CN112526887B - Self-adaptive friction compensation control method for electric power-assisted brake system - Google Patents

Self-adaptive friction compensation control method for electric power-assisted brake system Download PDF

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CN112526887B
CN112526887B CN202011504372.XA CN202011504372A CN112526887B CN 112526887 B CN112526887 B CN 112526887B CN 202011504372 A CN202011504372 A CN 202011504372A CN 112526887 B CN112526887 B CN 112526887B
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冯能莲
张卫强
雍加望
李岩松
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Beijing University of Technology
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
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Abstract

A self-adaptive friction compensation control method of an electric power-assisted braking system is characterized in that a friction model of the system is established based on an expanded GMS friction model, and each parameter of the expanded GMS friction model is identified by measuring each parameter of the electric power-assisted braking system, so that the accurate modeling of the friction model of the electric power-assisted braking system is realized; combining feed-forward control and feedback control, wherein the feed-forward control comprises static feed-forward friction compensation and adaptive dynamic feed-forward friction compensation; the self-adaptive dynamic feedforward friction compensation is obtained by two extended GMS friction models. According to the invention, the accurate output of the braking torque of the electric power-assisted braking system is realized by modeling the friction model of the electric power-assisted braking system and adopting dynamic and static feedforward friction compensation and feedback control.

Description

Self-adaptive friction compensation control method for electric power-assisted braking system
Technical Field
The invention relates to the technical field of new energy automobile brake control, in particular to an adaptive friction compensation control method for an electric power-assisted brake system.
Background
In recent years, an electric power-assisted brake system that generates braking force by driving a piston of a brake master cylinder with a motor has become a new research focus in the field of automobiles. The electric power-assisted brake system generally takes a motor as a power source, and converts the force of the motor into the thrust of a brake master cylinder ejector rod through a speed reduction and torque increasing mechanism and a motion conversion mechanism so as to push the brake master cylinder together with a driver to generate hydraulic pressure. The friction compensation of the system is the core and the difficulty of accurate control of the electric power-assisted brake system. Due to the characteristics of the transmission mechanism, machining and installation errors, abrasion and other factors, coulomb friction, hysteresis loss and the like exist in the system, and the influence of the working temperature of the system on viscous friction exists. These non-linear factors cause the speed and force relationship of the mechanism to exhibit significant non-linearity, which may lead to inaccurate motor assist and thus inaccurate system hydraulic pressure control. Therefore, an accurate friction model is needed, which characterizes the friction characteristics of the mechanical mechanism of the electric power assisting system and performs friction feedforward compensation on the nonlinearity caused by friction.
Disclosure of Invention
Aiming at the problems in the prior art, the self-adaptive friction compensation control method of the electric power-assisted brake system comprises the following steps:
1. establishing a dynamic equation of the electric power-assisted brake system:
the system comprises a motor, a speed reducing and moment increasing mechanism, a motion conversion mechanism and a brake master cylinder, wherein the motor output torque converts the motor force into the thrust of a brake master cylinder ejector rod through the speed reducing and moment increasing mechanism and the motion conversion mechanism so as to push the brake master cylinder together with a driver to generate hydraulic pressure.
The motion equation of the motor is as follows:
Figure BDA0002844524600000011
the motion equations of the speed reduction and torque increase mechanism and the motion conversion mechanism are as follows:
Figure BDA0002844524600000012
Figure BDA0002844524600000021
Figure BDA0002844524600000022
in the formula is TmFor the output of torque of the motor, JmIs equivalent rotational inertia of a motor shaft, theta is a motor rotation angle, TlAs the load torque, mcFor the mass of the ejector rod of the brake master cylinder, xcIn order to brake the displacement of the top rod of the main cylinder,
Figure BDA0002844524600000023
for braking the acceleration of the master cylinder ram, FsFor the force acting on the brake master cylinder, p is the hydraulic pressure of the brake master cylinder, A is the cross-sectional area of the brake master cylinder, eta is the transmission efficiency of the transmission mechanism, TbH is the displacement of a linear component corresponding to one rotation of a rotating component in the motion conversion mechanism, and F' is the total friction force of the system.
