JP4576530B2 - Servo gain calculation method, servo gain calculation program, and servo gain calculation device - Google Patents

Description

  The present invention relates to a servo gain calculation method, a servo gain calculation program, and a servo gain calculation device for a feedback control system.

  Currently, gain adjustment of servo systems such as NC machine tools and robots is performed by trial and error, so that advanced technology based on experience and a great deal of time are required. Many methods have been proposed to solve such problems. Among them, conventional examples that are considered to be closely related to the present invention are listed below.

<First Conventional Example>
When tuning the control system of the feed drive system that governs the shape creation of NC machine tools, first, the speed loop and position loop should be adjusted so that the gain margin and phase margin of the servo system are within empirically determined ranges. A control gain is determined, and then a feedforward gain is obtained by calculation so that the follow-up error with respect to the target value becomes zero (see Non-Patent Document 1 below).

<Second Conventional Example>
This is called the speed loop gain in the conventional compensator, trying to adjust the control gain of the integral-proportional derivative compensator with excellent disturbance suppression characteristics in the same way as the proportional-integral compensator used in the past. When a parameter α having the same meaning as the parameter is defined and the parameter α is designated, the control gain can be calculated by four arithmetic operations (see Patent Document 1 below).

<Third conventional example>
For the purpose of adjusting the control gain safely without causing overshoot, sliding mode control is applied.When automatic gain adjustment is performed, the mode automatically shifts to sliding mode control, and the variable gain for sliding mode control is adjusted. The number of times of switching is obtained, and the value of the adjustment unit is automatically adjusted based on the number of times of switching (see Patent Document 2 below).

<Fourth Conventional Example>
In order to enable the use of complex compensators for which design algorithms have been proposed, a model to be controlled is created, and this model and the actual controlled object are controlled by a compensator having the same structure and parameters, both Compare the feature quantity of the control amount, infer from the comparison result, modify the above model to make it a model close to the actual machine, repeat the re-determining the gain of the control system, and determine the final gain (See Patent Document 3 below).

<Fifth conventional example>
In the feed drive system of a numerically controlled machine tool, it is necessary for multiple axes to move in synchronization with high precision. By using a method called the model matching method, the characteristics of the two control axes differing in the mechanism characteristics Can be aligned. At that time, a feed drive mechanism composed of a motor and a table is considered as one mechanical system, and a control device designed using a model matching method is applied to this to constitute a feed drive system, and each axis of the XY table The performance of the feed drive system is improved at the same time as matching the performances of the above (see Non-Patent Document 2 below).

<Sixth Conventional Example>
When adjusting a positioning servo system mounted on a base with a low natural frequency, such as a vibration isolation table, the gain is first input instead of the limit sensitivity method that is used relatively frequently in actual adjustment sites. Then, the adjustment sequence for stabilizing the closed-loop system and making the steady position deviation zero, that is, applying initial tuning, reduces the risk of runaway of the precision stage mounted on the vibration isolation table (Non-Patent Document 3 below) reference).

<Seventh conventional example>
When adjusting various parameters of a numerically controlled machine tool based on the measurement results of a device called a grid encoder that can measure displacement in two directions at the same time, the characteristics of the speed loop are targeted for vibrations of the machine body of 100 Hz or less. Is ignored, and the position loop and the feed forward gain are tuned (see Non-Patent Document 4 below).

<Eighth Conventional Example>
Without tuning the control target many times before supplying the control method, gain tuning is performed using a characteristic equation that is closer to the control target, making it possible to perform optimal gain tuning without causing the control target to run out of control. In order to do this, several types of mathematical models are prepared in advance in the control device, the user selects the model according to the structure of the control target, and then features such as the position and angle actually measured in the control device The parameters of the model are automatically adjusted by comparing the quantity with those of the model, and the control gain is determined by genetic algorithm using the model, and the control gain is determined while checking the control performance by simulation ( See Patent Document 4 below).

Yoshiaki Kakino et al .: Study on total tuning of feed drive system in NC machine tools (2nd report), Journal of Japan Society for Precision Engineering, Vol.61, No.2, (1995) Takanori Yamazaki et al .: Multi-axis control of numerically controlled machine tool feed drive system using model matching method, Journal of Precision Engineering, Vol.65, No.5, (1999) Shinji Sakurai: A Study on PID Adjustment of Stage Position Control System, Journal of Precision Engineering, Vol.65, No.5, (1999) Yasuhiko Suzuki et al .: Study on CNC parameter tuning for improving the contour accuracy of machine tools, Journal of Precision Engineering, Vol.69, No.8, (2003) JP-A-8-6603 JP-A-8-194542 Japanese Patent No. 2758246 JP 2004-94336 A

  However, in the first, sixth, and seventh conventional examples described above, the adjustment procedure is determined. However, it is necessary to understand the frequency characteristics, pole arrangement, and the like for the adjustment. However, in the second conventional example, if one parameter is determined empirically, other parameters are also determined. However, in determining the first one parameter, there is a problem. There was a problem that advanced expertise was required. Further, in the fifth conventional example, it is necessary to solve a complicated differential equation inside the control device, and it is difficult to realize with a commercially available control device. Therefore, the feed drive system is configured according to this theory. Had the problem of requiring advanced expertise.

