JP3280049B2 - Vibration suppression positioning control method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a control system capable of realizing high-speed positioning and vibration suppression in a positioning servo system having a low rigidity load like a robot.

[0002]

2. Description of the Related Art In the control of a positioning servo system having a low rigidity load, if the command time is shortened for high-speed positioning, a large acceleration is applied to the load, and the load vibrates, and the vibration remains. As a countermeasure, a command value may be passed through a filter, but the positioning time becomes longer. For example, as shown in FIG. 8, a filter having a trapezoidal wave when a rectangular wave is inserted has been used. In such a conventional technique, there is a problem that the load vibrates when trying to speed up the positioning, and conversely, the positioning becomes slow when trying to suppress the vibration. To solve such a problem, there is one proposed in Japanese Patent Publication No. 60-29121. This is because when the positioning control target is provided with a constant acceleration or constant deceleration section to perform positioning control, the time for equal acceleration or constant deceleration in the constant acceleration or constant deceleration section is an integral multiple of the natural vibration period T ₀ of the control target. This is a positioning control method that is set to be equal to the time nT ₀ .

[0003]

However, the method described in Japanese Patent Publication No. Sho 60-29121 has a problem that the control system is not clear and cannot be easily realized. There is a problem that it cannot be shorter than twice T and that moving the short distance at high speed is not sufficiently effective. An object of the present invention is to provide a servo system having a low stiffness load in which positioning is sufficiently fast and vibration is effectively suppressed.

[0004]

Means for Solving the Problems A first method for solving the problems is as follows.
Means have one or more axes, each axis has a low stiffness load, and has position feedback and velocity feedback.
In a positioning control method of a robot manipulator driven by an actuator controlled by a lock loop , a rectangular waveform signal having a cycle equal to or inherently an integer multiple of 2 or more as the inherent vibration cycle of a low-rigidity load is output as a speed command. It is to be.

[0005] The second means has one or more axes, each axis has a low rigidity load, and a position feedback.
And the positioning control method of a robot manipulator which is driven by an actuator which is controlled by the velocity feedback loop, a target level I got from the upper
The total movement amount stored in the position command and basic pattern storage unit is 1
Using the form standardized to
To create a basic speed command pattern for the movement amount
With this pattern creation unit,
The generated basic speed command pattern is stored in the command delay section and command
It is paid out to the turn synthesis part, and the command delay part
Set the speed command pattern to の of the natural vibration period of low rigidity load
Create a pattern shifted by an odd multiple of
It is paid out to the synthesizing unit, and the command pattern synthesizing unit
Adds the command output from this pattern creation unit and command delay unit
The basic speed command pattern as a speed command.
Odd multiples of half the natural vibration period of
This is to output a signal having a waveform obtained by synthesizing the obtained pattern .

[0006]

According to the first aspect of the present invention, as shown in the block diagram of FIG. 7, in a positioning servo system having a low-rigidity load 5, a speed at which the input ends at an integral multiple of the natural oscillation period of the load is used. Enter a certain command. That is, in FIG. 7, the input R (t) is R (t) = v = constant 0 ≦ t ≦ Tn (n = 1, 2,...) 0 nT <t (1) is input as a command. (T = 2π / ω _n ) Assuming θ≡y−x in order to observe the vibration of the low rigidity load 5, the following equation is obtained: θ ″ + 2ζω _n θ ′ + ω _n ² θ = −x ″ (t) (2) . The ". Is set to _{+ K p x '= K p} R (t) ··· (3) and can be expressed When where zeta = 0, theta" control system primary type, i.e. x + ω _n ² θ = - x ″ (t) (4) Further, since the input to the control system is represented by the equation (1), x ″ (t) is x ″ (t) = A ₁ exp (−K _p t) 0 ≦ t ≦ Tn A ₂ exp (−K _p (t−nT)) nT <t (5) A ₁ ≡vK _p , A ₂ ≡vK _p (−1 + exp (−K _p nT) ) (6)

