CN110460277A - Single motor servo system friction non-linear compensation method based on particle swarm algorithm - Google Patents

Single motor servo system friction non-linear compensation method based on particle swarm algorithm Download PDF

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CN110460277A
CN110460277A CN201910661720.5A CN201910661720A CN110460277A CN 110460277 A CN110460277 A CN 110460277A CN 201910661720 A CN201910661720 A CN 201910661720A CN 110460277 A CN110460277 A CN 110460277A
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friction
motor
particle
stribeck
model
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吴益飞
张翠艳
刘洋
郭健
陈庆伟
高熠
李胜
宋恺
高珺宁
靳懿
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Nanjing Tech University
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    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02PCONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02PCONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/14Estimation or adaptation of machine parameters, e.g. flux, current or voltage
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02PCONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P25/00Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
    • H02P25/02Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor

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  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Feedback Control In General (AREA)

Abstract

The invention discloses a kind of single motor servo system friction non-linear compensation method based on particle swarm algorithm, including following procedure: the offline revolving speed for obtaining single motor servo-system and moment of friction data;According to the revolving speed and moment of friction data obtained offline, parameter identification is carried out to Stribeck friction model using particle swarm algorithm, the Stribeck friction model after being recognized;On-line operation single motor servo-system, moment of friction is obtained in real time according to the Stribeck friction model after identification, and moment of friction is compensated by feed-forward coefficients to current signal, the feedforward compensation structure based on Stribeck friction model is constructed, single motor servo system friction nonlinear compensation can be realized using the structure.The method of the present invention improves tracking accuracy of the motor servo system when tracking sinusoidal signal, can effectively solve since non-linear in tribology causes system to there are problems that static tracking error, holistic approach is simple, facilitates application.