  On the other hand, in the third, fourth, and eighth conventional examples, the servo system host controller is configured to correspond to a specific actuator, so that it is difficult to apply to a system in which general-purpose motors are mixed. It was.

  The present invention has been made in order to solve the above-described problems of the conventional example, and an object of the present invention is to calculate the servo gain relatively easily even if the operator does not have advanced technical knowledge. A servo gain calculation method, a servo gain calculation program, and a servo gain calculation device are provided.

  Another object of the present invention is to provide a servo gain calculation method, a servo gain calculation program, and a servo gain calculation device that can be applied to a system in which general-purpose motors are mixed.

In the present invention, the servo gain calculation device having the equation creating means, the conditional expression calculating means, the constant determining means, and the servo gain calculating means uses the transfer function having an ideal characteristic corresponding to the transfer function of the feedback control system. A servo gain calculation method for calculating a servo gain of a speed feedback loop having disturbance suppression characteristics and a servo gain of a position feedback loop having target value tracking characteristics of a feedback control system,
The equation creating means equalizing the transfer function of the feedback control system and the transfer function having the ideal characteristics to obtain simultaneous equations relating to the coefficients of the Laplace operator;
The conditional expression calculating means calculating a conditional expression of the coefficient from which the positive real number solution for the coefficient of the transfer function having ideal characteristics is obtained from the simultaneous equations;
The constant determining means calculates a value of some of the various constants necessary for calculating the servo gain of the feedback control system, and values of constants other than the some constants are known in advance. Determining from
The servo gain calculation means substitutes the determined various constants into a conditional expression of the coefficient that obtains a positive real number solution, and calculates a speed loop proportional gain and a speed loop integral gain that are servo gains of the speed feedback loop. Calculate the break frequency of the frequency characteristic of the speed feedback loop based on the calculated speed loop proportional gain and the speed loop integral gain by a predetermined arithmetic expression, and position based on the calculated break frequency Calculating a loop proportional gain;
Have.

The present invention provides a computer having an equation creating means, a conditional expression calculating means, a constant determining means, and a servo gain calculating means with a transfer function having ideal characteristics corresponding to the transfer function of the feedback control system and the transfer function of the feedback control system. A servo gain calculation program for storing a function and calculating a servo gain of a speed feedback loop having a disturbance suppression characteristic and a position feedback loop having a target value tracking characteristic of the feedback control system,
The equation creating means makes the transfer function of the feedback control system equal to the transfer function having the ideal characteristic to obtain simultaneous equations related to the coefficients of the Laplace operator;
A step of calculating a conditional expression of the coefficient by which a positive real solution for a coefficient of a transfer function having ideal characteristics is obtained from the simultaneous equations by the conditional expression calculating means;
The constant determination means calculates the values of some of the various constants necessary for calculating the servo gain of the feedback control system, and values of constants other than the some constants are known in advance. Determining from
By substituting the various constants determined by the servo gain calculation means into a conditional expression of the coefficient that provides a positive real number solution , a speed loop proportional gain and a speed loop integral gain, which are servo gains of the speed feedback loop, are obtained. Calculate the break frequency of the frequency characteristic of the speed feedback loop based on the calculated speed loop proportional gain and the speed loop integral gain by a predetermined arithmetic expression, and position based on the calculated break frequency Calculating a loop proportional gain;
Sequentially using the computer.

The present invention provides a position feedback having a servo gain of a speed feedback loop having a disturbance suppression characteristic and a target value tracking characteristic of the feedback control system using a transfer function having an ideal characteristic corresponding to the transfer function of the feedback control system. A servo gain calculation device for calculating a servo gain of a loop,
First transfer function storage means for storing a transfer function of the feedback control system;
Second transfer function storage means storing a transfer function having the ideal characteristics;
An equation creating means for equalizing the transfer function stored in the first transfer function storage means and the transfer function stored in the second storage means to create simultaneous equations relating to the coefficients of the Laplace operator;
A first computing unit that calculates a conditional expression of a coefficient that provides a positive real solution for a coefficient of a transfer function having ideal characteristics from the simultaneous equations created by the equation creating unit;
Constant determining means for calculating values of some of the various constants necessary for calculating the servo gain of the feedback control system and determining values of constants other than the some constants from previously known values When,
Substituting various constants determined by the constant determining means into the conditional expression of the coefficient calculated by the first arithmetic means, and calculating a speed loop proportional gain and a speed loop integral gain which are servo gains of the speed feedback loop. First servo gain calculating means for
Based on the calculated velocity loop proportional gain and the calculated velocity loop integral gain, a corner frequency of the frequency characteristic of the velocity feedback loop is calculated by a predetermined arithmetic expression, and the position loop proportional gain is calculated based on the calculated corner frequency. Second servo gain calculation means for calculating
Prepare.

