JP2007188322A - Pid controller and method for setting control elements of its pid control system - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method for determining control elements for performing positioning at high speed with accuracy over a target servo band in a PID controller. <P>SOLUTION: In the method for setting control elements of the PID control system, a frequency response characteristic of an object to be controlled is measured and a transfer function of a secondary delay system of a feedback control system approximated to the frequency response characteristic is identified. The transfer function of a controller for controlling the object to be controlled is set to an incomplete differentiation type including comparison, integral, and differential gain factors, an open loop transfer function expressed by an integration between a transfer function of the controller and the transfer factor of the object to be controlled is defined, the comparison, integral, and differential gain factors of the controller are obtained so as to cancel resonance characteristics owned by the object to be controlled, and they are set to the controller. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

    The present invention relates to a PID control device that realizes a target servo band and a method for setting control elements of the PID control system, and in particular, a control device for positioning an actuator including a piezoelectric element and a parallel spring mechanism with high speed and high accuracy. And a method of setting control elements of the control system.

With the development of hard disks, the recording capacity is rapidly increasing and a recording density of 200 Gbit / in ² is about to be achieved. The background of this increase in density is that the track density is significantly improved along with the increase in linear recording density. If a recording density of 1 Tbit / in ² is achieved in the near future, the track pitch is expected to be 50 nm or less. The The tracking error allowed on the recording track by the magnetic head is about 10% of the track pitch. In the magnetic recording evaluation apparatus (spin stand) used for the development of the magnetic head and media, the track profile or off-track margin is set. In order to measure, positioning technology of 1/10 or less, that is, sub-nanometer is required.

  Thus, in order to realize high-speed and high-accuracy tracking on a spin stand, the development of a fine-motion actuator (Nano-motion Actuator: NMA) and its control system is required.

From such a background, the inventors have already proposed a fine actuator for realizing high-speed and high-accuracy tracking in Patent Document 1, and further, for positioning control of this fine-movement actuator with high speed and high accuracy. There is a demand for improved control systems. A PID control device is applied as a control system, and the PID control device is configured by combining three elements of a proportional element (P), a differential element (D), and an integral element (I). The gains of the three elements are determined by trial and error so as to realize a servo band given as a specification. In order to determine the control element in this way, a wide band is realized by giving an anti-resonance characteristic to the PID control device so as to cancel the resonance characteristic of the mechanism that limits the servo band. Further, the gain is determined so as to suppress the overshoot amount in positioning. There is a control system that uses a notch filter to give anti-resonance characteristics to the PID control device so as to cancel the resonance characteristics of the mechanism that limits the servo band.
JP 2004-261167 A

  The PID control device is most widely used, but in the current situation, the three gain determination methods are determined empirically from infinite combinations. For this reason, in the prior art, (1) it is difficult to determine a gain so as to realize a desired servo band, (2) an overshoot in positioning is increased by the determined gain, and (3) resonance characteristics of the mechanism Because of this, the servo band is limited, so that there is a problem that high-speed positioning cannot be realized.

  On the other hand, in a general PID (proportional, integral, derivative) controller, a method of canceling by providing anti-resonance characteristics with a narrow-band notch filter is common. However, since the notch filter also causes phase inversion at the same time, there is a problem that the control performance cannot be drastically improved. That is, the controller with the notch filter has a problem that the responsiveness deteriorates.

  The present invention has been made to solve the above-described problems, and an object of the present invention is to provide a PID control device that realizes high-speed and high-precision positioning over a target servo band and a proportional element (P) of the control system. The present invention provides a method for determining a differential element (D) and an integral element (I).

  Another object of the present invention is to set a PID control device that realizes high-speed and high-precision positioning of a fine actuator using a laminated piezoelectric element and a displacement magnifying mechanism over a target servo band and a control element of the PID control system. It is to provide a way to do.

