CN100565391C - The vibration suppression control method and the device of multi-inertia resonance system - Google Patents

Abstract

The object of the present invention is to stabilize the resonance modes of a multi-inertia resonance system. For the first-order resonance mode, implement resonance ratio control effective for vibration control of the two inertial resonance systems, and for higher-order vibration modes higher than the first-order resonance mode, use phase lead compensation to stabilize all resonance poles. On the other hand, for a high-rigidity load in which the shaft torsional reaction force can be ignored, phase lead compensation is performed using only the external disturbance observer, and all resonance poles are stabilized.

Description

Vibration suppression control method and device for multi-inertia resonance system

technical field

The present invention relates to a vibration suppression control method and device for a multi-inertia resonance system, in particular to a vibration suppression control used in a motor control device such as an elastic manipulator or an XY robot.

Background technique

Generally, in a motor drive system using an elastic manipulator, or an XY robot such as a ball wire or a timing belt, as shown in FIG. 1 , the motor M and the load A are connected through a low-rigidity elastic shaft ( In the figure, the belt B) stretched between the pulleys is combined to form a resonant system, and there is a problem that shaft torsional vibration occurs.

Since an actual resonance system has a plurality of vibration modes or natural frequencies, it is modeled as a multi-inertia resonance system as illustrated in FIG. 2 . In Figure 2, Jm is the inertia of the motor M, Kf1, Kf2... are the spring coefficients, Ja1, Ja2...Jan is the inertia of the load A.

The multi-inertia resonance system is represented by a block diagram as shown in FIG. 3 . In Fig. 3, θm represents the rotation angle of the motor M (motor position), θa represents the rotation angle of the load A (load position), T represents the torque, s represents the Laplace operator, the subscript a represents the load, and the subscript a represents the load. The subscript dis means external disturbance, and the subscript reac means shaft twisting reaction force.

For vibration suppression and disturbance suppression control of such a resonant system, methods such as state feedback control or H∞ control, hysteresis disturbance observation control, and resonance ratio control (see Non-Patent Document 1) have been proposed.

However, state feedback control or H∞ control requires a high-speed and high-performance CPU due to its complex control system and huge amount of calculation, and thus has problems in being applicable to actual machines.

Corresponding to this, the hysteresis external disturbance observation control and the resonance ratio control are composed of a relatively simple control system, and their practicability is high.

However, in the non-resonant control described in Non-Patent Document 1, the system is modeled as two inertial resonance systems in which the motor and the bracket are connected through a flexible drive shaft, so although it has an excellent effect on the first-order resonance, However, there is a problem that the effect on high-order vibrations is low, such as the case where high-order resonance is induced in an actual multi-inertial system.

On the other hand, in Patent Document 1, it is described that a phase advance filter is provided in a servo (servo) system. However, the structure of this technology is complicated, and precise calculation is required, and the calculation time becomes long. device to achieve. In addition, the design is also complicated, and there is a problem that it is difficult to find parameters with stable responses.

[Patent Document 1] Patent No. 3381880

[Non-Patent Document 1] Yuzuo "Vibration Suppression Control of Two Inertial Resonant Systems Controlled by Resonance Ratio" Theory of Electricity D, Vol. 113 (Heisei 5) No. 10, pp. 1162-1169.

Contents of the invention

In view of this, an object of the present invention is to provide a method for stabilizing all resonance poles including not only the first-order resonance mode but also higher-order vibration modes higher than the first-order resonance mode with a simple structure.

In the present invention, in the case of vibration suppression control of a multi-inertia resonance system, resonance ratio control is performed for the first-order resonance mode, and phase lead compensation is performed for higher-order vibration modes higher than the first-order resonance mode so as to realize all resonances Stabilization of the poles, thereby solving the above-mentioned problems.

Also, the ratio of the nominal value of the motor inertia to the actual value of the motor inertia used in the disturbance observer used in the resonance ratio control is changed to perform the phase lead compensation described above, thereby eliminating the need for a separate phase lead compensation mechanism.