  Since the present invention is configured as described above, the servo gain can be obtained by algebraic calculation without performing trial and error or iterative calculation. Therefore, it is relatively easy even if the operator does not have advanced expertise. Since the servo gain can be calculated and various constants of the feedback control system are determined and substituted into the coefficient conditional expression, it can be applied to a system in which general-purpose motors are mixed.

Hereinafter, the present invention will be described in detail based on preferred embodiments shown in the drawings.
<First Embodiment>
FIG. 1 is a perspective view showing a schematic configuration of a drive mechanism 10 according to a first embodiment of the present invention. In FIG. 1, linear ball bearing guide rails 12 and 12 are mounted in parallel on both sides of the surface of a substrate 11 having a rectangular planar shape, and a motor fixing base 13 is mounted on one end in the longitudinal direction. Has been. A servo motor 14 is mounted on the outer end surface of the motor fixing base 13, and an output shaft of the servo motor 14 protrudes in an intermediate portion of the guide rails 12 and 12. On the extension of the output shaft of the servo motor 14, a pair of shaft support tables 15, 15 are mounted separately. End portions of the screw shafts 16 that engage with the nuts 17 of the ball screws are supported on the shaft support bases 15 and 15 via radial bearings. The end of the screw shaft 16 on the motor fixing base 13 side is coupled to the output shaft of the servo motor 14. A work table 18 is mounted so as to overlap a part of the guide rails 12 and 12 in the longitudinal direction. A linear ball bearing (not shown) is mounted on both sides of the work table 18 on the back side shown in the drawing, and a nut 17 is mounted on the center. Hereinafter, a block diagram of a servo system including the drive mechanism 10, a servo gain calculation method, and an actual calculation example of the servo gain will be described.

(1) Block diagram of servo system The drive mechanism 10 shown in FIG. 1 converts the rotation of the servo motor 14 into a linear motion of a work table 18 by means of a screw shaft 16 and a nut 17, and is a general NC machine tool. Used as part of the servo system. In such a servo system, since the natural frequency of the drive mechanism 10 is sufficiently larger than the natural frequency of the servo system, it can be expressed by a dynamic model as shown in FIG. The model can be expressed by the equation of motion shown in the following equation (1).

Where θ is the rotation angle of the servo motor [rad], x _t is the table displacement [m], l is the ball screw lead [m], T _m is the servo motor torque [Nm], and c is the motor shaft. [Nm / (rad / s)], and f is the friction torque [Nm] in terms of motor shaft. J is the total moment of inertia [kgm ² ] of the drive mechanism in terms of the motor shaft. From the moment of inertia J _b [kgm ² ] of the servo motor and ball screw and the mass M _t [kg] of the table and ball screw, It is calculated by the equation (2).

  The entire servo system obtained by adding a control system to the equation (1) can be represented by block diagrams as shown in FIGS. Most control systems have a double control loop, a speed feedback loop and a position feedback loop. FIG. 3 shows a servo system in which the position feedback loop is proportionally controlled and the speed feedback loop is proportionally-integratedly controlled. FIG. 4 shows an example in which the speed feedback loop is integral-proportional control. The difference from the proportional-integral control can be easily realized, but it is not very popular because a gain adjustment method has not been established. There is no current situation. However, it is said that the integral-proportional control system has many advantages as the characteristics of the control system. The present invention provides a servo gain calculation method applicable regardless of which control system is employed.

In the block diagram of FIG. 3, DA is the DA converter gain, T _rg is the torque command adjustment gain, T _f is the torque command filter time constant [s], and T is the torque control delay time constant [s]. _Kpp is a position loop proportional gain, _Kvp is a velocity loop proportional gain, and _Kvi is a velocity loop integral gain. Of these, three control gains K _pp , K _vp , and K _vi are adjustment targets. Note that r is a position command [m].

(2) Calculation of servo gain The servo system is required to have target value tracking characteristics and disturbance suppression characteristics. In the servo system having the drive mechanism 10 shown in FIG. 1, the frictional force is the largest disturbance element. In the present invention, the velocity loop proportional gain K _vp and the velocity loop integral gain K _vi are first calculated by paying attention to the disturbance suppression characteristics. In particular, in a machine tool, if an overshoot that exceeds the target position occurs, the material is cut too much, so that the position feedback loop is required to have a characteristic that does not cause an overshoot. The present invention also provides a method for obtaining a position loop proportional gain that does not cause overshoot from the characteristics of the velocity feedback loop designed for the disturbance suppression characteristics.

(2-1) Speed Loop Proportional Gain and Speed Loop Integral Gain First, a method for calculating the speed loop proportional gain K _vp and the speed loop integral gain K _vi will be described. A method called the partial model matching method is used for the design of the velocity feedback loop (Toshiyuki Kitamori: Control system design method based on partial knowledge of the controlled object, Transactions of the Society of Instrument and Control Engineers, Vol. 15, No. 4) (1979) pp 549-555). This partial model matching method is a method for determining a servo gain so that a transfer function having an ideal characteristic matches a transfer function to be adjusted. The present invention applies this method.

