JP2009110492A - Position controller - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a position controller, which can suppress the vibration of a structure to be driven even when accelerating and decelerating, reduce the following error of the position of the structure to be driven to a position command, simultaneously achieve vibration suppression and high-accuracy control of the position of the structure to be driven, and maintain high vibration suppression effect, without causing parts of a machine to vibrate, and even when mechanical parameters fluctuate, for the occurrence of vibration and a machine base displacement owing to the rigidity of a machine base part which supports and fixes a driving system. <P>SOLUTION: A structure is provided in which a thrust feed forward structure for operating a structure to be driven without vibration, and a control structure which simultaneously compensates for positional deviation caused by the thrust feed forward structure and position deviation caused by a machine base displacement are included in a position controller 3. Alternatively, a structure is provided in which an acceleration and deceleration process for achieving response of the position of the structure to be driven and machine base displacement without vibration and a control structure which determines a feed forward amount with respect to a position instruction value after the acceleration and deceleration process are provided for the position controller. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a position control device applied to axis control of a numerically controlled machine.

2. Description of the Related Art Conventionally, a control system is used in which a drive system for accelerating and decelerating a drive body is supported and fixed on a machine base, and a force displacement generated in the machine base due to a reaction force of the drive is compensated. FIG. 11 is a drive system model showing one axis of a schematic mechanism of a drive system in a machine tool which is one of numerical control machines. Driver C receives a driving force Fx by a servo motor (not shown), the upper also serves as a guide surface structure B, and a structure for moving the x ₂ direction. The structures A arranged on both sides of the structure B support and fix the structure B, and one side of each is fixedly installed on the ground. Furthermore, the driving member C receives a reaction force from the driver C and to acceleration and deceleration operations x ₂ direction, which is the machine base unit structure A is to generate and flexural oscillation in the x ₁ direction. Note that the structure B, a linear scale for detecting the driver position x ₂ (not shown) is installed.

Next, the drive system model in FIG. 11 is regarded as a target plant, and its equation of motion is derived. In this case, the driving body position x ₂ and the machine base displacement x ₁ may be taken as a generalized coordinate system, and the following two equations of motion are obtained.
(Mb + Mc) · d ² x ₁ / dt ² −Mc · d ² x ₂ / dt ² + Ra · x ₁ = 0 (1)
Mc {d ² x ₂ / dt ² −d ² x ₁ / dt ² } = Fx (2)
Mb is the mass Mb of the structure B, Mc is the mass Mc of the driving body C, and Ra is the x ₁ direction rigidity Ra of the structure A.

  Further, FIG. 12 is a block diagram showing the equations of motion of equations (1) and (2) for the target plant, and will be described in detail in an embodiment according to the present invention described later.

  FIG. 13 is a block diagram of a conventional position control device. A position command value X generated by a function from a host device (not shown) is input to the acceleration / deceleration processing unit 50. The position command value Xc that is the output of the acceleration / deceleration processing unit 50 is such that the second-order time derivative of dXc / dt is bounded even if the time derivative dX / dt of X is stepped. At 50, quadratic function type acceleration / deceleration processing is added. Further, in order to speed up the position command response, the position command value Xc is time-differentiated by differentiators 54 and 55 (S is an operator of Laplace transform), and the feedforward amount Vf, Af is derived. The conversion block Cb is a conversion block for obtaining a thrust feedforward amount Ff corresponding to the motor thrust that generates the acceleration Af. The conversion block Cb is normally substituted by multiplying the acceleration Mc by the mass Mc of the drive body C.

The position detection value of the target plant 58, using the driving member position x ₂ detected by the linear scale described above. The driving body position x ₂ is subtracted from the position command value Xc by the subtractor 51, and the output position deviation is amplified Gp times by the position deviation amplifier Gp, and the output is added by the Vf and the adder 52. Speed command value V. The subtracter 53 subtracts the driving body speed v obtained by time-differentiating the driving body position x ₂ by the differentiator 56 from V, and the speed deviation as an output thereof is amplified by the speed deviation amplifier Gv. Gv is generally composed of a proportional-integral amplifier and various filters for suppressing a high-frequency vibration phenomenon that occurs in the order of several hundred Hz in the target plant. The output of Gv and the Ff are added by the adder 57, and the output of the adder becomes the motor generated thrust, that is, the driving force Fx of the driving body C.

In FIG. 14, target plant parameters are set as Mb = 500 [Kg], Mc = 300 [Kg], Ra = 19.6 · 10 ⁶ [Nm / m], and the above-described Gp and Gv as control parameters are set. It is the result of having simulated the quadratic function type acceleration response (maximum acceleration 2 [m / sec < ² >]) of the conventional position control apparatus of FIG. 13 when it adjusted suitably. The position control device 200 in this case is intended to control the absolute position x ₂ -x ₁ of the target plant according to the position command value Xc from FIG. 11, but in the position control device 200 of FIG. Since no consideration is given to the machine base displacement x ₁ , a large absolute position error εo = Xc− (x ₂ −x ₁ ) occurs during acceleration in FIG.

FIG. 15 is a block diagram of another example of the conventional position control device. This is a configuration in which a compensation block for the machine base displacement x ₁ disclosed in Patent Document 1 is added. Hereinafter, the configuration of only the added part will be described.

