JP2003005838A - Method for servo control - Google Patents

Abstract

PROBLEM TO BE SOLVED: To improve contour motion accuracy by correcting an error due to elastic displacement and suppressing a synchronization error even in interpolation of a plurality of axes in a hybrid control method including a scale feedback and a full closed-loop control method. SOLUTION: A transfer function is calculated in each axis in accordance with the set value of a first-order lag time constant of feedback compensation by a machine position detection value and change of an angular velocity, and feedforward quantity is set so as to make the tranfer functions of respective axes to be mutually equal.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a servo control method for performing simultaneous multi-axis control, and more particularly to an NC for contour control.
The present invention relates to a servo control method for machine tools, robots and the like.

[0002]

2. Description of the Related Art In recent machine tools, in order to improve the machining efficiency, it is required to drive the machine at high speed and with high acceleration / deceleration, and to have higher precision contour control accuracy. The contour control is to continuously control the tool path by simultaneously associating the movements of two or more axes by linear interpolation, circular interpolation, or the like.

A problem at the time of high speed and high acceleration / deceleration is the influence of the inertial force due to the high acceleration / deceleration, and for example, the ball screw is stretched (because of elastic deformation) to extend beyond the commanded position. High-speed operation increases the radius reduction amount.

Normally, in a vertical machine, the table is placed on the saddle, so that the mass ratio becomes twice or more. Even in a horizontal machine, when the column is driven, the mass ratio between the spindle and the column is more than double. If the two axes are moved simultaneously in this state, the error due to inertial force will be more than doubled, and an elliptic error will occur in circular interpolation. At high speed, viscous friction increases and the speed cannot follow in a transient state. Therefore, a phase shift occurs, which causes an error that the axis of circular interpolation is tilted.

As a measure taken so far, a velocity tracking error is corrected by velocity feedforward for velocity, and acceleration tracking is also improved by acceleration feedforward. The linear scale detects and corrects the position error of the machine. and so on.

As a technique for correcting the amount of elastic deformation of a machine, in a semi-closed loop control system, elastic deflection due to the inertial force of the machine is corrected by acceleration feed forward (Japanese Patent Laid-Open No. 7-78031),
A device that predicts the rigidity of an elastic deflection due to the inertial force of a machine and corrects it by feedforward (JP-A-4-271)
290), in a semi-closed loop control system, in which elastic deflection of a machine is corrected by feedforward in consideration of load weight and viscous resistance (Japanese Patent Application Laid-Open No. 20-200200).
No. 00-172341), there is known one in which the elastic deflection of a machine is corrected by feedforward in consideration of load weight and viscous resistance (Japanese Patent Laid-Open No. 11-84529).

[0007]

When the countermeasure is implemented by the semi-closed drove control, it is impossible to correct the lead error of the ball screw, the error due to the thermal displacement, etc., so that the feed drive cannot be performed with high accuracy. If a measure is taken, the full closed loop control causes a delay of at least the sampling time, which becomes a tracking error and cannot be completely corrected. Further, due to the problem of stability, in a machine with a heavy load, the gain does not increase, so that the contour accuracy decreases. Also, if the measures are taken with hybrid control, a delay of the hybrid time constant will occur, and again,
It cannot be corrected. For this reason, in all cases, circular interpolation results in a diagonal elliptical error.

[0008] None of the above mentioned hybrid control systems in which scale feedback is added to encoder feedback as a first-order lag element.

In the hybrid control method, when the elastic deformation amount of the machine is corrected by the above-described method, the difference in mechanical characteristics is reflected in the transfer function by the scale feedback. This results in contour motion error, which reduces the motion accuracy of the machine.

However, since the conventional semi-closed loop control system cannot suppress mechanical errors such as lead error and thermal displacement of the ball screw, hybrid control and full closed loop control are
It is expected to become mainstream in the future.

