JP2563318B2 - Position control device for industrial machinery - Google Patents

Description

The present invention relates to a position control device for an industrial machine such as a laser beam machine or a machine tool, and particularly to a highly accurate positioning while improving the quick response and stability of the system. Is to achieve.

[Conventional technology]

A so-called soft servo system is widely adopted for position control devices of industrial machines such as machine tools and laser beam machines.

A conventional industrial machine such as a laser beam machine for cutting and welding has a laser oscillator 10 and a beam transmission line 1 as shown in FIG.
1. Beam scanner 12, drive means 3 for moving a movable body to which beam scanner 12 is attached along beam member 5 as a stationary body, and orthogonal for moving beam scanner 12 along rail 6 as a stationary body. Drive means 13, cutting station 16 as an absolute stationary body, welding station
The beam scanner 12 is composed of a work transfer means 15 for transferring a work to 17 and the like, a chiller unit, a dry air device, etc., and the beam scanner 12 can be positionally controlled in two axial directions orthogonal to the cutting station 16. Here, the driving means 3 as a controlled object relating to the position control of the one axis, as shown in FIG. 9, is a screw 34 and a mora 32 connected to a motor 32 for driving the movable body 35 in the lateral direction in the figure. And a preamplifier 31 that supplies control power to the. The position control device uses the drive means 3 and the outputs of the detector 33 connected to the motor 32 (motor rotation angular velocity ω, motor rotation angle θ) as feedback signals to output the position command from the position command value generation means 1. Value signal Is input to drive means 3 as input And the control means 2 for outputting The control system block of such a position control device could be represented as shown in FIG. That is, the control means 3 has a relatively high gain inside. Relatively low gain outside including speed control loop To form the position control loop.

Therefore, the speed control loop has a high gain Therefore, it has high rigidity against disturbances and parameter fluctuations, and the gain of the position control loop is low. Therefore, it has an advantage that an excessive impact (acceleration) is not given to the mechanical system such as the screw 34 and the movable body 35, and that no special attention is required in creating a machining program.

Then, if the position command value generating means 1 outputs a position designation value signal based on the machining program, the movable body 35 is automatically positioned along the beam member 5 as a stationary body while a predetermined shape is formed on a work such as a metal body. Laser cutting was possible. Incidentally, the orthogonal drive means 13 and the work transfer means 15 were also provided with position control devices having similar configurations.

[Problems to be solved by the invention]

However, the position control device for the conventional industrial machine described above has the following problems.

In other words, since quick response and system stability cannot be set independently, it must be carried out with either of them being insufficient, and even if a compromise is made in such a state, much effort is required for the comparison work itself. And there was a drawback of spending time. Furthermore, the control position accuracy is the gain of the position control loop. There was a problem that it was regulated by the maximum value of.

The latter problem, which has been emphasized in the high precision era, will be described in detail below. The characteristics of the position control loop in the conventional position control system shown in FIG. Is a soft servo with a primary delay, Can be approximated by

Here, the speed response characteristic V _{(t) with} respect to the stepwise speed command value (V _o / S ₎ is (However, P is -ω _o t. The same applies to the following.) Therefore, the acceleration required for this Is the first-order differentiation of equation (2), Was asked for.

Therefore, if the maximum feed rate of the mechanical system is V _{o max} , the maximum acceleration generated by the position control system Is Stipulated in.

On the other hand, from the viewpoint of the mechanical system, the maximum allowable acceleration A _max
Is the maximum acceleration above because the configuration is determined In relation to Must. Because of this, the maximum value of the gain of the position control loop Is Will be constrained.

Further, the positioning accuracy, that is, the shape accuracy of the beam scanner 12 when the driving means 3 and the orthogonal driving means 13 are simultaneously position-controlled in the above laser processing machine, for example, if the radius reduction rate δ when a perfect circle is drawn, Reduction rate δ
Was calculated by the following formula.

Incidentally, R represents the radius of the command circle (mm), ΔR is the amount of decrease in radius (mm), the V _o is the feed rate (mm / sec).

