CN111580539A - Friction identification and compensation control method for Lorentz inertially stabilized platform - Google Patents
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Abstract
The invention discloses a friction identification and compensation control method for a Lorentz inertially stabilized platform. Aiming at the nonlinear friction force existing between a bearing and a stator when the Lorentz inertially stabilized platform works, a LuGre friction model of static and dynamic friction characteristics under the deflection of the platform is established. Measuring a Stribeck curve through a uniform-speed deflection experiment, performing data fitting by adopting a linear regression equation based on a least square method, and identifying static parameters of a model; based on the viscous friction coefficient in the static parameters, the micro bristle deformation idea is adopted, the pre-sliding phenomenon is equivalent to second-order damped oscillation motion, and the dynamic parameters are calculated through the step response of a measurement system. And according to the identified static and dynamic parameters, constructing a Lyapunov function by adopting a backstepping recursion idea, completing the design of the nonlinear feedback compensation controller, and solving the problem of the interference of nonlinear friction torque on rotor deflection. The invention belongs to the field of inertially stabilized platform control, and is suitable for identification and compensation control of nonlinear friction torque of a platform.
Description
Technical Field
The invention relates to an inertially stabilized platform control technology, in particular to a friction identification and compensation control method for a Lorentz inertially stabilized platform.
Background
The chariot, the ship and the aircraft are difficult to shake in posture during driving, which causes the problems of inaccurate attack, unsmooth communication and unclear photographing. The existing stabilizer is divided into an integral type and a local type: the integral stabilizing device has large volume and mass and poor stability and precision, and is difficult to meet the high precision requirements in the fields of weapon stabilized aiming, ship-borne communication, unmanned aerial vehicle reconnaissance and the like; the local type anti-rolling device has the advantages of high control bandwidth, good stability precision, convenience in mounting and dismounting and the like, and is suitable for performing high-precision attitude compensation on local loads. The existing local anti-rolling device mainly comprises a servo platform, a stewart platform and a magnetic suspension platform, wherein the servo platform and the stewart platform are mainly used for bearing and transmitting through a mechanical bearing, and the control bandwidth and the stability precision are limited; the traditional magnetic suspension platform adopts a magnetic bearing technology, so that the control bandwidth and the stability precision are improved, but the adopted magnetic resistance magnetic bearing has the defect of nonlinearity of electromagnetic force and control current.
The Chinese application patent 202010295514.X an inner rotor Lorentz inertia stable platform and 202010295521.X a Lorentz inertia stable platform provide a scheme of adopting a spherical Lorentz force magnetic bearing, solve the non-linearity problem of the electromagnetic force of the magnetic resistance force magnetic bearing, further improve the control precision of the platform and realize large-angle deflection and quick response of the platform.
The Lorentz inertia stable platform outputs electromagnetic force by changing the winding current of the magnetic bearing to drive the rotor to deflect radially, so as to realize attitude compensation. The inside of the platform adopts a ball bearing structure, so that the friction between a rotor framework and a stator support body in the bearing is reduced to a certain degree, but obvious rolling friction and static friction force still exist. And because the working characteristics of the platform, the radial rotating speed of the rotor often passes zero, and the stability precision of the platform during starting and low-speed maneuvering is seriously influenced by the existence of friction interference.
Disclosure of Invention
The invention aims to provide a method for identifying and compensating the friction of a Lorentz inertially stabilized platform aiming at the inherent friction of a spherical ball bearing of the Lorentz inertially stabilized platform, so as to reduce the interference of the friction on the stabilization precision of the platform.
The purpose of the invention is realized by the following technical scheme:
the invention relates to a friction identification and compensation control method of a Lorentz inertially stabilized platform, which aims at the nonlinear friction force between a bearing and a stator when the Lorentz inertially stabilized platform works, and establishes a LuGre friction model of static and dynamic friction characteristics under the deflection of the platform;
measuring a Stribeck curve through a uniform-speed deflection experiment, performing data fitting by adopting a linear regression equation based on a least square method, and identifying static parameters of a model;
based on the viscous friction coefficient in the static parameters, the microscopic bristle deformation idea is adopted, the preslip phenomenon is equivalent to second-order damped oscillation motion, and the dynamic parameters are calculated through the step response of a measurement system;
and according to the identified static and dynamic parameters, constructing a Lyapunov function by adopting a backstepping recursion idea, completing the design of the nonlinear feedback compensation controller, and solving the problem of the interference of nonlinear friction torque on rotor deflection.
