CN105700470A - Method for reducing tracking error of machine tool servo feeding system - Google Patents

Abstract

The invention discloses a method for reducing tracking error of a machine tool servo feeding system. The method comprises following steps: 1) modeling for the machine tool servo feeding system and obtaining a system model for the servo feeding system; 2) establishing a frictional force mathematical model for the machine tool servo feeding system and identifying parameters; 3) performing pre-estimation to position variation of the servo feeding system by use of a Kalman state observer, calculating compensation frictional force for the servo feeding system according to the pre-estimated position variation, and performing real-time dynamic compensation to the servo feeding system frictional force according to the calculated compensation frictional force. According to the invention, Kalman state observer is used for realizing frictional force pre-estimation, and system tracking error is accurately controlled through frictional force compensation so that the frictional force real-time variation can be observed and pre-estimated in real time by the system and the frictional force can be compensated in the control system. The method can greatly reduces servo system tracking error.

Description

A kind of method for reducing lathe servo feed system tracking error

Technical field

The invention belongs to Computerized Numerical Control processing technology field, more particularly, to a kind of method for reducing lathe servo feed system tracking error。

Background technology

Servo feed system is widely used in machine-building and the course of processing of Digital Control。There is multiple nonlinear characteristic in this system, for instance friction, gap, hysteresis effect and external disturbance, these nonlinear characteristics bring very big impact can to the performance of system, and wherein non-linear friction is the most notable on the impact of the motor control performance of system。For high-precision workbench servo feed system, after eliminating ball-screw pitch error and gap, the friction existed in feed system becomes the main cause affecting motion control accuracy, and the impact how effectively eliminating friction becomes the key issue of accurately control。

Realized the control of servo feed system tracking error by the control and compensation of frictional force for how, prior art gives some researchs, currently existing scheme has certain effect based on the friciton compensation of classical model, but classical model is static models, it can not well show the dynamic characteristic of frictional force, and these dynamic characteristics will have a strong impact on systematic function, particularly tracking performance and positioning precision。Therefore, in the motor control that positioning accuracy request is higher, frictional force static models are adopted to compensate, it is difficult to meet performance requirement, and directly adopt frictional force feedforward compensation, or directly frictional force is incorporated into control system as disturbance, it is impossible to the change of enough real-time monitored frictional force, cannot regulating compensating parameter in real time so that frictional force to be compensated, the effect precision after therefore compensating is not high。

Summary of the invention

Disadvantages described above or Improvement requirement for prior art, the invention provides a kind of method for reducing lathe servo feed system tracking error, it realizes estimating frictional force by Kalman's observer, and pass through the compensation to frictional force thus reaching the purpose of accurately control, enable the system to real-time observation and estimate frictional force real-time change, and in the controls it is compensated, for reducing compensation control when servosystem tracking error is particularly slided in advance, there is remarkable result。

For achieving the above object, the present invention proposes a kind of method for reducing lathe servo feed system tracking error, it is characterised in that the method comprises the steps:

1) lathe servo feed system is modeled, it is thus achieved that the system model of servo feed system；

2) frictional force mathematical model the identified parameters of lathe servo feed system are set up；

3) utilize Kalman observer that the change in location of servo feed system is estimated, the compensation frictional force of servo feed system is calculated according to the change in location estimated, the frictional force of servo feed system is carried out Real-time and Dynamic compensation by the compensation frictional force according to calculating, and then realizes reducing the tracking error of lathe servo feed system。

As it is further preferred that described lathe servo feed system is modeled, it is thus achieved that the system model of servo feed system includes:

The system model setting up servo feed system isWherein, M_tRepresent the quality that the mechanical part of servo feed system is total, B_mRepresent the damping of servomotor, F_qRepresent the driving force of servo feed system,Representing the frictional force of servo feed system, x represents servo feed system feed shaft displacement, and z represents mane average deformation。

As it is further preferred that described mane average deformation z adopts following expression to express:

$\stackrel{\·}{z}=\stackrel{\·}{x}-\frac{{\mathrm{\δ}}_0}{g\left(\stackrel{\·}{x}\right)}z\left|\stackrel{\·}{x}\right|;$

