JP2010207011A - Device and method for control of motor - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a motor control device which suppresses the vibrations of an object to be controlled and allows a motor to operate smoothly. <P>SOLUTION: The device includes an instruction calculating unit which calculates instructions for each instruction issue cycle based on a speed/time function with a shift time tb and variables k and a regrading instruction order that represent variables depending on a shift distance, an instruction filter calculating unit which carries out filter calculation having a property of a quadratic transfer function GF(s) with s representing a Laplace operator and ωs, ωc, ζ representing variables, and a filter constant calculating unit which determines the value of ωs as the instruction filter variable based on the shift time tb and the variable k regarding instruction order. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

The present invention relates to a motor control device and a motor control method for operating a control target having a vibration element such as a two-inertia system without vibrating.

In recent years, industrial machines such as machine tools and robots have become more accurate, faster, lighter, and lower in cost, and the rigidity of the machine is becoming weaker. In particular, when the controlled object has a vibration element such as a two-inertia system or a machine base vibration system, there is a general technical problem that vibration occurs during acceleration / deceleration when driven by a motor control device. In order to solve this general technical problem, the conventional motor control device uses a special time function having the order as a parameter, and adjusts the order of the command to suppress vibrations (for example, Patent Documents). 1).
In some cases, vibration is suppressed by setting the nominal vibration frequency of the pre-filter according to the acceleration / deceleration time of the S-shaped command (for example, see Non-Patent Document 1).

FIG. 7 shows a flowchart of a method described in a conventional patent document. In this conventional example, first, as a command function, a special time function v (t) having a as a variable depending on a moving distance, tb as a moving time, and a degree k as a parameter is prepared, and v Based on (t), a command for each command payout period is calculated.
v (t) = a ・ t ^k・ (tb-t) ^k (1)

Processing will be described with reference to FIG. First, in S51, a movement distance dist and a movement time tb, which are operating conditions, are set. In step S52, the vibration period tf in question is input. In S53, x, which is the ratio of tb and tf, is calculated, and in S53, the order k of the command is determined according to the value of x. Since the relationship between x and k is determined in advance so as not to vibrate, a command that does not vibrate can be created.

FIG. 8 shows a block diagram of Non-Patent Document 1. Here, 61 is a position command amplitude, which is input to the S-shaped position command generator 62. 63 represents a pre-filter, which converts the natural vibration angular frequency ω _a to be controlled into ω _an . Gp (s) of 65 indicates the transfer characteristic by the motor speed / position control loop. 66 represents a transfer function from the motor position θ _M to the load position θ _L.

Normally, when a speed / position control loop is added to a two-inertia system control target, reaction torque due to shaft torsion is added as a disturbance. In this paper, however, the result is shown in order to remove the shaft torsion reaction force using a motor disturbance torque observer. Thus, the electric motor and the load block are separated. Therefore, as shown in FIG. 8, the transfer function from the motor position indicated by 66 to the load is separated.

For example, when proportional integral control ( _Ksp : proportional gain, _KSI : integral gain) is used for the speed compensator and proportional control ( _KPP : proportional gain) is used for the position compensator, the motor position command θ _M ^* The transfer function of θ _L with respect to is given by equation (2).
θ _L / θ _M ^* = ω _a ² / (s ² + ω _a ² ) * K _PP (sK _sp + K _SI ) / (s ³ J _Mn + s ² K _sp + s (K _SI + K _PP K _sp ) + K _PP K _sI )
= ω _a ² / (s ² + ω _a ² ) * Gp (s) (2)
Here, since Gp (s) is not related to the resonant vibration if well designed, vibration generated in the load as a result becomes a resonant vibration due to the natural vibration angular frequency omega _a of the controlled object, the load is oscillating when suppress this Will not.

On the other hand, in this conventional example as a method of suppressing vibration, as _a method of suppressing ω _a by setting the acceleration / deceleration time, the acceleration time is t _A = 2nπ / ω _a , or the deceleration start time is t _D = 2nπ / ω _a . It is described that vibration control is selected by selecting.

However, in this method, since the acceleration / deceleration time of the position command depends on the natural frequency of the system, an arbitrary position response time cannot be set, and the response time generally increases. Therefore, in this conventional example, it is described that the problem is solved by changing the natural vibration period of the system by multiplying the position command with a filter by paying attention to the transfer characteristic of the controlled object.

The command generator 62 generates an S-curve having a desired acceleration / deceleration time for the target position amplitude input at 61, and sets the pre-filter nominal vibration frequency ω _an according to the acceleration / deceleration time. Thus, vibration suppression control is realized. Assuming that the natural frequency angular frequency omega _a of the controlled object can be grasped, performs pre-filtering to the motor position command theta _M ^* by the relation expression of Expression (3), the theta _M ^** a new control command. As a result, the vibration pole ω _{a of the} system is nominally made arbitrary ω _an by pole-zero cancellation.
θ _M ^** = (ω _an ² / ω _a ² ) ・ (s ² + ω _a ² ) / (s ² + ω _an ² ) θ _M ^* (3)

Since ω _an can be arbitrarily set, the acceleration / deceleration time of the position command does not depend on the natural frequency of the system, and vibration can be suppressed while arbitrarily setting the acceleration / deceleration time.

As described above, the conventional motor control device uses a special time function having the order k as a parameter to adjust the order k of the command according to the vibration period tf, or the system vibration pole is pre-filtered. By converting it to an arbitrary pole, vibration is suppressed within the set acceleration / deceleration time.

Japanese Patent Laying-Open No. 2006-031111 (page 5-8, FIG. 1)

Makoto Iwasaki and Nobuyuki Matsui, “Optimum Position Command Design Method for Robot Arms Considering Vibration Suppression Effect” IEEJ Transactions C, The Institute of Electrical Engineers of Japan, December 20, 1996, Vol. 117-C, No. 1, p. 50-56

  The conventional motor control device disclosed in Patent Document 1 determines a variable k related to a command order so as not to vibrate using a function determined in advance by a variable x which is a ratio of a vibration period tf and a movement time tb. However, in most cases, the variable k becomes a non-integer (decimal number), so that not only cannot be calculated by a normal control device, but also when k can take a non-integer when calculating the variable a that depends on the moving distance. Therefore, in order to obtain the variable a, the variable a is set to 1, the movement distance Id for the entire movement time is obtained in advance, and finally the actual movement distance dist is obtained. There is a problem that it is necessary to obtain the variable a by dividing by Id, and it takes a long time to calculate the variable a. In addition, since it takes a lot of calculation time, there is a problem that the calculation time is not in time if the target value is changed during operation.