Therefore, considering that a circle with a constant radius R is drawn at a constant feed speed V _o as in equation (6), the radius reduction rate δ is 1 /
proportional to ω _o ² . (Inversely proportional to ω _o ² ). On the other hand, the maximum value of the gain of the position control loop, ω _{o max,} was constrained in relation to the mechanical system as shown in equation (5). That is, since the upper limit of the maximum value omega _{o max} gain by the permissible maximum acceleration A _max and maximum feed speed V _{o max} which is determined by the mechanical system in the position control system is approximated by the equation (1) is determined, the mechanical system (A _max , V _{o
If (max} ) is fixed, the upper limit of the maximum gain ω _{o max} is constrained, and the gain cannot be set higher than that. In the end, the accuracy (δ) is limited by the maximum gain ω _{o max} and There was a problem that accuracy improvement could not be achieved.

Therefore, there has been a strong demand for the development of a position control device in which the accuracy is not limited by the maximum gain value ω _{o max} without making a large modification to the mechanical system.

It is an object of the present invention to provide a position control device for an industrial machine that can achieve high-precision positioning while improving quick response and stability.

[Means for solving problems]

The present invention has been made in consideration of the above conventional problems, and is based on the optimal control theory and has an evaluation function. Special weighting function that adapts the weighting function of the system to the state of the system instead of a fixed constant By doing so, the prediction characteristics are remarkably improved.

That is, the speed control formed from the position command value generating means 1, the control means 2 and the drive means 3 as the control target shown in FIG. 1 in the position control system including the conventional speed control loop shown in FIG. Consider the system. In this speed control system, the state equation in the continuous time system is expressed by the differential equation (= ay + bv). On the other hand, when expressing a discrete-time system with a sampling period Ts _(sec) , the state variable vector of the system is Is However, Note that E is −ω _c · Ts.

Is.

Also, the evaluation function Is defined as in equation (8).

However, Here, the characteristic technical matter of the present invention is a weighting function. Instead of using a fixed constant, to immediately respond to the state of the system, _i = 1,2, ..., M ^Z = variable.

Therefore, the state variable vector of the system expressed by equation (7) With respect to, the quadratic form evaluation function shown in equation (8) Control input vector that minimizes Using optimal control theory, It can be expressed as.

However, Is a matrix of M constants corresponding to L = 1, 2, 3, ..., M, and has a size obtained as follows.

Also, Is a constant.

Furthermore, the boundary condition is In addition, the above Toki, Is the convergence value of.

Here, equation (10) (including the above boundary conditions)
Substituting equations (7) and (9) into Asking for However, Is a constant.

Therefore, in the position control system having the characteristics of the control system expressed by the formula (7), the evaluation function expressed by the formula (8) In order to perform the control so as to minimize the equation (11), the control loop shown in FIG. 2 may be configured, for example.

Further, from the viewpoint of deepening the understanding of the present invention, the control means 2
From the standpoint of implementing using a computer,
In equation (10), Etc. are constants, so it is not necessary to calculate each sampling, Is a variable that changes from sampling to sampling and Is the position command value From It is a value calculated from the values up to. Therefore, Needs to be calculated for each sampling.

here, From equation (10) Anyway, However, it is obtained based on the general formula of L = 1, 2, ..., M-1.

 That is, the following is obtained from the equation (13).

In addition, Is calculated in advance. Here second
The structure of the feedforward FF shown in the figure may be as shown in FIG.

Then, as the processing of the sample value control system by the computer, the equation (10) is However, Since it can be rewritten as follows, it is understood that the process shown in FIG. 4 can be performed based on the equation (14).

In other words, as a pre-processing before entering the real-time processing And then in real-time processing, When And then Than Is output to the driving means 3, and this is repeated thereafter.

Therefore, according to the present invention, the driving means for driving the movable body with respect to the stationary body, the position command value generating means for outputting the position command value signal, and the driving means are provided. In an industrial control device configured with a control unit that forms a position control loop, the control unit is a position command value signal output from the position command value generation unit. Is an input signal and is a state variable determined by the relationship between the stationary body and the movable body. Is defined as the feedback signal Control input signal sought to minimize Is configured to be output to the driving means to achieve the above object.

However, Is. Further, [R _{0 (k + M)} −X _{(k + M)} ] ^T , [R _{0 (j)} −X _(j) ] ^T , ▲ ^UT _(j-1) ▼ are respectively [R _{0 ( k + M)} -X _{(k + M)} ], [ _{R0 (j)} -X _(j) ], and U _(j-1) .