In addition, the pole and zero point of the above-mentioned phase lead compensation are arranged inside the pole of the resonance ratio control, so that the phase lead compensation and the resonance ratio control coexist.

Furthermore, in the present invention, for a high-rigidity load in which the shaft torsional reaction force can be ignored, phase lead compensation is performed using only the external disturbance observer, thereby achieving stabilization of all resonance poles.

The present invention also provides a vibration suppression control device for a multi-inertial resonance system characterized by a resonance ratio control mechanism suitable for first-order resonance modes and a phase lead compensation mechanism suitable for higher-order vibration modes above the second order.

In addition, the above-mentioned resonance ratio control means is constituted by an external disturbance observer and a shaft twist reaction force estimation observer.

The present invention also provides a vibration suppression control device for a multi-inertia resonance system characterized by using only an external disturbance observer to perform phase advance compensation for a high rigidity load in which the shaft torsional reaction force can be ignored.

Also, the nominal value of the motor inertia used in the external disturbance observer is set to a value larger than the actual motor inertia to perform the above-mentioned phase lead compensation, thereby eliminating the need for a separate phase lead compensation mechanism.

In the present invention, resonance ratio control is performed, plus phase lead compensation, so resonance ratio control effective for vibration control of two resonance systems is implemented for the first-order resonance mode, and for higher-order vibration modes higher than the first-order resonance mode Stabilization of the resonance poles is achieved using phase lead compensation, so that all resonance poles can be stabilized.

Here, in the phase lead compensation control, for example, the nominal value Jmn of the motor inertia used in the disturbance observer in the resonance ratio control is set to be larger than the actual value Jm of the motor inertia (Jmn>Jm) , so that phase lead compensation control can be realized without adding another phase lead compensation mechanism.

Also, in the case of performing control by a disturbance observer, it is possible to have a vibration suppression effect and also ensure robustness.

In addition, the control system is simpler than state feedback control or H∞ control, and the amount of calculation is less, so it is not necessary to use an expensive CPU or the like. In addition, design or adjustment are easy, too.

Also, for a load with high rigidity in which the shaft torsional reaction force can be ignored, phase lead compensation can be performed using only the external disturbance observer.

Description of drawings

FIG. 1 is a configuration diagram showing an example of an implementation object of the present invention.

Fig. 2 is a model diagram showing an example of an implementation object of the present invention.

FIG. 3 is a block diagram showing an example of an object of implementation of the present invention.

FIG. 4 is an overall block diagram of the first embodiment of the present invention.

FIG. 5 is a block diagram showing the configuration of a disturbance observer used in the first embodiment.

Fig. 6 is a block diagram of an acceleration control system constituted by the above-mentioned external disturbance observer.

Fig. 7 is a block diagram showing the configuration of an axial twist reaction force estimation observer used in the first embodiment.

Fig. 8 is a block diagram showing shaft twisting reaction force feedback used in the first embodiment.

FIG. 9 is an equivalent block diagram of FIG. 8 .

FIG. 10 is a block diagram showing phase compensation according to parameter variations of the disturbance observer used in the first embodiment.

Fig. 11 shows a diagram of poles and zeros of the multi-inertial resonance system used in the first embodiment.

Fig. 12 is a block diagram showing phase compensation performed in two inertial resonance systems used in the first embodiment.

13 is a diagram showing the arrangement of poles and zeros during phase lag compensation in a comparative example of 0<α<1.

14 is a diagram showing root loci when phase lag compensation is performed for three inertial systems of a comparative example of 0<α<1.

FIG. 15 is a diagram showing the arrangement of poles and zeros in the phase lead compensation of the present invention where α>1.

FIG. 16 is a diagram showing root loci when phase lead compensation according to the present invention is performed in three inertial resonance systems where α>1.

FIG. 17 is a diagram showing a pole arrangement of the first embodiment.

Fig. 18 is an overall block diagram of a second embodiment of the present invention.

