JPH0750417B2 - Position control device using piezoelectric actuator - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial field of application] The present invention is generally applicable to ultra-precision machining such as positioning of an exposure apparatus in semiconductor manufacturing, ultra-precision machining machine for laser optical parts, and precise and high-speed response piston lathe. The present invention relates to a position control device using a piezoelectric actuator used in a called field.

[Conventional technology]

FIG. 6 is a diagram showing a conventional example in which a small displacement control system is realized as a feedback control system, FIG. 7 is a block diagram of the feedback control system shown in FIG. 6, and FIG. 8 shows a root locus of the feedback control system. FIG. 9 and FIG. 9 are diagrams showing an example of a micro-displacement tool base using a piezoelectric element.

A control system as shown in Fig. 6 (Piezoelectric / electrostrictive actuator by Uchino, Morikita Shuppan, 1985, P123, Fig. 6.
17) In this feedback control system, the applied voltage E is given as an integral value of the difference between the target value e _i and the position signal e _o . A block diagram of this feedback control system is shown in FIG. 7. A transfer function of a mechanical vibration system in which a piezoelectric actuator and a certain block are composed of an actuator and a mass is shown. Here, ζ is a parameter representing the damping of the electrostrictive actuator.

Further, as a conventional example of a micro-displacement tool base using a piezoelectric element, there is a micro-displacement tool base shown in FIG. 9 (Nikkei Mechanical Co., Ltd., 1986, 9, 22). This example also performs closed-loop control of the piezoelectric actuator, and is characterized in that a notch filter is inserted in order to lower the gain near the natural frequency of the mechanical vibration system and improve the stability of the closed loop.

[Problems to be solved by the invention]

However, in the conventional feedback control system shown in FIG. 6 as described above, the parameter ζ representing the damping of the electrostrictive actuator is considerably small in an ordinary element, so that a mechanical vibration system having a poor damping property is constructed. Become. 7th
The response of the control system shown in the block diagram of FIG. The characteristics of the integrating amplifier and the piezoelectric actuator of FIG. 7 (a) are shown as the pole of the origin indicated by x and the pole of the secondary vibration system indicated by Δ on the S plane of FIG. 8, respectively. Here, the root locus of the poles of the closed loop when the gain K ₁ of the integrating amplifier is gradually increased from zero is shown by a solid line. The pole of the closed loop starting from the pole Δ of the secondary vibration system of the piezoelectric actuator moves to the right in the S plane as the gain K ₁ increases. In other words, it gradually loses stability. At the limit gain K _1c (the pole at this time is shown by ● in FIG. 8), the stability limit is reached. Gain K ₁ is the limit gain K _1c
When it becomes larger, the pole moves to the right half of the S plane and becomes unstable. Practically, in order to ensure stability, the gain K ₁ must be set to a value considerably smaller than the limit gain K _1c . As described above, in the conventional feedback control system shown in FIG. 6, in the case of an oscillating system having a poor damping property, a large closed loop gain cannot be obtained, so that the closed loop response becomes slow and the positioning accuracy cannot be increased. There is.

Further, in the feedback control system shown in FIG. 9, since the notch filter is inserted, the closed loop system does not excite the vibration by itself, but if the mechanical vibration system causes the natural frequency (cutoff of the notch filter) for some reason. If we start oscillating at (frequency), there is no operation at this frequency because of the notch filter. For this reason, there is a problem that the mechanical vibration system itself has only a damping action and the vibration continues for a long time. Further, since the gain of the integrator of FIG. 9 does not become ∞ when the frequency f → 0, there is a problem that an offset occurs in the low frequency range.

The present invention is to solve the above problems, and an object of the present invention is to provide a position control system using a piezoelectric actuator with respect to a mechanical vibration system in which a piezoelectric actuator is a spring system and a moving body is a mass. Then, the vibration system is stabilized by adding a control for increasing the damping.
Furthermore, by setting the gain of the position control loop high by this effect, the response of the position control system is made faster,
It is intended to improve the accuracy and to quickly damp vibrations generated by the action from the outside.