[Action]

In the present invention configured as described above, the evaluation function Weighting function for the second term of Is not a fixed constant but a special weighting function as a correction term according to the state Therefore, excellent preview control characteristics can be achieved, and high-accuracy industrial machine positioning control can be performed while ensuring quick response and stability.

Also, the evaluation function Is the control input vector for the controlled object Is executed by outputting Can be realized by a simple control system that satisfies

〔Example〕

An embodiment of a position control device for an industrial machine according to the present invention will be described with reference to the drawings.

The first embodiment is the mechanical system shown in FIG. 9 above, but the second and third embodiments are the same as the mechanical system shown in FIG. Orthogonal drive means
The 13 mechanical systems and their position controls shall also be activated. Therefore, in the case of the second and third embodiments, it can be understood that two positions of the position control device shown in FIGS. 1 and 2 are provided.

(First Embodiment) The first embodiment is a case where the position control system shown in FIGS. 1 and 2 is formed to draw a linear locus, and a ramp-shaped position command value (R = 20 mm) is input. The responsiveness when it was done was clarified.

The response waveforms of the preview position control system according to the present invention and the conventional position control system will be described below in comparison with each other. Even if the same ramp-shaped position command signal R is added as shown in FIG. The maximum value of the acceleration (Y ₃ ) of the previous system and the maximum value of the acceleration (X ₃ ) of the conventional system are almost the same value, but the response of the control system to the position command signal R is the same as the signal R in the case of the preview system (Y ₁ ). Compared to being controlled almost synchronously (specifically, in advance), in the case of the conventional system (X ₁ ), there is a time delay and finally a large delay of about 260 m sec, so the speed of the present invention is high. It is understood that the responsiveness is excellent. This is because it is possible to control in advance by about 60 m sec in the initial stage, and the weight Can be said to be an effect based on the fact that it became linear. There is no change in the maximum value for the relationship between speeds (Y ₂ , X ₂ ), but there is a time delay.

As described above, in the case of the present embodiment, the response of the conventional system causes a significant time delay, while it is controlled extremely quickly and synchronously and the maximum value of the acceleration (Y3, X
It was confirmed that the position accuracy is high while maintaining the stability of 3).

 The implementation conditions are as follows.

Gain of the sampling time Ts = 0.002sec foreseeable period M = 30times position control loop omega _{o =} 20 rad / gain of S Speed control loop ω _{c =} 120rad / S Constant Z = 0.3 Further, the gain ω _{1 of the} conventional system is 14.41 rad / S.

(Second Embodiment) This embodiment is also a case where a circular locus is drawn on a plane in the position control system shown in FIGS. 1 and 2, and the ramp-shaped position (radius) is the same as in the first embodiment. ) Command value (R = 10m
The responsiveness and accuracy when inputting m) are clarified.

Similar to the case of the first embodiment, comparing the preview position control system according to the present invention with the conventional position control system, FIG. 6 (dRx, dR
As for y, the shape accuracy is dRy in the case of foreseeing, as shown in (5 times scaling for drawing convenience).
While (= R−Ry) is 110 μm, in the case of the conventional system, dRy (= R−R _X ) is 812 μm, and in the case of the present invention, a remarkable improvement in accuracy is confirmed. Also in this case, the maximum acceleration was substantially the same in both systems as in the case of the first embodiment.

Note that this implementation condition is Ts, M, ω ₀ , ω _c , Both Z and ω ₁ are the same as the execution conditions of the first embodiment. In addition, the waveform (Si
n) The frequency is 1Hz.

(Third Embodiment) In this embodiment, a corner shape is drawn at a speed of 6 m / min instead of the circular locus of the second embodiment. With respect to the orthogonal corner, as shown in Fig. 7, the preview system shifts to 2.63mm in the X-axis direction with respect to the Y-axis length (20mm), while the conventional system causes a shift of 5.44mm in the X-axis direction. Here too, the accuracy of the prediction system could be significantly improved.

The implementation conditions of this example are Ts, M, ω ₀ , ω _c , Both Z and ω ₁ are the same as those in the first and second embodiments.