According to this invention,
Measure the frequency response characteristic of the controlled object and specify the transfer function of the controlled second-order lag system approximated to this frequency response characteristic.
Setting the transfer function of the controller for controlling the controlled object to an incomplete differential type including proportional, integral and differential gain coefficients (K _P , K _I , K _D );
An open-loop transfer function represented by the product of the transfer function of the controller and the transfer function of the control object is determined in the following equation (8) so as to cancel the resonance characteristic of the control object. The proportional, integral, and differential gain coefficients (K _P , K _I , K _D ) of the controller so that the relationship is satisfied, the parameter α included in the incomplete differentiator, and the gain included in the transfer function of the second-order lag system Determined by a relational expression including a constant K, a damping rate ζ and a natural angular frequency ω _n and a parameter L1 of the open loop transfer function,

The parameter L1 is determined so as to realize a servo band to be given as a specification,
Determining a parameter α included in the incomplete differentiator;
A control element of a PID control system that applies the proportional, integral and differential gain coefficients (K _P , K _I , K _D ) specified by the parameters L1 and α, the gain constant K, and the damping rate ζ to the controller as control elements A method of setting is provided.

Moreover, according to this invention,
A controlled object having a frequency response characteristic approximated by a transfer function of a second-order lag system of a model in a feedback control system;
A controller for controlling the controlled object in which a transfer function including proportional, integral and differential gain coefficients (K _P , K _I , K _D ) is set to an incomplete differential type, the resonance characteristic of the controlled object The open loop transfer function represented by the product of the transfer function of the controller and the transfer function of the controlled object is determined by the following equation (8), and the relationship of the equation (8) is satisfied. The proportional, integral and differential gain coefficients (K _P , K _I , K _D ) of the controller are the parameters α included in the incomplete differentiator, the gain constant K included in the transfer function of the second-order lag system, and the attenuation rate ζ. And a relational expression including the natural angular frequency ω _n and the parameter L1 of the open-loop transfer function,

The parameter L1 is determined so as to realize a servo band, and the proportional, integral and differential gain coefficients (K _P , K _I , K _D ) specified by the parameters L1 and α, the gain constant K, and the damping rate ζ are determined. A controller provided as a control element;
There is provided a PID control device characterized by comprising:

  According to the PID control apparatus for realizing the target servo band of the present invention, a desirable form of an open loop transfer function including a fine actuator and a controller is set, and a PID control apparatus for realizing this is determined without trial and error. Thus, a desirable servo band can be realized.

  Further, according to the PID control device of the present invention, in place of the widely used PID control system to which the notch filter is applied, the servo band is specified only by the PID control device, the resonance frequency is canceled, and the positioning is performed. Overshoot can be suppressed, and the number of control calculations can be suppressed by keeping the order of the control device low.

  Hereinafter, referring to the drawings as necessary, a PID control device that realizes a target servo band for positioning a fine actuator according to an embodiment of the present invention at high speed and high accuracy, and setting of a transfer function of the PID control device A method will be described.

  First, the structure of a fine actuator as a control object developed for realizing high-speed and high-accuracy tracking on a spin stand will be described with reference to FIGS.

  As a piezoelectric element, a laminated piezoelectric element with multiple layers of piezoelectric materials typified by PZT (PbZrO3-PbTiO3), which has excellent high-speed response and can generate large force, is a very effective driving element for high-precision positioning. is there. However, this piezoelectric element has a problem that the amount of displacement that can be driven is very small, approximately 1/1000 of the stacking height, and when a large shearing load is applied to the piezoelectric element itself, it is easy to break at the bonding surface of the piezoelectric material. is there. Therefore, it is necessary to consider the method of fixing and supporting the piezoelectric element and the relationship with the parts to be driven. When an attempt is made to use a single piezoelectric element as an actuator, there are aspects that are very difficult to use. In view of this, an actuator is proposed in which a small displacement generated by a piezoelectric element is geometrically expanded, and at the same time a displacement expanding mechanism that facilitates attachment to a fixed part or a driving component (see Patent Document 1). )

