CN110460277A - Friction nonlinearity compensation method for single motor servo system based on particle swarm optimization - Google Patents

Abstract

The invention discloses a friction nonlinear compensation method for a single-motor servo system based on a particle swarm algorithm, which includes the following process: obtaining the speed and friction torque data of the single-motor servo system off-line; according to the speed and friction torque data obtained off-line, using particle The group algorithm is used to identify the parameters of the Stribeck friction model to obtain the identified Stribeck friction model; run the single-motor servo system online, obtain the friction torque in real time according to the identified Stribeck friction model, and compensate the friction torque to the current signal through the feedforward coefficient. A feed-forward compensation structure based on the Stribeck friction model is constructed, and the friction nonlinear compensation of the single-motor servo system can be realized by using this structure. The method of the invention improves the tracking accuracy of the motor servo system when tracking sinusoidal signals, can effectively solve the problem of static tracking errors in the system due to non-linear friction, and the overall method is simple and convenient for application.

Description

Friction nonlinearity compensation method for single motor servo system based on particle swarm optimization

technical field

The invention relates to the field of motor control, in particular to a friction nonlinear compensation method for a single motor servo system based on particle swarm algorithm.

Background technique

In the motor servo system, due to some inherent mechanical characteristics of the transmission device, the system often exhibits friction nonlinearity. For the servo system, friction nonlinearity will have a certain influence on the dynamic performance and steady-state accuracy of the system. And for some high-precision servo systems, the impact caused by friction nonlinearity will be even greater.

The non-linear factor of friction is mainly caused by relative motion between bearing components or between two parts with contact surfaces. Friction models can be divided into two categories: static models and dynamic models.

In a servo system, the friction nonlinearity will have a great influence on the control performance of the system. Friction will increase the static difference of the system and cause system jitter during low-speed reversing movements. In order to reduce the impact of friction nonlinearity on the system, many compensation algorithms for friction nonlinearity have been proposed.

There are two main methods for existing friction compensation: one method is to only consider the linear part of the friction, that is, to only compensate Coulomb friction and viscous friction; the other method is to treat friction as an external disturbance and use the disturbance observation tor estimate compensation. With the improvement of control precision requirements, it is difficult for these two methods to achieve satisfactory results. The former method does not consider the influence of static friction. The Coulomb friction model mentioned in the paper "On the modeling of coulomb frinction" is a time-delay model in an ideal state. It does not describe the friction torque at zero speed, and it is considered that the friction The size and speed have nothing to do; the limitation of the latter method is that the disturbance observer is based on the linear system theory. Effectively estimate the precise friction torque.

Contents of the invention

The purpose of the present invention is to provide a friction nonlinear compensation method for a single-motor servo system based on particle swarm algorithm.

The technical solution for realizing the object of the present invention is: a friction nonlinear compensation method for a single-motor servo system based on particle swarm algorithm, comprising the following steps:

Step 1. Obtain the speed and friction torque data of the single-motor servo system offline;

Step 2. According to the rotational speed and friction torque data obtained off-line, use the particle swarm algorithm to identify the parameters of the Stribeck friction model, and obtain the identified Stribeck friction model;

Step 3. Run the single-motor servo system online, obtain the friction torque in real time according to the identified Stribeck friction model, and compensate the friction torque to the current signal through the feed-forward coefficient, and construct a feed-forward compensation structure based on the Stribeck friction model. Using this structure, It can realize friction nonlinear compensation of single motor servo system.

Compared with the prior art, the present invention has the remarkable advantages as follows: 1) the Stribeck friction model is adopted, which can well reflect the non-linear characteristics of friction such as pre-sliding displacement, friction hysteresis, changing critical friction force and viscous sliding, and improve the non-linear Reliability of compensation; 2) Using the Stribeck friction model can overcome the crawling motion and limit cycle phenomenon caused by friction nonlinearity, and improve the reliability of nonlinear compensation; 3) Use the particle swarm algorithm to identify the parameters of the Stribeck friction model of the system, The identification accuracy is higher, and then the compensation effect is improved; 4) The tracking accuracy of the motor servo system is improved when tracking the sinusoidal signal, and the problem of static tracking error in the system due to friction nonlinearity is effectively solved; 5) The method is simple and convenient for application.

Description of drawings

Fig. 1 is a structural diagram of the present invention based on the particle swarm algorithm for friction nonlinear compensation of a single-motor servo system.

Fig. 2 is a flowchart of the realization principle of the particle swarm optimization algorithm of the present invention.

Fig. 3 is a simplified block diagram of the control system of the single-motor servo system of the present invention.

Fig. 4 is a curve diagram of actually measured rotation speed and friction torque in the embodiment of the present invention.