[Means for solving problems]

Therefore, a position control device using a piezoelectric actuator of the present invention controls a position x of a moving body and an acceleration a in a position control system for controlling the position of a moving body having a mass by operating an applied voltage of the piezoelectric actuator. Detecting means, a primary delay circuit for integrating the signal of the acceleration a detected by the detecting means, and an output signal v of the primary delay circuit.
And a control circuit for controlling the applied voltage of the piezoelectric actuator from the position command r and the gain constants K ₁ and K _{2 so} that E = K ₁ ∫ (r−x) dt−K ₂ v. To do.

[Action]

In the position control device using the actuator of the present invention, the position and acceleration of the moving body are detected with respect to the mechanical vibration system in which the piezoelectric actuator is a spring system and the moving body is a mass, and the acceleration is the natural frequency of the mechanical vibration system. By feeding back to the piezoelectric actuator in an integrated amount near f _r , control that increases damping can be realized and the vibration system can be stabilized. Further, the gain of the position control loop can be set high, the response of the position control system can be speeded up, the accuracy can be improved, and the vibration generated by the action from the outside can be quickly attenuated.

〔Example〕

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

FIG. 1 is a diagram for explaining one embodiment of a position control device using an actuator according to the present invention, FIG. 2 is a diagram showing a gain characteristic of a first-order lag circuit, and FIG. 3 is an operational amplifier with a first-order lag circuit. It is a figure which shows the example comprised by.

In FIG. 1, 1-1 is a piezoelectric actuator, 1-2
Is a moving body, 1-3 is a position sensor, 1-4 is an amplifier, 1-
Reference numeral 5 is an integrating amplifier, 1-6 is a high voltage amplifier, 1-7 is an accelerometer, 1-8 is a first-order delay circuit, 1-9 is a subtractor, r is a position command, x is a position, and E is a piezoelectric actuator drive. Indicates the voltage.

As is clear from comparison between the position control system shown in FIG. 1 and the conventional position control system shown in FIG. 6, the control system of the position control system using the piezoelectric actuator according to the present invention is the accelerometer 1-7. , A first-order delay circuit 1-8 and an adder 1-9 are added. The accelerometer 1-7 is a piezoelectric actuator 1-
It measures the acceleration of the moving body 1-2 in the direction parallel to the displacement of 1, and is installed on the moving body 1-2. The first-order lag circuit 1-8 is for integrating the acceleration measured by the accelerometer 1-7, and its gain characteristic is an integral characteristic at a frequency f _r , that is, −20 dB / dec as shown in FIG. Has a slope of. Here, the frequency f _r is a natural frequency of a mechanical vibration system that configures the piezoelectric actuator 1-1 as a spring system and the moving body 1-2 as a mass, It is represented by. Note that K _p is the spring constant and M is the mass. The subtractor 1-9 outputs the output of the integrator 1-5 and the first-order delay circuit 1-
8 is subtracted from the output v to obtain the piezoelectric actuator 1-1.
The driving voltage E of E is set to E = K ₁ ∫ (r−x) dx−K ₂ v, and K ₁ and K ₂ are gain constants.

As described above, the position control device using the piezoelectric actuator according to the present invention detects the position x and the acceleration a of the moving body 1-2 by the position sensor 1-3 and the accelerometer 1-7, and the acceleration a is a primary value. The delay circuit 1-8 integrates the signal v to obtain the drive voltage E of the piezoelectric actuator 1-1. This allows the mechanical vibration system to be controlled so as to increase the damping, thereby reducing the mechanical vibration system. Can be stabilized. As a result, the gain of the position control loop can be set high.

