CN102023612B - Method for compensating frictional error of servo system of numerical control machine tool - Google Patents

Abstract

The invention discloses a device and a method for compensating a frictional error of a servo system of a numerical control machine tool. Position feedback control and friction feedforward compensation are realized to further eliminate the frictional error by adopting a multi-sampling rate control structure of a discrete system. In the multi-sampling rate control structure, the sampling frequency of friction feedforward is required to be higher than that of position feedback. The multi-sampling rate control structure can realize a detailed friction feedforward compensation function in the position feedback under the condition of not changing the structure and stability of a servo feed control system. In the calculation of the amount of detailed friction feedforward compensation, the output of a position interpolator of the servo feed control system is utilized to obtain more detailed compensation speed instruction input by a linear interpolation method, and the amplitude change of a frictional force is predicted and the amount of the compensation is determined by adopting an exponential friction model. In the compensation method, the characteristics of the multi-sampling rate control structure and the structure of the servo system are fully utilized to improve the output accuracy and output frequency of the friction compensation, thereby achieving a more accurate friction compensation effect.

Description

The compensation method of a kind of Servo System of CNC Machine Tool frictional error

Technical field

The invention belongs to the numerical control machine tool technique field, relate to a kind of error compensating method, especially a kind of frictional error compensation method to Servo System of CNC Machine Tool.

Background technology

Friction is a kind of strong and inevitable external disturbance factor in the Servo feeding System of NC Machine Tools.Because fricative error phenomenon is with the realization of limit number controlled machine High Accuracy Control seriously.Therefore elimination and the control about frictional error in the servo-drive system is the focus and the difficult point of high speed, high precision numerical control technical research always.Because the strong nonlinearity characteristic of friction, general linear feedback are difficult to solve pointedly the error characteristics of friction under conditions such as high speed, switching-over.Utilization is a kind of more direct and effective control method based on the feedforward compensation method of friction model.Can realize modeling and prediction based on friction model, and can specific aim export compensation rate, thereby realize the elimination of frictional error with the counteracting function of friction through feedforward compensation to frictional force amplitude and frictional error characteristic.

Yet for application conditions such as Servo System of CNC Machine Tool; Motion path has higher movement velocity and acceleration requirement, need carry out the speed switching-over continually, and change in friction force is strong; The action time of the compensation policy of simple direct compensation is less, and compensation effect receives certain restriction.Therefore need utilize servo-drive system control system structure to improve the effect of feedforward compensation method.For digital control system; The controlled quentity controlled variable input of controlled device is only in the sampling instantaneous variation; And in the whole time interval of adjacent two moments of sampling; No matter how the output of controlled device changes, and the characteristic of its input only changes according to the characteristic of retainer, and promptly at this moment The whole control system is in the open loop state of a control.

Summary of the invention

The objective of the invention is to overcome the shortcoming of prior art; The compensation method of a kind of Servo System of CNC Machine Tool frictional error is provided; Characteristic according to the servo-drive system control system proposes to utilize the multi-sampling rate control strategy to realize friciton compensation; This friciton compensation strategy inserts compensation cycle in control cycle, the friciton compensation effect is occurred under the non-FEEDBACK CONTROL state, has reduced the intercouple influence of position feedback control with the friction feedforward compensation; And improved the output accuracy and the output frequency of compensation, thereby realized more accurate friciton compensation effect.

The objective of the invention is to solve through following technical scheme:

This numerically-controlled machine servo-control system frictional error compensation method may further comprise the steps:

1) at first the position interpolator is to the instruction of difference engine outgoing position, and said difference engine calculates the speed command input signal according to position command, and passes to the friction instruction generator;

2) the friction instruction generator calculates according to the speed command input signal and generates the friciton compensation command signal;

3) the friciton compensation device calculates the friciton compensation value signal based on the friciton compensation command signal; The sampling period of being confirmed by first timer is realized the maintenance to the friciton compensation value signal of friciton compensation device output through first zero-order holder down again, said first zero-order holder output feedforward compensation amount signal;

4) in step 1) to 3) carry out in, after the position signalling that the position command signal that the position interpolator is generated and actual feedback measure is asked and is differed from, as the position feedback error signal; Make said position feedback error signal through feedback controller, under the sampling period that second timer is confirmed, obtain position feedback control amount signal; Then through exporting feedback control signal behind second zero-order holder; The feedforward compensation amount signal of said feedback control signal and step 3) is obtained the synthetic control signal after frictional error compensates according to following formula (A) summation:

$u_c\left(T_u^i\right)=u_{\mathrm{fd}}\left(T_{\mathrm{fd}}^j\right)+u_{\mathrm{cmp}}\left(T_{\mathrm{cmp}}^k\right)---\left(A\right)$

In the formula (1),

Be i synthetic controller amount output constantly signal u _cThe output sampling period;

Be j moment FEEDBACK CONTROL amount signal u _FdSampling period;

Be the k feedforward compensation amount signal u that rubs constantly _CmpSampling period.