2. Establishing a GMS friction model of the system:
the GMS friction model is a method for simulating a contact unit between two surfaces by adopting a certain number of springs without mass blocks and connected in parallel, and each basic block has inherent hysteresis characteristics; after corresponding displacement signals are input into the model, because conditions of different basic blocks in the model entering a pre-sliding stage and a sliding stage are different, the hysteresis curves of the respective hysteresis curves are integrated to form the overall hysteresis curve of the system.
[1] Establishing a mathematical model of the total extended GMS friction model:
Figure BDA0002844524600000024
in the formula
Figure BDA0002844524600000025
For the estimated total friction of the system, FC(z, ω, T) is the coulomb friction torque of the system, Fv(ω, t) is the viscous friction torque of the system; z is the state of the system, ω is the rotational speed of the motor, T is the torque of the mechanism, and T is the temperature of the system.
[2] Determining the coulomb friction torque of the system as follows:
FC(z,ω,T)＝F(T)H(z,ω)
wherein F (T) is a function of the Coulomb coefficient of friction; h (z, ω) is a hysteresis function.
The following assumptions are made for the GMS model:
1)F(T)＝FC,0+FC,1T2
wherein FC,0Is the Coulomb friction coefficient at no load, FC,1Is the coulomb friction coefficient under load.
2)
Figure BDA0002844524600000026
Wherein Fi＝kiδi，FiIs the friction force of the ith basic block, kiFor each basic block stiffness coefficient, δiElasticity of each basic blockDeformation; c-1(. cndot.) is a reversible function with a period of 2 pi as an output equation and the limit of spring deformation
Figure BDA0002844524600000031
Representing the sum of the M basic block friction forces.
[3] Determining the viscous friction torque of the system as follows:
Figure BDA0002844524600000032
wherein sgn (. cndot.) is a sign function, FSIs the Stribeck friction coefficient, F (0) ═ FC,0Exp (. cndot.) is an exponential function, |. cndot. | is an absolute value function, VSIs the Stribeck velocity, μ is the Stribeck form factor, FV,1，FV,2，FV，3A first, a second and a third coefficient of friction speed, Ft,1，Ft,2Respectively a first friction temperature coefficient and a second friction temperature coefficient, t0For a given temperature, 20 ℃ is generally chosen.
[4]And (3) identifying system parameters: according to the established GMS model of the electric power-assisted brake system, the static friction parameters of the model have four parameters which are respectively: fC,0，FC,1，FS，VS，μ，FV,1，FV,2，FV，3，Ft,1，Ft,2And the ten static parameters are obtained by applying a genetic algorithm and combining test result identification.
3. After the GMS friction model of the system is obtained, the adaptive dynamic coefficients are calculated:
the adaptive dynamic coefficient was obtained by a nonlinear synovium observer and the first extended GMS friction model. The nonlinear synovium observer estimates the state of the system according to measurable values, and the estimated state quantity of the system is used for driving the adaptive estimation. The measurable values include motor current, brake master cylinder hydraulic pressure and temperature. The estimation signals comprise the rotating speed, the torque and the temperature of each part of the system and the rotating speed of the rotating angle of the motor. Calculating the friction force F of the system according to the estimated state quantity of the system:
Figure BDA0002844524600000033
wherein KτIs a motor torque constant, B is a viscous friction coefficient,
Figure BDA0002844524600000034
for the purpose of the estimated motor current,
Figure BDA0002844524600000035
for the purpose of the estimated rotational speed of the motor,
Figure BDA0002844524600000036
is a derivative of the estimated rotational speed of the motor,
Figure BDA0002844524600000037
respectively estimated displacement, velocity and acceleration of the mechanism,
Figure BDA0002844524600000038
for the machine torque calculated from the inverse kinematic equation based on the estimated machine motion,
Figure BDA0002844524600000039
in order to be able to estimate the temperature,
Figure BDA00028445246000000310
is the viscous friction torque of the system found from the estimated state of the system.