In general, when x ″ = A _i exp (−K _p t), the solutions θ (t) and θ ′ (t) of the equation (2) have initial values (θ (0),
If θ ′ (0) = (θ ₀ , θ ′ ₀ ), θ (t) = {A _i / (K _p ² + ω _n ² )} ·｝ R _i cos (ω _n t + φ) −exp (−K _p t)｝ θ '(t) =-｛A _i / (K _p ² + ω _n ² )｝ ・ ｛R _i ω _n sin (ω _n t + φ) -K _p exp (-K _p t)｝ ... (7) where R _i = √ [｛((K _p ² + ω _n ² ) / A _i ) θ ₀ +1｝ ² + (1 / ω _n ² ) ｛((K _p ² + ω _n ² ) / A _i ) θ ′ ₀ −K _p ｝ ² ] (8) φ = tan ⁻¹ [｛(1 / ω _n ) θ ′ − (K _p / ω _n ) (A _i / (K _p ² + ω _n ²⁾ ))｝ / ｛Θ ₀ (K _p ² + ω _n ² ) + A _i ｝] (9) cosφ = (1 / R _i ) ｛θ ₀ (K _p ² + ω _n ² ) + A _i ｝, sin φ = − (1 / R _i ) ｛(1 / ω _n ) θ ′ − (K _p / ω _n ) (A _i / (K _p ² + ω _n ² ))｝ (10)

Therefore, when θ ₀ = θ ′ ₀ = 0 according to equation (7), when t = nT, sin (ω _n nT) = 0,
cos (ω _n nT) = 1, and from equation (10), cos φ = A _i /
Since R _i , sin φ = − (K _p / ω _n ) (A _i / R _i ), θ (nT) = {A _i / (K _p ² + ω _n ² )} · [1-exp (−K _p t) Θ ′ (nT) = − {K _p A _i / (K _p ² + ω _n ² )} · [1-exp (−K _p t)] (11) Using this result, t> nT From equation (8), the radius R of the vibration term is given by R ² = {((K _p ² + ω _n ² ) / A ₂ ) θ (nT) +1} ² + (1 / ω _n ² ) ｛((K _p ² + ω _n ² ) / A ₂ ) θ '(nT)-K _p ｝ ² = {(A ₁ / A ₂ ) (1-exp (-K _pn t) +1｝ ² + (1 / ω _n ² ) ｛ −K _p (A ₁ / A ₂ ) (1−exp (−K _p nT) −K _p ｝ ² (12) Assuming that exp (−K _p nT) = 0, A ₂ = − Since A ₁ , R = 0 from equation (12) (13) Therefore, after t> nT, (7), (8),
From equations (9) and (13), θ (t) = {A ₁ / (K _p ² + ω _n ² )} − exp (−K _p (t−nT)) θ ′ (t) = − ｛K _p A ₁ / ( _Kp ² + ω _n ² )｝ exp (−K _p (t−nT)) = − K _p θ (t) (14) From equation (14), θ (t), θ ′ (t ) Has no vibration component when t> nT, and exponentially becomes θ (t) → 0,
θ ′ (t) → 0. As described above, if a step input that ends with an integer value of the cycle T is input as the input in FIG. 7, the vibration component disappears after the command is completed, and positioning is performed quickly.

Next, in the second invention of the present application, the seventh invention
As shown in the block diagram in the figure, in a positioning servo system having a low rigidity load, two patterns shifted by an odd multiple of 1/2 of the natural vibration period of the load are combined and input as inputs. That is, input R (t) = v (t) + v (t−m · T / 2) (m = 2n + 1, n = 0, 1, 2,...) (V (t) is an arbitrary function, T Is input as a natural vibration cycle of the load = 2π / ω _n ) (21). Assuming that the difference between the displacement y (t) of the low rigidity load and the output x (t) from the control system is θ (t) = y (t) −x (t), θ ″ (t) + 2 ＋ ω _n θ ′ (t ) + Ω _n ² θ (t) = ω _n ² F (t) (22) F (t) = − (1 / ω _n ² ) x ″ (t) (23) , Ω _n : Considering the natural frequency, the state of vibration can be examined. Now, as a definitive and ζ = 0, 'When / ω _n, (22) equation θ "(t' t = t in order to simplify the formula) + θ (t ') = F (t') ·· (24) Here, t '= t, where T / 2 becomes π by changing the time scale.
If v is considered as a set of step inputs (see FIG. 6), the following equation is derived.