According to the technical scheme provided by the invention, the friction identification and compensation control method for the Lorentz inertially stabilized platform, provided by the embodiment of the invention, is used for establishing a friction model with static and dynamic friction characteristics under the deflection state of the Lorentz inertially stabilized platform, obtaining the friction torque of the platform by identifying friction parameters, and performing compensation control on the nonlinear friction torque, so that the stability precision of the platform is improved, and the method is suitable for identifying and compensating the nonlinear friction coefficient of the Lorentz inertially stabilized platform with a spherical rotor structure.
Drawings
Fig. 1 is a schematic flow chart of a method for identifying and compensating for friction of a lorentz inertially stabilized platform according to an embodiment of the present invention;
FIG. 2 is a diagram illustrating an example of a fitting curve for static parameter identification according to an embodiment of the present invention;
the example parameter values in fig. 2 are: coulomb friction torque Tc0.3Nm, maximum static friction moment TsIs 0.305Nm, critical Stribeck speed ws0.02rad/s, coefficient of viscous friction σ2Is 0.03 Nms/rad;
FIG. 3 is an exemplary diagram of a micro step response for dynamic parameter identification according to an embodiment of the present invention;
the example parameter values in fig. 3 are: coefficient of bristle stiffness σ0Is 2.6 × 106Nm/rad, bristle damping coefficient σ1Is 0.08 Nms/rad;
FIG. 4 is a schematic view of a rotor deflection system of a platform according to an embodiment of the present invention;
in fig. 4: the mark 1 is a rotor assembly, the mark 2 is magnetic steel, the mark 3 is a stator winding, the mark 4 is a spherical ball bearing, the mark 5 is an angular rate gyroscope, the mark 6 is a support body, and the mark 7 is a stator framework; x, Y after the stator windings are energized, the same and opposite ampere forces F are generated in the magnetic field of magnetic steeliDriving the rotor to deflect around X and Y axes, and deflecting angle signal theta of the rotorxAnd thetayMeasured by an angular rate gyroscope, the arm of deflection force is lm；
FIG. 5 is a block diagram of a control structure according to an embodiment of the present invention;
in fig. 5, the nonlinear element has an input of w and an output of g (w).
Detailed Description
The embodiments of the present invention will be described in further detail below. Details which are not described in detail in the embodiments of the invention belong to the prior art which is known to the person skilled in the art.
The invention discloses a friction identification and compensation control method for a Lorentz inertially stabilized platform, which has the following preferred specific implementation modes:
aiming at the nonlinear friction force existing between a bearing and a stator when a Lorentz inertially stabilized platform works, a LuGre friction model of static and dynamic friction characteristics under the deflection of the platform is established;
measuring a Stribeck curve through a uniform-speed deflection experiment, performing data fitting by adopting a linear regression equation based on a least square method, and identifying static parameters of a model;
based on the viscous friction coefficient in the static parameters, the microscopic bristle deformation idea is adopted, the preslip phenomenon is equivalent to second-order damped oscillation motion, and the dynamic parameters are calculated through the step response of a measurement system;
and according to the identified static and dynamic parameters, constructing a Lyapunov function by adopting a backstepping recursion idea, completing the design of the nonlinear feedback compensation controller, and solving the problem of the interference of nonlinear friction torque on rotor deflection.