According to the first extended GMS friction model:
Figure BDA00028445246000000311
in the formula
Figure BDA0002844524600000041
For adaptive dynamic parametersNumber, FC,0Is the Coulomb friction coefficient at no load, FC,1Is the Coulomb friction coefficient under load, Fi＝kiδi，FiIs the friction force of the ith basic block, kiFor each basic block stiffness coefficient, δiElastic deformation of each basic block; c-1(. cndot.) is a reversible function with a period of 2 pi as an output equation and the limit of spring deformation
Figure BDA0002844524600000042
Representing the sum of the M basic block frictional forces,
Figure BDA0002844524600000043
is the viscous friction torque of the system found from the estimated state of the system.
Substituting the estimated state quantity and the initial adaptive dynamic coefficient of the system into the first extended GMS friction model to obtain friction force
Figure BDA0002844524600000044
To be provided with
Figure BDA0002844524600000045
Calculating a self-adaptive dynamic coefficient for the target function by adopting a gradient descent method; the gradient descent method may be arbitrarily selected from those described in the prior art.
4. According to the target brake master cylinder hydraulic pressure p of the systemdAnd calculating the torque of each part of the system by combining the target hydraulic change rate with an inverse dynamic model of the system, and calculating the static feedforward compensation of the system.
5. Calculating and calculating the total output quantity of the control system:
Figure BDA0002844524600000046
wherein
Figure BDA0002844524600000047
For dynamic feed-forward compensation, T2Is based onTorque, u, calculated from inverse kinematic equation for system stateFFFor static feed-forward compensation, uFBFor the PID controller output, u is the total output, i.e., motor current value.
The invention has the beneficial effects that:
the invention provides a self-adaptive friction compensation control method for an electric power-assisted braking system. According to two same extended GMS friction models, the accurate output of the braking force of the electric power-assisted braking system is controlled by a control method of static feedforward and self-adaptive dynamic feedforward friction compensation and feedback, and the output torque of the electric power-assisted braking system is more accurate.
Drawings
Other features, objects and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments thereof, which is to be read in connection with the accompanying drawings.
FIG. 1 is a block diagram of adaptive friction compensation control based on GMS friction model, where pdIs a target master cylinder hydraulic pressure, e is a difference between the target master cylinder hydraulic pressure and an actually measured master cylinder hydraulic pressure, T is a torque of the mechanism calculated from the inverse dynamics model, u is a torque of the mechanism calculated from the inverse dynamics modelFFIs a feed-forward static friction compensation quantity uFBIs a PID feedback control amount of the feedback control,
Figure BDA0002844524600000051
is an adaptive dynamic friction compensation feed forward quantity based on the second extended GMS friction model,
Figure BDA0002844524600000052
is the dynamic adaptive coefficient, theta is the motor rotation angle, and t is the temperature of the mechanism.
FIG. 2 is a block diagram of dynamic adaptive coefficient estimation, where i is the measured current of the motor, p is the measured master cylinder hydraulic pressure, t is the measured system temperature, θ is the measured rotational angle of the motor,
Figure BDA0002844524600000053
is the value of the current that is estimated,
Figure BDA0002844524600000054
is the estimated rotational speed of the motor and,
Figure BDA0002844524600000055
is the estimated acceleration of the motor and,
Figure BDA0002844524600000056
is the value of the estimated temperature at which,
Figure BDA0002844524600000057
is the estimated displacement, velocity and acceleration of the mechanism, T is the torque of the mechanism calculated from the inverse dynamics model of the system, KτIs a motor torque constant, B is a viscous friction coefficient, F is a friction force calculated from a state quantity estimated by the system,
Figure BDA0002844524600000058
friction force estimated for friction of first extended GMS
Figure BDA0002844524600000059
The difference between the value of the first and second values of F,
Figure BDA00028445246000000510
is a dynamic adaptive coefficient calculated from the cost function.