In the case of the present embodiment as well, in the same way as the case of the second embodiment, theoretically the position control loop had to be increased to about 2.6 times in order to obtain the same shape accuracy as the preview system in the conventional system. Further, in that case, the maximum acceleration of the conventional system for the same ramp-shaped position input is 2.
It becomes 6 times, and it is added that it was practically difficult to realize due to its control and mechanical defects.

Therefore, according to this embodiment, the evaluation function as defined in equation (8) Since is a variable adapted to the state of the system, it is possible to dramatically improve the positioning accuracy of the industrial machine as compared with the position control device of the conventional system. On the other hand, when the accuracy is the same, the acceleration of the prediction system according to the present invention is 1 / 2.6 that of the conventional system.
It can be:

This is determined by the maximum value of the position control loop gain even if the allowable maximum acceleration and the maximum feed rate that determine the maximum value of the position control loop gain are restricted in the same mechanical system as the conventional industrial machine. Since it is possible to achieve a shape precision higher than the precision, it means that high precision and high speed machining can be guaranteed without any modification to the mechanical system. In addition, it has a practical industrial advantage that it can be easily applied to existing mechanical systems. Naturally, the stability of the system is secured.

Further, although the laser processing machine is disclosed in the above embodiments, the industrial machine of the present invention is not limited to this. That is, the position command value generating means 1, the control means 2 and the driving means 3 are formed and As long as it is an industrial machine that forms a position control loop, the machine tool that controls the position of the blade, the robot that controls the posture of the arm with respect to the main body, the drawing machine that controls the pen position on the drawing board, etc. It is applied as it is.

〔The invention's effect〕

INDUSTRIAL APPLICABILITY The present invention has an excellent effect that highly precise positioning of an industrial machine can be achieved while improving adaptability and stability.

[Brief description of drawings]

FIG. 1 is a block diagram of a position control device for an industrial machine according to the present invention, FIG. 2 is a detailed block diagram of the same, FIG. 3 is a feedforward arithmetic circuit configuration diagram, and FIG. 4 is a drive means that is also a control target. Control input vector to output to FIG. 5, FIG. 6, FIG. 7 and FIG. 7 are graphs showing the results of accuracy and the like in the case of carrying out by the block diagrams of FIG. 2, FIG. 3, and FIG. The first embodiment draws a straight line trajectory, FIG. 6 shows the second embodiment draws a circle trajectory, and FIG. 7 shows the third embodiment draws a corner. FIG. 8, FIG. 9, and FIG. 10 show a conventional industrial machine, FIG. 8 is a schematic configuration diagram mainly showing a mechanical system, FIG. 9 is a block diagram, and FIG. 10 is an overall configuration of a laser processing machine. It is a figure. 1 ... Position command value generating means, 2 ... Control means, 3 ... Driving means to be controlled, 5 ... Beam member as stationary body, 35 ...
… Movable body.

Claims (1)

(57) [Claims] 1. A driving means for driving a movable body with respect to a stationary body, a position command value generating means for outputting a position command value signal for commanding the position of the driving means, and X _{(k +1)} = Φ · X _(k) + G · U _(k) , a control means forming a position control loop, and a position control device for an industrial machine, the control means comprising: An evaluation function in which the position command value signal R _{0 (k)} output from the position command value generating means is used as an input signal, and the state variable X _(k) determined by the relationship between the stationary body and the movable body is defined as a feedback signal. A position control device for an industrial machine, which is configured to output a control input vector U _(k) obtained so as to minimize to the drive means. Where X _(k) : System state variable vector (n × 1) Φ: Control target coefficient matrix (n × n) G: Input matrix (n × m) U _(k) : Control input vector (m × 1) ) R _{0 (k)} : Enlarged position command value signal F _M : Final value matrix (n × n) Q: Semi-positive definite symmetric matrix (n × n) H _(i) : Positive definite symmetric matrix (m × m) i = 1 , ..., M (M is the prediction period, that is, the number of samplings). Also, [R _{0 (k + M)} −X _{(k + M)} ] ^T , [R _{o (j)} −X _(j) ] ^T , U ▲ ^T _(j-1) ▼ are respectively [R _{0 ( k + M)} -X _{(k + M)} ], [ _{R0 (j)} -X _(j) ], and U _(j-1) .