In addition, the conventional command design method of Non-Patent Document 1 can be applied to a control device that does not include an electric motor disturbance observer, or an inertia moment nominal value used in an electric motor disturbance observer has an error with respect to the actual motor inertia moment. Since the transfer function from the position to the load cannot be separated, the frequency of the natural vibration angular frequency ωa of the controlled object changes depending on the characteristics of the control system. Therefore, the frequency of the vibration generated when actually operating is the original ωa Will be different. Even when the controlled object does not have attenuation, it often has attenuation that cannot be ignored depending on the design of the control system. In this case, the conventional prefilter that cancels the resonance of ωa with pole-zero cancellation is assumed to be completely oscillating on the assumption that the transfer characteristic from the motor to the load position has no attenuation and is separated from the control unit. There was a problem that it could not be suppressed. In addition, even in the case of a controlled object having a controlled object, there is a problem that vibration cannot be completely suppressed because the conventional pre-filter has no term that considers the attenuation. In addition, the S-command is indispensable because the S-command command is used to set the pre-filter nominal pole according to the acceleration / deceleration time. There were the following problems with this method. FIG. 9B shows the result of simulating a conventional S-command and prefilter method for a control object of a two-inertia system. As is apparent from the figure, it can be seen from the result of (a) in which no prefilter is used, that both the motor and the load are vibrated. On the other hand, in (b), the motor and the load position respond without vibration, but it can be seen that the speed waveform of the motor is an irregular waveform. This is because the motor operates in such a way that the load does not vibrate, and this phenomenon frequently occurs when the acceleration / deceleration time is shortened by using the S-shaped command. appear. As described above, there are problems that the operation noise of the motor increases the noise of the machine and the other parts of the apparatus are vibrated.

  The present invention has been made in view of such a problem. A time function that can suppress vibration by adjusting a variable k related to the command order is used as a command. Resonance frequency ωs that can suppress vibration from tb and k, and a command filter that uses the natural vibration angular frequency and damping coefficient as numerator coefficients when approximating the entire system including the control unit and the controlled object with a second-order lag system By inputting the calculated signal to the control unit as a new command, even if the control calculation unit does not have a disturbance observer or if the inertia moment nominal value has an error, the control target Whether the vibration has a damping or the control system significantly changes the pole to be controlled, the vibration of the load can be suppressed while the motor operates smoothly, and the command parameters are displayed. And to provide even less motor controller time.

In order to solve the above problem, the present invention is configured as follows.
According to the first aspect of the present invention, the command calculation unit has a command time period based on a speed time function v (t) = a · t ^k · (tb−t) ^{k in} which a is a variable depending on the moving distance. The command filter operation unit calculates the following transfer function GF (s) = (ωs ² / ωc ² ) using ωs, ωc, and ζ as variables when s is a Laplace operator. A filter having a characteristic expressed by (s ² + 2 · ζ · ωc · s + ωc ² ) / (s ² + ωs ² ), which is a command filter variable based on the movement time tb and the variable k related to the command order. A certain ωs is obtained by calculation.
In the invention according to claim 2, the command calculation unit has an acceleration time function acceleration period in which ad is a variable depending on speed. 0 ≦ t ≦ ta α (t) = ad · t ^k · (ta−t)
Constant speed period ta ≦ t ≦ ta + tc α (t) = 0
Between reducers ta + tc ≦ t ≦ 2ta + tc α (t) =-ad ・ (t-ta-tc) ^k・ (2ta + tc-t) ^k
The command filter calculating unit calculates the following transfer function GF (s) using ωs, ωc, and ζ as variables when s is a Laplace operator. = (Ωs ² / ωc ² ) · (s ² + 2 · ζ · ωc · s + ωc ² ) / (s ² + ωs ² ) / (s ² + ωs ² ) Based on ta and the variable k related to the command order, the command filter variable ωs is obtained by calculation.

In the invention according to claim 3, when ωc and ζ, which are variables of the filter used in the command filter calculation unit, are approximated by a second-order lag system, the entire system including the control unit and the control target is approximated. The natural vibration angular frequency and the damping coefficient are set.
According to a fourth aspect of the present invention, in the method of approximating the entire system including the control unit and the controlled object, the frequency and the damping rate of the slowest vibration root of the entire system are set to the natural vibration angle of the secondary delay system. It approximates the frequency and attenuation coefficient.
In the invention according to claim 5, the method of approximating the entire system including the control unit and the controlled object is to measure the frequency characteristics from the input of the control unit to the output of the controlled object, and to measure the measured frequency response. The waveform is approximated so that the frequency response waveform of the second-order lag system matches.

According to the sixth aspect of the present invention, as a method of setting ωc and ζ, which are the variables of the filter used in the command filter calculation unit, ωc and ζ are adjusted while confirming a simulation or an actual machine response, and the vibration is minimized. It is characterized by being set to a value.
In the filter constant calculation unit, a position command obtained by integrating the speed time function v (t) is converted into a transfer function of a second order lag system having a damping coefficient of 0 and a natural vibration angular frequency of ωs. When inputting, ωs is calculated from the relationship between tb, k, and ωs derived by analytically solving based on boundary conditions where velocity and acceleration are 0 at time 0 and time tb. is there.
In the filter constant calculation unit, a position command obtained by second-order integration of the acceleration time function α (t) is transmitted in a second-order lag system having a damping coefficient of 0 and a natural vibration angular frequency of ωs. Ωs is calculated from the relationship between ta, k, and ωs derived by analytically solving based on the boundary condition in which the velocity and acceleration are 0 at time 0 and time tb when input to the function. Is.
In a ninth aspect of the invention, the filter constant calculation unit previously measures the relationship between tb and ωs by simulation or experiment so that the vibration of the controlled object is minimized for each value of k. In addition, ωs is set based on the measurement result.
In a tenth aspect of the present invention, the filter constant calculation unit previously measures the relationship between ta and ωs by simulation or experiment so that the vibration of the controlled object is minimized with respect to each k value. In addition, ωs is set based on the measurement result.

According to the eleventh aspect of the present invention, there is provided a command condition setting unit for setting a variable k relating to the moving distance dist, the moving time tb, and the command order, and a speed time function v (t) using a as a variable depending on the moving distance.
v (t) = a ・ t ^k・ (tb-t) ^k
When s is a Laplace operator, a command for each command payout period is calculated based on a time function ref (t) having a characteristic multiplied by a transfer function GF (s) having ωs, ωc, and ζ as variables. And a command constant calculation unit for calculating ωs, which is a variable of the transfer function GF (s), based on a variable k relating to the movement time tb and the command order.
Where GF (s) is
GF (s) = (ωs ² / ωc ² ) ・ (s ² +2 ・ ζ ・ ωc ・ s + ωc ² ) / (s ² + ωs ² )
It is.