Detailed Description
In the description of the present invention, it is to be understood that the terms indicating an orientation or positional relationship are based on the orientation or positional relationship shown in the drawings only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the elements referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus, should not be construed as limiting the present invention.
Embodiments of the present invention are further described below with reference to the accompanying drawings.
1. Establishing a dynamic equation of the electric power-assisted brake system:
the system comprises a motor, a speed reducing and moment increasing mechanism, a motion conversion mechanism and a brake master cylinder, wherein the motor output torque converts the motor force into the thrust of a brake master cylinder ejector rod through the speed reducing and moment increasing mechanism and the motion conversion mechanism so as to push the brake master cylinder together with a driver to generate hydraulic pressure.
The motion equation of the motor is as follows:
Figure BDA00028445246000000511
the motion equations of the speed reduction and torque increase mechanism and the motion conversion mechanism are as follows:
Figure BDA00028445246000000512
Figure BDA00028445246000000513
Figure BDA00028445246000000514
in the formula is TmFor the output of torque of the motor, JmIs equivalent rotational inertia of a motor shaft, theta is a motor rotation angle, TlAs the load torque, mcFor the mass of the ejector rod of the brake master cylinder, xcIn order to brake the displacement of the ejector rod of the main cylinder,
Figure BDA0002844524600000061
for braking the acceleration of the master cylinder ram, FsFor the force acting on the brake master cylinder, p is the hydraulic pressure of the brake master cylinder, A is the cross-sectional area of the brake master cylinder, eta is the transmission efficiency of the transmission mechanism, TbH is the displacement of a linear component corresponding to one rotation of a rotating component in the motion conversion mechanism, and F' is the total friction force of the system.
2. Establishing a GMS friction model of the system:
the GMS friction model is a method for simulating a contact unit between two surfaces by adopting a certain number of springs without mass blocks and connected in parallel, and each basic block has inherent hysteresis characteristics; after corresponding displacement signals are input into the model, because conditions of different basic blocks in the model entering a pre-sliding stage and a sliding stage are different, the hysteresis curves of the respective hysteresis curves are integrated to form the overall hysteresis curve of the system.
[1] Establishing a mathematical model of the total extended GMS friction model:
Figure BDA0002844524600000062
in the formula
Figure BDA0002844524600000063
For the estimated total friction of the system, FC(z, ω, T) is the coulomb friction torque of the system, Fv(ω, t) is the viscous friction torque of the system; z is the state of the system, ω is the rotational speed of the motor, T is the torque of the mechanism, and T is the temperature of the system.
[2] Determining the coulomb friction torque of the system as follows:
FC(z,ω,T)＝F(T)H(z,ω)
wherein F (T) is a function of the Coulomb coefficient of friction; h (z, ω) is a hysteresis function.
The following assumptions are made for the GMS model:
1)F(T)＝FC,0+FC,1T2
wherein FC,0Is the Coulomb friction coefficient at no load, FC,1Is the coulomb friction coefficient under load.
2)
Figure BDA0002844524600000064
Wherein Fi＝kiδi，FiIs the friction force of the ith basic block, kiFor each basic block stiffness coefficient, δiElastic deformation of each basic block; c-1(. cndot.) is a reversible function with a period of 2 pi as an output equation and the limit of spring deformation
Figure BDA0002844524600000065
Representing the sum of the M basic block friction forces.
[3] Determining the viscous friction torque of the system as follows:
Figure BDA0002844524600000071
wherein sgn (. cndot.) is a sign function, FSIs the Stribeck friction coefficient, F (0) ═ FC,0Exp (. cndot.) is an exponential function, |. cndot. | is an absolute value function, VSIs the Stribeck velocity, μ is the Stribeck form factor, FV,1，FV,2，FV，3A first, a second and a third coefficient of friction speed, Ft,1，Ft,2Respectively a first friction temperature coefficient and a second friction temperature coefficient, t0For a given temperature, 20 ℃ is generally chosen.