FIG. 3 shows an example in which the first-order delay circuit 1-8 is configured by the operational amplifier OP, and the cutoff frequency f _c = 1 / 2πR.
_As shown in FIG. 2, ₂ C is designed so that f _c <f _{r in} relation to the natural frequency f _r of the mechanical vibration system.

Generally, the stroke of the piezoelectric actuator is several μm, and it is difficult to directly detect the velocity. Therefore, it is practical to obtain the velocity by measuring the acceleration with an accelerometer and integrating it. Further, since the damping action only needs to be effective in the frequency band near the natural frequency f _r = ω _n / 2π of the vibration system, a first-order delay circuit having an integral characteristic near this natural frequency f _r can be used. . Furthermore, the natural frequency
In order to prevent oscillation in higher-order vibration modes higher than f _r and to increase stability in the low-frequency range, a band-pass filter whose center frequency is the natural frequency f _r in series with the first-order lag circuit, or It may be effective to insert a high-pass filter having a flat characteristic at the frequency f _r .

FIG. 4 is a diagram showing a gain characteristic of a bandpass filter having a center frequency f _r, and FIG. 5 is a diagram showing a gain characteristic of a high-pass filter flattening at a frequency f _r . This can be easily achieved by using a commercially available filter IC.

Next, a position control device using the piezoelectric actuator according to the present invention will be devised based on the position control system having the conventional basic structure.

FIG. 10 is a diagram showing a basic configuration of a closed loop position control system using a piezoelectric actuator, and FIG. 11 is a diagram showing a dynamic model of a portion of the piezoelectric actuator and a moving body.

10, the same reference numerals as those in FIG. 1 indicate the same components. This position control system has substantially the same structure as the conventional position control system shown in FIG. 6, and a dynamic model of the piezoelectric actuator 1-1 and the moving body 1-2 is shown in FIG. Is approximated as follows. Here, M is the mass of the moving body, f _p is the generated force of the piezoelectric actuator (this is approximated to be proportional to the applied voltage E), and x is the position.

Differential equation of this system _{is, M + K p x = f} p ...... (1) next to, and put the ^{_{ω n 2 = K p / M}} , the ^{_{+ ω n 2 x = f p}} / M ...... (2). The system represented by the equation (2) is an undamped vibration system, and as it is, it is inconvenient to construct a closed loop system. In practice, there is damping that occurs inside the piezoelectric actuator, but it is negligible. Therefore, the control for increasing the attenuation is realized by setting f _p = −g (3). At this time, the equation (2) is And becomes a secondary vibration system with damping. Therefore,
When the desired damping constant is ζ, g = 2ζω _n · M (5) can be set from 2ζω _n = g / M.

FIG. 12 is a block diagram showing the above relationship. However, the feedback control expressed by the equation (3) merely increases the damping of the vibration system, and the control for the purpose of position control must be separately configured.

Now, the position control system of the formula (1), since a localization of a system having _{x = f p / K p ......} (6) becomes an equilibrium point, in order to constitute an offset-free closed loop system integration It must be controlled. This integral control is performed by setting f _p = K _i ∫ (r−x) dt (7). Therefore, in order to perform the integral control and the control for increasing the attenuation at the same time, from the above equations (3) and (7), f _p = K _i ∫ (r−x) dt−2ζω _n M (8) It would be good. FIG. 13 shows a block diagram of the position control system when the feedback of the equation (8) is performed, and FIG. 14 shows a simplified speed feedback loop.

In the system shown in FIG. 14, when ζ = 1, the loop gain at the stability limit can be maximized and the response can be the fastest. FIG. 15 shows the root locus when the gain K _i is used as a parameter under the condition of ζ = 1.
In this case, further, a condition having a multiple root such that K _i is shown by the point A, , The transfer function of r → x is as shown in FIG. Becomes This setting gives the fastest response under the condition that the position loop is non-oscillatory. Such non-oscillation of the position loop is generally a desirable characteristic, and is an indispensable condition particularly when machining is performed by a method of removing a workpiece, for example, cutting and grinding. Also,
In the control method of the present invention represented by the equation (8), since the feedback that performs the damping action proportional to is always performed, the vibration generated by the external force can be quickly damped.