Above method; In step 2); Said friction instruction generator calculates the method that generates the friciton compensation command signal according to the speed command input signal: the friction instruction generator is according to the speed command input signal; The speed command input signal of friction instruction generator is carried out the linearization interpolation according to sampling period of first timer, obtain the friciton compensation command signal.

Above method, in step 3), the feedforward friciton compensation amount u that said friciton compensation device 3 generates _CmpCalculating adopt the index friction model to accomplish, said index friction model is suc as formula (B):

$u_{\mathrm{cmp}}\left(T_{\mathrm{cmp}}^k\right)=\left\{\begin{array}{cc}{\mathrm{\&alpha;}}_{\mathrm{cf}}[T_s^{+}{e}^{-{\mathrm{\&omega;}}_r\left(T_{\mathrm{cmp}}^k\right)/{\mathrm{\&Omega;}}_1^{+}}+T_c^{+}(1-e^{-{\mathrm{\&omega;}}_r\left(T_{\mathrm{cmp}}^k\right)/{\mathrm{\&Omega;}}_2^{+}})]& {\mathrm{\&omega;}}_r\left(T_{\mathrm{cmp}}^k\right)>{\mathrm{\&Omega;}}_{\mathrm{<figure-callout\; id="0"\; label="d"\; filenames="HDA0000035612510000022.png,HDA0000035612510000023.png"\; state="\{\{state\}\}">d</figure-callout>}}\\ 0& \left|{\mathrm{\&omega;}}_r\left(T_{\mathrm{cmp}}^k\right)\right|\&le;{\mathrm{\&Omega;}}_d\\ {\mathrm{\&alpha;}}_{\mathrm{cf}}[T_s^{-}{e}^{-{\mathrm{\&omega;}}_r\left(T_{\mathrm{cmp}}^k\right)/{\mathrm{\&Omega;}}_1^{-}}+T_c^{-}(1-e^{-{\mathrm{\&omega;}}_r\left(T_{\mathrm{cmp}}^k\right)/{\mathrm{\&Omega;}}_2^{-}})]& {\mathrm{\&omega;}}_r\left(T_{\mathrm{cmp}}^k\right)>{-\mathrm{\&Omega;}}_d\end{array}\right.---\left(B\right)$

Wherein

With

Be respectively the stiction amplitude of positive negative direction in the index friction model,

With

Be respectively positive negative direction coulomb friction amplitude,

With

Be respectively the Stribeck critical velocity of positive negative direction, α _CfBe the compensating gain coefficient, adjust Ω according to the control mode of servomotor and the parameter of friction model _dCritical velocity for the index friction model.

The present invention has following beneficial effect:

(1) the present invention adopts the multi-sampling rate control structure of discrete system to realize the position feedback control device and friction feedforward compensation device of servo-control system; This structure makes the position feedback control device be operated under the different SFs with friction feedforward compensation device; And require the SF of friction feedforward compensation device to be higher than the position feedback control device; To realize friciton compensation and the decoupling zero of position control on output time; Arrive the effect that shortens the output of friction feedforward compensation, can realize effectively to the frictional error compensate function under the conditions such as friction strong variations.

(2) change in friction force that the present invention is directed under high acceleration, the switching-over condition is violent; Realized multiply periodic friction feedforward compensation device, under the condition that does not change the system feedback control cycle, through the segmentation feedforward compensation cycle; Refinement friciton compensation command signal; Realized more meticulous repeatedly compensation rate signal output, particularly, can obtain better frictional error compensation effect to high acceleration, switching-over condition.What is more important adopts the multi-sampling rate controller architecture to realize a kind of open-loop compensation function under closed loop configuration, and close-loop feedback control is separated with the feedforward compensation method, has reduced interactional coupled relation.

Description of drawings

Fig. 1 is a servo-drive system multi-sampling rate friciton compensation controller architecture;

Fig. 2 is a friction-length velocity relation model Stribeck curve;

Fig. 3 adopts linear interpolation to realize the refinement of speed command;

Fig. 4 is the effect data figure of the straight path that obtains through the method for the invention;

Fig. 5 is the effect data figure of the round track that obtains through the method for the invention.