  Therefore, considering the transfer function from disturbance (friction force) to the rotational speed of the servo motor in the speed feedback loop, both the proportional-integral control system shown in FIG. 3 and the integral-proportional control system shown in FIG. (3) of the formula.

  When the transfer function of equation (3) is expressed in the denominator series, it can be written as the following equation (4).

  Two servo gains are calculated by equating the characteristic polynomial of equation (4) with a transfer function (reference model) having desirable characteristics. Here, the reference model is shown in the following equation (5).

If the servo gains to be obtained are the speed loop proportional gain K _vp and the speed loop integral gain K _vi , the servo gain can be calculated by using up to the third power of the Laplace operator s. In the formula (4), h ₁ to h ₃ are as shown in the following formula (6).

  Therefore, when the equations (4) and (5) are placed equally, the following simultaneous equations (7) can be obtained.

  If the simultaneous equations of Equation (7) are arranged for σ, the following cubic equation is obtained for σ.

  Obtain σ from the solution of the cubic equation. Since σ must be a positive real number, the following equation (9) is obtained.

Servo gains K _vp and K _vi to be obtained from σ calculated by equation (9) and equations (3) and (7) are calculated by the following equation (10).

  Through the above procedure, the servo gain of the speed feedback loop for matching the characteristics of the speed feedback loop with the reference model can be obtained.

(2-2) Position Loop Proportional Gain Next, the procedure for obtaining the position feedback loop proportional gain K _pp will be described. The position loop proportional gain K _pp of the position feedback loop is determined so as not to cause overshoot based on the characteristics of the speed feedback loop. When the transfer function from the speed command of the speed loop to the motor rotation speed is expressed in the denominator series, it can be written as the following equation (11).

Here, the transfer function from the speed command to the motor rotation speed is different between the proportional-integral control system and the integral-proportional control system, and each coefficient h ′ _i (i = 1 to 3) in the denominator series expression is proportional− In the case of integral control, the following equation (12) is obtained.

  In the case of integral-proportional control, the following equation (13) is obtained.

Note that a _{0 to} a ₃ are exactly the same as the equation (3). When calculating the servo gain of the speed loop, the terms up to the third power of the Laplace operator s are used, so the fourth power term of the Laplace operator s is ignored when considering the characteristics for the target value. I decided to.

The position loop proportional gain is calculated based on the frequency characteristics of the speed loop. Considering the speed loop as a third-order lag system, the frequency characteristics from the speed command to the motor rotation speed are as shown in FIG. In FIG. 5, ω _n is a break frequency [rad / s] and represents a frequency that can be responded to by the speed loop. In the case of a third-order lag system, in the range where the frequency is higher than the break frequency, the frequency decreases by 60 [dB] every time the frequency is increased 10 times. Using this fact, the corner frequency can be calculated from the transfer function of equation (11) as follows.
When an arbitrary frequency sufficiently higher than the response frequency of the speed loop is ω ′, the gain [dB] at the frequency ω ′ is expressed by the following equation (14).

Since the equation (14) and the gain slope are −60 [dB / decade], the corner frequency ω _n can be calculated by the following equation (15).

This corner frequency ω _n has the same meaning as the natural frequency in the second-order lag system. Therefore, the speed loop characteristic is considered as a second-order lag system of the natural frequency ω _n as shown in the following equation (16), and the position loop proportional gain is calculated.

FIG. 6 shows a block diagram of the entire servo system when the speed loop characteristics are expressed by the transfer function of equation (16). In FIG. 6, _Vr is a speed command [rad / s]. From this block diagram, the leads to the transfer function from the target value r to the table displacement x _t is (17) below is obtained.

  The servo system is required to quickly reach the target value without causing overshoot. The fastest response without overshoot occurs when the denominator of Eq. (17) has a triple root. In such a case, the position loop proportional gain can be calculated by Eq. (18) below. it can.

  By the procedure as described above, the position loop proportional gain that quickly follows the target value without causing overshoot can be calculated.

(3) Actual Calculation Example of Servo Gain FIG. 7 is a flowchart showing a specific processing procedure of the servo gain calculation method described above, and will be described with reference to this flowchart. First, in the first step 101, a speed feedback system in which a control system is added to the dynamic model expressing the drive mechanism is constructed, and the transfer function G _fθ (s) and (11) of the speed feedback loop shown in the expression (3) is expressed. The transfer function G _Vrθ (s) of the position feedback loop shown is determined, and the transfer function G _R (s) shown in the equation (5), which has been proposed as desirable so far, corresponding to the transfer function G _fθ (s) in step 102 is determined. ). Next, in step 103, the transfer function G _fθ (s) and the transfer function G _R (s) are equally placed in the form of a denominator series expression, and simultaneous equations relating to the coefficients of the Laplace operator as shown in equation (7). In step 104, a conditional expression of coefficients for obtaining a positive real number solution is calculated from the prepared simultaneous equations as shown in the equation (9). Next, in step 105, various constants of the feedback control system are determined, and in step 106, the determined constants are substituted into the conditional expression of the coefficient for obtaining a positive real solution, and the servo gain K _{vp of} the speed feedback loop is _calculated . Calculate K _vi . Servo gain _K vp of velocity feedback loop in the last step _107, calculates a proportional gain _{K pp} position feedback loop based on the _{K vi.}