The control system of the hybrid control system will be described with reference to the approximate block diagram shown in FIG. In FIG. 9, 11 is a servo motor system, 12 is a mechanical system including loads such as a feed screw and a table, 13 is a low-pass filter, and 14 is a front compensator. Also,
ω _o is a position loop gain, ω _h is a first-order lag frequency, s is a Laplace transform operator, and Gm (s) is a transfer function of a mechanical system.

The transfer function Gm (s) of the mechanical system is expressed by the following equation. Gm (s) = s ² + 2ζωn · s + ωn ² where ζ: damping ratio ωn: natural angular frequency.

The overall transfer function Gh (s) in this case is

[Equation 1] Becomes Solve this by substituting s = jω.

[0014] where

[Equation 2] And

However, A = ω _h ω _o ωn ² B = ω _o ωn ² ω C = ω ⁴ − {2ζωn (ω _h + ω _o ) + ωn ² } ω ² + ω _h
ω _o ω n ² D =-(ω _h + ω _o +2 ζω n)} ω ³ + (ω _h + ω _o ) ω n
² ω]

Here, the gain | Gh (jω) |

[Equation 3] And the phase ∠Gh (jω) is

[Equation 4] Is.

The natural angular frequency ωn is ωn = √ (k /
M) and the damping ratio ζ are ζ = c / 2√ (kM),
Gain Gh (jω) and phase ∠ in the case of hybrid control
Gh (jω) is mass M, spring constant k, viscous damping coefficient c, angular velocity ω, first-order lag frequency (hybrid frequency)
is a function of ω _h and the position loop gain ω _o .

Generally, in a hybrid control system, the hybrid frequency ω _h and the position loop gain ω _o are set to the same values for all axes to prevent gain deviation and the like. However, in most cases, the mass M, the spring constant k, and the viscous damping coefficient c are different for each axis in the mechanical system, in other words, the elastic displacement amount of each axis is different for each axis, and these mechanical values are different. Differences due to characteristics cause a shift in the gain and phase of each axis. As described above, when a gain or a phase shift occurs between the axes, a path error occurs in the circular interpolation motion in which the two axes are simultaneously controlled, and the perfect circle is as shown in FIG. It becomes an oblique ellipse.

The respective gains and phases of the X axis and the Y axis are as illustrated in FIGS. 11 (a), (b), 12 (a), and (b). In this example, since the X-axis has a low natural frequency, the gain peaks at the resonance point of the machine,
It can be seen that there is a large difference in the gain around this. Also, the phase difference is large near the resonance point. Therefore, the movement locus becomes an oblique ellipse.

Next, a control system of the full closed loop control system will be described with reference to the approximate block diagram shown in FIG. Also in this case, the transfer function Gm of the mechanical system
(S) is Gm (s) = s2 + 2ζωn · s + ωn2, and the overall transfer function G _full (s) is

[Equation 5] Becomes Solve this by substituting s = jω.

[0021] where

[Equation 6] And

However, A _f = ω _o ωn ² B _f = 0 C _f = −2ζωn ω ² + ω _o ωn ² D _f = −ω ³ + ωn ² ω

Here, the gain | G _full (jω) |
Is

[Equation 7] And the phase ∠G _full (jω) is

[Equation 8] Is.

The natural angular frequency ωn is ωn = √ (k /
M) and the damping ratio ζ are ζ = c / 2√ (kM),
In the case of full closed loop droop control, the gain G _full (jω) and the phase ∠G _full (jω) are functions of the mass M, the spring constant k, the viscous damping coefficient c, the angular velocity ω, and the position loop gain ω _o . is there.

The position loop gain ω _o is usually set to the same value for all axes to prevent gain deviation, but in most cases, the mass M, spring constant k, and viscous damping coefficient c are set for each axis. different.

Therefore, ideally, even in the case of the fully closed loop control capable of compensating the mechanical error, a delay of one cycle of the position loop occurs, and therefore the difference due to these mechanical characteristics is the gain of each axis. And cause a phase shift. In this way, when a gain or a phase shift occurs between the axes, if the biaxial circular interpolation motion is performed, the above-mentioned 1
It becomes an oblique ellipse as shown in 0.