The method specifically comprises the following steps:
(1) aiming at the problem of non-linearity of friction force between a bearing and a stator, a LuGre friction model is established:
wherein theta is the deflection angle of the rotor, z is the deformation of the bristles, and four static parameters Tc、Ts、wsAnd σ2Respectively comprising coulomb friction torque, maximum static friction torque, critical Stribeck speed and viscous friction coefficient, and two dynamic parameters sigma0And σ1The stiffness coefficient and damping coefficient of the bristles, T, respectivelyfIs the total friction torque;
(2) identifying static parameters:
according to the conservation law of angular momentum, under the state that the platform rotor deflects at a constant speed, the resultant torque is zero, namely the torque output by the Lorentz magnetic bearing is equal to the friction torque, and the corresponding friction torque is obtained by calculating through measuring the current in the magnetic bearing winding:
4nBLlmI+Tf＝0
wherein n is the number of turns of the coil, B is magnetic induction intensity, L is effective length of the electrified coil, and LmIs rotor deflection arm, I is winding current, 4nBLlmCan be recorded as deflection current stiffness Ki；
Under the constant speed state, the bristle deformation quantity z is kept constant, dz/dt is equal to 0, and the bristle deformation quantity z is substituted into a LuGre model to obtain a Stribeck friction model:
drawing a corresponding Stribeck friction curve by measuring friction torque data under a plurality of groups of constant-speed deflection angles, using a data fitting tool in MATLAB, and respectively adopting two linear regression equations T based on a least square method1＝σ2w+TcAnd T2＝kw+TsFitting, equation T1Has a slope of the coefficient of viscous friction σ2Intercept is Coulomb friction torque Tc，T2Intercept of (2) is the maximum static friction moment Ts，T1And T2The abscissa of the intersection point of the two equations is the critical Stribeck speed wsThereby obtaining four static parameters Tc、Ts、wsAnd σ2A value of (d);
(3) identifying dynamic parameters:
the static friction force in the preslip stage is related to the bristle deformation by identifying the bristle rigidity coefficient sigma0Mane damping coefficient sigma1Obtaining the friction torque of the pre-sliding stage by the two dynamic parameters; according to Newton's law of motion, a rotor deflection dynamic model is established:
j is radial rotational inertia of the rotor, and the bristle deformation z is approximate to a rotor deflection angle theta in the pre-sliding stage;
according to the Dahl effect, in the preslip phase, the bristles exhibit stiffness and damping characteristics, K, when the deflection force exerted by the magnetic bearing winding current disappearsiWhen I ═ 0, the motion appears as free vibration of a damped second order system, and the transfer function can be written in the form of a second order system:
wherein K is the equivalent gain of the second-order system, and the oscillation frequency w of the second-order system can be obtained by the formulanAnd damping ratio ζ:
zeta is a relation including0、σ1And σ2In which the static parameter σ2The method comprises the following steps of (1) knowing;
according to the steady state value theta of the second-order system response in the control theoryssAnd overshoot MpThe calculation formula is as follows:
the winding input current I is given a step signal of smaller amplitude, so that the deflection force K is giveniI is less than the maximum static friction force, and a response steady-state value theta is obtained by measuring a microscopic step response curve of the systemssAnd overshoot MpThe experimental value of (a);
the bristle stiffness coefficient sigma can be calculated by the calculation formula of the steady state value and the overshoot0And ζ:
further obtain the bristle damping coefficient sigma1；
(4) Designing a friction torque compensation controller by a backstepping method;
the mover deflection dynamics model is written in the form of state variables:
wherein, C0＝Ki/J，C1＝σ0/J，C2＝σ1J and C3＝(σ0+σ1) the/J are known amounts;
set the observer for the bristle deformation z:
defining a tracking error:
wherein, thetadAnd wdRespectively setting an angle and an angular speed;
according to the recursion design idea of a backstepping method, selecting e1Lyapunov function V1：
Will V1And (3) derivation of time:
to make V1The derivative of (a) is negative, then (theta)d-w) is to be equivalent to-k1·e1Namely, the following conditions are satisfied:
selection of e2Lyapunov function V2：
Will V2And (3) derivation of time:
make V2The derivative of (b) satisfies a negative definite condition:
the control law under asymptotically stable conditions can be determined:
aiming at the nonlinear friction force existing between the bearing and the stator when the Lorentz inertially stabilized platform works, the LuGre friction model of static and dynamic friction characteristics under the deflection of the platform is established. Measuring a Stribeck curve through a uniform-speed deflection experiment, performing data fitting by adopting a linear regression equation based on a least square method, and identifying static parameters of a model; based on the viscous friction coefficient in the static parameters, the micro bristle deformation idea is adopted, the pre-sliding phenomenon is equivalent to second-order damped oscillation motion, and the dynamic parameters are calculated through the step response of a measurement system. According to the identified static and dynamic parameters, a reverse step recursion idea is adopted to construct a Lyapunov function, the design of the nonlinear feedback compensation controller is completed, the problem of interference of nonlinear friction torque on rotor deflection is solved, and the method is suitable for identification and compensation control of the nonlinear friction torque of the platform.