[0010]

(Equation 1)

[0011] thinking that the control system (FIG. 7) so is a _{linear, R i (t) = v} i (u i (t) + u i (t · π · m)) ··· (26) comprising an input Assuming that the displacement of the arm with respect to (FIG. 4B) is y _i (t) and the output from the control system is x _i (t), θ (t) = y (t) −x (R (t) when R (t) is input. t) is

[0012]

(Equation 2)

## EQU1 ## Then, θ _i (t) and θ _i ′ (t) are
Assuming that θ _i (0) = θ _i ′ (0) = 0, (i) when 0 ≦ t <t _i , θ _i (t) = 0, θ _i ′ (t) = 0 (28) (ii) When t _i ≦ t ≦ t _i + π · m θ _i (t) = R ₀ cos (t−t _i + φ ₀ ) + F ₀ (t−t _i ) θ _i ′ (t) = − R ₀ sin (t−t _i + φ ₀ ) + F ₀ (t−t _i ) (29) R ₀ = √ (F ₀ (0) ² + F ₀ '(0) ² ) (30) cos φ _{0 = F 0 (0) / R} 0, sin φ 0 = -F 0 (0) / R 0 ··· (31) F 0 (t) = - {v i K p / (K p 2 + ω n 2) ｝ Exp ((− K _p / ω _n ) t) (32) (iii) When t _i + π · m <t θ _i (t) = R ₁ cos (t−mπ−t _i + φ ₁ ) + F ₁ (t−t _i −π · m) θ _i ′ (t) = − R ₁ sin (t−m π−t _i + φ ₁ ) + F ₁ (t−t _i −π · m) (33) ) R ₁ = √ ((θ _i (t _i −mπ) −F ₁ (0)) ² + (θ _i ′ (t _i −mπ) −F ₁ ′ (0) ² ) (34) cosφ _{1 = {θ 1 (t i} + πm) -F 1 (t i + πm + 0)} / R 1, sinφ 1 = - {θ 1 (t i + πm) -F 1 (t i + πm + 0)} _{R 1 ··· (35) F 1} (t) = - {v i K p / (K p 2 + ω n 2)} · (1-exp (-K p / ω n) πm exp ((- K p / Ω _n ) t)) (36) Here, θ _i (t) and θ _i ′ (t) are continuous at t = t _i + π · m, and from equation (29), θ _i (t _i + Mπ) = R ₀ cos (mπ + φ ₀ ) + F ₀ (mπ) = − R ₀ cos (φ ₀ ) + F ₀ (mπ) = − F ₀ (0) + F ₀ (mπ) (37) θ _i ′ (t _i + mπ) = − R ₀ sin (mπ + φ ₀ ) + F ₀ ′ (mπ) = R ₀ sin (φ ₀ ) + F ₀ ′ (mπ) = − F ₀ ′ (0) + F ₀ ′ (mπ)・ (38) From equation (36), F ₁ ′ (t) = F ₀ ′ (t) −F ′ (m π) exp ((− K _p / ω _n ) t) (39) (36) , (37), (38), and (39) into (34)
Substituting into the equation, R ₁ = {(2F ₀ (mπ)) ² + (2F ′ (m π)) ² } (40) where F ₀ (mπ) ≒ 0, F ₀ ′ ( If mπ) ≒ 0, (41) R ₁ ≒ 0 (42) Therefore, from equation (33), θ _i (t) = F ₁ (t−t _i −mπ) θ _i ′ (t) = F ₁ ′ (t−t _i −mπ), and F ₁ (t) is (36) ), Θ _i (t),
θ _i ′ (t) does not oscillate. Therefore, θ (t) represented by Expression (27) as a superposition of θ _i (t) is also expressed as t _{M + 1} <t
In, there is no vibration component. In other words, it is damped. Also, this method does not pass through the filter,
The positioning time does not become long. Note equation (41) of the condition _{exp (- (K p / ω} n) πm) = a _{exp (-K p (T / 2} ) m) ≒ 0 ··· (43), the damping effect in this range There is.

[0014]

DESCRIPTION OF THE PREFERRED EMBODIMENTS The present invention will be specifically described below based on embodiments. FIG. 1 is a block diagram (first embodiment) for implementing the first invention of the present application. In the figure, 1 is a pattern generator, 2 and 4 are integrators, 3 is an amplifier, and 5 is a low rigidity load. In this block diagram, when a position command is applied, the pattern generator 1 generates a step speed command having a length of nT. FIG. 2 shows the pattern (when n = 1). The speed command output from the pattern generator 1 is output as a position command after passing through the integrator 2, amplifier 3, and integrator 4, and is input to the position feedback system. As a result, the difference θ (t) and θ ′ (t) between the load and the output of the servo system becomes a motion in the phase space as shown in FIG. 3, and after t> T, there is no vibration and (θ, θ ′) )
= (0, 0). When the position command value is x _{0 in the} software servo, the pattern creator 1 obtains v = x ₀ / T
It can be easily realized simply by creating a program for calculating v where n (n = 1, 2,...).