In the figure: M-motor; A-load; 10-external disturbance observer; 20-axis twisting reaction force feedback device; 30-phase compensator.

Detailed ways

Embodiments of the present invention will be described in detail below with reference to the drawings.

FIG. 4 shows an overall block diagram of the control device according to the first embodiment of the present invention (the load is shown as two inertial resonance systems in the figure, but the same applies to the case of multiple inertial resonance systems).

In this control device, the external disturbance observer 10 shown in FIG. 5 and the shaft twisting reaction force estimation observer 20 shown in FIG. 7 are used to perform resonance ratio control and vibration suppression control of a multi-inertia resonance system. .

The external disturbance observer 10 is applied to the motor side so that the effects of various external disturbances acting on the motor can be counteracted and removed, and a robust acceleration control system as shown in FIG. 6 can be established.

That is, the disturbance torque Tdism acting on the motor can be represented by the following equation.

Tdism=(Jm-Jmn)(d ² θm/dt ² )+(Ktn-Kt)Ia ^ref

+Tfric+Dm(dθm/dt)+Treac ...(1)

Among them, Ia ^ref represents the reference current value, the first term on the right side of the formula represents the inertial variation torque, the second term represents the torque ripple (ripple), the third term represents the Coulomb friction torque, and the fourth term represents the viscous friction torque, The fifth term represents the shaft twisting reaction force.

The external disturbance torque Tdisa acting on the shaft is included in the shaft twisting reaction force Treac so as to act on the motor. When the reference current value Ia ^ref and the motor speed can be detected, the external disturbance torque Tdism defined in formula (1) is estimated as as follows. In FIG. 5 , Icmp is a compensation current for ensuring robustness by compensating for external disturbance torque.

【Number 1】

${\mathrm{<span\; class="notranslate">\; Tdism</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; =</span>\frac{\frac{\mathrm{<span\; class="notranslate">\; Jmn</span>}}{\mathrm{<span\; class="notranslate">\; jm</span>}}\mathrm{<span\; class="notranslate">\; Gdis</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; Kt</span>}}{\mathrm{<span\; class="notranslate">\; Ktn</span>}}\frac{\mathrm{<span\; class="notranslate">\; Jmn</span>}}{\mathrm{<span\; class="notranslate">\; jm</span>}}\mathrm{<span\; class="notranslate">\; Gdis</span>}}\mathrm{<span\; class="notranslate">\; Tdism</span>}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

This estimated external disturbance torque Tdism is fed back so that a control system robust to external disturbances can be established.

The robust control system based on the disturbance observer 10 becomes an acceleration control system as shown in FIG. 6 . It can be seen that the external disturbance observation gain Gdis is set to be larger in order to eliminate the influence of the external disturbance torque Tdism. In this way, the motor becomes a robust control system that eliminates the shaft torsional reaction force Treac and is not affected by the load side.

The external disturbance observer 10 is applied to the motor side in order to cancel and remove the shaft torsional reaction force Treac which is the only information on the load side, thereby causing vibrations on the load side.

Therefore, the axial torsion reaction force Treac is estimated using the axial torsion reaction force estimation observer 20 having substantially the same configuration as the external disturbance observer.

In the external disturbance torque Tdis in the formula (1), the nominal value Jmn of the motor inertia is taken as a value verified by the acceleration test, so that the influence of the variable torque of the motor inertia can be eliminated. Also, the Coulomb friction torque Tfric and the viscous friction torque Dm (d ² θm/dt ² ) are verified by a uniform velocity test, and the shaft torsional reaction force Treac is estimated by the following equation by the offset method.

Treac ^* ＝Tdism ^* -Tfric-Dm(dθm/dt) …(3)

FIG. 7 shows a block diagram of the shaft twist reaction force estimation observer 20 . Greac is the cutoff frequency of the first-order low-pass filter included in the shaft twist reaction force estimation observer 20 .