The present invention has been made in order to solve the above-mentioned problems, and in a hybrid control system or a fully closed loop control system including scale feedback which is feedback compensation based on a detected value of a machine position, elastic displacement is caused. An object of the present invention is to provide a servo control method that corrects an error, suppresses a synchronization error even in interpolation of a plurality of axes, and improves contour motion accuracy.

[0028]

In order to achieve the above-mentioned object, a servo control method according to the present invention, in multi-axis simultaneous control, sets a first-order lag time constant of feedback compensation based on a detected value of a machine position and a square measure. The transfer function according to the change of the degree is calculated for each axis, and the feedforward amount is set so that the transfer functions of the respective axes are the same.

Further, in the servo control method according to the present invention, the change in the load mass is detected, the change amount of the inertial force due to this is calculated, and the transfer function for each axis is calculated in consideration of the change amount of the inertial force. To do.

Further, in the servo control method according to the present invention, the amount of change in rigidity of each axis is calculated in accordance with the mechanical position of the load mass, and the amount of change in rigidity is added to calculate the transfer function for each axis. .

Further, in the servo control method according to the present invention, the transfer function for each axis is calculated in consideration of changes in the viscous damping coefficient and frictional force depending on the feed rate.

Further, in the servo control method according to the present invention, the difference in the thermal displacement amount between the axes is added to the elastic displacement amount.

[0033]

BEST MODE FOR CARRYING OUT THE INVENTION Embodiments of the present invention will be described in detail below with reference to the accompanying drawings. In the embodiments of the present invention described below, parts having the same configurations as those of the above-described conventional example are denoted by the same reference numerals as those of the above-described conventional example. FIG. 1 shows one embodiment of a servo control method according to the present invention. In FIG. 1, 11 is a servo motor system, 12 is a mechanical system including loads such as a feed screw and a table, 13 is a low-pass filter, 15 is a speed feedforward section, 16 is an acceleration feedforward section, and 17 is Reference numeral 18 denotes a calculation unit for the correction value K of the gain ratio between the axes, and 18 denotes a feedforward correction unit.

The calculation unit 17 has information on the position loop gain ω _o , the first-order lag frequency ω _h , the acceleration / deceleration time constant T _a, and the ratio of the biaxial transfer function depending on the angular velocity ω (angular velocity ω1, inclination a1, angular velocity ω2, Inclination a2 ...) is input as an NC parameter, mass M, spring constant k, viscous damping coefficient c, ball screw mounting distance L, λ (λ = ball screw cross-sectional area S / Young's modulus E), frictional force F _d , The friction torque Tv and the natural frequency f are input as mechanical parameters (mechanical parameters), and the correction value K of the gain ratio between the axes is calculated.

The feedforward correction unit 18 corrects the velocity feedforward K _v s and the acceleration feedforward K _a s ² with the correction value K.

The ratio of the angular velocity ω to the X-axis and Y-axis gains (|
Gx | / | Gy |) is as shown in FIG. 2, and as a result of the actual machine test, the angular velocity ω and the X-axis, Y
Optimal speed feedforward ratio of the axis (FFx / FF
The relationship with y) is as shown in FIG. 3, and the feedforward ratio (FFx / FFy) is almost the same as the relationship between the gain ratio (| Gx | / | Gy |) and the angular velocity ω. It is confirmed.

Therefore, if the gain ratio of each axis due to the angular velocity ω is obtained and is multiplied by the feedforward set value, even in the hybrid control, the elastic displacement is generated without causing a path error such as an oblique ellipse. It turns out that can be corrected.

Next, a method of calculating the mechanical parameters of the mass M, the spring constant k, and the viscous damping coefficient c will be described. In the calculation of these mechanical parameters, the control system of the target machine for parameter calculation is the semi-closed loop control system. Transfer function Gs (s) from command to motor position in case of semi-closed loop control system
Is

[Equation 9] Becomes

When the absolute value of the above equation is calculated,

[Equation 10] Since this is a function of ω _o , the transfer function (control) in this case is not mechanically affected.