  As shown in FIGS. 1 to 3, the actuator 10 includes a laminated piezoelectric element 12 and a displacement enlarging mechanism 14 that enlarges the displacement of the piezoelectric element 12. The displacement enlarging mechanism 14 includes a prismatic support 16, a prismatic movable element 18 facing the support 16 substantially in parallel with a gap, and a parallel extension extending between the support 16 and the movable element 18. It has a pair of link parts 20a and 20b, and is formed in a substantially rectangular frame shape as a whole. Both ends of each link part 20a, 20b are connected to the support part 16 and the mover 18 via the elastic hinge 22, respectively. Each link part 20a, 20b can perform an equivalent rotational movement with the elastic hinge 22 as a fulcrum by elastic deformation of the elastic hinge 22.

  The support portion 16 is formed with a screw hole 11 for screwing the support portion to a desired site. A pedestal 24 that protrudes toward the movable element 18 is formed integrally with the support 16, and one end of the piezoelectric element 12 is fixed to the pedestal 24. The other end of the piezoelectric element 12 is connected to one link portion 20 a via an insulator mechanism 26. When the piezoelectric element 12 is displaced, this displacement is increased by the lever mechanism 26 and transmitted to the one link portion 20a. Then, the link part 20a moves in the arrow A direction with respect to the support part 16. Accordingly, the mover 18 and the other link portion 20b move in the direction of arrow A. As a result, the displacement enlarging mechanism 14 having a substantially rectangular frame shape is displaced into a parallelogram frame shape. In this way, the displacement of the piezoelectric element 12 is magnified by the displacement enlarging mechanism 14 and output as the displacement of the mover 18.

  The support part 16, the movable element 18, the link parts 20a and 20b, the elastic hinge 22, and the lever mechanism 26 of the displacement magnifying mechanism 14 are made of, for example, a metal such as duralumin (high-strength aluminum), stainless steel, or a ceramic having high rigidity. It is molded integrally with the material. The movable element 18, the link parts 20 a and 20 b, the elastic hinge 22, and the lever mechanism 26 function as a movable part of the displacement enlarging mechanism 14.

  A restraining member 30 is fixed to the movable part of the displacement magnifying mechanism 14 via an elastic body or a viscoelastic body. The restraining member 30 is formed into a rectangular flat plate of aluminum, stainless steel, or the like, and an elastic body or viscoelastic body 32 is applied to the entire surface of one side to form an elastic body layer. For example, the plate thickness of the restraining member 30 is formed to about 0.2 to 1.0 mm, and the layer thickness of the viscoelastic body 32 is formed to about 0.04 to 0.2 mm. The restraining member 30 is fixed to the displacement enlarging mechanism with the viscoelastic body 32 side in surface contact with the surface of the displacement enlarging mechanism 14. Here, the restraining member 30 is fixed to the ends of the pair of link portions 20a and 20b on the side of the movable element 18, and is disposed so as to be bridged with the pair of link portions. For fixing the restraining member 30 to the displacement magnifying mechanism 14, an adhesive or the viscosity of the viscoelastic body 32 itself can be used.

  According to the actuator 10 having the above-described configuration, the restraint member 30 is bridged between the parallel link portions 20a and 20b to intentionally restrain the operation between the link portions, whereby viscoelasticity is obtained according to the vibration of the displacement magnifying mechanism 14. The body 32 is efficiently distorted. At the same time, by restraining deformation of the restraining member side surface of the viscoelastic body 32 by the restraining member 30, the distortion of the viscoelastic body 32 can be increased. The viscoelastic body 32 is distorted to convert vibration energy into heat energy and attenuate the vibration. Thereby, the resonance frequency can be increased while effectively attenuating a large resonance peak in which the actuator 10 composed of the displacement enlarging mechanism 14 and the laminated piezoelectric element 12 is present.