FIG. 5 is a graph of position error without friction compensation in an embodiment of the present invention.

FIG. 6 is a graph of position error including friction compensation in an embodiment of the present invention.

Detailed ways

The friction nonlinear compensation method of single motor servo system based on particle swarm algorithm in the present invention comprises the following steps:

Step 1. Obtain the speed and friction torque data of the single-motor servo system offline;

Step 2. According to the rotational speed and friction torque data obtained off-line, use the particle swarm algorithm to identify the parameters of the Stribeck friction model, and obtain the identified Stribeck friction model;

Step 3. Run the single-motor servo system online, obtain the friction torque in real time according to the identified Stribeck friction model, and compensate the friction torque to the current signal through the feed-forward coefficient, and construct a feed-forward compensation structure based on the Stribeck friction model. Using this structure, It can realize friction nonlinear compensation of single motor servo system. Figure 1 shows the structure diagram of friction nonlinear compensation of single motor servo system based on particle swarm optimization algorithm.

Further, step 1 obtains the speed and friction torque data of the single-motor servo system offline, specifically:

Step 1-1. In the offline situation, control the motor to track a constant speed v _m , measure the output of the speed controller, and obtain the current value I _q ;

Step 1-2. Obtain the friction torque F at the current moment according to I _q :

F＝C _t I _q

In the formula, C _t is the motor torque coefficient;

The data of the rotational speed v _m and the friction torque F are thus obtained.

Further, step 2 uses the particle swarm algorithm to identify the parameters of the Stribeck friction model, and obtains the identified Stribeck friction model. Combined with Figure 2, the details are as follows:

The Stribeck friction model is:

in,

In the formula, F is the friction force, v is the relative motion velocity, F _c is the Coulomb force, F _s is the maximum static friction force, v _s is the Stribeck velocity, B is the viscous friction coefficient, and δ _s is an empirical parameter;

Step 2-1. Set the population size of particles as n, learning factors c ₁ and c ₂ , parameter movement range as [s ₁ , s ₂ ], maximum number of iterations M, and randomly initialize the position vector of particles as and the velocity vector The speed range is [v ₁ ,v ₂ ];

Step 2-2. Calculate the fitness value f( _xi ) of the particle according to the initial position of the particle, and initialize the optimal position of the population with the position vector of the particle with the best fitness value;

Step 2-3, select the inertia algorithm factor ω, update the velocity and position vector of the particle, generate a new population, and judge whether the position and velocity of the particle are out of bounds, that is, whether it exceeds the range of motion of the parameter, and if it exceeds, the particle information will be discarded;

Among them, the particle update formula is:

v _id ＝ωv _id +c ₁ s ₁ (p _id -x _id )+c ₂ s ₂ (p _gd -x _id )

x _id = x _id +v _id

In the formula, i=1,2,...,n, d=1,2,...,D, c ₁ and c ₂ are the learning factors, v _id is the velocity of the particle, x _id is the position of the current particle, s ₁ and s ₂ are random numbers between (0, 1), p _id is the optimal position searched by particle i when searching for the solution of D-dimensional space, p _gd is the optimal position of the population, and the inertial algorithm factor ω adopts a linear decreasing method;

Step 2-4. Compare the particle’s current fitness value f( _xi ) with its own historical optimal value. If the current fitness value f( _xi ) is better than the historical optimal value, update its own optimal value to f ( _xi ) and particle position;

Step 2-5. Compare the current fitness value f( _xi ) of the particle with the optimal value of the population. If the current fitness value f( _xi ) is better than the optimal value of the population, update the optimal value of the population to f( x _i ) and particle position;

Step 2-6. Determine whether the number of iterations reaches the maximum number of iterations. If so, end the iterative process and obtain the optimal solution of the particle, which is the parameters of the identified Stribeck friction model. According to the identified parameters, the identified Stribeck friction model can be obtained; if not satisfied, skip to step 2-3.

Exemplarily preferably, the population size n of particles is 80, and the maximum number of iterations M=500; four parameters The motion range [s ₁ , s ₂ ] of the parameters is (0, 1), and the speed range [v ₁ , v ₂ ] is [-1, 1]; learning factors c ₁ =1.2, c ₂ =1.8.