According to the twelfth aspect of the present invention, there is provided a command condition setting unit for setting a variable k relating to the moving distance dist or the speed V, the acceleration time ta1, the constant speed time tc, the deceleration time ta2, and the command order, and a variable depending on the speed. a1 and a2, and a characteristic obtained by multiplying the case-dependent acceleration time function α (t) and the following transfer function GF (s) with ωs, ωc, and ζ as variables when s is a Laplace operator. The command calculation unit that calculates a command for each command payout period based on the function ref (t) of time, the acceleration / deceleration time ta1, the deceleration time ta2, and the variable k related to the command order of the transfer function GF (s) It is characterized by comprising a command constant calculation unit for obtaining ωs as a variable by calculation.
Where α (t) is
0 ≦ t ≦ ta1 α (t) = a1 ・ t ^k・ (ta1-t)
ta1 ≦ t ≦ ta1 + tc α (t) = 0
ta1 + tc ≦ t ≦ ta1 + tc + ta2 α (t) =-a2 ・ (t-ta1-tc) ^k・ (ta1 + tc + ta2-t) ^k
And GF (s) is
GF (s) = (ωs ² / ωc ² ) ・ (s ² +2 ・ ζ ・ ωc ・ s + ωc ² ) / (s ² + ωs ² )
It is.

The invention according to claim 13 is the transfer function of the second-order lag system according to claim 11, wherein the position command obtained by time-integrating the velocity time function v (t) is a damping coefficient 0 and the natural vibration angular frequency is ωs. Ωs is calculated from the relationship between tb, k, and ωs derived by analytically solving based on boundary conditions where the velocity and acceleration are 0 at time 0 and time tb. It is.
The invention according to claim 14 is the second-order lag system according to claim 12, wherein a position command obtained by integrating the acceleration time function α (t) with second-order time is a damping coefficient of 0 and the natural vibration angular frequency is ωs. When input to the transfer function, ωs is calculated from the relationship between ta1 or ta2, k, and ωs derived analytically based on the boundary condition where acceleration and jerk are 0 at time 0 and time ta1 or ta2. It is characterized by doing.

The invention according to claim 15 sets a variable k related to the moving distance dist, the moving time tb, and the command order, and sets a as a variable dependent on the moving distance, and a speed time function v (t) and s as Laplace. When an operator is used, a command for each command payout period is calculated based on a time function ref (t) having characteristics obtained by multiplying the following transfer function GF (s) with ωs, ωc, and ζ as variables. Thus, ωs, which is a variable of the transfer function GF (s), is calculated based on the movement time tb and the variable k related to the command order.
Where v (t) is
v (t) = a ・ t ^k・ (tb-t) ^k
And GF (s) is
GF (s) = (ωs ² / ωc ² ) ・ (s ² +2 ・ ζ ・ ωc ・ s + ωc ² ) / (s ² + ωs ² )
It is.

According to the sixteenth aspect of the present invention, the moving distance dist or the speed V, the acceleration time ta1, the constant speed time tc, the deceleration time ta2, and the variable k relating to the command order are set, and the speed dependent variables a1 and a2 are set. A time function ref () having characteristics obtained by multiplying the case-dependent acceleration time function α (t) and the following transfer function GF (s) with ωs, ωc, and ζ as variables when s is a Laplace operator. The command for each command payout cycle is calculated based on t), and ωs that is a variable of the transfer function GF (s) is calculated based on the variable k relating to the acceleration / deceleration time ta1, the deceleration time ta2, and the command order. It is characterized by calculating.
Where α (t) is
0 ≦ t ≦ ta1 α (t) = a1 ・ t ^k・ (ta1-t)
ta1 ≦ t ≦ ta1 + tc α (t) = 0
ta1 + tc ≦ t ≦ ta1 + tc + ta2 α (t) =-a2 ・ (t-ta1-tc) ^k・ (ta1 + tc + ta2-t) ^k
And GF (s) is
GF (s) = (ωs ² / ωc ² ) ・ (s ² +2 ・ ζ ・ ωc ・ s + ωc ² ) / (s ² + ωs ² )
It is.

According to a seventeenth aspect of the present invention, in the fifteenth aspect, the position command obtained by time-integrating the speed time function v (t) is a transfer function of a second-order lag system in which the damping coefficient is 0 and the natural vibration angular frequency is ωs. Ωs is calculated from the relationship between tb, k, and ωs derived by analytically solving based on boundary conditions where the velocity and acceleration are 0 at time 0 and time tb. It is.
According to an eighteenth aspect of the present invention, in the sixteenth aspect, a position command obtained by second-order integration of the acceleration time function α (t) is a second order lag system having a damping coefficient of 0 and a natural vibration angular frequency of ωs. When input to the transfer function, ωs is calculated from the relationship between ta1 or ta2, k, and ωs derived analytically based on the boundary condition where acceleration and jerk are 0 at time 0 and time ta1 or ta2. It is characterized by doing.

According to the first aspect of the present invention, since the variable k related to the order of the command can be arbitrarily selected, the variable k can be an integer. In order to obtain the variable a by making it possible, it is not necessary to obtain the movement distance Id for the entire movement time in advance by setting the variable a to 1, and finally to calculate the movement distance Id by dividing the actual movement distance dist by Id. Significantly shortened. As a result, the target value can be changed.
In addition, since there is a damping term in the numerator of the command filter, the case where the resonance of the controlled object is originally attenuated, or when the controlled object pole moves due to the design of the control system, it has complete attenuation. It is possible to suppress vibration.
In addition, since the natural vibration angular frequency ωc and the damping coefficient ζ when the entire system is approximated by a second-order lag system are set, vibration is completely suppressed even when the pole is moved by the control system and the pole frequency is changed. be able to.
Further, the control system can be designed in any way, and it is not necessary to use a motor disturbance observer as in the prior art.
In addition, by using a time function that can suppress vibration by adjusting a variable k related to the command order instead of an S-shape command, not only the load vibration but also the motor can be operated smoothly. .