The present invention is not limited to the above embodiment, and various modifications can be made.

〔The invention's effect〕

As is apparent from the above description, according to the present invention, the deviation e is different from that of the position control device using the piezoelectric actuator.
Since not only the integrated value of = v−x but also the integrated value of acceleration is fed back, the vibration characteristic is stabilized, and as a result, the integral gain can be increased. Therefore, it is possible to configure a position control device having higher response and higher accuracy than the conventional one. Further, since it is possible to obtain a non-oscillating position control system response, which was difficult with the conventional method, it becomes possible to use the device as a position control device for a device such as a cutting machine in which an oscillatory response is not allowed. As described above, the application of the position control device using the actuator according to the present invention has a great effect on the field of ultra-precision machining.

[Brief description of drawings]

FIG. 1 is a diagram for explaining one embodiment of a position control device using a piezoelectric actuator according to the present invention, FIG. 2 is a diagram showing a gain characteristic of a first-order lag circuit, and FIG. The figure which shows the example comprised by the amplifier, FIG. 4 is a figure which shows the gain characteristic of the band pass filter which makes center frequency f _r , FIG. 5 is the figure which shows the gain characteristic of the high pass filter which becomes flat at frequency f _r , FIG. 6 is a diagram showing a conventional example in which a small displacement control system is realized as a feedback control system,
FIG. 7 is a block diagram of the feedback control system shown in FIG. 6, FIG. 8 is a diagram showing a root locus of the feedback control system, and FIG. 9 is a diagram showing an example of a microdisplacement tool base using a piezoelectric element. FIG. 10 is a diagram showing a basic configuration of a closed-loop position control system using a conventional piezoelectric actuator, FIG. 11 is a diagram showing a dynamic model of a piezoelectric actuator and a moving body, FIG.
Fig. 12 is a block diagram of velocity feedback, Fig. 13 is a block diagram with feedback of integral control, and Fig. 14
The figure is a block diagram that simplifies velocity feedback.
FIG. 15 is a diagram showing a root locus when the gain K _i is a parameter under the condition of ζ = 1, and FIG. 16 is a diagram showing a transfer function between the position command and the position. 1-1: Piezoelectric actuator 1-2: Moving body, 1
-3 ... Position sensor, 1-4 ... Amplifier, 1-5 ... Integrating amplifier, 1-6 ... High-voltage amplifier, 1-7 ... Accelerometer, 1-8 ... First-order delay circuit, 1- 9 ... Subtractor.

Claims (4)

[Claims] 1. A position control system for controlling a position of a moving body having a mass by operating an applied voltage of a piezoelectric actuator, and a detecting means for detecting a position x and an acceleration a of the moving body, and the detecting means. The first-order delay circuit that integrates the signal of the acceleration a detected by, the output signal v of the first-order delay circuit, the position command r, and the gain constants K ₁ and K _{2 are used} to calculate the voltage applied to the piezoelectric actuator by E = K ₁ ∫ (r− x) A position control device using a piezoelectric actuator, which is provided with a control circuit for controlling dt−K ₂ v. 2. The first-order lag circuit has a mass of a moving body, M,
If the spring constant of the piezoelectric actuator is K _p , the natural frequency f _r determined by these is A position control device using a piezoelectric actuator according to claim 1, wherein a cutoff frequency f _c is set to be sufficiently smaller. 3. A position control device using a piezoelectric actuator according to claim 1, wherein a bandpass filter having a center frequency of the natural frequency f _r is connected in series to the first-order lag circuit. 4. A position control using a piezoelectric actuator according to claim 1, wherein a high-pass filter having flat characteristics at the natural frequency f _r is connected in series to the first-order lag circuit. apparatus.