[4]And (3) identifying system parameters: according to the established GMS model of the electric power-assisted brake system, the static friction parameters of the model have four parameters which are respectively: fC,0，FC,1，FS，VS，μ，FV,1，FV,2，FV，3，Ft,1，Ft,2And the ten static parameters are obtained by applying a genetic algorithm and combining test result identification.
3. After the GMS friction model of the system is obtained, the adaptive dynamic coefficients are calculated:
the adaptive dynamic coefficient was obtained by a nonlinear synovium observer and the first extended GMS friction model. The nonlinear synovium observer estimates the state of the system according to measurable values, and the estimated state quantity of the system is used for driving the adaptive estimation. The measurable values include motor current, brake master cylinder hydraulic pressure and temperature. The estimation signals comprise the rotating speed, the torque and the temperature of each part of the system and the rotating speed of the rotating angle of the motor. Calculating the friction force F of the system according to the estimated state quantity of the system:
Figure BDA0002844524600000072
wherein K isτIs a motor torque constant, B is a viscous friction coefficient,
Figure BDA0002844524600000073
for the purpose of the estimated motor current,
Figure BDA0002844524600000074
for the purpose of the estimated rotational speed of the motor,
Figure BDA0002844524600000075
is a derivative of the estimated rotational speed of the motor,
Figure BDA0002844524600000076
respectively estimated displacement, velocity and acceleration of the mechanism,
Figure BDA0002844524600000077
for the machine torque calculated from the inverse kinematic equation based on the estimated machine motion,
Figure BDA0002844524600000078
in order to be able to estimate the temperature,
Figure BDA0002844524600000079
is the viscous friction torque of the system found from the estimated state of the system.
According to the first extended GMS friction model:
Figure BDA00028445246000000710
in the formula
Figure BDA00028445246000000711
For adapting dynamic parameters, FC,0Is the Coulomb friction coefficient at no load, FC,1Is the Coulomb friction coefficient under load, Fi＝kiδi，FiIs the friction force of the ith basic block, kiFor each basic block stiffness coefficient, δiElastic deformation of each basic block; c-1(. cndot.) is a reversible function with a period of 2 pi as an output equation and the limit of spring deformation
Figure BDA00028445246000000712
Representing the sum of the M basic block frictional forces,
Figure BDA0002844524600000081
is the viscous friction torque of the system found from the estimated state of the system.
Substituting the estimated state quantity and the initial adaptive dynamic coefficient of the system into the first extended GMS friction model to obtain friction force
Figure BDA0002844524600000082
To be provided with
Figure BDA0002844524600000083
Calculating a self-adaptive dynamic coefficient for the target function by adopting a gradient descent method; the gradient descent method may be arbitrarily selected from those described in the prior art.
4. According to the target brake master cylinder hydraulic pressure p of the systemdAnd calculating the torque of each part of the system by combining the target hydraulic change rate with an inverse dynamic model of the system, and calculating the static feedforward compensation of the system.
5. Calculating and calculating the total output quantity of the control system:
Figure BDA0002844524600000084
wherein
Figure BDA0002844524600000085
For dynamic feed-forward compensation, T2According to the state of the systemTorque, u, calculated against the kinetic equationFFFor static feed-forward compensation, uFBFor the PID controller output, u is the total output, i.e., motor current value.