The machine base vibration monitor corresponding block 59 in FIG. 15 is a block corresponding to the machine base vibration monitor of Patent Document 1. In the case of this example, since there is no damping element in the machine vibration, according to Patent Document 1, the operation of this part becomes Xsw = McS ² / (MbS ² + Ra) Xc, which becomes an unstable transfer function. Xsw = (McS ² / Ra) Xc is set with emphasis on the operation under constant acceleration. Here, Xsw is a machine vibration compensation command value. Xsw is added to Xc by the adder 60 to become a control position command value Xco. On the other hand, Xsw is time-differentiated by the differentiators 61 and 63 to derive the machine vibration compensation speed command value Vsw and the machine vibration compensation acceleration command value Asw. Vsw is added to Vf by the adder 62, and Asw is multiplied by the drive body mass Mc to obtain a machine vibration compensation thrust command value Fsw, which is added to Ff by the adder 64.

FIG. 16 is a result of simulating the response when subject plant parameters, control parameters, and quadratic function type acceleration processing similar to FIG. 14 are applied to the conventional position control device of FIG. The absolute position error εo is reduced because of the control structure that compensates for the machine base displacement, but since there is no damping in the machine base vibration, the jerk command value Bc (= d ³ Xc / dt ³ ) The response is that the vibration remains at the start and end points of acceleration, and the greater the Bc, the greater the vibration.

  FIG. 17 is a block diagram of still another example of the conventional position control device. This is an application of the technology announced in Non-Patent Document 1, and achieves thrust feedforward using the reverse transfer function of the target plant to suppress machine vibration. Hereinafter, a different part from the conventional position control apparatus demonstrated so far is demonstrated.

The transfer function P ₂ indicates a transfer function from the driving force Fx to the driving body position x _2, and is given by equation (3) from FIG.
P ₂ = {(Mb + Mc) S ² + Ra} / {McS ² (MbS ² + Ra)} (3)
Since the inverse transfer function P ₂ ^-1 of P ₂ is not stable, with a first-order lag element of stabilizing pole (S = -ωo), in order to set the P ₂ ^-1 · F, with (4) Consider the transfer function F shown.
F = {ωo / (S + ωo)} {(Mb + Mc) S ² + Ra} / Ra (4)
Therefore, P ₂ ^-1 · F is
P ₂ ⁻¹ · F = {ωoMcS ² (MbS ² + Ra)} / {(S + ωo) Ra} (5)
Thus, Ff = P ₂ ⁻¹ · F · Xc is calculated, and the thrust feedforward amount Ff in FIG. 11 can be calculated because the third-order time derivative of the position command value Xc is determined to be bounded.

FIG. 18 is a result of simulating a response when subject plant parameters, control parameters, and quadratic function type acceleration processing similar to those of FIG. 14 are applied to the conventional position control device of FIG. 17 set to the parameter ωo = 10000. . In principle, the drive body position x ₂ is configured so as to coincide with the control position command value Xco, so that the response non-vibration can be achieved, but if the speed command value Vc ≠ 0, the position Due to the generation of the command deviation εc = Xc−Xco, the absolute position error εo remains during the axis operation.

JP 2007-025961 A Yasuhiro Yamamoto, 4 others, “High-speed positioning control of linear motor drive table to suppress machine vibration”, Journal of Precision Engineering, Japan Society for Precision Engineering, 2004, Vol. 70, no. 5, p. 645-650

  As described above, with respect to the occurrence of vibration and machine base displacement due to the rigidity of the machine base portion that supports and fixes the drive body, the conventional position control device takes both of these into account and accurately determines the drive body position. Could not be controlled. The problem to be solved by the present invention is to provide a position control device that can suppress the vibration of the driving body even during acceleration / deceleration and reduce the tracking error of the driving body position with respect to the position command. Furthermore, the problem to be solved by the present invention is to provide a position control device that realizes vibration induction prevention of each part of the machine and vibration suppression when machine parameters fluctuate.

  According to the present invention, a thrust feedforward structure for causing the drive body to perform a vibration-free operation and a control structure for simultaneously compensating for a position deviation caused by this structure and a position deviation caused by a machine base displacement are added to the position control device. The problem is solved.

  A position control device according to the present invention is a control device in which a drive system for accelerating and decelerating a drive body is supported and fixed by a machine base part, and compensates for a force displacement generated in the machine base part by a reaction force of the drive body, By detecting the position of the drive body driven by the servo motor, the post-compensation position command value is calculated according to the position command value from the host device, and the position command value is input in the position control device that controls the absolute position of the drive body As an input, the third-order time differential value of the output position command value is set to be bounded, and the acceleration / deceleration processing unit that outputs the post-acceleration / deceleration position command value and the post-compensation position command value are input. From the adjustment transfer function block that outputs the position command value, the block that calculates the thrust feedforward from the compensated position command value and adds it to the driving force of the servo motor, and the time differential value of the post-acceleration / deceleration position command value A block for calculating a position deviation compensation amount that compensates for a position command deviation and machine unit displacement by the adjustment transfer function, and subtracting the position deviation compensation amount from the post-acceleration / deceleration position command value, and the compensated position command And a block as a value.

  In the position control device according to the present invention, the position deviation compensation amount is calculated as a position command deviation compensation amount by the adjustment transfer function.