Wherein,δ₀Represent mane rigidity, f_cRepresent coulomb frictional force, f_sRepresent maximum static friction force, v_sRepresent the characteristic velocity of Stribeck effect。

As it is further preferred that the described frictional force mathematical model setting up lathe servo feed system identified parameters include:

2.1) the frictional force mathematical model of lathe servo feed system is set up:

$F(\stackrel{\·}{x},z)={\mathrm{\δ}}_{0}z+{\mathrm{\δ}}_1(\stackrel{\·}{x}-{\mathrm{\δ}}_0\frac{\left|\stackrel{\·}{x}\right|}{g\left(\stackrel{\·}{x}\right)}z)+{\mathrm{\μ}}_v\stackrel{\·}{x};$

Wherein, δ₀Represent mane rigidity, δ₁Represent microcosmic damped coefficient, μ_vRepresent servo feed system feed shaft viscous friction coefficient；

2.2) parameter δ in identification frictional force mathematical model₀、δ₁、μ_v、f_c、f_sAnd v_sValue。

As it is further preferred that parameter δ in described identification frictional force mathematical model₀、δ₁、μ_v、f_c、f_sAnd v_sValue include:

Select to optimize cost function J_s, and minimize it, calculate and obtain parameter δ₀、δ₁、μ_v、f_c、f_sAnd v_sValue, described J_sEmploying following expression represents:

$J_s=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{e}_{ss}^2(X_s,{\stackrel{\·}{x}}_i)+\max \left\{\right|e_{ss}\left(X_s,\stackrel{\·}{x}\right)\left|\right\};$

In formula, N_sIt is the number of composition Stribeck effect point,Represent workbench steady-state error at various speeds respectively, wherein DescribedWithRepresenting the frictional force under stable state, it is by actually measured, described inWithRepresent estimation stable state under frictional force, it is by step 2.1) in frictional force mathematical model express。

As it is preferred that, described utilize Kalman observer that the change in location of servo feed system is estimated, the compensation frictional force of servo feed system is calculated according to the change in location estimated, the frictional force of servo feed system is carried out Real-time and Dynamic compensation by the compensation frictional force according to calculating, and then the tracking error realizing reducing lathe servo feed system includes:

3.1) expression formula that frictional force is associated is set up with state variable X:

$F=-M_t\[\begin{array}{ccc}0& a_{22}& a_{23}\end{array}\]X-B_m\stackrel{\·}{x};$

Wherein, $a_{22}=-\frac{1}{M_t}({\mathrm{\δ}}_1+{\mathrm{\μ}}_v+B_m),a_{23}=-\frac{1}{M_t}({\mathrm{\δ}}_0-{\mathrm{\δ}}_0{\mathrm{\δ}}_1\frac{\left|\stackrel{\·}{x}\right|}{g\left(\stackrel{\·}{x}\right)}),X=\left[\begin{array}{c}x\\ \stackrel{\·}{x}\\ z\end{array}\right];$

3.2) the kinetic model discrete form of servo feed system is set up:

X (k+1)=AX (k)+Bu (k)+v (k)；

Y (k+1)=CX (k)+n (k)；

$\hat{X}\left(k+1\right)=\hat{X}\left(k\right)+K\[Y\left(k\right)-C\widehat{X\left(K\right)}\];$

In formula, X (k+1), X (k) represent the state variable X position in k+1, k moment respectively, Represent that state variable X is in the estimation position in k+1, k moment respectively, Y (k), Y (k+1) represent the servo feed system output state variable in k+1, k moment respectively, v (k), n (k) are k moment white noise signal, u (k) represents servo feed system action function, K is yield value $A=\left[\begin{array}{ccc}0& 1& 0\\ 0& a_{22}& a_{23}\\ 0& 1& a_{33}\end{array}\right],$ $B=\left[\begin{array}{c}0\\ \frac{1}{M_t}\\ 0\end{array}\right],$ C=[100], $a_{33}=-{\mathrm{\δ}}_0\frac{\left|\stackrel{\·}{x}\right|}{g\left(\stackrel{\·}{x}\right)};$

3.3) covariance of state variable error is set upAnd calculate covariance forecast P (k+1), make covariance forecast P (k+1) converge to zero, calculate and obtain yield value K, this yield value K-band is entered formulaIn, calculate and obtain state variable in the position in k+1 moment

