0112] c.sub.d: an internal parameter of the LuGre model

[0113] F.sub.c: A friction level

[0114] F.sub.s: A static friction level

[0115] When the LuGre model is applied to the considered model power steering system, we obtain:

[00003]$\begin{array}{cc}\stackrel{.}{\hat{v}}=\frac{1}{M}\left(\mathrm{RFE}-{\hat{F}}_{\mathrm{Friction}}+\hat{G}\gamma +\hat{D}\right)& \left[\mathrm{Math}11\right]\\ \stackrel{.}{\hat{z}}=v-{\hat{\sigma }}_0.Math.\frac{.Math.v.Math.}{g\left(v\right)}.Math.\hat{z}& \left[\mathrm{Math}12\right]\\ {\hat{F}}_{\mathrm{Friction}}={\hat{\sigma }}_0.Math.\hat{z}+{\sigma }_1.Math.\left(v-{\hat{\sigma }}_0.Math.\frac{.Math.v.Math.}{g\left(v\right)}.Math.\hat{z}\right)+{\hat{\sigma }}_2.Math.v& \left[\mathrm{Math}13\right]\end{array}$

[0116] With:

[0117] {circumflex over ({circle around (v)})}: the acceleration of the model mass M,

[0118] RFE: the sum of the model motor force T.sub.MO and the model driver force T.sub.TB, expressed in the reference of the rack 6

[0119] {circumflex over (D)}: internal parameter corresponding to a possible constant error on the measurements, such as for example the presence of an offset on the measurements of the steering wheel torque T3 or of the lateral acceleration γ of the vehicle

[0120] {circumflex over ({circle around (z)})}: derivative of the internal state of the LuGre model

[0121] In order to make the mathematical model representative of the actual steering system 1, only the model mass M could be assumed to be known. The other internal parameters {circumflex over (σ)}.sub.0{circumflex over (σ)}.sub.1, {circumflex over (σ)}.sub.2, {circumflex over (D)}, Ĝ, {circumflex over (z)} are too variable to be accurately estimated a priori.

[0122] The method also comprises a step of measuring, on the power steering system 1, a value of at least one input variable. In the example of FIGS. 1 and 2, the input variables are the control torque T12 of the control motor 12, the steering wheel torque T3, and the lateral acceleration γ of the vehicle.

[0123] The method then comprises a step of calculating at least one output parameter by means of the mathematical model and of the at least one input variable.

[0124] The step of calculating at least one output parameter makes it possible to determine the speed {circumflex over (v)} of the model mass M corresponding to the rotational speed v of the control motor 12 as a function of the input variables. More specifically, the input variables are integrated in the mathematical model described above, which makes it possible to deduce the speed D of the model mass M.

[0125] The method then comprises a step of measuring, on the portion of the power steering system 1, a value of at least one output variable representing a physical quantity similar to the at least one output parameter.

[0126] During the step of measuring a value of at least one output variable, the rotational speed v of the control motor 12 is measured on the power steering system 1. The method comprises a step of calculating at least one deviation e between the at least one output parameter and the at least one output variable.

[0127] In other words, the deviation e is equal to the at least one output variable minus the at least one output parameter.

[0128] In the present case, the deviation e is equal to the speed P of the model mass M minus the rotation speed v of the control motor 12.

e={circumflex over (v)}−v  [Math 14]

[0129] The deviation e, also called the prediction error, symbolically represents imperfections in the mathematical model. In other words, when the mathematical model is perfect, the deviation e is zero.

[0130] The method comprises a step of correcting a value of at least one internal parameter of said mathematical model as a function of the prediction error.

[0131] In this way, the mathematical model is corrected in order to make it more representative of the power steering system 1. To correct the mathematical model, the values of the internal parameters {circumflex over (σ)}.sub.0{circumflex over (σ)}.sub.1, {circumflex over (σ)}.sub.2, {circumflex over (D)}, Ĝ, {circumflex over (z)} are modified.

[0132] The modification of the values of the internal parameters {circumflex over (σ)}.sub.0{circumflex over (σ)}.sub.1, {circumflex over (σ)}.sub.2, {circumflex over (D)}, Ĝ, {circumflex over (z)} requires solving equations, not reproduced here, which reveal nonlinear terms.

[0133] To solve this problem, it is known to dissociate the nonlinear terms using a structure comprising two estimates of the internal state z. Then expressions of the internal coefficients are defined after applying Lyapunov theorem.

[0134] The method comprises a step of determining the value of the frictional force from the at least one corrected internal parameter.

[0135] Finally, the model frictional force {circumflex over (F)}.sub.friction corresponding to the frictional force {circumflex over (F)}.sub.friction exerted on the actual power steering system 1 can then be determined according to the equation:

[00004]$\begin{array}{cc}{\hat{F}}_{\mathrm{friction}}={\hat{\sigma }}_0{\hat{z}}_0+{\hat{\sigma }}_{1}h\left(v\right)\left(v-\frac{.Math.v.Math.}{g\left(v\right)}.Math.{\hat{z}}_1\right)+{\hat{\sigma }}_{2}v& \left[\mathrm{Math}15\right]\end{array}$

[0136] With:

[0137] {circumflex over (σ)}.sub.0{circumflex over (σ)}.sub.1, {circumflex over (σ)}.sub.2: internal parameters of the mathematical model, representing respectively a bonding stiffness, an internal damping, and a viscous coefficient of friction according to a LuGre model,

[0138] {circumflex over (z)}: internal state of the LuGre model

[0139] v: rotational speed of the control motor 12 corresponding to the speed of the model mass M

[0140] Determining the value of the frictional force makes it possible to modify, by increasing or decreasing, the value of the control torque T12 so as to reach a target frictional value. In other words, by modifying the control torque T12, it is possible to more or less compensate the value of the frictional force so that two vehicles of the same series have equivalent behaviors.

[0141] Of course, the invention is not limited to the embodiments described and represented in the appended figures. Modifications are still possible, in particular with regards to the constitution of the various elements or by substitution of technical equivalents, yet without departing from the scope of protection of the invention.