Claims (3)

1. An adaptive friction compensation control method of an electric power-assisted brake system is characterized in that feedforward control and feedback control are combined, wherein the feedforward control comprises static feedforward friction compensation and adaptive dynamic feedforward friction compensation;
the static feedforward friction compensation is obtained by calculating an inverse dynamics model of the electric power-assisted braking system according to the state of the system;
the self-adaptive dynamic feedforward friction compensation is to calculate the numerical value of the self-adaptive feedforward friction compensation according to the estimated system state in each sampling period, and comprises two parts of self-adaptive dynamic coefficient estimation and self-adaptive friction compensation friction calculation; the self-adaptive dynamic feedforward friction compensation is obtained through two extended GMS friction models, wherein a first extended GMS friction model is applied in self-adaptive dynamic coefficient estimation, and a second extended GMS friction model is applied in system friction torque estimation in self-adaptive friction feedforward compensation;
the method for establishing the expanded GMS friction model comprises the following steps:
[1] establishing a mathematical model of the total extended GMS friction model:
Figure FDA0002844524590000011
in the formula
Figure FDA0002844524590000012
For the purpose of estimating the total friction of the system,
Figure FDA0002844524590000013
for adaptive dynamic coefficients, FC(z, ω, T) is the coulomb friction torque of the system, Fv(ω, t) is the viscous friction torque of the system; z is the state of the system, ω is the rotational speed of the motor, and T is the motorThe torque of the structure, t is the temperature of the system;
[2] the coulomb friction torque of the system is:
FC(z,ω,T)＝F(T)H(z,ω)
wherein F (T) is a function of the Coulomb coefficient of friction; h (z, ω) is a hysteresis function;
the following assumptions are made for the GMS model:
1)F(T)＝FC,0+FC,1T2
wherein FC,0Is the Coulomb friction coefficient at no load, FC,1Is the coulomb friction coefficient under load;
2)
Figure FDA0002844524590000014
wherein Fi＝kiδi，FiIs the friction force of the ith basic block, kiFor each basic block stiffness coefficient, δiElastic deformation of each basic block; c-1(. cndot.) is a reversible function with the period of 2 pi, and is used as an output equation and the deformation limit of the spring,
Figure FDA0002844524590000015
representing the sum of M basic block friction forces;
[3] the viscous friction torque of the system is:
Figure FDA0002844524590000016
wherein sgn (. cndot.) is a sign function; fSIs the Stribeck coefficient of friction; f (0) ═ FC,0Exp (·) is an exponential function; | is an absolute value function; vSIs the Stribeck speed; μ is the Stribeck shape factor; fV,1，FV,2，FV，3A first friction speed coefficient, a second friction speed coefficient and a third friction speed coefficient respectively; ft,1，Ft,2A first friction temperature coefficient and a second friction temperature coefficient respectively; t is t0Is a specified temperature;
[4]identifying system parameters: according to the established GMS model of the electric power-assisted brake system, the static friction parameters of the model have four parameters which are respectively: fC,0，FC,1，FS，VS，μ，FV,1，FV,2，FV，3，Ft,1，Ft,2And the ten static parameters are obtained by applying a genetic algorithm and combining test result identification.
2. The method of claim 1, further comprising: the self-adaptive dynamic coefficient is obtained by a nonlinear synovial observer and an extended GMS friction model; the nonlinear synovium observer is used for estimating the state of the system according to measurable values, and the estimated state quantity of the system is used for driving the adaptive estimation; the measurable values comprise motor current and rotation angle, brake master cylinder hydraulic pressure and temperature; the estimation signals comprise displacement speed and acceleration of each part of the system, torque and temperature, and motor rotation angle and rotation speed; calculating the friction force F of the system according to the estimated state quantity of the system, and substituting the estimated state quantity of the system and the initial adaptive dynamic coefficient into the first extended GMS friction model to obtain the estimated friction force
Figure FDA0002844524590000021
To be provided with
Figure FDA0002844524590000022
And calculating the self-adaptive dynamic coefficient for the target function by adopting a gradient descent method.
3. The method of claim 1, further comprising: and substituting the self-adaptive dynamic coefficient, the torque calculated according to the inverse dynamics model and the temperature into the second GMS friction model to obtain the friction torque compensated by the self-adaptive dynamic friction of the system.
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