Here, the case of the XY axis plane will be described as an example. The circular interpolation motion of the XY axes is commanded for two or more rounds. At this time, the command value of each axis (actually the position calculated from the rotation angle of the servo motor) and the position of the machine are detected. In addition, pre-compensation is set to eliminate the effect of the radius reduction amount.

Here, the commands x ^* and y ^* for the x and y axes are as follows: x ^* = Rcosωt y ^* = Rsinωt (see FIG. 4). However, R: arc radius, ω: angular velocity, t: time.

The command velocity v and the acceleration α are as follows: v _x = -Rωsinωt v _y = Rω cosωt α _x = -Rω ² cosωt α _y = -Rω ² sinωt.

When the elastic displacement σ is calculated from the equation of motion,

[Equation 11] Becomes

When ωt = 2nπ (n is an integer, except for the movement start point and the end point, which may be influenced by other factors), v _x = 0 v _y = Rω α _x = −Rω ² α _{Since y} = 0,

[Equation 12] Become.

The elastic displacement σ can be measured as a difference between the motor position and the machine position, the mass M can be calculated from a design value or torque, and the arc radius R and the angular velocity ω can be read from a program.

Therefore,

[Equation 13] And rigidity is obtained.

When ωt = π / 2, v _x = −Rω v _y = 0 α _x = 0 α _y = −Rω ²

[Equation 14] Therefore,

[Equation 15] And rigidity is obtained.

When the arc radius R is small, k _x =
_{k 'x, k y = k} ' and _y, because regarded,

[Equation 16] And the viscous damping coefficient is obtained.

The method of obtaining the rigidity and viscous damping coefficient of each axis by performing the circular interpolation operation in the semi-closed loop control system and comparing the position calculated from the servo motor with the machine position has been described above.

In addition to the above, from the actual measurement of lost motion, static rigidity test, friction measurement, etc., axial rigidity and friction force,
The viscous damping coefficient can also be obtained.

Here, k _x = k ′ _x , k _y = k ′ _y
The calculation was performed by assuming that the axial rigidity k does not change depending on the machine position.However, when using a ball screw drive, the axial rigidity of the screw shaft is the same at the position where the load acts (machine position). different.

These can be measured and calculated by the above-mentioned method if the start position of circular interpolation is changed. However, since this increases the number of measurements, the rigidity of the ball screw shaft is obtained as a function of the load acting position, and the rigidity change due to the load acting position is calculated in advance to obtain an almost exact solution and minimize the measurement. can do.

In the case of ball screw drive, the total axial rigidity is

[Equation 17] Becomes However, k _b : Ball screw shaft rigidity k _T : Other total rigidity.

[0054] Ball screw shaft stiffness k _b when the ball screw mounting both ends fixed,

[Equation 18] Becomes However, λ = SE (S: cross-sectional area of ball screw, E: Young's modulus, constant) L: distance between ball screw attachments 1: indicates load acting position.

The other total rigidity k _T includes the rigidity of the ball screw nut, the rigidity of the ball screw supporting bearing, the rigidity of the nut and the bearing mounting portion, and the like. When the radius of the arc is large, the stiffness k corrected for the calculation of the viscous damping coefficient is used.

Up to now, the case where the viscous damping coefficient c is considered to be almost constant has been described. However, as in the case of a slide guide, when the frictional force varies depending on the sliding speed along the Stribeck curve, or when the lubricant When the kinematic viscosity is high and the friction force is not proportional to the speed, there is a method of actually measuring the relationship between the feed speed and the friction force to obtain the relationship between the viscous damping coefficient and the feed speed. The Coulomb friction is compensated by the torque feedforward control by the quadrant projection correction at the time of axis reversal.

An example of the relationship between the feed rate and the frictional force due to the difference in kinematic viscosity is shown in FIG. As an example of the method of measuring the relationship between speed and frictional force, there is a method of detecting and recording the steady-state (non-accelerated) feed axis torque at the time of uniaxial linear interpolation at each feed rate. It suffices to have a memory for recording the difference between.