3.4) by step 3.3) middle acquisitionValue brings expression formula into as the input value of XIn, calculate the compensation frictional force obtaining servo feed system；

3.5) according to the compensations frictional force calculated, the frictional force of servo feed system carried out Real-time and Dynamic compensation, and then realize the tracking error of minimizing lathe servo feed system。

As it is further preferred that the covariance of described state variable errorEmploying following expression is expressed:

$\hat{P}\left(k\right)=\left\{\[\hat{X}\left(k\right)-E\left\{X\left(k\right)\right\}\]{\[\hat{X}\left(k\right)-E\left\{X\left(k\right)\right\}\]}^T\right\};$

In formula, E is covariance matrix。

As it is further preferred that described covariance forecast P (k+1) adopts following expression to express:

$P(k+1)=(I-KC)\left(A\hat{P}\right(k)A^T+V)\×{(I-KC)}^T+{\mathrm{KNK}}^T;$

In formula, I is vector matrix, and V, N represent the covariance matrix of white noise signal v (k), n (k) respectively。

As it is further preferred that described white noise signal v (k), n (k) covariance matrix particularly as follows:

$V=\left[\begin{array}{ccc}0.0008& 0& 0\\ 0& 9.6\×{10}^5& 0\\ 0& 0& 1\end{array}\right],N=\mathrm{0.34.}$

As it is further preferred that covariance forecasts that P (k+1) obtains yield value K when converging to zero and is: K=PC^T[CPC^T+N]^-1, wherein P is the covariance matrix of covariance forecast P (k+1)。

In general, by the contemplated above technical scheme of the present invention compared with prior art, mainly possess following technological merit:

1. in the present invention, the state variable of Frictional model is observed by introducing state observer, realize real-time monitored change in location thus realizing estimating in real time change in friction force, the frictional force moment of the servo feed system estimated is added in torque signals as compensation, by the frictional force torque compensation of the servo feed system of estimation to the moment after PID controller regulates realizing the accurate control to servo feed system so that feed shaft tracking error is obviously improved。

2. in the present invention, introduce dynamic friction model and not only describe the static characteristic of frictional force, dynamic characteristic such as the sudden change power of change, frictional force hysteresis phenomenon, stopping-sliding motion etc. are also presented, the real-time monitored to dynamic friction is realized by design point observer, and in the controls it being compensated, the tracking error for reducing servo feed axle compensates control when particularly sliding in advance and has remarkable result。

3. design con-trol device process of the present invention is easy, it is possible to system parameter is estimated；By on semi-physical simulation platform, the real-time adjustment to design parameter can be realized, frictional force being compensated with simple and flexible, it is achieved control the tracking error of servo feed system, has the accuracy of higher motility, stability, observability and tracking error。

Accompanying drawing explanation

Fig. 1 be the embodiment of the present invention based on Friction Compensation closed-loop control system structural representation；

Fig. 2 is the method flow diagram for reducing lathe servo feed system tracking error of the embodiment of the present invention；

Fig. 3 (a) is that precision machine tool servo feed system zerofriction force compensates the tracking error design sketch controlled；

Fig. 3 (b) is the tracking error design sketch that precision machine tool servo feed system has Friction Compensation to control。

Detailed description of the invention

In order to make the purpose of the present invention, technical scheme and advantage clearly understand, below in conjunction with drawings and Examples, the present invention is further elaborated。Should be appreciated that specific embodiment described herein is only in order to explain the present invention, is not intended to limit the present invention。As long as just can be mutually combined additionally, technical characteristic involved in each embodiment of invention described below does not constitute conflict each other。

A kind of method for reducing lathe servo feed system tracking error of the present invention, it is regulated by PID and realizes controlling based on the Friction Compensation of Kalman observer, as shown in Figure 1, its ultimate principle is: the servo parameter of PID regulable control device, the motor making drive system rotates in a predetermined manner, thus driving feed system (such as workbench) according to predetermined orbiting motion, working table movement process is measured its actual frictional force, the positional information of workbench is obtained by semi-physical simulation platform, Kalman observer is utilized to realize estimating of the change in location to workbench, and utilize frictional force estimator to realize estimating in real time change in friction force according to the change in location of the workbench estimated, according to the change in friction force estimated, frictional force is carried out real-Time Compensation, in general, it reduces the purpose of servo feed system tracking error by the monitoring of change in friction force is achieved。