Further, step 3 obtains the friction torque in real time according to the identified Stribeck friction model, and compensates the friction torque to the current signal through the feedforward coefficient to construct a feedforward compensation structure based on the Stribeck friction model, specifically:

Step 3-1. Taking the speed as an input variable, the friction torque F is obtained in real time according to the identified Stribeck friction model, and the friction torque F is compensated to the current signal through the feedforward coefficient. The formula used is:

Among them, feed-forward friction compensation current I _F (t) = k _F × F, k _F is the friction feedback coefficient, I _q (t) is the current after applying feed-forward compensation, is the current before no feed-forward compensation is applied;

Step 3-2, will Substituting the single-motor dynamic model to obtain the dynamic model of the feed-forward compensation structure based on the Stribeck friction model is:

Among them, the single-motor dynamic model is:

In the formula, U _q (t) is the equivalent voltage of the motor on the q-axis; I _q (t) is the equivalent current of the motor on the q-axis; R _q is the equivalent resistance of the motor on the q-axis; L _q is the motor on the q-axis The equivalent inductance of the q-axis, C _e is the back electromotive force coefficient of the motor; θ _m (t) is the angle of the motor; is the angular velocity of the motor; is the angular acceleration of the motor; C _t is the torque coefficient of the motor; k _s is the stiffness coefficient of the motor; i _m is the reduction ratio between the pinion and the gear; J _m and b _m are the moment of inertia and viscosity coefficient of the motor, respectively; J _L and b _L are the moment of inertia and viscosity coefficient of the load; τ _m is the elastic moment between the motor and the load; θ _L (t) is the load angle; is the load angular velocity; is the load angular acceleration; T _L is the load torque.

Below in conjunction with embodiment the present invention is described in further detail.

Example

According to the Stribeck friction model of the single-motor servo system, the parameters to be identified are In the offline situation, a set of constant speed is input into the single-motor servo system as an input command. The speed controller in the system adopts a PI controller, and the input speed range is selected to be -1rad/s～1rad/s, and the sampling period is 0.03 rad/s to obtain a set of friction torque values, as shown in Figure 4.

The parameters of initializing the particle swarm are the particle population size n is 80; the maximum number of iterations M=500; four parameters Parameter motion range [s ₁ , s ₂ ] is (0, 1), speed range [v ₁ , v ₂ ] is [-1, 1]; learning factors c ₁ = 1.2, c ₂ = 1.8, through particle swarm The results of the offline identification of the Stribeck friction model by the algorithm are shown in Table 1 below:

Table 1 Identification results of Stribeck friction model

It can be seen from Table 1 that the Stribeck friction model identified by particle swarm optimization algorithm has small error and accurate model identification.

After obtaining the identified Stribeck friction model, add it to the single motor system, the current loop PI controller in the system is P=17.90, I=0.009; the parameters of the speed loop PI controller are P=0.2, I=0.45 , the position controller adopts the feedforward control based on the characteristic model and the consistent controller of the discrete second-order sliding mode, and the friction compensation coefficient is k _F =0.3. Input 60°/s, 60°/s2 equivalent sinusoidal signal, run the single motor servo system online, and obtain the friction torque in real time according to the identified friction model, according to the formula Compensate the real-time friction torque to the current signal through the feed-forward coefficient.

The position error curves without friction compensation and the position error curves with friction compensation are shown in Figure 5 and Figure 6 respectively. It can be seen from the figure that the position error with friction compensation is significantly reduced.

The invention uses the Stribeck friction model to well overcome the creeping motion and limit cycle phenomenon caused by non-linear friction, and reflects various non-linear characteristics of friction, and uses the particle swarm algorithm to identify the parameters of the Stribeck friction model of the system, with higher identification accuracy , thereby improving the accuracy of nonlinear compensation. In addition, the method of the invention improves the tracking accuracy of the motor servo system when tracking sinusoidal signals, and can effectively solve the problem of static tracking errors in the system due to non-linear friction. The overall method is simple and convenient for application.

Claims (5)