The viscous damping coefficient c under the condition of the above method
_Ask for ₀ . The viscous damping coefficient for any feed rate is

[Formula 19] Can be found at. However, Tv _n and Tv ₀ are friction torques at arbitrary feed rates.

Here, in the case of ball screw driving, the relationship between the friction torque T and the friction force F _d is

[Equation 20] Becomes However, P is the lead of the ball screw, and the rate of change in torque with the feed rate corresponds to the rate of change in friction.

Further, a change in the moving mass can be detected, and a change in the inertial force due to the change can be calculated and corrected. Next, a method of detecting a mass change when the moving mass changes will be described. Before and after the load mass is placed on the work table, etc., linear interpolation motion of one axis is commanded at the same feed rate, and the steady-state torque is measured. The moment of inertia can be approximated from the amount of increase in torque at this time, and the load mass can be estimated from this.

When the natural frequency in the axial direction of the machine can be detected, such as when the open-loop transfer function of speed control can be measured, the change in mass can be obtained from the change in natural frequency. The natural frequency f is

[Equation 21] Than,

[Equation 22] Therefore, the change in mass is inversely proportional to the square of the change in natural frequency.

Next, a method of measuring the difference in elastic displacement due to the biaxial inertial force will be described. Here, an example in which the difference in elastic displacement due to the biaxial inertial force is obtained by actual measurement will be described. A command for linear interpolation motion of 45 degrees in two axes is issued to detect an error Δσ during acceleration / deceleration. An example of the measurement result is shown in FIG. This is the difference in elastic displacement due to the biaxial inertial force.

Assuming that friction is almost the same in both axes, the elastic displacement of each axis is

[Equation 23] And Δσ = σ _x −σ _y . If the mass is known in advance, the rigidity of each axis can be calculated by performing this measurement under the condition of two or more accelerations.

There may be a case where the position detector (scale or the like) provided in the machine has an Abbe error, or the structure may include a deflection. If there is an Abbe error, the position of the machine is not detected by the scale, and the above-mentioned circular interpolation accuracy measurement is performed using a biaxial plane scale and compared with the command value. When the deflection of the structure is large, it is possible to measure at several points and obtain the relationship between the measurement position and the deflection.
In addition, the deflection of the structure is calculated in advance by structural analysis,
The calculated value may be added to the correction.

Next, a method of correcting the difference between the biaxial transfer functions will be described. The relationship between the ratio of the transfer functions of the two axes and the angular velocity is as shown in FIG. 2, but it is very laborious to exactly solve this value. Therefore, approximation may be performed based on this curve.

Example 1: The transfer function of a hybrid contains a first-order lag element. Therefore, the approximation is performed with an exponential function. Example 2: When the angular velocity is low, the gain deviation is small and can be regarded as almost 1. Therefore, the coefficient by this correction is set to 1 up to a certain angular velocity. The curve from the angular velocity at which the gain change becomes large is linearly approximated by a plurality of straight lines. The correction pattern of Example 2 is shown in FIG.

This simplifies a complicated operation, and N
The calculation processing of C can be reduced. In FIG. 7, the solid line shows the exact solution and the dotted line shows the correction line. In FIG. 7, the angular velocity ω1 = 18, the inclination a1 = 0, the angular velocity ω2 = 45, the inclination a2 = 0.0009, the angular velocity ω3 = ∞, and the inclination a3 = 0.0.
This is an example approximated by three straight lines of 002.

FIG. 8 shows an embodiment of the servo control method according to the present invention in the case where viscous friction varies depending on conditions. In addition, in FIG. 8, portions corresponding to those in FIG. 1 are denoted by the same reference numerals as those in FIG. 1, and description thereof will be omitted.

The correction value calculation unit 17 inputs the NC parameter and the mechanical parameter and calculates the correction coefficient K1 for the velocity feedforward and the correction coefficient K2 for the acceleration feedforward, respectively, as in the above-described embodiment.