As in figure 2 it is shown, the described method for reducing lathe servo feed system tracking error, mainly comprise the steps:

1) lathe servo feed system is modeled, it is thus achieved that the system model of servo feed system so that it is be prone to design and the stability analysis of Friction Compensation, itself particularly as follows:

The servo feed system of the present embodiment adopts the control system of closed-loop structure, output is the displacement of lathe, the closed-loop control system of design is broadly divided into Kalman observer, frictional force estimator and three parts of system model, and its topology layout is as shown in Figure 1。

The system model setting up servo feed system is as follows:

$M_t\stackrel{\·\·}{x}+B_m\stackrel{\·}{x}=F_q-F(\stackrel{\·}{x},z)---\left(1\right);$

Wherein, M_tRepresent the quality that the mechanical part of servo feed system is total, B_mRepresent the damping of servomotor, F_qRepresent the driving force of servo feed system,Representing the frictional force of servo feed system, x represents servo feed system feed shaft displacement,For the first derivative of x, it is relative sliding velocity v, z and represents mane average deformation。

Further, described mane average deformation z adopts following expression to express:

$\stackrel{\·}{z}=\stackrel{\·}{x}-\frac{{\mathrm{\δ}}_0}{g\left(\stackrel{\·}{x}\right)}z\left|\stackrel{\·}{x}\right|---\left(2\right);$

Wherein,This functionDescribe Stribeck (this Trebek) effect (frictional force phasic Chang), δ₀Represent mane rigidity, f_cRepresent coulomb frictional force, f_sRepresent maximum static friction force, v_sRepresent the characteristic velocity of Stribeck effect。

2) frictional force mathematical model the identified parameters of lathe servo feed system are set up:

2.1) setting up the frictional force mathematical model of lathe servo feed system, it is (frictional force is produced by the flexure of mane) that the present embodiment specifically sets up the frictional force mathematical model at platen rail plate place:

$F(\stackrel{\·}{x},z)={\mathrm{\δ}}_{0}z+{\mathrm{\δ}}_1(\stackrel{\·}{x}-{\mathrm{\δ}}_0\frac{\left|\stackrel{\·}{x}\right|}{g\left(\stackrel{\·}{x}\right)}z)+{\mathrm{\μ}}_v\stackrel{\·}{x}---\left(3\right);$

Wherein, δ₀Represent mane rigidity, δ₁Represent microcosmic damped coefficient, μ_vRepresent servo feed system feed shaft viscous friction coefficient；

2.2) parameter δ in identification frictional force mathematical model₀、δ₁、μ_v、f_c、f_sAnd v_sValue:

Select to optimize cost function J_s, and minimize it, calculate and obtain parameter δ₀、δ₁、μ_v、f_c、f_sAnd v_sValue, the present embodiment calculate obtain δ₀=2.79 × 10⁷(N/m), δ₁=4.32 × 10³(N s/m), μ_v=2.45 × 10³(N s/m), f_c=64.2 (N), f_s=86.2 (N), v_s=6.04 × 10^-4(m/s)。

Further, described J_sEmploying following expression represents:

$J_s=\underset{i=1}{\overset{N_s}{\mathrm{\Σ}}}{e}_{ss}^2(X_s,{\stackrel{\·}{x}}_i)+max\left\{\right|e_{ss}\left(X_s,\stackrel{\·}{x}\right)\left|\right\}---\left(4\right);$