The specific embodiment is as follows:
as shown in fig. 1, in the implementation process, the implementation steps of the present invention are as follows:
1. aiming at the problem of non-linearity of friction force between a bearing and a stator, a LuGre friction model is established:
wherein theta is the deflection angle of the rotor, z is the deformation of the bristles, and four static parameters Tc、Ts、wsAnd σ2Respectively comprising coulomb friction torque, maximum static friction torque, critical Stribeck speed and viscous friction coefficient, and two dynamic parameters sigma0And σ1The stiffness coefficient and damping coefficient of the bristles, T, respectivelyfIs the total friction torque.
2. Identifying static parameters:
according to the conservation law of angular momentum, under the state that the platform rotor deflects at a constant speed, the resultant torque is zero, namely the torque output by the Lorentz magnetic bearing is equal to the friction torque, and the corresponding friction torque is obtained by calculating through measuring the current in the magnetic bearing winding:
4nBLlmI+Tf＝0
wherein n is the number of turns of the coil, B is the magnetic induction intensity, L is the effective length of the electrified coil, and LmIs rotor deflection arm, I is winding current, 4nBLlmCan be recorded as deflection current stiffness Ki。
Under the constant speed state, the bristle deformation quantity z is kept constant, dz/dt is equal to 0, and the bristle deformation quantity z is substituted into a LuGre model to obtain a Stribeck friction model:
drawing a corresponding Stribeck friction curve by measuring friction torque data under a plurality of groups of constant-speed deflection angles, using a data fitting tool in MATLAB, and respectively adopting two linear regression equations T based on a least square method1＝σ2w+TcAnd T2＝kw+TsFitting, equation T1Has a slope of the coefficient of viscous friction σ2Intercept is Coulomb friction torque Tc，T2Intercept of (2) is the maximum static friction moment Ts，T1And T2The abscissa of the intersection point of the two equations is the critical Stribeck speed wsThereby obtaining four static parameters Tc、Ts、wsAnd σ2The value of (c).
3. Identifying dynamic parameters:
the static friction force in the preslip stage is related to the bristle deformation by identifying the bristle rigidity coefficient sigma0Mane damping coefficient sigma1Obtaining the friction torque of the pre-sliding stage by the two dynamic parameters; according to Newton's law of motion, a rotor deflection dynamic model is established as follows:
wherein J is the radial rotational inertia of the rotor, and the bristle deformation z is approximate to the rotor deflection angle theta in the pre-sliding stage.
According to the Dahl effect, in the preslip phase, the bristles exhibit stiffness and damping characteristics, K, when the deflection force exerted by the magnetic bearing winding current disappearsiWhen I ═ 0, the motion appears as free vibration of a damped second order system, and the transfer function can be written in the form of a second order system:
wherein K is the equivalent gain of the second-order system, and the oscillation frequency w of the second-order system can be obtained by the formulanAnd damping ratio ζ:
zeta is a relation including0、σ1And σ2In which the static parameter σ2Are known.
According to the steady state value theta of the second-order system response in the control theoryssAnd overshoot MpThe calculation formula is as follows:
the winding input current I is given a step signal of smaller amplitude, so that the deflection force K is giveniI is less than the maximum static friction force, and a response steady-state value theta is obtained by measuring a microscopic step response curve of the systemssAnd the experimental value of the overshoot Mp, and the bristle stiffness coefficient sigma can be calculated by the calculation formula of the steady state value and the overshoot0And ζ:
further obtain the bristle damping coefficient sigma1。
4. The friction torque compensation controller is designed by a backstepping method. The mover deflection dynamics model is written in the form of state variables:
wherein, C0＝Ki/J，C1＝σ0/J，C2＝σ1J and C3＝(σ0+σ1) The values of/J are known.