  Further, by providing the restraining member 30 and the viscoelastic body in the upper surfaces of the link portions 20a and 20b, that is, in a plane parallel to the moving direction of the movable portion, the actuator 10 is restrained in the moving plane, and the displacement other than the moving direction. Deformation such as an unnecessary twist generated in the enlargement mechanism 14 can be effectively suppressed.

  The restraining member 30 and the viscoelastic body 32 may be provided not only on the upper surface side of the actuator 10 but also on the back surface side. That is, the restraining member 34 similar to the restraining member 30 is fixed across the pair of link portions 20 a and 20 b on the back side of the actuator 10 and faces the restraining member 30. The restraining member 34 is fixed to the displacement magnifying mechanism 14 via the viscoelastic body 36, and the adhesive or the viscosity of the viscoelastic body 32 itself can be used for the fixing.

  By providing a restraining member on both the upper surface side and the back surface side of the actuator 10 via a viscoelastic body or an elastic body, the resonance peak of the actuator is further reduced to about ½ compared to the case where it is provided only on one side. Can be attenuated.

  In the actuator 10 shown in FIGS. 1 to 3, when a voltage is applied to the piezoelectric element 12 (PZT) and expanded and contracted as indicated by an arrow, the center on the elastic hinge 22 is fixed to the fulcrum and the pedestal 24. The lever mechanism 26 provided at the other end of the piezoelectric element 12 has a mechanism in which the center of the lever mechanism 26 is a force point and the point on the movable element 18 is an action point to expand a minute displacement of the piezoelectric element 12. Has been.

  Note that an arm provided with a magnetic head (not shown) at the tip is fixed to the mover 18, and the arm 18 is finely moved in the radial direction of the rotating magnetic disk as the mover 18 is finely moved. Will track the target track on the magnetic disk.

  This lever mechanism (actuator) can express a transmission characteristic from an input to the piezoelectric element 12 (PZT) to a displacement of a point on the movable element 18 by a second-order lag element by a set of springs, masses, and dampers. . The actuator 10 is suitable for high-speed positioning control of several milliseconds or less because one main resonance peak is in a high frequency band of 5 kHz or more.

  FIG. 4 shows a control system for controlling the actuator 10. In the control system shown in FIG. 4, a piezoelectric element drive amplifier 112 for driving the piezoelectric element 12 (PZT) of the actuator 10 is connected to the electrode of the piezoelectric element 12 (PZT). In order to optically measure the displacement of the mover 18 of the actuator 10, an optical fiber sensor 118 is provided on the side of the actuator 10, and the displacement of the mover is measured without contact. The optical fiber sensor 118 irradiates a side surface of the movable element 18 with a laser beam, detects a light beam reflected from the side surface, and detects a displacement as indicated by an arrow A of the movable element 18. A measurement signal from the optical fiber sensor 118 is output to the operational amplifier 120, amplified by the operational amplifier 120, and input to the A / D converter 122.

  In the A / D converter 122, the input analog measurement signal is converted into a digital measurement signal and input to a digital signal processor 124 (DSP: digital signal processor). The target displacement is input to the digital signal processor 124 from the target displacement input unit 132 via the A / D converter 130. This target displacement corresponds to the amount of displacement necessary for the magnetic head to shift from the current track currently being tracked on the magnetic disk to the target track to be tracked next. Therefore, when a track address is assigned on the magnetic disk, the track address read by the magnetic head is input to the target displacement input unit 132, and the target displacement may be determined based on the track address. . The digital signal processor 124 is connected to a PC (personal computer) 126, and the proportional (P), integral (I) and derivative (D) gains in the digital signal processor 124 are set by setting from the PC 126. The digital measurement signal is processed with the set gain, and the PID control signal is output from the digital signal processor 124.