[0070] Speed feed forward correction unit 19 the speed feedforward _{K v} s is corrected by the correction value K1, the acceleration feedforward correction unit 20 correction value K2
Correcting the acceleration feedforward _K a ^{s 2} by.

As described above, when the viscous friction varies depending on the conditions, the velocity feedforward K _vs is corrected,
The correction of the acceleration feedforward _K a ^{s 2,} can be carried out by individual correction values K1, K2.

In any of the embodiments, the heat change correction is performed by multiplying the friction by the heat correction coefficient and adding the difference in the thermal displacement amount to the elastic displacement amount for the axes having very different heat conductions. You can also

Further, the servo control method according to the present invention can be applied to not only the hybrid control method but also the full closed loop control method.

[0074]

As can be understood from the above description, according to the servo control method of the present invention, a gain deviation due to a mechanical difference between axes caused by hybrid control or full closed loop control of a plurality of axes occurs. It is possible to correct and improve the contour movement error. In particular, diagonal elliptical error during high-speed circular interpolation operation or orbit boring,
It is effective in reducing the contour motion error in the transient state.

[Brief description of drawings]

FIG. 1 is a block diagram showing an embodiment of a servo control method according to the present invention.

FIG. 2 is a graph showing a relationship between an angular velocity and a gain ratio between two axes.

FIG. 3 is a graph showing an actually measured value of a relationship between a ratio of correction values of two axes and an angular velocity.

FIG. 4 is an explanatory diagram showing circular interpolation motion.

FIG. 5 is a graph showing the relationship between frictional force and feed rate (comparison of kinematic viscosity).

FIG. 6 is a graph showing measured values of differences in elastic displacement due to biaxial inertial forces.

FIG. 7 is a graph showing an example of a correction straight line that approximates the relationship between the gain ratio and the angular velocity.

FIG. 8 is a block diagram showing another embodiment of the servo control method according to the present invention.

FIG. 9 is an approximate block diagram of a hybrid control system.

FIG. 10 is an explanatory diagram showing an example of an oblique ellipse error.

FIG. 11A and FIG. 11B are graphs showing biaxial gain characteristics.

12A and 12B are graphs showing biaxial phase characteristics.

FIG. 13 is an approximate block diagram of a full closed loop control system.

[Explanation of symbols]

11 Servo motor system 12 Mechanical system 13 Low-pass filter 15 Speed feed forward section 16 Acceleration feed forward section 17 Correction value calculation unit 18 Feedforward correction unit 19 Velocity feedforward correction unit 20 Acceleration feedforward correction unit

   ─────────────────────────────────────────────────── ─── Continued front page    F-term (reference) 3C001 KA05 TA01 TA04 TD01                 5H269 BB03 CC01 DD01 EE01 EE03                       EE05 FF06 GG01 GG09 JJ01                 5H303 AA01 AA10 BB02 BB07 CC01                       CC07 CC08 DD01 DD25 EE03                       EE07 FF03 KK23 KK25 KK29                       MM05

Claims (5)

[Claims] 1. In multi-axis simultaneous control, a transfer function is calculated for each axis according to a set value of a first-order lag time constant for feedback compensation based on a detected value of a machine position and a change in angular velocity, and the transfer functions of the respective axes are mutually calculated. A servo control method characterized in that the feedforward amount is set to be the same. 2. A transfer function for each axis is calculated by detecting a change in the load mass, calculating a change amount of the inertial force due to the change, and taking the change amount of the inertial force into consideration. 1
The servo control method described in. 3. The transfer function for each axis is calculated by calculating the amount of change in rigidity of each axis according to the mechanical position of the load mass and adding the amount of change in rigidity. Alternatively, the servo control method described in 2. 4. The servo control according to claim 1, wherein the transfer function is calculated for each axis in consideration of changes in a viscous damping coefficient and a frictional force depending on a feed speed. Method. 5. The servo control method according to claim 1, wherein a difference in thermal displacement between the axes is added to the elastic displacement.