FIG. 8 shows a system in which the shaft twisting reaction force Treac is fed back in a control object in which the external disturbance observer 10 is applied to the motor side to constitute an acceleration control system. Kr is the feedback gain of the shaft twisting reaction force Treac, which can be set arbitrarily.

The transfer function from the acceleration reference value (d ² θm/dt ² ) ^ref of this system to the motor position θm and the transfer function from the motor position θm to the load position θa are as follows.

【Number 2】

$\mathrm{<span\; class="notranslate">\; \&theta;m</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; Jay</span>}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="s"\; filenames="C2006101000790015H1.png"\; state="\{\{state\}\}">s</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; Kf</span>}}{\mathrm{<span\; class="notranslate">\; js</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="s"\; filenames="C2006101000790015H1.png"\; state="\{\{state\}\}">s</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; Kf</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; KrJ</span>}<span\; class="notranslate">\; )</span>}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d"\; filenames="C2006101000790015H1.png"\; state="\{\{state\}\}">d</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&theta;m</span>}}{{\mathrm{<span\; class="notranslate">\; dt</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; ref</span>}}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

$\mathrm{<span\; class="notranslate">\; \&theta;a</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; Kf</span>}}{\mathrm{<span\; class="notranslate">\; Jay</span>}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="s"\; filenames="C2006101000790015H1.png"\; state="\{\{state\}\}">s</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; Kf</span>}}\mathrm{<span\; class="notranslate">\; \&theta;m</span>}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

In addition, the motor resonance frequency ωm and the load resonance frequency ωa are defined as follows.

【Number 3】

$\mathrm{<span\; class="notranslate">\; \&omega;m</span>}<span\; class="notranslate">\; =</span>\sqrt{\frac{\mathrm{<span\; class="notranslate">\; Kf</span>}}{\mathrm{<span\; class="notranslate">\; Jay</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; KrJ</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

$\mathrm{<span\; class="notranslate">\; \&omega;a</span>}<span\; class="notranslate">\; =</span>\sqrt{\frac{\mathrm{<span\; class="notranslate">\; Kf</span>}}{\mathrm{<span\; class="notranslate">\; Jay</span>}}}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

Here, the resonance ratio K is defined by the following formula.

$\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&omega;m</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; \&omega;a</span>}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; =</span>\sqrt{\mathrm{}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; KrJ</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

The load resonance frequency ωa is an anti-resonance frequency acting as a zero point on the motor side. ωa, does not contain any parameters but is determined by the control object. Also, the state feedback on the motor side cannot be controlled.

On the other hand, ωm is the resonant frequency on the motor side, and can be arbitrarily set by the shaft torsion reaction force feedback gain Kr.

Using formulas (6) and (7), figure 8 is equivalently transformed into the frame diagram of figure 9 . It can be seen from Fig. 9 that the resonance pole ωa on the load side cancels the anti-resonance zero point on the motor side as long as there is no zero point operation through the motor side feedforward and there is no pole point zero point cancellation on the motor side.

The resonance ratio control feeds back the shaft torsion reaction force Treac, and the resonance ratio K can be set arbitrarily by the shaft torsion reaction force feedback gain Kr.

Controlling the resonance ratio K is equivalent to controlling the virtual motor inertia. When the resonance ratio K is large, that is, when the feedback gain Kr is large, the motor inertia becomes smaller for the load inertia and is easily affected by the load side. In addition, the same applies in the opposite case.

Set the resonance ratio K as

$\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; =</span>\sqrt{\mathrm{}}\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

, so that for any two inertial resonance systems, vibration suppression and adaptive gain setting can also be achieved.

The respective gains are as follows.

Kr＝4/Ja …(11)

Kp = ωa ² ... (12)

Kv＝4ωa ...(13)

Here, if the external disturbance applied to the motor M is composed only of the external disturbance torque Tdism that varies according to the parameters, it will be represented by the following equation.