  The control output from the digital signal processor 124 is converted into an analog control signal by the D / A converter 134, amplified by the operational amplifier 136, and input to the piezoelectric element drive amplifier 112. Accordingly, the piezoelectric element 12 (PZT) of the actuator 10 is operated according to the target displacement, and the magnetic head is shifted to the target track.

  In the control system shown in FIG. 4, the PID controller 140 is mounted on the DSP 124 by a program such as C language. That is, the control system shown in FIG. 4 can be equivalently represented by a block diagram of a PID control system as shown in FIG. That is, the actual displacement amount (sensor output) is subtracted from the target displacement and input to the PID controller 140, and the feedback amount is calculated based on this subtraction value to control the actuator 10. In FIG. 5, the frequency characteristics of the drive amplifier 112 for the piezoelectric element or the optical sensor 118 are omitted. Since the actuator 10 in FIG. 5 is the control target P (s), if the actuator 10 is replaced with the control target P (s), a feedback control system as shown in FIG. 6 can be represented by a block diagram.

  The discussion regarding the determination of the general control element examined by the inventor with reference to FIG. 6 will be described, and the PID control apparatus according to the embodiment of the present invention based on this consideration and the control element of the PID control system The method for setting the will be described below.

In the control system shown in FIG. 6, the controlled object is well known.

  As shown, it is expressed as a transfer characteristic of a second-order lag system.

Here, ζ is an attenuation factor, ω _n is a natural angular frequency, and K is a gain constant.

  A transfer function L (s) = P (s) · K (s) obtained by multiplying the control object P (s) and the controller K (s) is called an open-loop transfer function (or a round transfer function).

  When positioning the actuator at high speed and high accuracy, the gain crossover frequency of the frequency response in the open loop transfer function L (s) is a measure of the response speed. The higher the gain crossover frequency is in the high frequency band, the faster the positioning response rises, and the gain of the open-loop transfer function increases, resulting in lower sensitivity and the effects of disturbances or characteristic fluctuations mixed in the system. Can be suppressed.

As the controller 140 for controlling the actuator, a PID controller given by the following equation is generally used, and is usually the most widely used.

Here, K _P represents a proportional element, K _I / s represents an integral element, and K _D S represents a differential element.

However, as described in the background art, in general, the three gains K _P , K _I , and K _D are obtained by trial and error so that the frequency response of the open loop transfer function L (s), the response related to positioning, and the like become desirable. It has been adjusted.

  As explained in the background art, since there are an infinite number of combinations of PID controller gains, it takes time longer than necessary to set gains to achieve high-speed and high-accuracy in a trial and error design. Cost. Further, in the design by trial and error, it is difficult to design the system so as not to become unstable when setting the servo band to a high frequency band.

  The actuator can be model-approximate as a second-order lag element even if there are individual differences or an HGA (Head Gimbals Assembly) and a fixture are attached, but the resonance frequency is affected by these effects. Therefore, the gain of the PID controller 140 must be adjusted according to the characteristics. For this reason, the gain of the PID controller needs to be determined without trial and error.

An example of the frequency response of the actuator 10 is shown in FIGS. 7 (a) and 7 (b). It can be seen that this actuator 10 has a resonance peak characteristic at a frequency of 5 kHz. In the case of such a control target, it is generally known that a PID controller 140 is often used in combination with a notch filter. The transfer function of the notch filter is as follows.

Here, since the anti-resonance characteristics can be created by selecting the notch filter coefficients ω _n2 and ζ ₂ so that ω _n = ω _n2 and ζ = ζ ₂ , the resonance peak of the actuator 10 is canceled out. Therefore, it can be expected that the servo band has a high frequency. However, when the PID controller 140 is combined with a notch filter, the transfer function of the controller 140 is

  Therefore, there is a problem that the degree becomes higher and the number of times of control calculation when mounted on the DSP is increased.

  When the order of the transfer function of the controller increases, the order of the transfer function from the target displacement to the displacement also increases in the block diagram of FIG.