In formula, N_sIt is the number of composition Stribeck effect point,Represent the speed under corresponding each effect point i,Represent workbench steady-state error at various speeds respectively, wherein $e_{ss}(X_s,{\stackrel{\·}{x}}_i)=F_{ss}\left({\stackrel{\·}{x}}_i\right)-F_{ss}({\stackrel{\·}{x}}_i,z)e_{ss}(X_s,\stackrel{\·}{x})=F_{ss}\left(\stackrel{\·}{x}\right)-F_{ss}(\stackrel{\·}{x},z),$ DescribedWithRepresenting the frictional force under stable state, it is by actually measured, described inWithRepresent estimation stable state under frictional force, it is by step 2.1) in frictional force mathematical model and formula (3) express, for instance $F_{ss}({\stackrel{\·}{x}}_i,z)={\mathrm{\δ}}_{0}z+{\mathrm{\δ}}_1({\stackrel{\·}{x}}_i-{\mathrm{\δ}}_0\frac{\left|{\stackrel{\·}{x}}_i\right|}{g\left({\stackrel{\·}{x}}_i\right)}z)+{\mathrm{\μ}}_v{\stackrel{\·}{x}}_i,F_{ss}(\stackrel{\·}{x},z)={\mathrm{\δ}}_{0}z+{\mathrm{\δ}}_1(\stackrel{\·}{x}-{\mathrm{\δ}}_0\frac{\left|\stackrel{\·}{x}\right|}{g\left(\stackrel{\·}{x}\right)}z)+{\mathrm{\μ}}_v\stackrel{\·}{x}.$

3) utilize Kalman observer that the change in location of servo feed system is estimated, the compensation frictional force of servo feed system is calculated according to the change in location estimated, the frictional force of servo feed system is carried out Real-time and Dynamic compensation by the compensation frictional force according to calculating, and then realizing reducing the tracking error of lathe servo feed system: the Kalman observer and the frictional force estimation module that the simulink module inside Matlab7.0 are designed by semi-physical simulation platform download on semi-physical simulation platform, realized the driving of servomotor and the reading to lathe displacement signal by semi-physical simulation platform, the purpose introducing Kalman observer is in that to export the estimation making state vector X (k) based on Y (k) measurement。

It comprises the following steps:

3.1) expression formula that frictional force is associated is set up with state variable X

First, the state-space expression of this system is set up:

$\stackrel{\·}{X}=AX+Bu---\left(5\right)$

$X=\left[\begin{array}{c}x\\ \stackrel{\·}{x}\\ z\end{array}\right]---\left(6\right)$

Y=CX=[100] X (7)

Wherein, X represents that system state variables, Y represent output state variable, u=F_q, A, B are matrix；

Bring formula (6) into formula (5) to draw:

$\left[\begin{array}{c}\stackrel{\·}{x}\\ \stackrel{\·\·}{x}\\ \stackrel{\·}{z}\end{array}\right]=A\left[\begin{array}{c}x\\ \stackrel{\·}{x}\\ z\end{array}\right]+Bu---\left(8\right)$

In formula (8), $\stackrel{\·\·}{x}=\frac{F_q-F(\stackrel{\·}{x},z)-B_m\stackrel{\·}{x}}{M_t}=\frac{F_q-({\mathrm{\δ}}_{0}z+{\mathrm{\δ}}_1(\stackrel{\·}{x}-{\mathrm{\δ}}_0\frac{\left|\stackrel{\·}{x}\right|}{g\left(\stackrel{\·}{x}\right)}z)+{\mathrm{\μ}}_v\stackrel{\·}{x})-B_m\stackrel{\·}{x}}{M_t},$ $\stackrel{\·}{z}=\stackrel{\·}{x}-\frac{{\mathrm{\δ}}_0}{g\left(\stackrel{\·}{x}\right)}z\left|\stackrel{\·}{x}\right|;$

According to formula (8), utilize trial and error procedure obtain A, B matrix be:

$A=\left[\begin{array}{ccc}0& 1& 0\\ 0& a_{22}& a_{23}\\ 0& 1& a_{33}\end{array}\right]---\left(9\right)$

$B=\left[\begin{array}{c}0\\ \frac{1}{M_t}\\ 0\end{array}\right]---\left(10\right)$

In formula (9), matrix element a₂₂,a₂₃,a₃₃It is respectively as follows:

$a_{22}=-\frac{1}{M_t}({\mathrm{\δ}}_1+{\mathrm{\μ}}_v+B_m)---\left(11\right)$

$a_{23}=-\frac{1}{M_t}({\mathrm{\δ}}_0-{\mathrm{\δ}}_0{\mathrm{\δ}}_1\frac{\left|\stackrel{\·}{x}\right|}{g\left(\stackrel{\·}{x}\right)})---\left(12\right)$