FIG. 8 is a flowchart showing a more detailed processing procedure of step 105. Here, the parameters necessary for calculating the servo gain are the total moment of inertia J [kgm ² ] of the drive mechanism, the viscosity coefficient c [Nm / (rad / s)] of the motor shaft, the filter time constant T _f , and torque control. There are a total of six system delays T [s], DA converter gain DA, and torque command adjustment gain T _rg . Of these, the moment of inertia J can be calculated accurately from the design value of the drive mechanism, and the filter time constant _Tf , the torque control system delay T, the DA converter gain DA, and the torque command adjustment gain T _rg are known. . However, it is necessary to identify the viscosity coefficient c.
Therefore, the moment of inertia J is calculated in step 1051, the filter time constant T _f , the torque control system delay T, the DA converter gain DA, and the torque command adjustment gain T _rg are checked in step 1052, and the viscosity is determined in step 1053. The coefficient c is identified.

A general-purpose servo system has a function of rotating a motor at a constant speed by a sequence input and a function of monitoring the motor torque. The viscosity coefficient c is identified using these functions. That is, the motor is rotated at a speed ω ₁ [rad / s] that is a state where the motor is assembled to the drive mechanism, and the motor torque T _m1 [Nm] at that time is recorded. Next, the motor is rotated at a speed ω ₂ [rad / s] different from the speed ω _1, and the motor torque T _m2 [Nm] at that time is recorded. From these four values, the motor shaft equivalent viscosity coefficient c is calculated by the following formula (19) (Shinji Shinji: Identification method of physical parameters of positioning mechanism, Journal of Precision Engineering, Vol.60, No2, (1994) , pp.211-214.).

FIG. 9 is a flowchart showing a detailed processing procedure for calculating the servo gain of the speed feedback loop in step 106. Here, in step 1061, from the six parameters J, T _f , T, DA, T _rg , c and the three servo gains K _vp , K _vi , K _pp , a ₀ , a ₁ shown in the equation (3) , A ₂ , a ₃ , a ₄ , b ₁ , b ₂ are defined. In step 1062, simultaneous equations α ₀ , α ₁ σ, α ₂ σ ² , and α ₃ σ ³ shown in Equation (7) are obtained. Next, in step 1063, the simultaneous equations are arranged with respect to σ, and a cubic equation of σ shown in equation (8) is obtained. Subsequently, in step 1064, a conditional expression having a positive real solution for the cubic equation related to σ, that is, a conditional expression shown in the expression (9) is obtained. In the last step 1065, the proportional gain K _vp and integral gain K _vi of the speed control loop are calculated according to the equation (10).

FIG. 10 is a flowchart showing a detailed processing procedure for calculating the servo gain of the position feedback loop in step 107. In this case, in step 1071, if the speed feedback loop is proportional-integral control, h ₁ ', h ₂ ', h ₃ 'shown in equation (12) is used. If the speed feedback loop is integral-proportional control, H ₁ ′, h ₂ ′, and h ₃ ′ shown in the equation (13) are obtained. In step 1072, the above-mentioned h ₁ ′, h ₂ ′, h ₃ ′ and the angular frequency ω ′ having a frequency sufficiently higher than the response frequency of the speed feedback loop (about 10000 rad / s) are used (15) The corner frequency ω _n is obtained by calculating the equation. In the final step 1073, the proportional gain K _pp of the position feedback loop is calculated according to the equation (18).

  According to the servo gain calculation method based on the above processing procedure, the servo gain can be obtained by algebraic calculation without performing trial and error or repeated calculation, and various constants of the feedback control system are determined to determine the condition of the coefficient. Since it is substituted in the equation, it can be applied to a system in which general-purpose motors are mixed.

  In addition, it is possible to statically record a program that implements the servo gain calculation method described above on a recording medium such as a CD-ROM, set it up in a computer, and sequentially input necessary data to calculate the servo gain. Further, the servo gain can be easily obtained by dynamically transmitting the program through a network connected by a wired line or a wireless line and setting it up in a computer.