Thus, the inventors have come up with the idea that the differential element of the PID controller 140 is an incomplete differentiator given by the following equation.

  This rewriting is generally performed, and it is possible to prevent an increase in gain in the high frequency range of the differential element and to suppress the influence of high frequency noise mixed in the system. Here, α is a parameter that can be arbitrarily determined.

By rewriting the differentiator of the PID controller 140, the transfer characteristics are as follows.

  From this equation, it can be seen that the numerator polynomial is a quadratic equation, and an anti-resonance characteristic for canceling the resonance characteristic of the controlled object can be created using this quadratic polynomial. That is, by making the numerator polynomial of the PID controller 140 using the incomplete differentiator equal to the denominator polynomial of the actuator, it is possible to cancel the resonance characteristics of the controlled object. For this reason, it is necessary to rewrite the differential element in the previous section, which is one key point of the present invention. This canceling operation means that it is not necessary to use a notch filter, which can suppress an increase in the order of the open-loop transfer function.

The open loop transfer function when an incomplete differentiator is used is as follows.

The open loop transfer function after the denominator polynomial of the control object P (s) and the numerator polynomial of the PID controller are canceled is set as follows:

Here, L ₁ is an adjustable parameter in order to realize the servo band given as a specification. When the equations (5) and (6) are regarded as equivalent and the gain of the PID controller 140 is obtained, the following equation is obtained.

A method for determining the parameter L1 will be described. Setting the servo band given as specifications and omega _d, the omega _d, a frequency gain diagram of the open-loop transfer function crosses the 0 dB. Thus, the gain in the omega _d of L (s) determines the L1 to be 1.

In other words, L ₁ can be obtained by the following equation, and an arbitrary servo band can be realized by selecting L ₁ .

FIG. 8 shows the gain characteristics of the open loop transfer function. According to the experimental results in the control system according to the embodiment of the present invention, the gain characteristic of the open-loop transfer function has a servo band of ω _d , an approximate straight line with a low gain characteristic of −20 dB / dec, and a high band of − 40 dB / dec, and by introducing an incomplete differentiator, the intersection of the two approximate curves becomes the frequency α.

The transfer function F (s) from the target displacement to the displacement is as follows.

  The formula used to determine the PID gain in Equation (9) cannot be realized by a control system in which a notch filter is added to a PID controller that is widely used in general.

  In the determination method according to the embodiment of the present invention, it becomes negative when the proportional gain Kp is 2ζα <ωn. Since the PID gain is normally determined as a positive value, the gain as in the present determination method cannot be realized by determination by trial and error. As an example, in the result shown in FIG. 9, the proportional gain is negative.

In the method of setting the control elements of the PID control system based on the above-described consideration, as shown in step S10 of FIG. 10, first, the frequency response of the controlled object is obtained and expressed by the model of equation (1). It is. That is, in the PID control system, the frequency response characteristics as shown in FIGS. 7A and 7B of the actuator 10 that is the control target P (s) shown in FIG. 1 are experimentally obtained. This frequency response characteristic is indicated by a solid line in FIGS. 7 (a) and 7 (b). The parameters K, ζ and ω _{n of the} mathematical model shown by the equation (1) approximated to the curve shown by the solid line are determined. The frequency response characteristics of this mathematical model are indicated by broken lines in FIGS. 7 (a) and 7 (b).

Next, as shown in step S12 of FIG. 10, the differential element of the PID controller 140 is an incomplete differentiator represented by equation (5). Next, as shown in step S14, the parameter L1 of the open loop transfer function (L (S)) included in equation (9) is determined so as to realize the servo band given as the specification. Thereafter, as shown in step S16, the parameter α included in the incomplete differentiator represented by the equation (5) is determined in consideration of the influence of noise and the amount of overshoot in the high frequency range. Finally, as shown in step S18, the gains K _p , K _I , and K of the PID controller so that the open-loop transfer function expressed as the multiplication of the controlled object 10 and the controller 140 becomes the equation (8). _D is determined using K, ω _n , ζ, L1 and α. Here, the proportional gain Kp is preferably determined to a value that is a negative assumption 2ζα <ω _n.