In addition, according to the invention described in claim 2, there is no problem even when the maximum speed value is limited or the operation speed is specified by using a command in which acceleration, constant speed, and deceleration sections are separated. This idea can be used, and the same effect as that of claim 1 can be obtained.
According to the invention described in claim 3, since the natural vibration angular frequency ωc and the damping coefficient ζ when the whole system is approximated by a second-order lag system are set, the pole is moved by the control system and the frequency of the pole is changed. The vibration can be completely suppressed even when it changes or when it comes to have damping. Further, the control system can be designed in any way, and it is not necessary to use a motor disturbance observer as in the prior art.
Further, according to the invention described in claim 4, since the slowest vibration root can be calculated analytically by the mathematical formula and ωc and ζ that are the variables of the command filter can be determined as they are, the control object can be easily obtained. Variables can be set.

Further, according to the invention described in claim 5, since the whole system can be approximated by a quadratic system by matching frequency characteristics, and the natural vibration angular frequency ωc and the damping coefficient ζ can be set. Even if it is difficult to solve, the command filter variables can be set easily.
Further, according to the invention described in claim 6, since the command filter variable can be set while adjusting the waveform while observing the simulation and the actual machine, the control object can be obtained even when there is no knowledge of control or when frequency characteristics cannot be obtained. Can be suppressed.
According to the seventh and eighth aspects of the invention, since the relationship between the movement time tb or the acceleration / deceleration time ta and ωs can be obtained analytically based on the boundary condition, the variable k and the movement time tb or the acceleration / deceleration are obtained. When time ta is given, ωs can be accurately calculated by a mathematical expression, and the denominator variable of the command filter can be automatically set.
According to the ninth and tenth aspects of the present invention, since the relationship between the movement time tb or the acceleration / deceleration time ta and ωs can be adjusted while observing the waveform with simulation and actual equipment, the movement time tb can be obtained even when there is no knowledge of control. Alternatively, the relationship between the acceleration / deceleration time ta and ωs can be obtained in advance, and the denominator variable of the command filter can be set automatically.

According to the invention of claim 11 and claim 15, by using a time function ref having both a special time function and a special transfer characteristic as a command function, vibration can be suppressed only by a position command, and no command filter is used. This eliminates the problem that the original damping effect is deteriorated when the calculation accuracy of the filter is not sufficiently obtained. Further, it is not necessary to add a process for clamping the output of the filter. In addition, it is not necessary to monitor the position after the command filter processing, and the amount of calculation is reduced.
In addition, according to the inventions described in claims 12 and 16, it is possible to realize a movement that operates at a constant speed, such as a so-called trapezoidal speed command, divided into sections such as acceleration, constant speed, and deceleration. An effect equivalent to the effect 1 is obtained.
In addition, according to the inventions of claims 13 and 14 and claims 17 and 18, if parameter k is determined, ωs that can suppress vibration can be automatically obtained by calculation, so parameters that are actually set or adjusted. Since only the vibration frequency ωc and the damping coefficient ζ, which are variables of the transfer function of the denominator when approximated by a second-order lag system, are sufficient, a position command can be created easily.

The block diagram of the motor control apparatus which shows 1st Example of this invention. The figure which shows the transfer function of the command filter of this invention The block diagram explaining the process of the control calculating part of this invention The flowchart explaining the procedure of the processing of the present invention The block diagram of the motor control apparatus which shows 3rd Example of this invention. The block diagram of the motor control apparatus which shows 4th Example of this invention. Flowchart explaining the processing procedure of a conventional motor control device Configuration diagram of a conventional motor control device The figure which shows the simulation result of the past and this invention

  Hereinafter, embodiments of the present invention will be described with reference to the drawings.

FIG. 1 is a configuration diagram of a motor control device of the present invention. In the figure, reference numeral 1 denotes a command condition setting unit, which sets a command distance kst, a travel distance dist, a travel time tb, and a command order variable k. A command calculation unit 2 calculates a command for each command payout period based on a speed time function v (t) where a is a variable depending on the moving distance.
v (t) = a ・ t ^k・ (tb-t) ^k (4)

Reference numeral 3 denotes a command filter calculation unit. When the position command ref output from the command calculation unit is input and s is a Laplace operator, ωs, ωc, and ζ are variables as follows. The filter having the characteristics shown is calculated and a command refc after the filter calculation is output.
GF (s) = (ωs ² / ωc ² ) ・ (s ² +2 ・ ζ ・ ωc ・ s + ωc ² ) / (s ² + ωs ² ) (5)
FIG. 2 shows the input / output relationship of the command filter arithmetic unit 3. Since the motor control device is digitally processed, the command filter calculation unit 3 normally performs calculation by discretizing this filter. Any method of discretization may be used, but it is usually easy to use backward difference, forward difference or bilinear transformation. In addition, when the amount of calculation permits, it may be discretized by Z conversion that strictly considers the zeroth-order hold.

Reference numeral 4 denotes a filter constant calculation unit, which calculates ωs, which is a variable of the command filter, based on the moving speed time tb and the variable k related to the command order. Further, ωc and ζ which are variables of the command filter 3 are set to the natural vibration angular frequency and the damping coefficient when the entire system including the control system and the control target is approximated by a second-order lag system.

Reference numeral 5 denotes a control calculation unit that inputs the filtered command refc and the motor position xfb detected by the detector 200 added to the controlled object 100, performs position / speed control, and outputs a torque command tref. FIG. 3 shows an example of position / speed control of the control calculation unit. When the 35 differential operation units are digitally processed, differentiation using difference approximation may be used. Kp of 31 represents a position control proportional gain, Kv of 32 represents a speed control proportional gain, Ki used in the integral calculation unit 33 represents an integral gain, and Jn of 34 represents an inertia moment nominal value. Further, after the normal torque command, the current loop is processed and the voltage is output to the motor, but this is not shown in FIG. 1 because it is not related to the present invention.

Next, a method for setting each variable of the command filter will be described in detail with reference to the flowchart of FIG. 4 showing the processing procedure of the present invention.

First, in S1, a variable k related to the command distance, that is, the command distance, the travel distance dist, the travel time tb, and the command order is input. The value of k can be set arbitrarily, but a positive integer should be selected so that it can be easily calculated by a normal computing unit. In this embodiment, k = 1 is set so that the calculation can be performed most easily.

  Next, in S2, ωc and ζ, which are variables of the command filter expressed by Expression (5), are set. As a method for setting the variables ωc and ζ, the natural vibration angular frequency and damping coefficient of the slowest vibration root of the entire system including the control target and the control calculation unit may be set as ωc and ζ. This is because most of the vibrations that become a problem when the control target is actually operated are the same as those of the slowest vibration root of the entire system. In this way, by setting the natural vibration angular frequency and damping coefficient of the slowest vibration root of the entire system on the numerator of the command filter, that is, the zero point side, pole zero cancellation occurs with the actual system, and vibration can be completely suppressed. It is. It should be noted that the slowest vibration root of the entire system is the vibration root that was originally moved by the control system, and the natural vibration angular frequency of the vibration root of the control object Even if the damping coefficient is set as it is as a numerator variable of the command filter, vibration cannot be suppressed.