Description

Single-motor servo system friction nonlinear compensation method based on particle swarm optimization
Technical Field
The invention relates to the field of motor control, in particular to a single-motor servo system friction nonlinear compensation method based on a particle swarm algorithm.
Background
In motor servo systems, the system often exhibits frictional non-linear conditions due to some inherent mechanical characteristics of the transmission. For servo systems, friction non-linearity has some effect on the dynamic performance and steady state accuracy of the system. And for some high precision servo systems the effect of frictional non-linearity will be greater.
The frictional non-linearity is mainly caused by the relative motion between the bearing parts or between two parts with contact surfaces. Friction models can be divided into two broad categories: static models and dynamic models.
In servo systems, frictional non-linearity can have a large impact on system control performance. Friction increases the static difference of the system and causes the system to shake during low speed reverse motion. In order to reduce the influence of friction nonlinearity on the system, many compensation algorithms for friction nonlinearity are proposed.
There are two main methods for friction compensation: one approach is to consider only the linear part of the friction, i.e. to compensate only the coulomb and viscous friction forces; another approach is to treat the friction as an external disturbance and estimate the compensation with a disturbance observer. With the increase of the control precision requirement, the two methods can hardly achieve satisfactory effect. The former method does not consider the influence of static friction force, and the coulomb friction model mentioned in the thesis of "On the modeling of the coulomb friction" is a time delay model in an ideal state, does not describe the friction torque at the zero-speed moment, and considers that the friction force is independent of the speed; the limitation of the latter method is that the disturbance observer is based on a linear system theory, and the thesis "review on characteristics, modeling and control compensation of frictional nonlinear links" realizes the disturbance observer based on the linear theory, but it is difficult to effectively estimate the accurate frictional torque.
Disclosure of Invention
The invention aims to provide a single-motor servo system friction nonlinear compensation method based on a particle swarm algorithm.
The technical scheme for realizing the purpose of the invention is as follows: the single motor servo system friction nonlinear compensation method based on the particle swarm algorithm comprises the following steps:
step 1, obtaining the rotating speed and friction torque data of a single motor servo system in an off-line manner;
step 2, performing parameter identification on the Stribeck friction model by using a particle swarm algorithm according to the rotating speed and friction torque data obtained offline to obtain an identified Stribeck friction model;
and 3, operating the single motor servo system on line, acquiring friction torque in real time according to the identified Stribeck friction model, compensating the friction torque to a current signal through a feedforward coefficient, constructing a feedforward compensation structure based on the Stribeck friction model, and realizing the friction nonlinear compensation of the single motor servo system by using the structure.
Compared with the prior art, the invention has the following remarkable advantages: 1) by adopting a Stribeck friction model, the friction nonlinear characteristics of pre-sliding displacement, friction lag, changed critical friction force, viscous sliding and the like can be well reflected, and the reliability of nonlinear compensation is improved; 2) by adopting the Stribeck friction model, the creeping motion and limit cycle phenomena caused by friction nonlinearity can be overcome, and the reliability of nonlinear compensation is improved; 3) parameter identification is carried out on the Stribeck friction model of the system by adopting a particle swarm algorithm, so that the identification precision is higher, and the compensation effect is further improved; 4) the tracking precision of the motor servo system in tracking the sine signal is improved, and the problem of static tracking error of the system caused by friction nonlinearity is effectively solved; 5) the method is simple and convenient to apply.
Drawings
FIG. 1 is a structural diagram of friction nonlinear compensation of a single motor servo system based on a particle swarm optimization.
FIG. 2 is a flow chart of the implementation principle of the particle swarm optimization algorithm of the present invention.
FIG. 3 is a simplified block diagram of a single motor servo control system according to the present invention.
Fig. 4 is a graph of actual measured rotational speed versus friction torque in an embodiment of the present invention.