  The position control device according to the present invention is a control device that compensates for a force displacement generated in the machine base portion by a reaction force of the drive body, in which a drive system for accelerating / decelerating the drive body is supported and fixed by the machine base portion. In the position control device that controls the absolute position of the driving body according to the position command value from the host device by detecting the position of the driving body driven by the servo motor, the position command value is output as the position command value. And the acceleration / deceleration processing unit for outputting the post-acceleration / deceleration position command value, the driving force output by the servo motor, and the driving position obtained by the driving force, And a notch filter with the transfer pole of the transfer function as a notch angular frequency, and the post-acceleration / deceleration position command value output from the acceleration / deceleration processing unit is output as a control position command value Block to calculate the thrust feedforward amount that corresponds the absolute position of the drive body to the control position command value, and calculates the machine base displacement from the control position command value and adds it to the control position command value Then, a block for calculating a position command value corresponding to the driving body position and a block for calculating a speed feedforward amount by differentiating the position command value corresponding to the driving body position with respect to time are provided.

  Further, in the position control device according to the present invention, the block that outputs the post-acceleration / deceleration position command value output from the acceleration / deceleration processing unit as the control position command value includes the driving force output by the servomotor, and the drive A notch filter with a transfer function that expresses the relationship between the drive position obtained by force and the transfer zero of the transfer function as a notch angular frequency, and controls the post-acceleration / deceleration position command value output from the acceleration / deceleration processor It is output as an upper position command value.

According to the position control device of the present invention, the thrust feedforward structure that controls the drive body according to the control position command value, the position command deviation generated by the introduction of this structure, and the position deviation generated by the machine base displacement, By having the position deviation compensation structure that compensates simultaneously and precisely, the generated body vibration is suppressed during the shaft operation including acceleration / deceleration, and the absolute position x ₂ -x ₁ of the target plant is obtained as the position command value Xc. There is an effect that the follow-up operation can be performed with high accuracy. Further, since the control amount is suitably varied according to the magnitudes of the acceleration command value Ac and jerk command value Bc, there is an effect that a high control effect can be obtained regardless of these magnitudes.

  Furthermore, the position control device according to the present invention has a notch filter structure that has a feedforward structure of thrust and speed for controlling the drive body in accordance with the position command value in the control, and has a slight introduction effect on the position command value. A position command value for control is calculated by adding acceleration / deceleration processing. Thereby, various feedforward amounts are made non-vibrating, and the driving body position and the machine base displacement response can be controlled non-vibrating and with high accuracy. Further, the non-vibration of the driving body position and the machine base displacement response does not induce the vibration of each part of the machine, and there is an effect that a high vibration suppression effect can be maintained even when the machine parameter varies.

Hereinafter, an example of the best mode for carrying out the present invention (hereinafter referred to as an example) will be described. One of the characteristic features of this embodiment is that vibration is suppressed by thrust feedforward Ff = P ₂ ⁻¹ M · Xc using the adjustment transfer function M (s). In principle, the driving body position x ₂ does not match Xc because it matches the control position command value Xco = M · Xc. Therefore, the post-compensation position command value Xc ^* is introduced to form Xco = M · Xc ^*, and Ff = P ₂ ⁻¹ M · Xc ^* is determined. Further, a position deviation compensation structure for compensating simultaneously for the position command deviation Xc ^* -Xco generated by M (s) and the position deviation due to the machine base displacement x _{1 is} adopted.

Consider controlling the absolute position x ₂ -x ₁ of the target plant according to the position command value Xc. Therefore, when the restriction items for achieving both vibration suppression and position deviation compensation are studied, the following items (restriction a) to (restriction c) are obtained.
(Constraint a): The adjustment transfer function M (s) is indispensable and can be expressed by the equation (6) using a stable polynomial Go (s).
M = {(Mb + Mc) S ² + Ra} / Go (6)
(Constraint b): Thrust feedforward Ff of equation (7) can be calculated.
Ff = P ₂ ⁻¹ M · Xc ^* = ({McS ² (MbS ² + Ra)} / Go) Xc ^* (7)

Here, x ₂ = Xco = M · Xc ^* = ({(Mb + Mc) S ² + Ra} / Go) Xc ^* , and from FIG. 12, x ₁ / x ₂ = McS ² / {(Mb + Mc) S ² + Ra}. , X ₁ = (McS ² / Go) Xc ^* , so that the driver absolute position x ₂ −x ₁ can be expressed by the following equation (8).
x ₂ −x ₁ = {(MbS ² + Ra) / Go} Xc ^* (8)
Therefore, consider a position deviation compensation structure in which the position deviation compensation amount is defined as α (Xc) as a function of the original position command value Xc, and the relationship between Xc and Xc ^* is defined as Xc ^* = Xc−α (Xc). Then, the constraint of position deviation compensation is
Xc− (x ₂ −x ₁ ) = {Xc−Xc ^* } + {Xc ^* − (x ₂ −x ₁ )}
= Α (Xc) + {(Go−MbS ² −Ra) / Go} Xc ^*
= Α (Xc) + {(Go−MbS ² −Ra) / Go} {Xc−α (Xc)}
= 0 (9)
And solving equation (9) for α (Xc)
(Constraint c): The positional deviation compensation amount α (Xc) satisfies the expression (10).
α (Xc) = {(MbS ² + Ra−Go) / (MbS ² + Ra)} Xc (10)
Get.