As a method of setting ωc and ζ, which are command filter variables, frequency characteristics from the input of the control unit to the output of the controlled object are measured, and the measured frequency response waveform matches the frequency response waveform of the second-order lag system. As such, ωc and ζ may be adjusted and set.

Alternatively, ωc and ζ may be adjusted while confirming simulation or actual machine response, and set to a value at which vibration is minimized.

  Next, the denominator of the command filter expressed by the equation (5), that is, the pole-side variable ωs, is set from the variable k related to the movement time tb and the command order set in the command condition setting unit in S3.

Here, when this command filter is used, as described in S2, the vibration of the entire system including the controlled object and the control operation unit is completely canceled by pole-zero cancellation, and a new natural angular frequency ωs, attenuation = 0. Is converted to a system with vibration roots. Since the value of ωs can be set arbitrarily, if the natural vibration angular frequency ωs is determined by the input command so that the system does not vibrate, the system operates without any vibration.

Here, using a speed time function v (t) in which a shown in Expression (4) is a variable depending on the moving distance, and k = 1, ωs is expressed by Expression (6) using the moving time tb. Is calculated as follows.
ωs = 1.4303 * 2 ・ π / tb (6)

Next, a method for deriving Equation (6) is shown.
Consider a second-order lag system with natural vibration angular frequency ωs and damping = 0 as shown in equation (7), where G (s) is the transfer function of the system that inputs the command.
G (s) = ωs ² / (s ² + ωs ² ) (7)

The speed vy (t), which is the output when the speed time function v (t) shown in Expression (4) is input to such a system as a speed command, is obtained by solving the differential equation shown in Expression (8). Can do.
vy ⁽²⁾ (t) + ωs ²・ vy (t) = ωs ²・ v (t) (8)

When k = 1, solving the differential equation of equation (8) to obtain vy (t) yields equation (9). Further, when the acceleration αy (t) is obtained by differentiating the speed vy (t) with respect to time, the equation (10) is obtained.
vy (t) = {12ωs-6t ^{2 ・} ωs ³ + 6t ・ tb ・ ωs ³ -12ωs ・ cos (t ・ ωs)
-6tb ・ ωs ²・ sin (t ・ ωs)} / (6 ・ ωs ⁵ ) （9）
αy (t) = {- 12t · ωs 3 + 6tb · ωs 3 -6tb · ωs 3 · cos (t · ωs)
+ 12ωs ²・ sin (t ・ ωs)} / (6 ・ ωs ⁵ ) (10)

Here, when the boundary condition that the velocity vy and the acceleration αy are 0 at the time t = 0 and the time t = tb is applied to the equations (9) and (10), the relationship of the equation (11) is obtained. It is done.
cos (tb ・ ωs) = {4- (tb ・ ωs) ² } / {4+ (tb ・ ωs) ² }
sin (tb ・ ωs) = 4 (tb ・ ωs) / {4+ (tb ・ ωs) ² }
(11)

That is, if the relationship between tb and ωs satisfying this condition is obtained, vibration can be prevented from occurring when the variable k = 1. Then, equation (6) is derived by analytically obtaining equation (11).

Similarly, when k = 2, 3, the results are as shown in equations (12) and (13).
ωs = 1.8354 ・ 2π / tb (12)
ωs = 2.2255 ・ 2π / tb (13)

Although the method of analytically deriving the relationship between k, tb, and ωs has been described here, the relationship between tb and ωs that minimizes the vibration of the controlled object for each k value is simulated or A method may be used in which ωs is set based on the measurement result after measurement by experiment.

The present invention is different from the prior art in that the command is calculated based on a special speed time function in which the variables k and a relating to the movement time tb and the command order depend on the movement distance, and s is Laplace as a command filter. A filter having the characteristics of a second-order transfer function having ωs, ωc, and ζ as variables when it is used as an operator, and ωs that is a variable of the command filter is obtained by calculation based on the movement time tb and the variable k related to the command order. , Ωc and ζ, which are variables of the command filter, are set to the natural angular vibration frequency and the damping coefficient when the entire system including the control system and the controlled object is approximated by a second-order lag system.

The simulation result when using the present invention is shown in FIG. As can be seen from the figure, if the present invention is used, vibration can be suppressed and the motor can operate smoothly.

In the second embodiment, the command calculation is performed based on the acceleration / deceleration time function α (t) using a1 and a2ad represented by Expression (14) as variables depending on the speed as the command function. Here, when the command payout is used as the position command, the function of Expression (14) is used after second-order time integration.
Acceleration period 0 ≦ t ≦ ta α (t) = ad ・ t ^k・ (ta-t)
Constant speed period ta ≦ t ≦ ta + tc α (t) = 0
Between reducers ta + tc ≦ t ≦ 2ta + tc α (t) =-ad ・ (t-ta-tc) ^k・ (2ta + tc-t) ^k
(14)

When this command is used, as in the first embodiment, the transfer function of the system that inputs the command is G (s), and the second order lag system with natural vibration angular frequency ωs and damping = 0 as shown in Equation (7) The acceleration time function α (t) shown in equation (14) is input to this system as an acceleration command, the differential equation is solved, and boundary conditions are applied to analyze the relationship between the acceleration / deceleration time ta and ωs at each k. Ask for. However, as a boundary condition in this case, a condition is used in which both acceleration and jerk become 0 at the time of t = 0 and t = ta.

In this case, as a result, the relational expression between ta and ωs corresponding to k = 1, k = 2, and k = 3 is the movement time tb in the expressions (6), (12), and (13). The acceleration / deceleration time ta is changed.

In this way, by using the command of equation (14) that separates acceleration, constant speed, and deceleration sections as commands, there is no problem even when the maximum speed value is limited or the operation speed is specified. The invention can be used, and the same effect as that of the first embodiment can be obtained.