FIG. 5 is a graphical representation of a position error without friction compensation in an embodiment of the present invention.
FIG. 6 is a graphical representation of a position error curve including friction compensation in an embodiment of the present invention.
Detailed Description
The invention relates to a single motor servo system friction nonlinear compensation method based on a particle swarm algorithm, which comprises the following steps of:
step 1, obtaining the rotating speed and friction torque data of a single motor servo system in an off-line manner;
step 2, performing parameter identification on the Stribeck friction model by using a particle swarm algorithm according to the rotating speed and friction torque data obtained offline to obtain an identified Stribeck friction model;
and 3, operating the single motor servo system on line, acquiring friction torque in real time according to the identified Stribeck friction model, compensating the friction torque to a current signal through a feedforward coefficient, constructing a feedforward compensation structure based on the Stribeck friction model, and realizing the friction nonlinear compensation of the single motor servo system by using the structure. FIG. 1 is a structural diagram of friction nonlinear compensation of a single-motor servo system based on a particle swarm optimization.
Further, step 1 obtains the data of the rotating speed and the friction torque of the single motor servo system in an off-line manner, specifically:
step 1-1, controlling a motor to track constant rotating speed v under the offline conditionmMeasuring the output of the speed controller to obtain a current value Iq
Step 1-2, according to IqObtaining the friction torque F at the current moment:
F=CtIq
in the formula, CtIs the motor torque coefficient;
whereby the rotational speed v is obtainedmAnd friction torque F.
Further, step 2, performing parameter identification on the Stribeck friction model by using a particle swarm algorithm to obtain an identified Stribeck friction model, and specifically referring to fig. 2:
the Stribeck friction model is:
wherein,
wherein F is friction, v is relative movement velocity, and FcIs coulomb force, FsAt maximum static friction, vsIs the Stribeck velocity, B is the viscous friction coefficient, deltasIs an empirical parameter;
step 2-1, setting the population scale of particles as n and learning factor c1、c2The parameter motion range is [ s ]1,s2]Maximum number of iterations M, and randomly initializing a position vector of particles asAnd velocity vectorVelocity range of [ v ]1,v2];
Step 2-2, calculating particles according to initial positions of the particlesAdaptation value f (x) of childi) Initializing the optimal position of the population by using the position vector of the particle with the optimal adaptation value;
2-3, selecting an inertial algorithm factor omega, updating the speed and position vector of the particle, generating a new population, judging whether the position and speed of the particle are out of range, namely whether the position and speed of the particle exceed the parameter motion range, and discarding the particle information if the position and speed of the particle exceed the parameter motion range;
wherein, the updating formula of the particles is as follows:
vid=ωvid+c1s1(pid-xid)+c2s2(pgd-xid)
xid=xid+vid
wherein i is 1,2, 1, n, D is 1,2, D, c1、c2Is a learning factor, vidIs the velocity, x, of the particleidAs the position of the current particle, s1、s2Is a random number between (0, 1), pidFor the optimal position, p, of the particle i searched when searching the solution in the D-dimensional spacegdFor the optimal position of the population, the inertial algorithm factor omega adopts a linear decreasing mode;
step 2-4, the current adaptive value f (x) of the particlesi) Comparing with the self historical optimal value, and if the current adaptive value f (x)i) If the optimal value is better than the historical optimal value, the optimal value of the self is updated to be f (x)i) And a particle location;
step 2-5, the current adaptive value f (x) of the particlesi) Comparing with the population optimal value, if the current adaptive value f (x)i) If the optimal value of the population is better than the optimal value of the population, the optimal value of the population is updated to be f (x)i) And a particle location;
step 2-6, judging whether the iteration times reach the maximum iteration times, if so, ending the iteration process, and obtaining the optimal particle solution, namely the parameters of the identified Stribeck friction modelObtaining an identified Stribeck friction model according to the identified parameters; if notAnd if so, jumping to the step 2-3.
Exemplarily and preferably, the population size n of the particles is 80, and the maximum number of iterations M is 500; four parametersParameter range of motion s1,s2]Are all (0, 1), velocity range [ v1,v2]Is [ -1, 1 [ ]](ii) a Learning factor c1=1.2、c2=1.8。