Among the above restrictions, (constraint c) cannot be satisfied strictly because (10) is not a stable rational function, but using an implementable approximation form, s) and α (Xc) are determined.
Go (s) = Ra,
α (Xc) = (S ² / {S ² + βS + (Ra / Mb)}) Xc (11)
However, β is an arbitrary parameter that is a positive real number. As β → 0, the approximation as the position deviation compensation increases, but the position deviation compensation amount α (Xc) becomes oscillating.

Then, M, P ₂ ⁻¹ M, Xc ^* are obtained from the equations (6), (7), etc.
M = {(Mb + Mc) S ² + Ra} / Ra (12)
P ₂ ⁻¹ M = {McS ² (MbS ² + Ra)} / Ra (13)
Xc ^* = Xc− (S ² / {S ² + βS + (Ra / Mb)}) Xc (14)
It becomes.

FIG. 1 is a block diagram of a position control apparatus according to the present invention. Hereinafter, a different part from the conventional position control apparatus demonstrated so far is demonstrated. The position deviation compensation amount α (Xc) is configured by using the acceleration command value Ac (= d ² Xc / dt ² ) as an input from the equation (11). As described above, the post-compensation position command value Xc ^* is calculated by subtracting the position deviation compensation amount α (Xc) from the position command value Xc by the subtractor 2. Based on the above, the control position command value Xco is configured as Xco = M · Xc ^* . Further, the thrust feedforward Ff is configured by Ff = P ₂ ⁻¹ M · Xc ^* .

Here, the actual equations for calculating various quantities are given by the equations (15), (16), and (17).
Ff = P ₂ ⁻¹ M · Xc ^*
= ({McS ² (MbS ² + Ra)} / Ra) (Xc− [S ² / {S ² + βS + (Ra / Mb)}] Xc)
= McAc + {McMbβS ² / (Ra {S ² + βS + (Ra / Mb)})} Bc (15)
Xco = M · Xc ^*
= ({(Mb + Mc) S ² + Ra} / Ra) {Xc− (S ² / {S ² + βS + (Ra / Mb)}) Xc}
= Xc + [{(Mb + Mc) βS + (McRa / Mb)} / (Ra {S ² + βS + (Ra / Mb)})] Ac (16)
Vf = dXco / dt
= Vc + [{(Mb + Mc) βS + (McRa / Mb)} / (Ra {S ² + βS + (Ra / Mb)})] Bc (17)
However, Bc = d ³ Xc / dt ³ .

Therefore, the acceleration / deceleration processing unit 1 performs a quadratic function type acceleration / deceleration process as a position command so that Bc = d ³ Xc / dt ^3, which is a second-order time derivative of the speed command value Vc = dXc / dt, is determined to be bounded. In addition to the value X, the processing unit outputs a position command value Xc.

FIG. 2 is a result of simulating a quadratic function type acceleration response when the parameter β = 4 is set in the position control apparatus according to the present invention of FIG. 1 and the same target plant parameters and control parameters as in FIG. 14 are given. . In the quadratic function type acceleration process, the same conditions as the quadratic function type acceleration process shown in FIGS. 14, 16, and 18 are selected. Further, when the standard expression S ² + 2ζωnS + ωn ² and S ² + βS + (Ra / Mb) are associated with each other, β = 4 corresponds to an attenuation factor ζ = 0.01. As a result, according to the position control device of the present invention, the generation amount and vibration of the absolute position error εo during the shaft operation including acceleration / deceleration can be suppressed to be very small.

As described above, according to the position control apparatus of the present invention, the thrust feedforward structure that controls the drive body in accordance with the position command value in the control, and the position command deviation generated by the introduction of this structure and the machine base displacement are generated. The position deviation compensation structure that compensates the position deviation simultaneously and precisely to suppress the generated vibration during the shaft operation including acceleration / deceleration, and the absolute position x ₂ -x ₁ of the target plant is determined. Thus, the tracking operation can be performed with high accuracy according to the position command value Xc. Further, since the control amount is suitably varied according to the magnitudes of the acceleration command value Ac and jerk command value Bc, a high control effect can be obtained regardless of these magnitudes.

Next, the case where the position control device according to the present invention is applied to a control shaft whose purpose is to control the position of the driving body C on the structure B in FIG. 11 will be described. In this case, to control the street position instruction value Xc will drive member position x ₂ of the target plant. Here, the constraints for establishing vibration suppression are the above-described (constraint a) and (constraint b), and further, the constraint for establishing positional deviation compensation is Xc ^* −x ₂ = ({Go− ( From Mb + Mc) S ² -Ra} / Go) Xc ^*
Xc−x ₂ = {Xc−Xc ^* } + {Xc ^* −x ₂ }
= Α (Xc) + ({Go− (Mb + Mc) S ² −Ra} / Go) Xc ^*
= Α (Xc) + ({Go− (Mb + Mc) S ² −Ra} / Go) {Xc−α (Xc)} = 0 (18)
If the equation (18) is solved for α (Xc),
(Constraint d): The position deviation compensation amount α (Xc) satisfies the equation (19).
α (Xc) = [{(Mb + Mc) S ² + Ra−Go)} / {(Mb + Mc) S ² + Ra)}] Xc (19)
Get.