FIG. 11 is a block diagram showing the configuration of a servo gain calculation apparatus that implements the servo gain calculation method described above. This servo gain calculation device 30 is configured with the drive mechanism 10 shown in FIG. 1 as a driving target, and stores the first transfer function storage in which the transfer function G _fθ (s) of the speed feedback loop of the feedback control system shown in FIG. 3 is stored. Means 31, second transfer function storage means 32 storing a transfer function G _R (s) having ideal characteristics corresponding to this transfer function G _fθ (s), and first transfer function storage means 31 Of the transfer function G _fθ (s) stored in the second transfer function storage means 32 and the transfer function G _R (s) stored in the second transfer function storage means 32 are equally arranged to create simultaneous equations relating to the coefficients of the Laplace operator Means 33, a conditional expression calculating means 34 for calculating a conditional expression of a coefficient for obtaining a positive real number solution from the simultaneous equations created by the equation creating means 33, and a constant determining means 35 for determining various constants of the feedback control system. And constant A first servo gain calculating means 36 for calculating the servo gain of the speed feedback loop by substituting various constants determined by the number determining means 35 into the conditional expression of the coefficient calculated by the conditional expression calculating means 34; The corner frequency ω _n of the frequency characteristic of the speed feedback loop is detected based on the feedback gain calculated by the servo gain calculating means 36 of the servo gain, and the feedback gain of the position feedback loop is calculated based on the detected corner frequency ω _n. Second servo gain calculation means 37.

The operation of the servo gain calculation apparatus configured as described above will be described below. The first transfer function storage means 31 stores the transfer function G _fθ (s) of the speed feedback loop shown in equation (3), and the second transfer function storage means 32 corresponds to the transfer function G _fθ (s). Thus, the transfer function G _R (s) shown in the equation (5) which has been proposed as desirable so far is stored. The equation creating means 33 _equalizes the transfer function G _fθ (s) of the first transfer function storage means 31 and the transfer function G _Vrθ (s) of the second transfer function storage means 32 in the form of a denominator series expression. Create simultaneous equations for coefficients of Laplace operator as shown in Eq. (7). The conditional expression calculation means 34 calculates a conditional expression of coefficients for obtaining a positive real number solution from the simultaneous equations created by the equation creating means 33 as shown in the expression (9). On the other hand, the constant determining means 35 determines a constant of the feedback control system. Therefore, the first servo gain calculation means 36 substitutes the various constants determined by the constant determination means 35 into the conditional expression of the coefficient that provides a positive real number solution, and calculates the servo gains K _vp and K _vi of the speed feedback. . Servo gain _K vp of the second servo gain calculating means 37 velocity feedback _loop, calculates the proportional gain _{K pp} position feedback loop based on the _{K vi.} In this manner, according to the servo gain calculation apparatus shown in FIG. 11, the servo gain calculation method shown in the flowcharts of FIGS. 7 to 10 can be implemented.

  As a result, the servo gain can be obtained by algebraic calculation without trial and error or repeated calculations.Furthermore, various constants of the feedback control system are determined and substituted into the conditional expression of the coefficient. A servo gain calculation apparatus that can be applied to a mixed system is provided.

<Second Embodiment>
FIG. 12 is a perspective view showing a schematic configuration of a drive mechanism according to the second embodiment of the present invention. In this drive mechanism, the drive mechanism 10 described above is mounted on another drive mechanism 20 as a work table, and the drive mechanism 10 is an X-axis drive mechanism that drives the work table 18 in the X-axis direction. Then, the drive mechanism 20 is a drive mechanism for the Y axis that drives the drive mechanism 10 in the Y axis direction, and these constitute an XY table. The details of the drive mechanism 20 are basically the same as those of the drive mechanism 10, and thus detailed description thereof is omitted.

  FIG. 13 is a block diagram showing the configuration of an X-axis servo gain calculation device 30 applied to the XY table shown in FIG. 12 and a Y-axis servo gain calculation device 40 for calculating the servo gain of the drive mechanism 20. . In FIG. 13, the servo gain calculation device 30 is configured in the same manner as that shown in FIG. 11, and the servo gain calculation device 40 is also configured in the same manner as the servo gain calculation device 30, so that the detailed configuration is omitted. ing. With such a configuration, it is possible to calculate the respective servo gains by simultaneously moving the X axis and the Y axis.

  In the second embodiment, the servo gain calculation device 30 and the servo gain calculation device 40 are provided corresponding to the X-axis drive mechanism 10 and the Y-axis drive mechanism 20, but a multi-axis having three or more axes. By providing a servo gain calculation device similar to the servo gain calculation device 30 for each drive mechanism, the servo gain for each axis of the multi-axis drive mechanism can be calculated simultaneously.

Hereinafter, specific servo gain tuning when the XY table shown in FIG. 12 is driven by a personal computer and the servo gain calculation apparatus according to the present embodiment is applied will be described.
Here, the servo gain is calculated when the speed feedback loop is an integral-proportional control system and proportional-integral system, and the step response when the position command is changed stepwise and the X and Y axes are moved simultaneously. The trajectory error when circular interpolation motion was performed was investigated. For comparison, a comparison was made with a case where the servo gain of a proportional-integral control system generally used in the past was adjusted by trial and error.