Tdism=(Jm-Jmn)(d ² θm/dt ² )+(Ktn-Kt)Ia ^ref ...(14)

When parameter variation is considered and substituted into the calculation, the transfer function from the acceleration reference value (d ² θm/dt ² ) ^ref of the motor to the acceleration response value d ² θm/dt ² is as follows.

$\frac{\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d"\; filenames="C2006101000790015H1.png"\; state="\{\{state\}\}">d</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&theta;m</span>}}{{\mathrm{<span\; class="notranslate">\; dt</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}{{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d"\; filenames="C2006101000790015H1.png"\; state="\{\{state\}\}">d</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&theta;m</span>}}{{\mathrm{<span\; class="notranslate">\; dt</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; ref</span>}}}<span\; class="notranslate">\; =</span>\frac{\frac{\mathrm{<span\; class="notranslate">\; Kt</span>}}{\mathrm{<span\; class="notranslate">\; Ktn</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; Gdi</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{<span\; class="notranslate">\; *</span>}}{\frac{\mathrm{<span\; class="notranslate">\; jm</span>}}{\mathrm{<span\; class="notranslate">\; Jmn</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; G</span>}{\mathrm{<span\; class="notranslate">\; dis</span>}}^{<span\; class="notranslate">\; *</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 15</span>}<span\; class="notranslate">\; )</span>$

Here, the variation in torque is minimized, and the nominal values Jmn and Ktn used in the external disturbance observer 10 are set as follows.

Jmn=αJm ... (16)

Ktn＝Kt ...(17)

Conventionally, Jm=Jmn, that is, α=1 is controlled.

When formula (16) and (17) are substituted into formula (15), the following formula can be obtained.

$\frac{\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d"\; filenames="C2006101000790015H1.png"\; state="\{\{state\}\}">d</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&theta;m</span>}}{{\mathrm{<span\; class="notranslate">\; dt</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}{{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d"\; filenames="C2006101000790015H1.png"\; state="\{\{state\}\}">d</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&theta;m</span>}}{{\mathrm{<span\; class="notranslate">\; dt</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; ref</span>}}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="Gdis"\; filenames="C2006101000790015H1.png,C2006101000790017H1.png"\; state="\{\{state\}\}">Gdis</figure-callout></span>}}{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; Gdis</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 18</span>}<span\; class="notranslate">\; )</span>$

When this formula (18) is represented by a block diagram, it will be shown in FIG. 10 .

It can be seen from Fig. 10 that, for the acceleration reference value (d ² θm/dt ² ) ^ref , plus the phase compensation 30 of (s+Gdis)/{(1/α)s+Gdis}, and for the external disturbance Tdism, make It is equivalent that the cutoff frequency of the high-pass filter is multiplied by α.

here,

When α<1, the phase lag compensation and the gain reduction of the external disturbance observer

When α>1, the phase advance compensation and the gain of the external disturbance observer increase

That is, change the ratio α of the nominal value Jmn of the motor inertia used in the external disturbance observer 10 to the actual value Jm of the motor inertia, so that the phase compensation of changing the acceleration reference value and the cut-off frequency of the external disturbance observer can be obtained. Effect.

Next, in the multi-inertia resonance system, the vibration suppression effect when the nominal value Jmn of the motor inertia used in the external disturbance observer 10 is changed is represented by a root locus.

In FIG. 11 , the poles (* symbols) and zero points (◯ symbols) of the multi-inertial resonance system are shown on the complex plane. Re is a real axis, and Im is an imaginary axis. It can be seen that the poles and zeros of the multi-inertia resonance system alternate with each other and exist on the imaginary axis Im.

In the following description, a case where phase compensation is performed using two inertial resonance systems as loads for simplicity will be explained. FIG. 12 shows a block diagram for phase compensation of two inertial resonance systems. Here, θcmd is the position command value (can be set arbitrarily), and Cp is the gain of proportional control.

The transfer function of Fig. 12 is as follows.