Embodiment

Numerically-controlled machine servo-control system frictional error of the present invention compensation method may further comprise the steps:

1) at first position interpolator 2 is to the instruction of difference engine outgoing position, and said difference engine calculates the speed command input signal according to position command, and passes to friction instruction generator 1;

2) friction instruction generator 1 calculates according to the speed command input signal and generates friciton compensation command signal C _r

3) friciton compensation device 3 is according to friciton compensation command signal C _rCalculate the friciton compensation value signal, the sampling period of being confirmed by first timer 7 is again realized the maintenance to the friciton compensation value signal of friciton compensation device 3 outputs through first zero-order holder 5 down, said first zero-order holder, 5 output feedforward compensation amount signal u _Cmp

4) in step 1) to 3) carry out in, the position command signal X that position interpolator 2 is generated _rThe position signalling X that measures with actual feedback _aAfter asking difference, as the position feedback error signal; Make said position feedback error signal through feedback controller 4, under the sampling period that second timer 8 is confirmed, obtain position feedback control amount signal; Then through second zero-order holder (6) back output feedback control signal u _FdWith said feedback control signal u _FdFeedforward compensation amount signal u with step 3) _CmpObtain the synthetic control signal u after frictional error compensates according to following formula (A) summation _c:

$u_c\left(T_u^i\right)=u_{\mathrm{fd}}\left(T_{\mathrm{fd}}^j\right)+u_{\mathrm{cmp}}\left(T_{\mathrm{cmp}}^k\right)---\left(A\right)$

In the formula (A),

Be i synthetic controller amount output constantly signal u _cThe output sampling period;

Be j moment FEEDBACK CONTROL amount signal u _FdSampling period;

Be the k feedforward compensation amount signal u that rubs constantly _CmpSampling period.

Below in conjunction with accompanying drawing the present invention is done and to describe in further detail:

1, adopts the structure of the control structure of multi-sampling rate as position feedback control and friction feedforward compensation.

Multi-sampling rate control structure of the present invention is as shown in Figure 1.This control structure mainly contains by friction instruction generator 1, position interpolator 2, friciton compensation device 3, feedback controller 4, zero-order holder 5, zero-order holder 6, timer 7 and timer 8 and constitutes.The friction feedforward compensation part that constitutes of friciton compensation device 3, zero-order holder 5 and timer 7 wherein.The position feedback control part that feedback controller 4, zero-order holder 6 and timer 8 constitute.Friction instruction generator 1 is according to the position output computing velocity command input signals of position interpolator 2, and then generation friciton compensation command signal C _r, be specially: friction instruction generator 1 is according to the speed command input signal, the speed command input signal of friction instruction generator 1 carried out the linearization interpolation according to sampling period of first timer 7, obtains friciton compensation command signal C _rAccording to friciton compensation command signal C _r, friciton compensation device 3 calculates the friciton compensation value, under the sampling period of being confirmed by timer 7, realizes feedforward compensation device compensation rate u through zero-order holder 5 _CmpOutput keep.Position command signal X according to 2 generations of position interpolator _rThe position signalling X that measures with actual feedback _aAfter asking difference, as the position feedback error.Obtain position feedback control amount signal according to the position feedback error through positioner 4, under the sampling period of confirming by timer 8, realize feedback control signal u then through zero-order holder 6 backs _FdOutput keep.But this structure is characterised in that the output sampling frequency rate of zero-order holder 5 and is higher than the output sampling frequency rate of zero-order holder 6, to realize the output of more meticulous compensation rate.Final synthetic controller amount output signal u _cCan be expressed as FEEDBACK CONTROL amount signal u _FdWith feedforward friciton compensation amount signal u _CmpTwo parts sum, the form shown in the promptly above-mentioned formula (A).The synthetic controlled quentity controlled variable u of i sampling instant _cBy the j sampling instant FEEDBACK CONTROL amount u that is operated under the different sample frequency _FdWith k sampling instant feedforward compensation device compensation rate u _CmpOutput comes common definite.

2, the utilization index friction model is realized the calculating of friciton compensation amount.

The function of friciton compensation of the present invention is the feedforward friciton compensation amount u that generates through friciton compensation device 3 _CmpRealize.And should feedforward friciton compensation amount u _CmpCalculating adopt the index friction model to accomplish.The index friction model is through exponential form friction as shown in Figure 2-length velocity relation Stribeck curve to be carried out parametric modeling, and then can realize friction force amplitude T through speed omega _fPrediction.Under the structure of multi-sampling rate friciton compensation device, the output of the index friciton compensation device of discrete form is expressed suc as formula shown in (B).