As in the first embodiment, for (d), Go (s) and α (Xc) are determined by the following equation (20) using an approximate form.
Go (s) = Ra,
α (Xc) = [S ² / (S ² + βS + {Ra / (Mb + Mc)})] Xc (20)
Then, M and P ₂ ⁻¹ M can be expressed by the following expressions (21) and (13), and Xc ^* can be expressed by the following expression (21).
Xc ^* = Xc− [S ² / (S ² + βS + {Ra / (Mb + Mc)})] Xc (21)

FIG. 3 is a block diagram of a position control apparatus according to the present invention. The post-compensation position command value Xc ^* is the same as that of the first embodiment shown in FIG. The actual equations for calculating various quantities are given by the equations (22), (23) and (24).
Ff = P ₂ ⁻¹ M · Xc ^*
= ({McS ² (MbS ² + Ra)} / Ra) (Xc− [S ² / {S ² + βS + Ra / (Mb + Mc)}] Xc)
= McAc + {(MbMcβS ² − {Mc ² Ra / (Mb + Mc)} S) / (Ra {S ² + βS + Ra / (Mb + Mc)})} Bc (22)
Xco = M · Xc ^*
= ({(Mb + Mc) S ² + Ra} / Ra) {Xc− (S ² / {S ² + βS + Ra / (Mb + Mc)}) Xc}
= Xc + {(Mb + Mc) βS / (Ra {S ² + βS + Ra / (Mb + Mc)})} Ac (23)
Vf = dXco / dt
= Vc + {(Mb + Mc) βS / (Ra {S ² + βS + Ra / (Mb + Mc)})} Bc (24)

4 shows that the parameter β corresponding to the attenuation rate ζ = 0.01 is set in the position control device 4 according to the present invention shown in FIG. 3 in the same manner as in FIG. It is the result of simulating a quadratic function type acceleration response. As a result, the generation amount and vibration of the position error Xc-x ₂ during the shaft operation including acceleration / deceleration can be suppressed to a very small level, and the position control device according to the present invention can operate the driving body C on the structure B. It can be seen that the control is effective as well when the absolute position of the driving body C is controlled.

  One of the characteristic features of this embodiment is that after the normal acceleration / deceleration processing is performed in order to make various feedforward amounts and compensation amounts non-vibrated in order to make the driving body position and machine base displacement response non-vibrating. The position command value is further subjected to an acceleration / deceleration processing function that has a slight influence on introduction, and the position command value for control is determined.

In this example, the final objective is to control the drive unit absolute position x ₂ -x ₁ of the target plant in accordance with the position command value Xc. First, the position command value Xc after the quadratic function type acceleration / deceleration processing is used. As an input, let us consider introducing an acceleration / deceleration processing function H (s) that outputs a control position command value Xco and controlling Xco = x ₂ −x ₁ . The effect of introducing the acceleration / deceleration processing function H (s) will be described later.

From FIG. 12, the relationship between the driving force Fx and the driving body absolute position x ₂ −x ₁ is expressed by the equation (25).
x ₂ −x ₁ = {1 / (McS ² )} Fx (25)
Therefore, the thrust feedforward amount Ff for controlling Xco = x ₂ −x ₁ is expressed by equation (26).
Ff = McS ² (x ₂ −x ₁ ) = McS ² Xco = McS ² HXc (26)
Responses of the drive body position x ₂ and the machine base displacement x ₁ with respect to Ff are expressed by equations (27) and (28).
x ₂ = [{(Mb + Mc) S ² + Ra} / {McS ² (MbS ² + Ra)}] McHAc (27)
x ₁ = {1 / (MbS ² + Ra)} McHAc = McP ₁ HAc (28)
However, P ₁ indicates a transfer function from the driving force Fx to the machine base displacement x ₁ and is given by the equation (29) from FIG.
P ₁ = 1 / (MbS ² + Ra) (29)
Therefore, equations (30) and (31) are considered as corresponding feedforward configurations.
Xco * = Xco + x ₁ = HXc + McS ² P ₁ HXc (30)
Vf = dXco * / dt = SHXc + McS ² P ₁ HSXc (31)
Incidentally, Xco * is the position command value corresponding to the drive member position x _2.

Here, the acceleration / deceleration processing function H (s) is defined by the equation (32) in order to make the response of the driving body position x ₂ and the machine base displacement x ₁ non-vibrating and to minimize the influence of introduction.
H (s) = (MbS ² + DS + Ra) / (MbS ² + αS + Ra) (32)
However, α and D are positive and real arbitrary parameters. When α → 0, the influence of introduction of H (s) becomes slight, but the driving body position and the machine base displacement response become oscillating. D has an approximate value when a damping element exists in the structure A.

FIG. 5 is a block diagram of the position control device 5 according to the present invention. Hereinafter, a different part from the conventional position control apparatus demonstrated so far is demonstrated. The position command value Xc, which is the output of the acceleration / deceleration processing unit 50, is the input of the acceleration / deceleration processing function H (s) of the notch filter structure having the transmission pole of the target plant 58 at the notch angular frequency shown in the equation (32). Become. The output of the acceleration / deceleration processing function H (s) becomes the control position command value Xco. The adder 3 adds the first term and the second term on the right-hand side of (30) outputs the position command value Xco ^* corresponding to the drive member position x _2. The adder 52 differentiates the position command value Xco ^* with the differentiator 4 and outputs a speed feedforward amount Vf shown in the equation (31). Further, by multiplying the control position command value Xco by McS ² , the thrust feedforward amount Ff shown in the equation (26) is calculated and input to the adder 57.