【Number 6】

$\frac{\mathrm{<span\; class="notranslate">\; \&theta;m</span>}}{\mathrm{<span\; class="notranslate">\; \&theta;cmd</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 19</span>}<span\; class="notranslate">\; )</span>$

n(s)=Cp(s ³ +αGdis·s ² +ωa ² s+αGdis·ωa ² ) …(20)

$\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="5"\; label="s"\; filenames="C2006101000790026H1.png"\; state="\{\{state\}\}">s</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&alpha;Gdis</span>}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\mathrm{<span\; class="notranslate">\; \&omega;</span>}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="m"\; filenames="C2006101000790015H1.png"\; state="\{\{state\}\}">m</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; Cp</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&alpha;Gdis</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="m"\; filenames="C2006101000790015H1.png"\; state="\{\{state\}\}">m</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; Cp\&alpha;Gdis</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="s"\; filenames="C2006101000790015H1.png"\; state="\{\{state\}\}">s</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$

$<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; Cp</span>}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; Cp\&alpha;Gdis</span>}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; twenty\; one</span>}<span\; class="notranslate">\; )</span>$

$\frac{\mathrm{<span\; class="notranslate">\; \&theta;a</span>}}{\mathrm{<span\; class="notranslate">\; \&theta;m</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&omega;</span>}{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="s"\; filenames="C2006101000790015H1.png"\; state="\{\{state\}\}">s</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; twenty\; two</span>}<span\; class="notranslate">\; )</span>$

The characteristics vary by the value of the phase compensator 30 . That is, the phase compensator 30 performs phase lag compensation when 0<α<1. In this case, the pole and the zero point are represented as Plag and Zlag as follows.

Plag＝[0, 0, jωm, -jωm, -αGdis] ... (23)

Zlag＝[jωa，-jωa，Gdis] …(24)

These poles and zeros are shown in Fig. 13 . × is a pole, and ○ is a zero.

Here, the angle formed by the pole -αGdis of the phase lag compensator 30 and the vibration pole s=jωm and the angle formed by the anti-resonant zero point s=jωa are respectively θp and φp. Also, the angle formed by the zero point -Gdis of the phase lag compensator 30 and the vibration pole s=iωm and the angle formed by the anti-resonance zero point s=jωa are respectively referred to as θz and φz.

In this case, the outgoing angle θi ^d (i=1-5) of each pole and the incident angle θi ^a (i=1-3) of the zero point are calculated as follows.

θ1 ^d = -π

θ2 ^d = -π

^θ3d = θz-θp+(π/2)

θ4 ^d = -{θz-θp+(π/2)}

θ1 ^a ＝-Φz+φp-(π/2)

θ2 ^a ＝-{-Φz+Φp-(π/2)}

In FIG. 14, the root locus when the phase lag compensation is performed for the three inertial resonance systems is shown. If the proportional control gain Cp is changed, it can be determined that the system must move in an unstable direction.

On the other hand, the phase compensator 30 performs phase advance compensation when α>1. If the pole and zero in this case are Plead and Zlead, they are expressed as follows.

Plead＝[0, 0, jωm, -jωm, -Gdis] ... (25)

Zlead＝[jωa, -jωa, Gdis] ... (26)

When these poles and zeros are shown in the figure, it becomes as shown in FIG. 15 .

Here, the angle formed by the pole -αGdis of the phase lead compensator 30 and the vibration pole s=jωm and the angle formed by the anti-resonant zero point s=iωa are respectively θp and φp. In addition, the angle formed by the zero point -Gdis of the phase lead compensator 30 and the vibration pole s=iωm, and the angle formed by the anti-resonance zero point s=jωa are respectively referred to as θz and φz.

In this case, the outgoing angle θi ^d (i=1-5) of each pole and the incident angle θi ^a (i=1-3) of the zero point are calculated as follows.