Next, an embodiment (second embodiment) of the second invention of the present application will be described. In the first embodiment, since the command is limited to a rectangular shape, acceleration and deceleration may be rapid, and a sufficient effect may not be obtained. In the second embodiment, this point is improved. are doing. In FIG. 1, when a position command is given, 1/2.
A pattern obtained by combining two patterns shifted by m (m = 1, 3, 5,...) is created as a speed command. FIGS. 4A, 4B, and 4C show examples of such patterns. 4D, 4E, and 4F are obtained by synthesizing patterns shifted by T / 2 from the basic patterns shown in FIGS. The speed command output from the pattern generator 1 is
After passing through the amplifier 3 and the integrator 4, it is output as a position command and input to the position control system. As a result, low rigidity load 5
Does not vibrate at the end of the command. For example, FIG.
When the waveform (a) is input, the output is as shown in FIG. The pattern creator 1 may be made by hardware or may be calculated by software.

[0016]

As described above, according to the present invention,
In a servo system having a low rigidity load, vibration of the load can be suppressed without delaying the positioning time. Not only the control of the robot manipulator but also the positioning time of the automation device mainly used for the positioning control of the indexing table and the like can be remarkably speeded up as compared with the conventional method.

[Brief description of the drawings]

FIG. 1 is a block diagram showing an example of a control system for implementing the present invention.

FIG. 2 is a waveform diagram showing an example of a pattern output from the pattern generator of FIG.

FIG. 3 is a phase diagram showing an output movement with respect to the pattern of FIG. 2;

FIG. 4 is a waveform diagram showing each example of a pattern output from the pattern generator of FIG. 1;

FIG. 5 is a diagram of output θ with respect to the pattern of FIG.

FIG. 6 is a waveform diagram showing an example when an input is considered as a group of step signals.

FIG. 7 is a block diagram of a positioning servo system having a low rigidity load.

FIG. 8 is a diagram showing the relationship between input and output of a filter often used in conventional vibration suppression control.

[Explanation of symbols]

1 pattern creator, 2, 4 integrator, 3 amplifier, 5
Low rigidity load

Continued on the front page (72) Inventor Hisao Ozono 2-1 Kurosaki Castle Stone, Yawatanishi-ku, Kitakyushu-shi, Fukuoka Prefecture Inside Yaskawa Electric Corporation (56) References JP-A-63-308603 (JP, A) (58) Fields investigated (Int.Cl. ⁷ , DB name) G05D 3/00-3/20 G05B 11/00-13/04

Claims (2)

(57) [Claims] Claims: 1. An apparatus having one or more axes, each axis having a low stiffness load, and having position feedback and velocity feedback.
In a positioning control method of a robot manipulator driven by an actuator controlled by a feedback loop , a signal having a rectangular waveform having a period equal to or an integer multiple of 2 or more as a natural vibration period of a low-rigidity load is used as a speed command. A vibration control positioning control method characterized by output. 2. One or more axes, each axis having a low stiffness load, and position feedback and velocity feedback.
In the positioning control method of the robot manipulator driven by the actuator controlled by the feedback loop , the target position command and basic pattern
Where the total amount of motion stored in the
For the movement amount of 1/2 of the target position command.
Basic pattern creation unit that creates basic speed command patterns
The basic speed created by the basic pattern creation unit
The command pattern is paid to the command delay section and command pattern synthesis section.
In the command delay section, the basic speed command pattern
Is shifted by an odd multiple of 1/2 of the natural vibration period of low rigidity load
Created pattern and paid out to command pattern synthesis unit
The command pattern synthesizing section includes a basic pattern creating section
And the command coming out of the command delay section,
The basic speed command pattern and low rigidity load
A pattern shifted by an odd multiple of 1/2 the natural oscillation period
A vibration suppression positioning control method characterized by outputting a signal having a waveform obtained by combining the above .