  The characteristics of this determination method are applicable even when the resonance frequency is deviated because the parameter included in the gain of Expression (7) is 1: 1 with the parameter of the actuator.

Parameters L1 described above, ζ, α, ω _n and the gain _{K p, K I,} DSP124 shown in FIG. 4 so as to constitute a controller 140 with a _{K D} of set controlled by PC 126.

  As described above, a servo band of 2 kHz is designated for the actuator 10 having the frequency characteristics shown in FIG. 7, and a PID controller is designed. When the obtained PID controller was mounted on a DSP and the frequency response of the open loop transfer function was obtained, the experimental results shown in FIGS. 9A and 9B were obtained. 9 (a) and 9 (b), the experimental results and the simulation results are in good agreement, and it has been found that both achieve a servo bandwidth of 2 kHz.

  The above-described method for setting the control elements of the PID control system is not limited to the actuator as shown in FIG. 1, and can be applied to various control targets. In particular, a control target that requires high-speed and high-precision control. It is applicable to.

  As described above, according to the present invention, there is provided a PID control device that realizes a servo band given as a required specification in order to position a fine actuator with high speed and high accuracy. This PID control device has an anti-resonance characteristic that cancels the resonance characteristic of the fine actuator in order to realize a wider servo band.

  Further, according to the present invention, there is preferably provided a PID control device that cancels the pole of the fine actuator and the zero point of the controller so that the order of the controller mounted on the DSP is lowered. Furthermore, according to the present invention, it is more preferable to provide a PID control device that keeps the order of the transfer function of the feedback control system low so that the target value response does not overshoot.

  With a marked increase in recording density of a hard disk device, a technique for positioning a magnetic head at high speed and high accuracy is required in a magnetic recording evaluation device for evaluating a recording / reproducing signal of a magnetic disk. The present invention relates to a fine-motion actuator PID control device for positioning a magnetic head, and can design a control device without trial and error that has been conventionally performed. Therefore, the present invention can greatly contribute to improving the performance of a magnetic recording evaluation device.

It is a perspective view which shows roughly the structure of the actuator as an example of the control object in the PID control apparatus of this invention. It is a top view of the actuator shown in FIG. It is a side view of the actuator shown in FIG. It is a block diagram which shows the control system which controls the actuator shown in FIG. It is the block diagram which simplified the control system shown by FIG. FIG. 6 is a block diagram of the control system shown in FIG. 5. (A) And (b) is a graph which shows an example of the frequency response characteristic of the actuator 10 shown in FIG. It is a graph which shows the gain characteristic of the open loop transfer function in the control system shown by FIG. (A) And (b) is the graph which shows the frequency characteristic obtained by the experimental result and simulation in the PID control apparatus by which the gain was set according to the setting method of the transfer function of the PID control apparatus which concerns on one embodiment of this invention It is. It is a flowchart which shows the setting method of the control element of the PID control diameter which concerns on the Example of this invention.

Explanation of symbols

  10. . . Actuator, 12. . . Piezoelectric element, 14. . . Displacement expansion mechanism, 16. . . Support, 18. . . Mover, 20a, 20b. . . Link, 22. . . Hinge, 112. . . Drive amplifier for piezoelectric element, 120. . . Operational amplifier, 118. . . Fiber optic sensors 122, 130. . . A / D converter, 124. . . 126. digital signal processor; . . PC, 132. . . Target displacement input unit 136. . . Operational amplifier

Claims (12)