Set the observer for the bristle deformation z:
defining a tracking error:
wherein, thetadAnd wdRespectively an angle given value and an angular speed given value.
According to the recursion design idea of a backstepping method, selecting e1Lyapunov function V1：
Will V1And (3) derivation of time:
to make V1The derivative of (a) is negative, then (theta)d-w) is to be equivalent to-k1·e1Namely, the following conditions are satisfied:
selection of e2Lyapunov function V2：
Will V2And (3) derivation of time:
make V2The derivative of (b) satisfies a negative definite condition:
the control law under asymptotically stable conditions can be determined:
the above formula belongs to a backstepping method to design the control rate, and is easy to realize in control.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (2)
1. A method for identifying and compensating friction of a Lorentz inertially stabilized platform is characterized by comprising the following steps:
aiming at the nonlinear friction force existing between a bearing and a stator when a Lorentz inertially stabilized platform works, a LuGre friction model of static and dynamic friction characteristics under the deflection of the platform is established;
measuring a Stribeck curve through a uniform-speed deflection experiment, performing data fitting by adopting a linear regression equation based on a least square method, and identifying static parameters of a model;
based on the viscous friction coefficient in the static parameters, the microscopic bristle deformation idea is adopted, the preslip phenomenon is equivalent to second-order damped oscillation motion, and the dynamic parameters are calculated through the step response of a measurement system;
and according to the identified static and dynamic parameters, constructing a Lyapunov function by adopting a backstepping recursion idea, completing the design of the nonlinear feedback compensation controller, and solving the problem of the interference of nonlinear friction torque on rotor deflection.
2. The method for identifying and compensating for the friction of the lorentz inertially-stabilized platform as recited in claim 1, wherein:
the method specifically comprises the following steps:
(1) aiming at the problem of non-linearity of friction force between a bearing and a stator, a LuGre friction model is established:
wherein theta is the deflection angle of the rotor, z is the deformation of the bristles, and four static parameters Tc、Ts、wsAnd σ2Respectively comprising coulomb friction torque, maximum static friction torque, critical Stribeck speed and viscous friction coefficient, and two dynamic parameters sigma0And σ1The stiffness coefficient and damping coefficient of the bristles, T, respectivelyfIs the total friction torque;
(2) identifying static parameters:
according to the conservation law of angular momentum, under the state that the platform rotor deflects at a constant speed, the resultant torque is zero, namely the torque output by the Lorentz magnetic bearing is equal to the friction torque, and the corresponding friction torque is obtained by calculating through measuring the current in the magnetic bearing winding:
4nBLlmI+Tf＝0
wherein n is the number of turns of the coil, B is magnetic induction intensity, L is effective length of the electrified coil, and LmIs rotor deflection arm, I is winding current, 4nBLlmCan be recorded as deflection current stiffness Ki；
Under the constant speed state, the bristle deformation quantity z is kept constant, dz/dt is equal to 0, and the bristle deformation quantity z is substituted into a LuGre model to obtain a Stribeck friction model:
drawing a corresponding Stribeck friction curve by measuring friction torque data under a plurality of groups of constant-speed deflection angles, using a data fitting tool in MATLAB, and respectively adopting two linear regression equations T based on a least square method1＝σ2w+TcAnd T2＝kw+TsFitting, equation T1Has a slope of the coefficient of viscous friction σ2Intercept is Coulomb friction torque Tc，T2Intercept of (2) is the maximum static friction moment Ts，T1And T2The abscissa of the intersection point of the two equations is the critical Stribeck speed wsThereby obtaining four static parameters Tc、Ts、wsAnd σ2A value of (d);
(3) identifying dynamic parameters:
the static friction force in the preslip stage is related to the bristle deformation by identifying the bristle rigidity coefficient sigma0Mane damping coefficient sigma1Obtaining the friction torque of the pre-sliding stage by the two dynamic parameters; according to Newton's law of motion, a rotor deflection dynamic model is established:
j is radial rotational inertia of the rotor, and the bristle deformation z is approximate to a rotor deflection angle theta in the pre-sliding stage;
according to the Dahl effect, in the preslip phase, the bristles exhibit stiffness and damping characteristics, K, when the deflection force exerted by the magnetic bearing winding current disappearsiWhen I ═ 0, the motion appears as free vibration of a damped second order system, and the transfer function can be written in the form of a second order system:
wherein K is the equivalent gain of the second-order system, and can be obtained by the formulaOscillation frequency w of the second order systemnAnd damping ratio ζ:
zeta is a relation including0、σ1And σ2In which the static parameter σ2The method comprises the following steps of (1) knowing;
according to the steady state value theta of the second-order system response in the control theoryssAnd overshoot MpThe calculation formula is as follows:
the winding input current I is given a step signal of smaller amplitude, so that the deflection force K is giveniI is less than the maximum static friction force, and a response steady-state value theta is obtained by measuring a microscopic step response curve of the systemssAnd overshoot MpThe experimental value of (a);
the bristle stiffness coefficient sigma can be calculated by the calculation formula of the steady state value and the overshoot0And ζ:
further obtain the bristle damping coefficient sigma1；
(4) Designing a friction torque compensation controller by a backstepping method;
the mover deflection dynamics model is written in the form of state variables:
wherein, C0＝Ki/J，C1＝σ0/J，C2＝σ1J and C3＝(σ0+σ1) the/J are known amounts;
set the observer for the bristle deformation z:
defining a tracking error:
wherein, thetadAnd wdRespectively setting an angle and an angular speed;
according to the recursion design idea of a backstepping method, selecting e1Lyapunov function V1：
Will V1And (3) derivation of time:
to make V1The derivative of (a) is negative, then (theta)d-w) is to be equivalent to-k1·e1Namely, the following conditions are satisfied:
selection of e2Lyapunov function V2：
Will V2And (3) derivation of time:
make V2The derivative of (b) satisfies a negative definite condition:
the control law under asymptotically stable conditions can be determined:
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| CN113110305A (en) * | 2021-04-30 | 2021-07-13 | 华中科技大学 | Friction modeling method of electromechanical system and application thereof |
| CN114184192A (en) * | 2021-12-27 | 2022-03-15 | 北京计算机技术及应用研究所 | Method for obtaining angular velocity measurement channel transfer function of inertial measurement unit |
| CN114527710A (en) * | 2022-02-21 | 2022-05-24 | 天津大学 | Feed direct torque control method and device based on friction compensation and storage medium |
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| CN112799304A (en) * | 2021-01-06 | 2021-05-14 | 武汉理工大学 | Dual-motor synchronous control method and device based on time-varying friction compensation |
| CN112799304B (en) * | 2021-01-06 | 2022-06-14 | 武汉理工大学 | Dual-motor synchronous control method and device based on time-varying friction compensation |
| CN112859743A (en) * | 2021-01-21 | 2021-05-28 | 华中科技大学 | Method and device for monitoring health state of numerical control machine tool based on friction identification |
| CN113110305A (en) * | 2021-04-30 | 2021-07-13 | 华中科技大学 | Friction modeling method of electromechanical system and application thereof |
| CN114184192A (en) * | 2021-12-27 | 2022-03-15 | 北京计算机技术及应用研究所 | Method for obtaining angular velocity measurement channel transfer function of inertial measurement unit |
| CN114184192B (en) * | 2021-12-27 | 2023-09-26 | 北京计算机技术及应用研究所 | Method for acquiring angular velocity measurement channel transfer function of inertial measurement device |
| CN114527710A (en) * | 2022-02-21 | 2022-05-24 | 天津大学 | Feed direct torque control method and device based on friction compensation and storage medium |
| CN114527710B (en) * | 2022-02-21 | 2023-09-26 | 天津大学 | Friction compensation-based feed direct torque control method, apparatus and storage medium |
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