θ1 ^d = -π

θ2 ^d = -π

^θ3d = θz-θp+(π/2)

θ4 ^d = -{θz-θp+(π/2)}

θ1 ^a ＝-Φz+Φp-(π/2)

θ2 ^a ＝-{-Φz+Φp-(π/2)}

In FIG. 16, the root locus when phase lead compensation according to the present invention is performed in three inertial resonance systems is shown. If the proportional control gain Cp is changed, it can be confirmed that the system will definitely move towards a stable direction.

These, for the higher order resonance system, can also obtain the same result. That is, it can be seen that the vibration suppression control of the multi-inertia resonance system can be performed by performing phase lead compensation.

In the present embodiment, the ratio α of the nominal value Jmn of the motor inertia to the actual value Jm of the motor inertia Jm used in the external disturbance observer 10 used in the resonance ratio control is changed, and the phase lead compensation is not newly added. device 30 to implement these phase lead compensations.

In order to make the phase lead compensation and the resonance ratio control coexist, it is necessary to arrange the pole and the zero point of the phase lead compensation inside the pole of the resonance ratio control. That is, the pole configuration of the entire control system is set as shown in FIG. 17 so that the first-order vibration mode is not actively controlled by the resonance ratio control, and the higher-order vibration than the first-order vibration mode mode, due to the small influence of the original, the stability can be guaranteed by phase lead compensation.

Also, in the first embodiment, the motor and the load are connected through a flexible drive shaft, and the control system with low rigidity where shaft twist is a problem is targeted. However, when the rigidity of the load and shaft is high, no shaft twist compensation is required. In the case of , as in the second embodiment shown in FIG. 18 , the reaction force estimation observer can be omitted, and the phase advance compensation control can be constituted only by the outer orbiting observer 10 .

Also in this second embodiment, the resonance pole can be stabilized similarly to the first embodiment due to the phase advance compensation effect.

In addition, in the above-mentioned embodiment, P (proportional) control is used in the speed calculation part, but the control type of the speed calculation is not limited to this, and PI (proportional-integral) control, PD (proportional-derivative) control, PID control, etc. may also be used. (proportional integral differential) control, etc. In addition, instead of using the shaft torsion reaction force estimation observer, a linear encoder or the like may be used to measure the position on the load side. The implementation objects are not limited to elastic manipulators or XY robots.

Claims (8)

1, a kind of vibration suppression control method of multi-inertia resonance system,

For the first order resonant pattern, implement resonance than control, for the high frequent vibration pattern higher, implement phase lead compensation than first order resonant pattern.

2, the vibration suppression control method of multi-inertia resonance system as claimed in claim 1 is characterized in that,

By being used in resonance, carry out described phase lead compensation than the outer value of disturbing the nominal value of the motor inertia in the observer in the control greater than the motor inertia of reality.

3, as the vibration suppression control method of claim 1 or 2 described multi-inertia resonance systems, it is characterized in that,

With the pole and zero of described phase lead compensation, be configured in than the limit inside of resonance than control.

4, a kind of vibration suppression control method of multi-inertia resonance system is characterized in that,

For the high load of rigidity that can ignore axle distortion counter-force, disturb observer outside only using and carry out phase lead compensation.

5, a kind of vibration suppression control device of multi-inertia resonance system is characterized in that possessing:

Resonance is than control gear, and it is suitable for the first order resonant pattern; With

Phase lead compensation mechanism, it is suitable for the high frequent vibration pattern more than the second order.

6, the vibration suppression control device of multi-inertia resonance system as claimed in claim 5 is characterized in that,

Described resonance is inferred observer and is constituted by disturbing an observer and an axle distortion counter-force outward than control gear.

7, a kind of vibration suppression control device of multi-inertia resonance system is characterized in that,

It is arranged to for the high load of rigidity that can ignore axle distortion counter-force, disturbs observer outside only using and carries out phase lead compensation.

8, as the vibration suppression control device of claim 5 or 6 described multi-inertia resonance systems, it is characterized in that,

Be set at value by being used in described outer nominal value of disturbing the motor inertia in the observer, carry out described phase lead compensation greater than the motor inertia of reality.

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