FIG. 5 is a block diagram showing the configuration of the present invention. In the figure, reference numeral 1 denotes a command condition setting unit, which sets a variable k relating to a command distance, a movement distance dist, a movement time tb, and a command order.
The command condition setting unit further sets ωc and ζ, which are parameters of a transfer characteristic GF described later. ωc and ζ are set to the natural vibration angular frequency and the damping coefficient when the entire system including the control system and the controlled object is approximated by a second-order lag system. Reference numeral 2 denotes a command calculation unit that calculates and outputs a command ref for each command payout sampling. Reference numeral 6 denotes a command constant calculation unit that calculates ωs, which is a variable of the command filter, based on the moving speed time tb and the variable k related to the command order. Reference numeral 5 denotes a control calculation unit which inputs a command ref and a motor position xfb detected by the detector 200 added to the control object 100, performs position / speed control, and outputs a torque command tref.

As a method of setting ωc and ζ, use design values or measure frequency characteristics from the input of the control unit to the output of the controlled object, and the measured frequency response waveform matches the frequency response waveform of the second-order lag system. Thus, ωc and ζ may be adjusted and set. Alternatively, ωc and ζ may be adjusted while confirming simulation or actual machine response, and set to a value at which vibration is minimized.

The present invention is different from the first and second embodiments in that a command is not created and passed through a command filter, but a time function having a command filter characteristic is used as a command.
Hereinafter, the details of the commands actually created by the command calculation unit will be described.
Here, the parameterer k for determining the order is described as 1. However, it is possible to create a command in the same way even when k changes.

When k = 1, the speed function v (t) is expressed by Expression (15).
v (t) = a · t · (tb−t) (15)
Here, a is automatically calculated from the movement distance dist.
a = dist * 6 / tb ^ 3.
Here, formula (15) is Laplace transformed to derive formula (16).
V (s) = a ・ ((tb / s ² )-(2 / s ² )) (16)
On the other hand, the transfer characteristic GF (s) is expressed as in Expression (17).
GF (s) = (ω _s ² / ω _c ² ) (s ² + 2ζω _c + ω _c ² ) / (s ² + ω _s ² ) (17)

Here, the vibration frequency ωc and the damping coefficient ζ are adjustment parameters, and ωs is automatically calculated from the movement time tb and the order k. A method for calculating ωs will be described later.
The equation (16) is multiplied by the equation (17), and further, the integral is multiplied to make the velocity a position, thereby obtaining an equation (18).

By performing inverse Laplace transform on equation (18), the time function at the position of equation (19) is obtained.

At the time of mounting, a position command is calculated by substituting n * Ts at time t in the equation (7) for each command calculation cycle. n is a natural number.
Here, using the velocity time function v (t) shown in equation (16), when k = 1, ωs is calculated as in equation (20) using the movement time tb.
ωs = 1.4303 * 2 ・ π / tb (20)

Next, a method for deriving equation (20) is shown.
Consider a second order lag system with natural vibration angular frequency ωs and damping = 0 as shown in equation (21), where G (s) is the transfer function of the system to which the command is input.
G (s) = ωs ² / (s ² + ωs ² ) (21)
The speed vy (t), which is the output when the speed time function v (t) shown in Expression (16) is input to such a system as a speed command, is obtained by solving the differential equation shown in Expression (22). Can do.
vy ⁽²⁾ (t) + ωs ²・ vy (t) = ωs ²・ v (t) (22)

When k = 1, solving the differential equation of equation (22) to obtain vy (t) yields equation (23). Further, when the acceleration αy (t) is obtained by differentiating the speed vy (t) with respect to time, the following equation (24) is obtained.
vy (t) = {12ωs-6t ^{2 ・} ωs ³ + 6t ・ tb ・ ωs ³ -12ωs ・ cos (t ・ ωs) -6tb ・ ωs ²・ sin (t ・ ωs)} / (6 ・ ωs ⁵ ) ( 23)
αy (t) = {-12t ^・ ωs ³ + 6tb ・ ωs ³ -6tb ・ ωs ³・ cos (t ・ ωs) + 12ωs ²・ sin (t ・ ωs)} / (6 ・ ωs ⁵ )
(24)
Here, when the boundary condition that the speed vy and the acceleration αy are 0 at the time t = 0 and the time t = tb is applied to the expressions (23) and (24), the relationship of the expression (25) is obtained. It is done.
cos (tb ・ ωs) = {4- (tb ・ ωs) ² } / {4+ (tb ・ ωs) ² }
sin (tb ・ ωs) = 4 (tb ・ ωs) / {4+ (tb ・ ωs) ² }
(25)

That is, if the relationship between tb and ωs satisfying this condition is obtained, vibration can be prevented from occurring when the variable k = 1. Then, equation (20) is derived by analytically obtaining equation (25).
Similarly, when k = 2, 3, the results as shown in equations (26) and (27) are obtained.
ωs = 1.8354 ・ 2π / tb (26)
ωs = 2.2255 ・ 2π / tb (27)

Here, the method of analytically deriving the relationship between k, tb, and ωs has been described. However, the relationship between tb and ωs that minimizes the vibration of the controlled object with respect to each k value is simulated or A method may be used in which ωs is set based on the measurement result after measurement by experiment.

FIG. 2 is a diagram showing the configuration of the fourth embodiment. This embodiment is different from Embodiment 3 in that the command is divided into acceleration, constant speed, and deceleration sections.
When k = 1, the acceleration function α (t) is expressed by Expression (28).
α (t) ＝ a ・ t ・ (ta-t) (28)
Here, a is automatically calculated from the moving speed V.
a = V * 6 / tb ^ 3
Equation (16) is Laplace transformed to derive Equation (29).
α (s) = a ・ (ta / s ² -2 / s ³ ) (29)
On the other hand, the transfer characteristic GF (s) is expressed as in Expression (30).
GF (s) = (ωs ² / ωc ² ) ・ (s ² +2 ・ ζ ・ ωc ・ s + ωc ² ) / (s ² + ωs ² ) (30)

Here, the vibration frequency ωc and the damping coefficient ζ are adjustment parameters, and ωs is automatically calculated from the movement time tb and the order k.
Multiplying Expression (29) and Expression (30), and further multiplying the second-order integral to obtain the position of acceleration, yields Expression (31).

By performing inverse Laplace transform on Equation (31), the time function at the position of Equation (32) is obtained.

At the time of mounting, a position command is calculated by substituting n * Ts at time t in the equation (32) for each command calculation cycle. n is a natural number.

When this command is used, as in the first embodiment, the transfer function of the system to which the command is input is G (s), and the second-order lag system with natural vibration angular frequency ωs and damping = 0 as shown in Equation (21) The acceleration time function α (t) shown in Equation (16) is input to the system as an acceleration command, and the differential equation is solved and boundary conditions are applied to analyze the relationship between the acceleration / deceleration time ta and ωs at each k. Ask for.
However, as a boundary condition in this case, a condition is used in which both acceleration and jerk become 0 at the time of t = 0 and t = ta.