Further, step 3, acquiring friction torque in real time according to the identified Stribeck friction model, compensating the friction torque to a current signal through a feedforward coefficient, and constructing a feedforward compensation structure based on the Stribeck friction model, specifically:
step 3-1, taking the rotating speed as an input variable, acquiring a friction torque F in real time according to the identified Stribeck friction model, and compensating the friction torque F to a current signal through a feedforward coefficient, wherein the formula is as follows:
wherein the friction compensation current I is fed forwardF(t)=kF×F,kFAs coefficient of friction feedback, Iq(t) is the current after applying the feedforward compensation,the current before applying feedforward compensation is obtained;
step 3-2, mixingSubstituting the single motor dynamic model to obtain a dynamic model of a feedforward compensation structure based on the Stribeck friction model, wherein the dynamic model comprises the following steps:
wherein, the single-motor dynamics model is as follows:
in the formula of Uq(t) is the equivalent voltage of the motor on the q axis; i isq(t) is the equivalent current of the motor on the q axis; rqThe equivalent resistance of the motor on the q axis; l isqIs the equivalent inductance of the motor in the q axis, CeIs the motor back electromotive force coefficient; thetam(t) is the motor angle;the angular velocity of the motor;the angular acceleration of the motor; ctIs the motor torque coefficient; k is a radical ofsIs the stiffness coefficient of the motor; i.e. imThe reduction ratio between the small gear and the big gear; j. the design is a squaremAnd bmRespectively the rotational inertia and the viscosity coefficient of the motor; j. the design is a squareLAnd bLMoment of inertia and viscosity coefficient of the load; tau ismThe elastic moment between the motor and the load; thetaL(t) is the load angle;is the load angular velocity;is the angular acceleration of the load; t isLIs the load torque.
The present invention will be described in further detail with reference to examples.
Examples
According to the Stribeck friction model of the single motor servo system, the parameters needing to be identified areUnder the off-line condition, a group of constant rotating speeds are input into a single motor servo system as input instructions, a speed controller in the system adopts a PI controller, the selected input speed interval is-1 rad/s, and sampling is carried outThe period was 0.03rad/s and a set of friction torque values were obtained as shown in FIG. 4.
Initializing each parameter of the particle swarm to enable the population scale n of the particles to be 80; the maximum iteration number M is 500; four parametersRange of motion of parameter s1,s2]Are all (0, 1), velocity range [ v1,v2]Is [ -1, 1 [ ]](ii) a Learning factor c1=1.2、c21.8, the results of the offline identification of the Stribeck friction model by the particle swarm algorithm are shown in the following table 1:
table 1 identifies Stribeck friction model results
As can be seen from Table 1, the Stribeck friction model identified by the particle swarm algorithm has small error and accurate model identification.
After obtaining the identified Stribeck friction model, adding the Stribeck friction model into a single motor system, wherein a current loop PI controller in the system is P-17.90, and I-0.009; the parameter of the speed loop PI controller is P ═ 0.2, I ═ 0.45, the position controller adopts the feature model-based feedforward control and the discrete second-order sliding mode conforming controller, the friction compensation coefficient is kF0.3. Inputting equivalent sinusoidal signals of 60 degrees/s and 60 degrees/s 2, operating a single-motor servo system on line, acquiring friction torque in real time according to the identified friction model, and obtaining the friction torque according to the formulaThe real-time friction torque is compensated to the current signal through a feedforward coefficient.
The position error curves without friction compensation and the position error curves with friction compensation are shown in fig. 5 and 6, respectively, and it can be seen from the graphs that the position error with friction compensation is significantly reduced.
According to the invention, the Stribeck friction model can well overcome crawling motion and limit cycle phenomena caused by friction nonlinearity, various friction nonlinearity characteristics are reflected, the parameter identification is carried out on the Stribeck friction model of the system by adopting a particle swarm algorithm, the identification precision is higher, and the precision of nonlinear compensation is further improved. In addition, the method improves the tracking precision of the motor servo system when tracking the sine signal, can effectively solve the problem of static tracking error of the system caused by friction nonlinearity, and has simple integral method and convenient application.