$a_{33}=-{\mathrm{\δ}}_0\frac{\left|\stackrel{\·}{x}\right|}{g\left(\stackrel{\·}{x}\right)}---\left(13\right)$

According to formula (1)And formula (11)-(13), set up the expression formula that frictional force is associated with state variable X:

$F=-M_t\[\begin{array}{ccc}0& a_{22}& a_{23}\end{array}\]X-B_m\stackrel{\·}{x}---\left(14\right)$

3.2) the kinetic model discrete form of servo feed system is set up:

X (k+1)=AX (k)+Bu (k)+v (k) (15)

Y (k+1)=CX (k)+n (k) (16)

$\hat{X}\left(k+1\right)=\hat{X}\left(k\right)+K\[Y\left(k\right)-C\widehat{X\left(K\right)}\]---\left(17\right)$

In formula, X (k+1), X (k) represent the state variable X position in k+1, k moment respectively, Represent that state variable X is in the estimation position in k+1, k moment respectively, Y (k), Y (k+1) represent the servo feed system output state variable in k+1, k moment respectively, v (k), n (k) are k moment white noise signal, u (k) represents servo feed system action function, K is yield value $A=\left[\begin{array}{ccc}0& 1& 0\\ 0& a_{22}& a_{23}\\ 0& 1& a_{33}\end{array}\right],$ $B=\left[\begin{array}{c}0\\ \frac{1}{M_t}\\ 0\end{array}\right],$ C=[100], $a_{33}=-{\mathrm{\δ}}_0\frac{\left|\stackrel{\·}{x}\right|}{g\left(\stackrel{\·}{x}\right)};$

3.3) in estimation procedure, there is noise, in order to eliminate influence of noise, set up the covariance of state variable errorAnd calculate covariance forecast P (k+1), make covariance forecast P (k+1) converge to zero, calculate and obtain yield value K, this yield value K-band is entered formulaIn, calculate and obtain state variable in the position in k+1 moment

Further, the covariance of described state variable errorEmploying following expression is expressed:

$\hat{P}\left(k\right)=\left\{\[\hat{X}\left(k\right)-E\left\{X\left(k\right)\right\}\]{\[\hat{X}\left(k\right)-E\left\{X\left(k\right)\right\}\]}^T\right\}---\left(18\right)$

In formula, E is covariance matrix。

More specifically, described covariance forecast P (k+1) adopts following expression to express:

$P(k+1)=(I-KC)\left(A\hat{P}\right(k)A^T+V)\×{(I-KC)}^T+{\mathrm{KNK}}^T;$

In formula, I is vector matrix, and V, N represent the covariance matrix of white noise signal v (k), n (k) respectively。

It is further preferred that described white noise signal v (k), n (k) covariance matrix particularly as follows:

$V=\left[\begin{array}{ccc}0.0008& 0& 0\\ 0& 9.6\×{10}^5& 0\\ 0& 0& 1\end{array}\right],N=\mathrm{0.34.}$

Concrete, covariance forecast P (k+1) obtains yield value K when converging to zero and is:

K=PC^T[CPC^T+N]^-1；

Wherein, P is the covariance matrix of covariance forecast P (k+1)。

3.4) by step 3.3) middle acquisitionValue brings expression formula into as the input value of X $F=-M_t\[\begin{array}{ccc}0& a_{22}& a_{23}\end{array}\]X-B_m\stackrel{\·}{x}$ Namely, in formula (14), calculate the compensation frictional force obtaining servo feed system, frictional force is estimated；

3.5) according to the compensation frictional force calculated, the frictional force of servo feed system is carried out Real-time and Dynamic compensation, and then realizing reducing the tracking error of lathe servo feed system: the frictional force moment of the servo feed system of estimation is added in torque signals as compensation, and this Friction Compensation control algolithm realizes the also drive motor of downloading of algorithm is driven the acquisition of working table movement and data by Dspace semi-physical simulation platform；By the frictional force torque compensation of the servo feed system of estimation to the moment after PID controller regulates realizing the accurate control to servo feed system, feed shaft tracking error is obviously improved, as shown in Fig. 3 (a) and (b)。