In this case, as a result, the relational expression between ta and ωs corresponding to k = 1, k = 2, and k = 3 is the movement time tb in the expressions (20), (26), and (27). The acceleration / deceleration time ta is changed.
The result when k = 1 is shown in Expression (33).
ωs = 1.4303 * 2 ・ π / ta (33)
In this way, by using the command of Equation (32) that separates acceleration, constant speed, and deceleration sections as commands, there is no problem even when the maximum speed value is limited or the operation speed is specified. The invention can be used, and the same effect as that of the first embodiment can be obtained.

Concretely, the equation (32) is used, and the equation when the velocity V, the acceleration time ta1, the constant velocity time tc, and the deceleration time ta2 are separated is shown below.
When accelerating, ta in equation (32) and equation (33) is ta1 and ref1 (t), and during deceleration, ta in equation (32) and equation (33) is ta2 and ref2 (t).
An equation that uses these cases is shown in Equation (34).
Acceleration 0 ≦ t ≦ ta1 ref1 (t)
Constant speed ta1 ≦ t ≦ ta1 + tc V (ta1 ・ ωc + 4 ・ ζ) / 2ωc + V (t-ta1)
Deceleration ta1 + tc ≦ t ≦ ta1 + tc + ta2 V (ta1 ・ ωc + 4 ・ ζ) / 2ωc + V ・ tc + V (t-ta1-tc)
-ref2 (t-ta1-tc)
(34)

DESCRIPTION OF SYMBOLS 1 Command condition setting part 2 Command calculating part 3 Command filter calculating part 4 Filter constant calculating part 5 Control calculating part 6 Command constant calculating part 100 Control object 200 Detector 31 Position control proportional control part 32 Speed control proportional control part 33 Speed control integration Control unit 34 Moment of inertia nominal value multiplication unit 35 Differentiation calculation unit 61 Position command amplitude setting unit 62 S-shaped position command generation unit 63 Prefilter 65 Speed / position control unit 66 Transfer function of load from motor

Claims (18)