$u_{\mathrm{cmp}}\left(T_{\mathrm{cmp}}^k\right)=\left\{\begin{array}{cc}{\mathrm{\&alpha;}}_{\mathrm{cf}}[T_s^{+}{e}^{-{\mathrm{\&omega;}}_r\left(T_{\mathrm{cmp}}^k\right)/{\mathrm{\&Omega;}}_1^{+}}+T_c^{+}(1-e^{-{\mathrm{\&omega;}}_r\left(T_{\mathrm{cmp}}^k\right)/{\mathrm{\&Omega;}}_2^{+}})]& {\mathrm{\&omega;}}_r\left(T_{\mathrm{cmp}}^k\right)>{\mathrm{\&Omega;}}_{\mathrm{<figure-callout\; id="0"\; label="d"\; filenames="HDA0000035612510000022.png,HDA0000035612510000023.png"\; state="\{\{state\}\}">d</figure-callout>}}\\ 0& \left|{\mathrm{\&omega;}}_r\left(T_{\mathrm{cmp}}^k\right)\right|\&le;{\mathrm{\&Omega;}}_d\\ {\mathrm{\&alpha;}}_{\mathrm{cf}}[T_s^{-}{e}^{-{\mathrm{\&omega;}}_r\left(T_{\mathrm{cmp}}^k\right)/{\mathrm{\&Omega;}}_1^{-}}+T_c^{-}(1-e^{-{\mathrm{\&omega;}}_r\left(T_{\mathrm{cmp}}^k\right)/{\mathrm{\&Omega;}}_2^{-}})]& {\mathrm{\&omega;}}_r\left(T_{\mathrm{cmp}}^k\right)>{-\mathrm{\&Omega;}}_d\end{array}\right.---\left(B\right)$

Wherein With

Be respectively the stiction amplitude of positive negative direction in the index friction model,

With

Be respectively positive negative direction coulomb friction amplitude,

With

Be respectively the Stribeck critical velocity of positive negative direction, α _CfBe the compensating gain coefficient, adjust Ω according to the control mode of servomotor and the parameter of friction model _dCritical velocity for the index friction model.

3, adopt linear interpolation method to realize the refinement of compensating instruction

Friction instruction generator 1 of the present invention is used to realize friciton compensation command signal C _rCalculating: at first, obtain the speed command input signal, again with friction feedforward compensation device cycle T through difference engine according to the position command of position interpolator 2 output _Cmp, promptly the sampling period of timer 7 is a chronomere, and this speed value is carried out linear interpolation.Be about to this speed command and carry out the five equilibrium refinement, as shown in Figure 3.As working as FEEDBACK CONTROL amount sampling period T _FdBe friction feedforward compensation device sampling period T _Cmp3 times the time, just need carry out 3 five equilibriums to speed command, the speed command that has obtained refinement is friciton compensation command signal C _r, as the speed input of friction feedforward compensation device.Adopt this method can not increase the computation burden of servo-control system, do not produce redundant data.

4, FEEDBACK CONTROL of the present invention partly is any controller form common in the digital control system, like proportional controller, pi controller and proportional plus integral plus derivative controller.Feedback controller is mainly used in the feedback regulation of position command, does not realize the effect of frictional error elimination targetedly.

Below provide the test result of a kind of specific embodiment of the present invention:

Controlling object is for adopting the X-Y axle elaborate servo worktable of peace river AC servo, and the major parameter of servomotor is:

It is 20mm/s that Fig. 4 provides for speed of feed, and acceleration is 200mm/s ²Straight-line trajectory under, be that the Reinshaw grating chi of 0.1um carries out the error result contrast that position probing obtains through positional precision.Fig. 4 a is the error result that does not adopt friciton compensation method of the present invention to obtain, the error result of Fig. 4 b for adopting friciton compensation method of the present invention to obtain.Can find out that the friciton compensation method that realizes through the present invention has obvious reduction effect to the frictional error spike under the straight path condition.

It is under the 40mm/s that Fig. 5 has provided the speed of feed condition, and radius is under the round orbiting motion of 20mm, is that the Reinshaw grating chi of 0.1um carries out the error result contrast that position probing obtains through positional precision.The error result of Fig. 5 a for not adopting friciton compensation method of the present invention to obtain, the error result of Fig. 5 b for adopting friciton compensation method of the present invention to obtain.Can find out that the friciton compensation method that realizes through the present invention has obvious reduction effect equally to the frictional error spike under the circle tracking condition.