  The target response tracking characteristics can be evaluated by step response, and the motion direction of each axis is reversed by circular interpolation motion, especially by looking at the size of the projection-like trajectory error (quadrant projection) caused by the influence of frictional force. Properties can be evaluated. In the adjustment by trial and error, the adjustment was performed so that the size of the quadrant protrusions was as small as possible. The servo gain calculated according to the present embodiment and the servo gain adjusted by trial and error are shown in Table 1 below.

In the calculation of the servo gain here, the coefficient α of the reference model was determined as follows.
[Α ₀ , α ₁ , α ₂ , α ₃ ] = [1,1,0.375,0.0625] (20)
Note that the coefficient α of the reference model is a reference model having other characteristics (Takashi Shigemasa, Yasuo Takagi et al .: Practical general-purpose reference model for control system design, Transactions of the Society of Instrument and Control Engineers, Vol. 19, Vol. No., (1983) pp.592-594) can also be used.

  14 and 15 show the results of experiments on step response and circular interpolation motion using the servo gain shown in Table 1. Among these, FIG. 14 shows a step response when the target value is 200 μm. According to FIGS. 14A and 14B, when the servo gain calculated according to the present invention is used, a response with no overshoot is shown on both the X axis and the Y axis. Further, it can be seen that the X-axis and the Y-axis have almost the same response. This is important when performing 2-axis synchronous control. Further, comparing the case where the speed feedback loop is set to integral-proportional control and the case where proportional-integral control is used, the target value is reached more quickly when integral-proportional control is used.

  As shown in FIG. 14C, when the speed feedback loop is set to proportional-integral control and the servo gain is adjusted by trial and error, an overshoot occurs on the Y axis having a large mass. Also, the response characteristics are greatly different between the X axis and the Y axis. However, it is very difficult to match the response characteristics of the two axes by trial and error.

  FIG. 15 shows a circular arc locus when circular interpolation motion with a radius of 25 mm and a feed rate of 3000 mm / min is performed. The results are shown with the radial error magnified 1000 times. When the motion direction of each axis is reversed, the direction of the frictional force generated by the bearing, the linear motion guide, or the like also changes abruptly, resulting in a projection-like locus error (quadrant projection). The smaller the size of this quadrant protrusion, the better the disturbance suppression. According to FIG. 15, it can be seen that when the servo gain calculated according to the present invention is used, the disturbance characteristic is almost the same as that obtained when the servo gain is adjusted by trial and error so that the quadrant protrusion is reduced.

  As described above, according to the present embodiment, the servo gain can be calculated only by algebraic calculation without performing iterative calculation, and can be calculated by a general desk calculator. In addition, since the calculation is not repeated, the servo gain can be calculated at a very high speed on a personal computer, so that the servo gain can be changed in real time in accordance with the change in the characteristics of the control target. Furthermore, if the servo gain is adjusted, the characteristics of a plurality of axes having different masses can be matched, which is advantageous when performing a multi-axis synchronous control motion.

  When trying to adjust the servo gain by trial and error to achieve high-speed and high-accuracy exercise, even those with advanced expertise usually spend about 1 week to 1 month. Although it is normal, according to the present invention, it can be adjusted in about one day, so the effect of implementing this is extremely great.

  As described above, according to the present invention, the servo gain can be calculated relatively easily even if the operator does not have a high level of expertise, and further, it can be applied to a system in which general-purpose motors are mixed. Therefore, it can be widely applied not only to numerically controlled machine tools but also to other machine tools. Further, if the dynamic model shown in FIG. 2 is replaced with, for example, a temperature control system or a water level control system, it can be applied to all control systems having a double control loop. For example, when controlling the temperature of the tank jacket to further control the temperature of the tank, when controlling the opening of the valve to control the water level of the tank, or by controlling the air volume, the temperature of the room For example.

It is a perspective view showing a schematic structure of a drive mechanism concerning a 1st embodiment of the present invention. It is a dynamic model expressing the drive mechanism shown in FIG. FIG. 2 is a block diagram illustrating a configuration of an entire servo system in which a control system is added to the drive mechanism illustrated in FIG. 1. It is a block diagram which shows the structure of the whole servo system which added another control system to the drive mechanism shown in FIG. FIG. 4 is a diagram showing frequency characteristics from a speed command of the servo system shown in FIG. 3 to a motor rotation speed. FIG. 4 is a block diagram of the entire servo system when the characteristics of the speed feedback loop are expressed by a transfer function of a second-order lag system of the natural frequency in the servo system shown in FIG. 3. It is a flowchart which shows the specific process sequence of the servo gain calculation method which concerns on the 1st Embodiment of this invention. It is a flowchart which shows the detailed process sequence of the flowchart shown in FIG. It is a flowchart which shows the detailed process sequence of the flowchart shown in FIG. It is a flowchart which shows the detailed process sequence of the flowchart shown in FIG. It is a block diagram which shows the structure of the servo gain calculation apparatus which concerns on the 1st Embodiment of this invention. It is a perspective view which shows schematic structure of the drive mechanism which concerns on the 2nd Embodiment of this invention. It is the block diagram which showed the structure of the servo gain calculation apparatus for every axis | shaft of the drive mechanism shown in FIG. It is a figure which shows the step response of the result of having experimented using the specific servo gain in the 2nd Embodiment of this invention. It is a figure which shows the circular interpolation motion of the result of having experimented using the specific servo gain in the 2nd Embodiment of this invention.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10, 20 Drive mechanism 11 Board | substrate 12 Guide rail 13 Motor fixing stand 14 Servo motor 15 Shaft support stand 16 Screw shaft 17 Nut 18 Work table 30, 40 Servo gain calculation apparatus 31 1st transfer function memory | storage means 32 2nd transfer function Storage means 33 Equation creation means 34 Conditional expression calculation means 35 Constant determination means 36 First servo gain calculation means 37 Second servo gain calculation means