A command condition setting unit, a command calculation unit, a command filter calculation unit, and a filter constant calculation unit for calculating some constants of the command filter calculation unit from conditions set by the command condition setting unit, In a motor control device that performs a control calculation based on the output of and the signal detected by the detector added to the controlled object,
The command condition setting unit is configured to set a variable k related to the travel distance dist, the travel time tb, and the command order,
The command calculation unit is configured to calculate a command for each command payout period based on a speed time function v (t) in which a is a variable depending on a moving distance,
The command filter calculation unit is a filter having a characteristic represented by the following transfer function GF (s) with ωs, ωc, and ζ as variables when s is a Laplace operator,
The motor control device according to claim 1, wherein the filter constant calculation unit calculates ωs, which is a variable of the command filter, based on a movement time tb and a variable k related to the command order.
Where v (t) is
v (t) = a ・ t ^k・ (tb-t) ^k
And GF (s) is
GF (s) = (ωs ² / ωc ² ) ・ (s ² +2 ・ ζ ・ ωc ・ s + ωc ² ) / (s ² + ωs ² )
It is. A command condition setting unit, a command calculation unit, a command filter calculation unit, a filter constant calculation unit for calculating some constants of the command filter calculation unit from the conditions set in the command condition setting unit, and an output of the command filter And a motor control device including a control unit that performs a control calculation based on a signal detected by a detector added to the control target,
The command condition setting unit is configured to set a variable k relating to a moving distance dist or a speed V, an acceleration / deceleration time ta, a constant speed time tc, and a command order.
The command calculation unit is configured to calculate a command for each command payout period based on an acceleration time function α (t) where ad is a variable depending on speed.
The command filter calculation unit is a filter having a characteristic represented by the following transfer function GF (s) with ωs, ωc, and ζ as variables when s is a Laplace operator,
The motor control apparatus characterized in that the filter constant calculation unit calculates ωs, which is a variable of the command filter, based on a variable k related to the acceleration / deceleration time ta and the command order.
Where α (t) is
Acceleration period 0 ≦ t ≦ ta α (t) = ad ・ t ^k・ (ta-t)
Constant speed period ta ≦ t ≦ ta + tc α (t) = 0
Between reducers ta + tc ≦ t ≦ 2ta + tc α (t) =-ad ・ (t-ta-tc) ^k・ (2ta + tc-t) ^k
And GF (s) is
GF (s) = (ωs ² / ωc ² ) ・ (s ² +2 ・ ζ ・ ωc ・ s + ωc ² ) / (s ² + ωs ² )
It is. Set ωc and ζ, which are the variables of the filter used in the command filter calculation unit, to the natural vibration angular frequency and damping coefficient when the entire system including the control unit and the control target is approximated by a second-order lag system. 3. The motor control device according to claim 1, wherein the motor control device is a motor control device. The method of approximating the entire system including the control unit and the controlled object approximates the frequency and damping rate of the slowest vibration root of the entire system as the natural vibration angular frequency and damping coefficient of a second-order lag system. The motor control device according to claim 3. The method of approximating the whole system combining the control unit and the controlled object is to measure the frequency characteristics from the input of the control unit to the output of the controlled object, and to measure the measured frequency response waveform and the frequency response waveform of the second order lag system. The motor control device according to claim 3, wherein the motor control devices are approximated so as to match. The method for setting ωc and ζ, which are the variables of the filter used in the command filter calculation unit, is to adjust ωc and ζ while confirming a simulation or an actual machine response, and set to a value at which vibration is minimized. The motor control device according to claim 1 or 2.   In the filter constant calculation unit, when a position command obtained by integrating the speed time function v (t) is input to a transfer function of a second-order lag system having a damping coefficient of 0 and a natural vibration angular frequency of ωs, time 0 and time tb 2. The motor control device according to claim 1, wherein ωs is calculated from the relationship between tb, k, and ωs derived by analytically solving based on boundary conditions where the velocity and acceleration are zero.   In the filter constant calculation unit, when a position command obtained by second-order integration of the acceleration time function α (t) is input to a transfer function of a second-order lag system having a damping coefficient of 0 and a natural vibration angular frequency of ωs, 3. The motor control device according to claim 2, wherein ωs is calculated from a relationship between ta, k, and ωs derived by analytically solving based on a boundary condition in which the velocity and acceleration are zero at time ta.   In the filter constant calculation section, the relationship between the tb and ωs is measured in advance by simulation or experiment so that the vibration to be controlled becomes the smallest for each value of k, and ωs is set based on the measurement result. The motor control device according to claim 1.   The filter constant calculation unit previously measures the relationship between ta and ωs by simulation or experiment so that the vibration to be controlled becomes the smallest for each value of k, and sets ωs based on the measurement result. The motor control device according to claim 2, wherein A command condition setting unit; a command calculation unit; and a command constant calculation unit that calculates constants used in the command calculation unit from conditions set in the command condition setting unit. In the motor control device that performs control calculation based on the signal detected by the added detector,
The command condition setting unit is configured to set a variable k related to the travel distance dist, the travel time tb, and the command order,
The command calculation unit has the following transfer function GF (s) with ωs, ωc, and ζ as variables, where a is a speed time function v (t) where a is a variable depending on the moving distance, and s is a Laplace operator. ) And a command for each command payout period based on a function ref (t) of time having a characteristic multiplied by
The motor control apparatus, wherein the command constant calculation unit is configured to calculate ωs, which is a variable of the transfer function GF (s), based on a variable k relating to a movement time tb and a command order.
Where v (t) is
v (t) = a ・ t ^k・ (tb-t) ^k
And GF (s) is
GF (s) = (ωs ² / ωc ² ) ・ (s ² +2 ・ ζ ・ ωc ・ s + ωc ² ) / (s ² + ωs ² )
It is. A command condition setting unit; a command calculation unit; and a command constant calculation unit that calculates constants used in the command calculation unit from conditions set in the command condition setting unit. In the motor control device that performs control calculation based on the signal detected by the added detector,
The command condition setting unit is configured to set a variable k relating to a moving distance dist or a speed V, an acceleration time ta1, a constant speed time tc, a deceleration time ta2, and a command order.
The command calculation unit uses the variables a1 and a2 depending on the speed, the acceleration time function α (t) classified according to the case, and the following transmission using ωs, ωc, and ζ as variables when s is a Laplace operator. A command for each command payout period is calculated based on a time function ref (t) having a characteristic multiplied by the function GF (s).
The command constant calculator is configured to calculate ωs, which is a variable of the transfer function GF (s), based on a variable k related to the acceleration / deceleration time ta1, the deceleration time ta2, and the command order. Motor control device.
Where α (t) is
Acceleration period 0 ≦ t ≦ ta1 α (t) = a1 ・ t ^k・ (ta1-t)
Constant speed period ta1 ≦ t ≦ ta1 + tc α (t) = 0
Between reducers ta1 + tc ≦ t ≦ ta1 + tc + ta2 α (t) =-a2 ・ (t-ta1-tc) ^k・ (ta1 + tc + ta2-t) ^k
And GF (s) is
GF (s) = (ωs ² / ωc ² ) ・ (s ² +2 ・ ζ ・ ωc ・ s + ωc ² ) / (s ² + ωs ² )
It is. When a position command obtained by time-integrating the speed time function v (t) is input to a transfer function of a second-order lag system with a damping coefficient of 0 and a natural vibration angular frequency of ωs, the speed and acceleration are 0 at time 0 and time tb. 12. The motor control device according to claim 11, wherein ωs is calculated from a relationship between tb, k, and ωs derived by analytically solving based on a boundary condition.   When a position command obtained by integrating the acceleration time function α (t) with the second-order time is input to a transfer function of a second-order lag system having a damping coefficient of 0 and a natural vibration angular frequency of ωs, acceleration is performed at time 0 and time ta1 or ta2. 13. The motor control device according to claim 12, wherein ωs is calculated from a relationship between ta1 or ta2 and k and ωs derived analytically based on a boundary condition where the jerk is zero. A command condition setting unit; a command calculation unit; and a command constant calculation unit that calculates constants used in the command calculation unit from conditions set in the command condition setting unit. In the motor control device that performs control calculation based on the signal detected by the added detector,
When a variable k related to the moving distance dist, moving time tb, and command order is set, a is a speed time function v (t) where a variable depends on the moving distance, and s is a Laplace operator, ωs, ωc, ζ A command for each command payout period is calculated based on a time function ref (t) having a characteristic obtained by multiplying the following transfer function GF (s) with a variable as a variable. A motor control method, wherein ωs, which is a variable of the transfer function GF (s), is calculated based on a variable k.
Where v (t) is
v (t) = a ・ t ^k・ (tb-t) ^k
And GF (s) is
GF (s) = (ωs ² / ωc ² ) ・ (s ² +2 ・ ζ ・ ωc ・ s + ωc ² ) / (s ² + ωs ² )
It is. A command condition setting unit; a command calculation unit; and a command constant calculation unit that calculates constants used in the command calculation unit from conditions set in the command condition setting unit. In the motor control device that performs control calculation based on the signal detected by the added detector,
A variable k relating to the moving distance dist or the speed V and the acceleration time ta1, the constant speed time tc, the deceleration time ta2 and the command order is set as variables a1 and a2 depending on the speed. And a command for each command payout period based on a time function ref (t) having characteristics obtained by multiplying the following transfer function GF (s) with ωs, ωc, and ζ as variables when s is a Laplace operator. Is calculated, and ωs, which is a variable of the transfer function GF (s), is calculated based on the acceleration / deceleration time ta1, the deceleration time ta2, and the variable k related to the command order.
Where α (t) is
0 ≦ t ≦ ta1 α (t) = a1 ・ t ^k・ (ta1-t)
ta1 ≦ t ≦ ta1 + tc α (t) = 0
ta1 + tc ≦ t ≦ ta1 + tc + ta2 α (t) =-a2 ・ (t-ta1-tc) ^k・ (ta1 + tc + ta2-t) ^k
And GF (s) is
GF (s) = (ωs ² / ωc ² ) ・ (s ² +2 ・ ζ ・ ωc ・ s + ωc ² ) / (s ² + ωs ² )
It is. When a position command obtained by time-integrating the speed time function v (t) is input to a transfer function of a second-order lag system with a damping coefficient of 0 and a natural vibration angular frequency of ωs, the speed and acceleration are 0 at time 0 and time tb. The motor control method according to claim 15, wherein ωs is calculated from a relationship between tb, k, and ωs derived by analytically solving based on a boundary condition that satisfies   When a position command obtained by integrating the acceleration time function α (t) with the second-order time is input to a transfer function of a second-order lag system having a damping coefficient of 0 and a natural vibration angular frequency of ωs, acceleration is performed at time 0 and time ta1 or ta2. 17. The motor control method according to claim 16, wherein ωs is calculated from a relationship between ta1 or ta2 and k and ωs derived by analytically solving based on a boundary condition where the jerk is zero.