In sum, the present invention adopts the index friction model to realize modeling and identification to friction force in order to realize the prediction to friction force.For the index friction model, just can calculate the friction force amplitude according to the speed command signal of refinement through this model by analytic expression, realize prediction and calculation to the friction force amplitude.This predicted value multiply by behind certain gain coefficient the output as friction feedforward compensation device, thereby realize counteracting friction force.

Claims (3)

1. numerically-controlled machine servo-control system frictional error compensation method is characterized in that, may further comprise the steps:

1) at first position interpolator (2) is to the instruction of difference engine outgoing position, and said difference engine calculates the speed command input signal according to position command, and passes to friction instruction generator (1);

2) friction instruction generator (1) calculates according to the speed command input signal and generates friciton compensation command signal C _r

3) friciton compensation device (3) is according to friciton compensation command signal C _rCalculate the friciton compensation value signal; The sampling period of being confirmed by first timer (7) is again realized the maintenance to the friciton compensation value signal of friciton compensation device (3) output through first zero-order holder (5) down, said first zero-order holder (5) output feedforward compensation amount signal u _Cmp

4) in step 1) to 3) carry out in, the position command signal X that position interpolator (2) is generated _rThe position signalling X that measures with actual feedback _aAfter asking difference, as the position feedback error signal; Make said position feedback error signal through feedback controller (4), under the sampling period that second timer (8) is confirmed, obtain position feedback control amount signal; Then through second zero-order holder (6) back output feedback control signal u _FdWith said feedback control signal u _FdFeedforward compensation amount signal u with step 3) _CmpObtain the synthetic control signal u after frictional error compensates according to following formula (A) summation _c:

$u_c\left(T_u^i\right)=u_{\mathrm{fd}}\left(T_{\mathrm{fd}}^j\right)+u_{\mathrm{cmp}}\left(T_{\mathrm{cmp}}^k\right)---\left(A\right)$

In the formula (A),

Be i synthetic controller amount output constantly signal u _cThe output sampling period; Be j moment FEEDBACK CONTROL amount signal u _FdSampling period;

Be the k feedforward compensation amount signal u that rubs constantly _CmpSampling period.

2. error compensating method according to claim 1 is characterized in that: step 2) in, said friction instruction generator (1) calculates according to the speed command input signal and generates friciton compensation command signal C _rMethod be: friction instruction generator (1) is according to the speed command input signal, the speed command input signal of friction instruction generator (1) carried out the linearization interpolation according to sampling period of first timer (7), obtains friciton compensation command signal C _r

3. error compensating method according to claim 1 is characterized in that: in the step 3), and the feedforward friciton compensation amount u that said friciton compensation device 3 generates _CmpCalculating adopt the index friction model to accomplish, said index friction model is suc as formula (B):

$u_{\mathrm{cmp}}\left(T_{\mathrm{cmp}}^k\right)=\left\{\begin{array}{cc}{\mathrm{\&alpha;}}_{\mathrm{cf}}[T_s^{+}{e}^{{-\mathrm{\&omega;}}_r\left(T_{\mathrm{cmp}}^k\right)/{\mathrm{\&Omega;}}_1^{+}}+T_c^{+}(1-e^{{-\mathrm{\&omega;}}_r\left(T_{\mathrm{cmp}}^k\right)/{\mathrm{\&Omega;}}_2^{+}})]& {\mathrm{\&omega;}}_r\left(T_{\mathrm{cmp}}^k\right)>{\mathrm{\&Omega;}}_d\\ 0& \left|{\mathrm{\&omega;}}_r\left(T_{\mathrm{cmp}}^k\right)\right|\&le;{\mathrm{\&Omega;}}_d\\ {\mathrm{\&alpha;}}_{\mathrm{cf}}[T_s^{-}{e}^{{-\mathrm{\&omega;}}_r\left(T_{\mathrm{cmp}}^k\right)/{\mathrm{\&Omega;}}_1^{-}}+T_c^{-}(1-e^{{-\mathrm{\&omega;}}_r\left(T_{\mathrm{cmp}}^k\right)/{\mathrm{\&Omega;}}_2^{-}})]& {\mathrm{\&omega;}}_r\left(T_{\mathrm{cmp}}^k\right)<{-\mathrm{\&Omega;}}_d\end{array}\right.---\left(B\right)$

Wherein With Be respectively the stiction amplitude of positive negative direction in the index friction model,

With Be respectively positive negative direction coulomb friction amplitude, With

Be respectively the Stribeck critical velocity of positive negative direction, a _CfBe the compensating gain coefficient, adjust Ω according to the control mode of servomotor and the parameter of friction model _dCritical velocity for the index friction model.

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