Measure the frequency response characteristic of the controlled object and specify the transfer function of the controlled second-order lag system approximated to this frequency response characteristic.
Setting the transfer function of the controller for controlling the controlled object to an incomplete differential type including proportional, integral and differential gain coefficients (K _P , K _I , K _D );
An open loop transfer function expressed by the product of the transfer function of the controller and the transfer function of the control object is determined in the following equation (8) so as to cancel the resonance characteristic of the control object, and the equation (8) The proportional, integral, and differential gain coefficients (K _P , K _I , K _D ) of the controller so that the relationship is satisfied, the parameter α included in the incomplete differentiator, and the gain included in the transfer function of the second-order lag system Determined by a relational expression including a constant K, a damping rate ζ, a natural angular frequency ωn, and a parameter L1 of the open-loop transfer function;

The parameter L1 is determined so as to realize a servo band to be given as a specification,
Determining a parameter α included in the incomplete differentiator;
PID given to the controller as control elements using the parameters L1 and α and the proportional, integral and differential gain coefficients (K _P , K _I , K _D ) specified by the gain constant K, the attenuation factor ζ, and the natural angular frequency ω n A method for setting the control elements of the control system. The transfer function of the second-order lag system is expressed by the following equation (1)

The control element of the PID control system according to claim 1, wherein ζ is an attenuation factor, ω _n is a natural angular frequency, and K is a gain constant. how to. The transfer function of the controller has a transfer characteristic K1 (s) represented by the following equation (6), and is incompletely differential including the proportional, integral and differential gain coefficients (K _P , K _I , K _D ). 2. The method for setting a control element of a PID control system according to claim 1, wherein the control element is set.

The parameters L1, the method for setting the control elements of the PID control system of claim 1 in which the gain, characterized in that the determined to be 1 in the angular frequency omega _d of the frequency response of the L (s). The method for setting a control element of a PID control system according to claim 1, wherein the parameter is defined by the following equation (11).

The proportional gain K _p, a method of setting the control element of claim 1 of the PID control system damping factor as determined in the negative, the parameter α is equal to or defined in relation to 2ζα <ωn. A controlled object having a frequency response characteristic approximated by a transfer function of a second-order lag system of a model in a feedback control system;
A controller for controlling the controlled object in which a transfer function including proportional, integral and differential gain coefficients (K _P , K _I , K _D ) is set to an incomplete differential type, the resonance characteristic of the controlled object The open loop transfer function represented by the product of the transfer function of the controller and the transfer function of the controlled object is determined by the following equation (8), and the relationship of the equation (8) is satisfied. The proportional, integral and differential gain coefficients (K _P , K _I , K _D ) of the controller are the parameters α included in the incomplete differentiator, the gain constant K included in the transfer function of the second-order lag system, and the attenuation rate ζ. And a relational expression including the natural angular frequency ω _n and the parameter L1 of the open-loop transfer function,

The parameter L1 is determined so as to realize a servo band, and the proportional, integral and differential gain coefficients (K _P , K) specified by the parameters L1 and α, the gain constant K, the damping rate ζ, and the natural angular frequency ω _n are determined. _I , K _D ) as a control element,
A PID control device comprising: The transfer function of the second-order lag system is expressed by the following equation (1)

The PID control apparatus according to claim 7, wherein ζ is an attenuation factor, ω _n is a natural angular frequency, and K is a gain constant. The transfer function of the controller has a transfer characteristic K1 (s) represented by the following equation (6), and is incompletely differential including the proportional, integral and differential gain coefficients (K _P , K _I , K _D ). The PID control device according to claim 7, wherein the PID control device is set.

The parameters L1 is, PID control apparatus according to claim 7 in which the gain is equal to or define to be 1 in the angular frequency omega _d of the frequency response of the L (s). The PID control apparatus according to claim 7, wherein the parameter is defined by the following equation (11).

The proportional gain K _p, the attenuation factor as determined negatively, PID control apparatus according to claim 7 in which the parameter α is equal to or defined in relation to 2ζα <ωn.

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