Those skilled in the art will readily understand; the foregoing is only presently preferred embodiments of the present invention; not in order to limit the present invention, all any amendment, equivalent replacement and improvement etc. made within the spirit and principles in the present invention, should be included within protection scope of the present invention。

Claims (10)

1. the method for reducing lathe servo feed system tracking error, it is characterised in that the method comprises the steps:

1) lathe servo feed system is modeled, it is thus achieved that the system model of servo feed system；

2) frictional force mathematical model the identified parameters of lathe servo feed system are set up；

3) utilize Kalman observer that the change in location of servo feed system is estimated, the compensation frictional force of servo feed system is calculated according to the change in location estimated, the frictional force of servo feed system is carried out Real-time and Dynamic compensation by the compensation frictional force according to calculating, and then realizes reducing the tracking error of lathe servo feed system。

2. the method for reducing lathe servo feed system tracking error as claimed in claim 1, it is characterised in that described lathe servo feed system is modeled, it is thus achieved that the system model of servo feed system includes:

The system model setting up servo feed system isWherein, M_tRepresent the quality that the mechanical part of servo feed system is total, B_mRepresent the damping of servomotor, F_qRepresent the driving force of servo feed system,Representing the frictional force of servo feed system, x represents servo feed system feed shaft displacement, and z represents mane average deformation。

3. the method for reducing lathe servo feed system tracking error as claimed in claim 2, it is characterised in that described mane average deformation z adopts following expression to express:

$\stackrel{\·}{z}=\stackrel{\·}{x}-\frac{{\mathrm{\δ}}_0}{g\left(\stackrel{\·}{x}\right)}z\left|\stackrel{\·}{x}\right|;$

Wherein,δ₀Represent mane rigidity, f_cRepresent coulomb frictional force, f_sRepresent maximum static friction force, v_sRepresent the characteristic velocity of Stribeck effect。

4. the method being used for as claimed in claim 2 or claim 3 reducing lathe servo feed system tracking error, it is characterised in that the described frictional force mathematical model setting up lathe servo feed system identified parameters include:

2.1) mathematical model of the frictional force of lathe servo feed system is set up:

$F(\stackrel{\·}{x},z)={\mathrm{\δ}}_{0}z+{\mathrm{\δ}}_1(\stackrel{\·}{x}-{\mathrm{\δ}}_0\frac{\left|\stackrel{\·}{x}\right|}{g\left(\stackrel{\·}{x}\right)}z)+{\mathrm{\μ}}_v\stackrel{\·}{x};$

Wherein, δ₀Represent mane rigidity, δ₁Represent microcosmic damped coefficient, μ_vRepresent the viscous friction coefficient of servo feed system feed shaft；

2.2) parameter δ in identification frictional force mathematical model₀、δ₁、μ_v、f_c、f_sAnd v_sValue。

5. the method for reducing lathe servo feed system tracking error as claimed in claim 4, it is characterised in that parameter δ in described identification frictional force mathematical model₀、δ₁、μ_v、f_c、f_sAnd v_sValue include:

Select to optimize cost function J_s, and minimize it, calculate and obtain parameter δ₀、δ₁、μ_v、f_c、f_sAnd v_sValue, described J_sEmploying following expression represents:

$J_s=\underset{i=1}{\overset{N_s}{\mathrm{\Σ}}}{e}_{ss}^2(X_s,{\stackrel{\·}{x}}_i)+max\left\{\right|e_{ss}(X_s,\stackrel{\·}{x})\left|\right\};$

In formula, N_sIt is the number of composition Stribeck effect point,Represent workbench steady-state error at various speeds respectively, wherein DescribedWithRepresenting the frictional force under stable state, it is by actually measured, described inWithRepresent estimation stable state under frictional force, it is by step 2.1) in frictional force mathematical model express。

6. the method for reducing lathe servo feed system tracking error as claimed in claim 4, it is characterized in that, described utilize Kalman observer that the change in location of servo feed system is estimated, the compensation frictional force of servo feed system is calculated according to the change in location estimated, the frictional force of servo feed system is carried out Real-time and Dynamic compensation by the compensation frictional force according to calculating, and then the tracking error realizing reducing lathe servo feed system includes:

3.1) expression formula that frictional force is associated is set up with state variable X:

$F=-M_t\left[\begin{array}{ccc}0& a_{22}& a_{23}\end{array}\right]X-B_m\stackrel{\·}{x};$

Wherein, $a_{22}=-\frac{1}{M_t}({\mathrm{\δ}}_1+{\mathrm{\μ}}_v+B_m),$ $a_{23}=-\frac{1}{M_t}({\mathrm{\δ}}_0-{\mathrm{\δ}}_0{\mathrm{\δ}}_1\frac{\left|\stackrel{\·}{x}\right|}{g\left(\stackrel{\·}{x}\right)}),$ $X=\left[\begin{array}{c}x\\ \stackrel{\·}{x}\\ z\end{array}\right];$

3.2) the kinetic model discrete form of servo feed system is set up:

X (k+1)=AX (k)+Bu (k)+v (k)；

Y (k+1)=CX (k)+n (k)；

$\hat{X}(k+1)=\hat{X}\left(k\right)+K\[Y\left(k\right)-C\widehat{X\left(k\right)}\];$

In formula, X (k+1), X (k) represent the state variable X position in k+1, k moment respectively, Represent that state variable X is in the estimation position in k+1, k moment respectively, Y (k), Y (k+1) represent the servo feed system output state variable in k+1, k moment respectively, v (k), n (k) are k moment white noise signal, u (k) represents servo feed system action function, K is yield value $A=\left[\begin{array}{ccc}0& 1& 0\\ 0& a_{22}& a_{23}\\ 0& 1& a_{33}\end{array}\right],$ $B=\left[\begin{array}{c}0\\ \frac{1}{M_t}\\ 0\end{array}\right],$ C=[100], $a_{33}=-{\mathrm{\δ}}_0\frac{\left|\stackrel{\·}{x}\right|}{g\left(\stackrel{\·}{x}\right)};$

3.3) covariance of state variable error is set upAnd calculate covariance forecast P (k+1), make covariance forecast P (k+1) converge to zero, calculate and obtain yield value K, this yield value K-band is entered formulaIn, calculate and obtain state variable in the position in k+1 moment

3.4) by step 3.3) middle acquisitionValue brings expression formula into as the input value of X $F=-M_t\left[\begin{array}{ccc}0& a_{22}& a_{23}\end{array}\right]X-B_m\stackrel{\·}{x}$ In, calculate the compensation frictional force obtaining servo feed system；

3.5) according to the compensations frictional force calculated, the frictional force of servo feed system carried out Real-time and Dynamic compensation, and then realize the tracking error of minimizing lathe servo feed system。

7. the method for reducing lathe servo feed system tracking error as claimed in claim 6, it is characterised in that the covariance of described state variable errorEmploying following expression is expressed:

$\hat{P}\left(k\right)=\{\[\hat{X}\left(k\right)-E\{X\left(k\right)\}\]{\[\hat{X}\left(k\right)-E\left\{X\left(k\right)\right\}\]}^T\};$

In formula, E is covariance matrix。

8. the method for reducing lathe servo feed system tracking error as claimed in claims 6 or 7, it is characterised in that described covariance forecast P (k+1) adopts following expression to express:

$P\left(k+1\right)=\left(I-KC\right)\left(A\hat{P}\left(k\right)A^T+V\right)\×{\left(I-KC\right)}^T+{\mathrm{KNK}}^T;$

In formula, I is vector matrix, and V, N represent the covariance matrix of white noise signal v (k), n (k) respectively。

9. the method for reducing lathe servo feed system tracking error as claimed in claim 8, it is characterised in that described white noise signal v (k), n (k) covariance matrix particularly as follows:

$V=\left[\begin{array}{ccc}0.0008& 0& 0\\ 0& 9.6\×{10}^5& 0\\ 0& 0& 1\end{array}\right],N=\mathrm{0.34.}$

10. the method for reducing lathe servo feed system tracking error as claimed in claim 8, it is characterised in that covariance forecast P (k+1) obtains yield value K when converging to zero and is: K=PC^T[CPC^T+N]^-1, wherein P is the covariance matrix of covariance forecast P (k+1)。