FIG. 6 shows the second order when the parameter α = 198 · 10 ³ is set in the position control apparatus of the present invention shown in FIG. 5 and the same target plant parameters, control parameters, and quadratic function type acceleration conditions as those in FIG. 16 are given. It is the result of simulating a functional acceleration response. If the standard expression S ² + 2ζωnS + ωn ^{2 of} the second-order system is associated with the denominator polynomial MbS ² + αS + Ra of H (s), α = 198 · 10 ³ corresponds to the attenuation rate ζ = 1. As a result, according to the position control device of the present invention, Xco = x ₂ −x ₁ can be controlled including acceleration and deceleration (upper right diagram in FIG. 6). Further, since the thrust feedforward amount Ff and the speed feedforward amount Vf can be made non-vibrated by increasing the damping rate ζ, the driving force Fx (the lower left diagram in FIG. 6) and the machine base displacement x ₁ (in FIG. 6). The vibration shown in the lower right figure is suppressed.

  FIG. 7 is a result of simulating a quadratic function type acceleration response when only the rigidity Ra of the structure A on the target plant side is reduced (−10%) with respect to the conditions of FIG. 6. Since the rigidity Ra used in the control-side calculation is the same as that in FIG. 6, this result simulates the response when the machine parameter changes. The machine displacement x1 increases (lower right diagram in FIG. 7) due to the decrease in rigidity Ra, and this amount becomes a control error during acceleration (upper right diagram in FIG. 7), but the vibration suppression performance is the conventional control of FIG. High enough for the example.

  In the present embodiment, the final object is to control the drive body position x2 of the target plant in accordance with the position command value Xc. In this case, as in the third embodiment, first, after the quadratic function type acceleration / deceleration processing is performed. It is considered that an acceleration / deceleration processing function Hr (s) with the position command value Xc of the input as an input and an output of the position command value Xco on the control is introduced to control Xco = x2. The effect of introducing the acceleration / deceleration processing function Hr (s) will be described later.

From FIG. 12, the relationship between the driving force Fx and the driving body position x2 is expressed by equation (33).
x ₂ = P ₂ Fx = [{(Mb + Mc) S ² + Ra} / {McS ² (MbS ² + Ra)}] Fx (33)
Therefore, thrust feed forward amount Ff for controlling the Xco = x ₂ is (34).
Ff = P ₂ ⁻¹ Xco = P ₂ ⁻¹ HrXc = [{McS ² (MbS ² + Ra)} / {(Mb + Mc) S ² + Ra}} HrXc (34)
Responses of the driving body position x ₂ and the machine base displacement x ₁ with respect to Ff are expressed by equations (35) and (36).
x ₂ = P ₂ Ff = Xco = HrXc (35)
x ₁ = {1 / (MbS ² + Ra)} Ff = [McS ² / {(Mb + Mc) S ² + Ra}] HrXc (36)
Therefore, equations (37) and (38) are considered as corresponding feedforward configurations.
Xco = HrXc (37)
Vf = dXco / dt = SHrXc (38)
Here, the acceleration / deceleration processing function Hr (s) is defined by the equation (39) in order to make the response of the driving body position x ₂ and the machine base displacement x ₁ non-vibrating and to minimize the influence of introduction.

Hr (s) = {(Mb + Mc) S ² + DS + Ra} / {(Mb + Mc) S ² + γS + Ra} (39)
However, γ and D are positive and optional arbitrary parameters. When γ → 0, the influence of introduction of Hr (s) becomes slight, but the driving body position and the machine base displacement response become oscillating. D has an approximate value when a damping element exists in the structure A.

FIG. 8 is a block diagram of the position control apparatus 10 according to the present invention. Hereinafter, a different part from the position control apparatus demonstrated so far is demonstrated. Position command value Xc which is the output of the deceleration processing unit 50 (39) shown formula, the transmission zeros from the driving force Fx of the object plant 59 to the driving member position x ₂ of the notch filter structure having a notch angular frequency The acceleration / deceleration processing function Hr (s) is input. The output of the acceleration / deceleration processing function Hr (s) becomes the control position command value Xco. The speed feedforward amount Vf shown in the equation (38) is configured by differentiating Xco by the differentiator 54. Furthermore, the thrust feedforward amount Ff shown in the equation (35) can be configured by multiplying Xc by P ₂ ⁻¹ Hr because P ₂ ⁻¹ Hr is converted into a stable rational function.

A standard representation S ² + 2ζωnS + ωn ² secondary system, made to correspond to the denominator polynomial ^{(Mb + Mc) S 2 +} γS + Ra of Hr (s), γ = 250 · 10 3 corresponds to an attenuation factor zeta = 1. FIG. 9 shows 2 when the parameter γ = 250 · 10 ³ is set in the position control apparatus according to the present invention shown in FIG. 8 and the same target plant parameters, control parameters, and quadratic function type acceleration conditions as in FIG. 6 are given. It is the result of simulating a quadratic function type acceleration response. According to the position control device of the present invention, Xco = x ₂ can be controlled including acceleration / deceleration (upper right diagram in FIG. 9). Further, since the thrust feedforward amount Ff and the speed feedforward amount Vf can be made non-vibrated by increasing the damping rate ζ, the driving force Fx (lower left diagram in FIG. 9) and the machine table displacement x ₁ (in FIG. 9). The vibration in the lower right diagram) can also be suppressed as in the first embodiment.