Claims (5)

1. A single motor servo system friction nonlinear compensation method based on particle swarm optimization is characterized by comprising the following steps:
step 1, obtaining the rotating speed and friction torque data of a single motor servo system in an off-line manner;
step 2, performing parameter identification on the Stribeck friction model by using a particle swarm algorithm according to the rotating speed and friction torque data obtained offline to obtain an identified Stribeck friction model;
and 3, operating the single motor servo system on line, acquiring friction torque in real time according to the identified Stribeck friction model, compensating the friction torque to a current signal through a feedforward coefficient, constructing a feedforward compensation structure based on the Stribeck friction model, and realizing the friction nonlinear compensation of the single motor servo system by using the structure.
2. The particle swarm algorithm-based single-motor servo system friction nonlinear compensation method according to claim 1, wherein the step 1 of obtaining the rotation speed and friction torque data of the single-motor servo system offline specifically comprises:
step 1-1, controlling a motor to track constant rotating speed v under the offline conditionmMeasuring the output of the speed controller to obtain a current value Iq
Step 1-2, according to IqObtaining the friction torque F at the current moment:
F=CtIq
in the formula, CtIs the motor torque coefficient;
whereby the rotational speed v is obtainedmAnd friction torque F.
3. The single motor servo system friction nonlinearity compensation method according to claim 1, wherein the step 2 of performing parameter identification on the Stribeck friction model by using the particle swarm algorithm to obtain the identified Stribeck friction model specifically comprises:
the Stribeck friction model is:
wherein,
wherein F is friction, v is relative movement velocity, and FcIs coulomb force, FsAt maximum static friction, vsIs the Stribeck velocity, B is the viscous friction coefficient, deltasIs an empirical parameter;
step 2-1, setting the population scale of particles as n and learning factor c1、c2The parameter motion range is [ s ]1,s2]Maximum number of iterations M, and randomly initializing a position vector of particles asAnd velocity vectorVelocity range of [ v ]1,v2];
Step 2-2, calculating the adaptive value f (x) of the particle according to the initial position of the particlei) Initializing the optimal position of the population by using the position vector of the particle with the optimal adaptation value;
2-3, selecting an inertial algorithm factor omega, updating the speed and position vector of the particle, generating a new population, judging whether the position and speed of the particle are out of range, namely whether the position and speed of the particle exceed the parameter motion range, and discarding the particle information if the position and speed of the particle exceed the parameter motion range;
wherein, the updating formula of the particles is as follows:
vid=ωvid+c1s1(pid-xid)+c2s2(pgd-xid)
xid=xid+vid
wherein i is 1,2, 1, n, D is 1,2, D, c1、c2Is a learning factor, vidIs the velocity, x, of the particleidAs the position of the current particle, s1、s2Is a random number between (0, 1), pidFor the optimal position, p, of the particle i searched when searching the solution in the D-dimensional spacegdFor the optimal position of the population, the inertial algorithm factor omega adopts a linear decreasing mode;
step 2-4, the current adaptive value f (x) of the particlesi) Comparing with the self historical optimal value, and if the current adaptive value f (x)i) If the optimal value is better than the historical optimal value, the optimal value of the self is updated to be f (x)i) And a particle location;
step 2-5, the current adaptive value f (x) of the particlesi) Comparing with the population optimal value, if the current adaptive value f (x)i) If the optimal value of the population is better than the optimal value of the population, the optimal value of the population is updated to be f (x)i) And a particle location;
step 2-6, judging whether the iteration times reach the maximum iteration times, if so, ending the iteration process, and obtaining the optimal particle solution, namely the parameters of the identified Stribeck friction modelObtaining an identified Stribeck friction model according to the identified parameters; if not, jumping to the step 2-3.
4. The particle swarm algorithm-based single-motor servo system friction nonlinear compensation method according to claim 3, wherein the population size n of the particles is 80, and the maximum iteration number M is 500; four parametersParameter range of motion s1,s2]Are all (0, 1), velocity range [ v1,v2]Is [ -1, 1 [ ]](ii) a Learning factor c1=1.2、c2=1.8。
5. The single-motor servo system friction nonlinear compensation method based on the particle swarm optimization according to claim 1, wherein step 3 is to obtain friction torque in real time according to the identified Stribeck friction model, compensate the friction torque to a current signal through a feedforward coefficient, and construct a feedforward compensation structure based on the Stribeck friction model, specifically:
step 3-1, taking the rotating speed as an input variable, acquiring a friction torque F in real time according to the identified Stribeck friction model, and compensating the friction torque F to a current signal through a feedforward coefficient, wherein the formula is as follows:
wherein the friction compensation current I is fed forwardF(t)=kF×F,kFAs coefficient of friction feedback, Iq(t) is the current after applying the feedforward compensation,the current before applying feedforward compensation is obtained;
step 3-2, mixingSubstituting the single motor dynamic model to obtain a dynamic model of a feedforward compensation structure based on the Stribeck friction model, wherein the dynamic model comprises the following steps:
wherein, the single-motor dynamics model is as follows:
in the formula of Uq(t) is the equivalent voltage of the motor on the q axis; i isq(t) is the equivalent current of the motor on the q axis; rqThe equivalent resistance of the motor on the q axis; l isqIs the equivalent inductance of the motor in the q axis, CeIs the motor back electromotive force coefficient; thetam(t) is the motor angle;the angular velocity of the motor;the angular acceleration of the motor; ctIs the motor torque coefficient; k is a radical ofsIs the stiffness coefficient of the motor; i.e. imThe reduction ratio between the small gear and the big gear; j. the design is a squaremAnd bmRespectively the rotational inertia and the viscosity coefficient of the motor; j. the design is a squareLAnd bLMoment of inertia and viscosity coefficient of the load; tau ismThe elastic moment between the motor and the load; thetaL(t) is the load angle;is the load angular velocity;is the angular acceleration of the load; t isLIs the load torque.
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