Claims (3)

A servo gain calculating apparatus having an equation creating means, a conditional expression calculating means, a constant determining means, and a servo gain calculating means uses a transfer function having an ideal characteristic corresponding to the transfer function of the feedback control system. A servo gain calculation method for calculating a servo gain of a speed feedback loop having disturbance suppression characteristics and a servo gain of a position feedback loop having target value tracking characteristics,
The equation creating means equalizing the transfer function of the feedback control system and the transfer function having the ideal characteristics to obtain simultaneous equations relating to the coefficients of the Laplace operator;
The conditional expression calculating means calculating a conditional expression of the coefficient from which the positive real number solution for the coefficient of the transfer function having ideal characteristics is obtained from the simultaneous equations;
The constant determining means calculates a value of some of the various constants necessary for calculating the servo gain of the feedback control system, and values of constants other than the some constants are known in advance. Determining from
The servo gain calculation means substitutes the determined various constants into a conditional expression of the coefficient that obtains a positive real number solution, and calculates a speed loop proportional gain and a speed loop integral gain that are servo gains of the speed feedback loop. Calculate the break frequency of the frequency characteristic of the speed feedback loop based on the calculated speed loop proportional gain and the speed loop integral gain by a predetermined arithmetic expression, and position based on the calculated break frequency Calculating a loop proportional gain;
Servo gain calculation method. A computer having an equation creating means, a conditional expression calculating means, a constant determining means, and a servo gain calculating means stores a transfer function of a feedback control system and a transfer function having ideal characteristics corresponding to the transfer function of the feedback control system. A servo gain calculation program for calculating a servo gain of a speed feedback loop having a disturbance suppression characteristic and a position feedback loop having a target value tracking characteristic of the feedback control system,
The equation creating means makes the transfer function of the feedback control system equal to the transfer function having the ideal characteristic to obtain simultaneous equations related to the coefficients of the Laplace operator;
A step of calculating a conditional expression of the coefficient by which a positive real solution for a coefficient of a transfer function having ideal characteristics is obtained from the simultaneous equations by the conditional expression calculating means;
The constant determination means calculates the values of some of the various constants necessary for calculating the servo gain of the feedback control system, and values of constants other than the some constants are known in advance. Determining from
By substituting the various constants determined by the servo gain calculation means into a conditional expression of the coefficient that provides a positive real number solution , a speed loop proportional gain and a speed loop integral gain, which are servo gains of the speed feedback loop, are obtained. Calculate the break frequency of the frequency characteristic of the speed feedback loop based on the calculated speed loop proportional gain and the speed loop integral gain by a predetermined arithmetic expression, and position based on the calculated break frequency Calculating a loop proportional gain;
A servo gain calculation program that is sequentially executed using the computer. Servo gain of velocity feedback loop having disturbance suppression characteristics and servo gain of position feedback loop having target value tracking characteristics of the feedback control system using a transfer function having ideal characteristics corresponding to the transfer function of the feedback control system Servo gain calculation device for calculating
First transfer function storage means for storing a transfer function of the feedback control system;
Second transfer function storage means storing a transfer function having the ideal characteristics;
An equation creating means for equalizing the transfer function stored in the first transfer function storage means and the transfer function stored in the second storage means to create simultaneous equations relating to the coefficients of the Laplace operator;
A first computing unit that calculates a conditional expression of a coefficient that provides a positive real solution for a coefficient of a transfer function having ideal characteristics from the simultaneous equations created by the equation creating unit;
Constant determining means for calculating values of some of the various constants necessary for calculating the servo gain of the feedback control system and determining values of constants other than the some constants from previously known values When,
Substituting various constants determined by the constant determining means into the conditional expression of the coefficient calculated by the first arithmetic means, and calculating a speed loop proportional gain and a speed loop integral gain which are servo gains of the speed feedback loop. First servo gain calculating means for
Based on the calculated velocity loop proportional gain and the calculated velocity loop integral gain, a corner frequency of the frequency characteristic of the velocity feedback loop is calculated by a predetermined arithmetic expression, and the position loop proportional gain is calculated based on the calculated corner frequency. Second servo gain calculation means for calculating
Servo gain calculation device provided.

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