10 is a quadratic function type acceleration when only the rigidity Ra of the structure A on the target plant side is reduced (−10%) with respect to the condition of FIG. 9 in the same manner as the condition of FIG. 7 with respect to FIG. It is the result of simulating the response. Since the rigidity Ra used in the control-side calculation is the same as that in FIG. 9, this result simulates the response when the machine parameter fluctuates. Due to the decrease in the rigidity Ra, the machine base displacement x ₁ increases (the lower right diagram in FIG. 10), but the control error defined by Xco-x ₂ (the upper right diagram in FIG. 10) does not directly affect the third. High vibration suppression performance can be maintained as in the example.

Here, the introduction effect of the acceleration / deceleration processing function H (s) shown in the equation (32) will be described. Since H (s) has the same structure as the acceleration / deceleration processing function Hr (s) shown in the equation (39), the following discussion is made on the normalized F (s) in the equation (40). Go.
F (s) = (S ² + c) / (S ² + bS + c) = (S ² + ωn ² ) / (S ² + 2ζωnS + ωn ² ) (40)
Further, the influence of introduction is that linear acceleration / deceleration processing L (s) = (1-e ^−TS ) / TS (where T is a time constant in linear acceleration / deceleration processing), which is a general position acceleration / deceleration processing. Consider by comparison.

The direct influence of the acceleration / deceleration process on the position command is that a delay occurs between the position command X before the acceleration / deceleration process and the position command Xo after the acceleration / deceleration process. Therefore, a position command delay εp = X−Xo in a steady state with respect to the step speed command dX / dt = V is considered. For linear acceleration / deceleration processing,
εp = (T / 2) V (41)
Whereas, εp of the acceleration / deceleration processing function F (s) in the present invention is
εp (s) = (V / S ² ) − {(S ² + c) / (S ² + bS + c)} (V / S ² )
= {BS / (S ² + bS + c)} (V / S ² ) (42)
Therefore, using the relationship between the final value theorem and the equation (40), it is expressed by the equation (43).
εp = (b / c) V = (2ζ / ωn) V (43)

On the other hand, it is known that the acceleration / deceleration process generates a trajectory error when a plurality of axes are operated synchronously. Therefore, considering the response radius Ro after acceleration / deceleration processing in a steady state with respect to the arc position command (radius R, angular velocity ω) by synchronous operation of two orthogonal axes, acceleration / deceleration is performed with an arc diameter reduction amount ΔR = R−Ro. Evaluate trajectory error due to processing. If this response radius Ro is equal to the steady amplitude of Xo (t) with respect to X (t) = Rcosωt,
Xo (s) = {(1−e ^−TS ) / TS} {RS / (S ² + ω ² )} (44)
In addition, since ωT << 1 is established in general operation, the response radius Ro is
Ro = (R / ωT) ( 2-2cosωT) 1/2 ≒ (R / ωT) {ωT- (ωT) 3/24}
^{= R-R (ωT) 2} /24 ··· (45)
Thus, the arc diameter reduction amount ΔR can be approximated by the equation (46).
ΔR = R-Ro = {( ωT) 2/24} R ··· (46)

In the case of the acceleration / deceleration processing function F (s) in the present invention,
Xo (s) = {(S ² + c) / (S ² + bS + c)} {RS / (S ² + ω ² )} (47)
And Laplace inverse transform, and the response radius Ro is
Ro = R (c−ω ² ) / {(bω) ² + (c−ω ² ) ² } ^1/2 = R cos θ (48)
Thus, the arc diameter reduction amount ΔR is expressed by equation (49).
ΔR = R−Ro = (1−cos θ) R (49)
However, θ = tan ⁻¹ {bω / (c−ω ² )} = tan ⁻¹ {2ζωnω / (ωn ² −ω ² )}.

  If T = 200 ms, ωn = 200 rad / sec, V = 0.4 m / sec, and ζ = 1 are selected as conditions close to the conditions used in the above-described simulation, the position command delay εp is the linear acceleration / deceleration process: In the case of εp = 40 mm and the acceleration / deceleration processing function F (s) in the present invention: εp = 4 mm. On the other hand, when R = 0.1 m and ω = 2 rad / sec are selected as the arc operating conditions, the arc diameter reduction amount ΔR is ΔR≈670 μm in the case of linear acceleration / deceleration processing, and the acceleration / deceleration processing function F (s ): ΔR≈20 μm. That is, the position command delay and the trajectory error generated by introducing the acceleration / deceleration processing functions H (s) and Hr (s) according to the present invention are the position command delay and the position command delay generated by the existing acceleration / deceleration processing unit. It can be seen that the trajectory error is sufficiently small and the effect of introduction is negligible.