1. A single motor servo system friction nonlinear compensation method based on particle swarm algorithm, is characterized in that, comprises the following steps: Step 1. Obtain the speed and friction torque data of the single-motor servo system offline; Step 2. According to the rotational speed and friction torque data obtained off-line, use the particle swarm algorithm to identify the parameters of the Stribeck friction model, and obtain the identified Stribeck friction model; Step 3. Run the single-motor servo system online, obtain the friction torque in real time according to the identified Stribeck friction model, and compensate the friction torque to the current signal through the feed-forward coefficient, and construct a feed-forward compensation structure based on the Stribeck friction model. Using this structure, It can realize friction nonlinear compensation of single motor servo system. 2. The non-linear compensation method for friction of a single-motor servo system based on the particle swarm optimization algorithm according to claim 1, wherein the offline acquisition of the speed and friction torque data of the single-motor servo system described in step 1 is specifically: Step 1-1. In the offline situation, control the motor to track a constant speed v _m , measure the output of the speed controller, and obtain the current value I _q ; Step 1-2. Obtain the friction torque F at the current moment according to I _q : F＝C _t I _q In the formula, C _t is the motor torque coefficient; The data of the rotational speed v _m and the friction torque F are thus obtained. 3. the single-motor servo system friction nonlinear compensation method based on particle swarm algorithm according to claim 1, it is characterized in that, the described step 2 utilizes particle swarm algorithm to carry out parameter identification to Stribeck friction model, obtains the Stribeck friction after identification model, specifically: The Stribeck friction model is: in, In the formula, F is the friction force, v is the relative motion velocity, F _c is the Coulomb force, F _s is the maximum static friction force, v _s is the Stribeck velocity, B is the viscous friction coefficient, and δ _s is an empirical parameter; Step 2-1. Set the population size of particles as n, learning factors c ₁ and c ₂ , parameter movement range as [s ₁ , s ₂ ], maximum number of iterations M, and randomly initialize the position vector of particles as and the velocity vector The speed range is [v ₁ ,v ₂ ]; Step 2-2. Calculate the fitness value f( _xi ) of the particle according to the initial position of the particle, and initialize the optimal position of the population with the position vector of the particle with the best fitness value; Step 2-3, select the inertia algorithm factor ω, update the velocity and position vector of the particle, generate a new population, and judge whether the position and velocity of the particle are out of bounds, that is, whether it exceeds the range of motion of the parameter, and if it exceeds, the particle information will be discarded; Among them, the particle update formula is: v _id ＝ωv _id +c ₁ s ₁ (p _id -x _id )+c ₂ s ₂ (p _gd -x _id ) x _id = x _id +v _id In the formula, i=1,2,...,n, d=1,2,...,D, c ₁ and c ₂ are the learning factors, v _id is the velocity of the particle, x _id is the position of the current particle, s ₁ and s ₂ are random numbers between (0, 1), p _id is the optimal position searched by particle i when searching for the solution of D-dimensional space, p _gd is the optimal position of the population, and the inertial algorithm factor ω adopts a linear decreasing method; Step 2-4. Compare the particle’s current fitness value f( _xi ) with its own historical optimal value. If the current fitness value f( _xi ) is better than the historical optimal value, update its own optimal value to f ( _xi ) and particle position; Step 2-5. Compare the current fitness value f( _xi ) of the particle with the optimal value of the population. If the current fitness value f( _xi ) is better than the optimal value of the population, update the optimal value of the population to f( x _i ) and particle position; Step 2-6. Determine whether the number of iterations reaches the maximum number of iterations. If so, end the iterative process and obtain the optimal solution of the particle, which is the parameters of the identified Stribeck friction model. According to the identified parameters, the identified Stribeck friction model can be obtained; if not satisfied, skip to step 2-3. 4. the single motor servo system friction nonlinear compensation method based on particle swarm optimization algorithm according to claim 3, is characterized in that, the population size n of described particle is 80, and maximum number of iterations M=500; Four parameters The motion range [s ₁ , s ₂ ] of the parameters is (0, 1), and the speed range [v ₁ , v ₂ ] is [-1, 1]; learning factors c ₁ =1.2, c ₂ =1.8. 5. The friction nonlinear compensation method for single-motor servo system based on particle swarm optimization algorithm according to claim 1, characterized in that, step 3 obtains the friction torque in real time according to the identified Stribeck friction model, and passes the friction torque through the front The feed coefficient is compensated to the current signal, and a feedforward compensation structure based on the Stribeck friction model is constructed, specifically: Step 3-1. Taking the speed as an input variable, the friction torque F is obtained in real time according to the identified Stribeck friction model, and the friction torque F is compensated to the current signal through the feedforward coefficient. The formula used is: Among them, feed-forward friction compensation current I _F (t) = k _F × F, k _F is the friction feedback coefficient, I _q (t) is the current after applying feed-forward compensation, is the current before no feed-forward compensation is applied; Step 3-2, will Substituting the single-motor dynamic model to obtain the dynamic model of the feed-forward compensation structure based on the Stribeck friction model is: Among them, the single-motor dynamic model is: In the formula, U _q (t) is the equivalent voltage of the motor on the q-axis; I _q (t) is the equivalent current of the motor on the q-axis; R _q is the equivalent resistance of the motor on the q-axis; L _q is the motor on the q-axis The equivalent inductance of the q-axis, C _e is the back electromotive force coefficient of the motor; θ _m (t) is the angle of the motor; is the angular velocity of the motor; is the angular acceleration of the motor; C _t is the torque coefficient of the motor; k _s is the stiffness coefficient of the motor; i _m is the reduction ratio between the pinion and the gear; J _m and b _m are the moment of inertia and viscosity coefficient of the motor, respectively; J _L and b _L are the moment of inertia and viscosity coefficient of the load; τ _m is the elastic moment between the motor and the load; θ _L (t) is the load angle; is the load angular velocity; is the load angular acceleration; T _L is the load torque.