As described above, the position control device according to the present invention has a feedforward structure of thrust and speed for controlling the drive body in accordance with the position command value for control, and the introduction effect is small in the position command value. A position command value for control is calculated by adding acceleration / deceleration processing with a notch filter structure. Thereby, various feedforward amounts are made non-vibrating, and the driving body position and the machine base displacement response can be controlled non-vibrating and with high accuracy. This effect is because the control amount is suitably varied according to the magnitude of the acceleration command value Ac (= d ² Xc / dt ² ) or jerk command value Bc (= d ³ Xc / dt ³ ). A high control effect can be obtained regardless of the size of Bc and Bc. Further, since the drive body position and the machine base displacement response are made non-vibrating, vibrations of each part of the machine are not induced, and a high vibration suppressing effect can be maintained even when the machine parameters change.

It is a block diagram which shows the structure of 1st Example of the position control apparatus by this invention. It is explanatory drawing explaining the acceleration response of the object plant by the position control apparatus of FIG. It is a block diagram which shows the structure of 2nd Example of the position control apparatus by this invention. It is explanatory drawing explaining the acceleration response of the object plant by the position control apparatus of FIG. It is a block diagram which shows the structure of 3rd Example of the position control apparatus by this invention. It is explanatory drawing explaining the acceleration response of the object plant by the position control apparatus of FIG. It is explanatory drawing explaining the acceleration response of the object plant by the position control apparatus of FIG. 5 at the time of a machine parameter fluctuation | variation. It is a block diagram which shows the structure of the position control apparatus by 4th Example of the position control apparatus by this invention. It is explanatory drawing explaining the acceleration response of the object plant by the position control apparatus of FIG. It is explanatory drawing explaining the acceleration response of the object plant by the position control apparatus of FIG. 8 at the time of a machine parameter fluctuation | variation. It is a schematic mechanism diagram of a target plant. It is a block diagram describing the motion of the object plant of FIG. It is a block diagram which shows the 1st structural example of the conventional position control apparatus. It is explanatory drawing explaining the acceleration response of the object plant by the position control apparatus of FIG. It is a block diagram which shows the 2nd structural example of the conventional position control apparatus. It is explanatory drawing explaining the acceleration response of the object plant by the position control apparatus of FIG. It is a block diagram which shows the 3rd structural example of the conventional position control apparatus. It is explanatory drawing explaining the acceleration response of the object plant by the position control apparatus of FIG.

Explanation of symbols

  1, 50 Acceleration / deceleration processing unit, 2, 51, 53 Subtractor, 3, 4, 5, 6, 200, 201, 202 Position control device, 52, 57, 60, 62, 64 Adder, 54, 55, 56 , 61, 63 Differentiator, 58 Target plant, 59 Machine stand vibration monitor compatible block.

Claims (4)

A drive system for accelerating / decelerating the drive body is supported and fixed by the machine base part, and is a control device that compensates for the force displacement generated in the machine base part by the reaction force of the drive body, and the position of the drive body driven by the servo motor By detecting the position command value after compensation according to the position command value from the host device, in the position control device for controlling the absolute position of the drive body,
With the position command value as an input, an acceleration / deceleration processing unit that outputs a position command value after acceleration / deceleration processing, in which the third-order time differential value of the output position command value is defined as bounded,
An adjustment transfer function block that outputs a position command value on control with the post-compensation position command value as an input,
A block that calculates thrust feedforward from the post-compensation position command value and adds it to the driving force of the servo motor;
A block for calculating a position deviation compensation amount for compensating for a position command deviation and a machine unit displacement by the adjustment transfer function from a time differential value of the post-acceleration / deceleration position command value;
A block that subtracts the position deviation compensation amount from the post-acceleration / deceleration position command value to obtain the post-compensation position command value;
A position control device comprising: The position control device according to claim 1,
The position control device is characterized in that the position deviation compensation amount is calculated as a compensation amount of a position command deviation by the adjustment transfer function. A drive system for accelerating / decelerating the drive body is supported and fixed by the machine base part, and is a control device that compensates for the force displacement generated in the machine base part by the reaction force of the drive body, and the position of the drive body driven by the servo motor In the position control device that controls the absolute position of the driving body in accordance with the position command value from the host device,
With the position command value as an input, the second-order time differential value of the output position command value is set to be bounded, and an acceleration / deceleration processing unit that outputs the post-acceleration / deceleration position command value;
The relationship between the driving force output by the servo motor and the driving position obtained by the driving force is expressed by a transfer function, and a notch filter with the transfer pole of the transfer function as a notch angular frequency is provided and output from the acceleration / deceleration processing unit A block for outputting the post-acceleration / deceleration position command value as a control position command value;
A block for calculating a thrust feedforward amount for making the absolute position of the driving body correspond to a position command value for control;
A block that calculates the machine base displacement from the control position command value, adds it to the control position command value, and calculates the position command value corresponding to the drive body position;
A block that calculates the speed feedforward amount by differentiating the position command value corresponding to the driver position with respect to time,
A position control device comprising: The position control device according to claim 3, wherein
A block that outputs the post-acceleration / deceleration position command value output from the acceleration / deceleration processing unit as a position command value for control,
The relationship between the driving force output by the servo motor and the driving position obtained by the driving force is expressed by a transfer function, and a notch filter with the transfer zero of the transfer function as a notch angular frequency is provided and output from the acceleration / deceleration processing unit A position control device that outputs the post-acceleration / deceleration position command value as a control position command value.

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