JP2005208975A - Method for controlling active vibration of smart board in which piezoelectric fiber with metallic core is embedded - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an active vibration controlling method in which a smart board obtained by embedding a piezoelectric fiber with a metallic core in a CFRP board is used as a controlled target, the piezoelectric fiber is used as a sensor/actuator and a large damping effect can be obtained. <P>SOLUTION: In the active vibration controlling method, the smart board in which the piezoelectric fiber with the metallic core is embedded is used as a controlled target, a finite element model for the controlled target is led out, a low-dimensional model for design of a control system is found out, and the piezoelectric fiber is used as a sensor or an actuator. Then the low-dimensional model is transformed into a linear fraction transform (LFT) in which the ununiformity of an actuator coefficient is considered as perturbation, a generalized plant including the obtained LFT expression is constituted and the active vibration of the smart board for designing the control system by μ design is controlled. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  The present invention relates to an active vibration control method for a smart board, and more particularly to an active vibration control system design method using a piezoelectric fiber as a sensor / actuator for a smart board embedded with a piezoelectric fiber with a metal core.

  Research has been actively conducted on smart structures in which structural members, sensors, and actuators are integrated, and the materials themselves detect abnormalities and control them. As a research on the vibration control, there has been a conventional research for controlling a vibration by attaching a single piezoelectric element or a piezoelectric film to a cantilever structure and using it as a sensor / actuator and performing feedback control. However, this method has a drawback that it is vulnerable to an external impact because the piezoelectric ceramic or piezoelectric film is exposed on the surface of the structure.

In order to eliminate the above-mentioned drawbacks, the present inventors have made a surface of lead zirconate titanate using a fine metal wire as a core and suitable as a piezoelectric material embedded as a sensor or actuator in a composite material such as carbon fiber reinforced plastic (CFRP). A composite type piezoelectric wire coated with (PZT) ceramics (hereinafter referred to as “piezoelectric fiber with a metal core”) has been proposed (see Non-Patent Document 1).
Up to now, it has been reported that passive vibration control using an RL shunt circuit was performed by embedding a metal core-containing piezoelectric fiber in a CFRP plate. However, since the piezoelectric fiber has a small capacitance, it is difficult to obtain a large control effect (see Non-Patent Document 2).
Koji Sato, Yoshiro Shimojo, Tadashi Sekiya, “Fabrication of a piezoelectric fiber with a thin metal wire as a core and its application to a smart boat”, Proceedings of the Japan Opportunity Society (A), Volume 69, No. 184 (2003), pp 1805 1810 Sato, H., Shimojo, Y., Sekiya, T., “Development of the Piezoelectric Fiber and Application for the SmartBoard, Proceedings of ISSS-SPIE 2002, pp242-246.

  The present invention provides an active vibration control method for a smart board capable of obtaining a large vibration suppression effect by using a smart board in which a piezoelectric fiber with a metal core is embedded in a CFRP plate as a control target and using the piezoelectric fiber as a sensor / actuator. With the goal.

Further, when a plurality of embedded piezoelectric fibers are simultaneously driven by a single piezo amplifier, the non-uniformity becomes a problem. Piezoelectric fibers have (1) non-uniformity of force generated when a voltage is applied due to the internal metal core being slightly shifted from the center, and (2) minute sintering conditions when producing the piezoelectric fiber. Individual differences occur due to individual differences in ceramics due to differences, (3) the influence of the interface between the piezoelectric fiber and the CFRP composite material, and non-uniformity in the actuator coefficient. When multiple piezoelectric fibers are used, if an optimal control system is designed for each and driven independently, that many piezo amplifiers and controllers are required, leading to increased costs. become.
Therefore, another object of the present invention is to provide an active vibration control method for a smart board by an optimal control system design method for driving a plurality of piezoelectric fibers with a single piezo amplifier.

  As a result of intensive studies to solve the above-mentioned problems, the present inventors have derived a finite element model to be controlled, obtained a reduced-order model for control system design, and reduced the reduced-order model to non-uniform actuator coefficients. Is converted into a linear fractional transformation (LFT) expression that considers the perturbation as a perturbation, and a generalized plant including the obtained LFT expression is constructed, and when μ design is performed, a control system that reflects the non-uniformity of piezoelectric characteristics Found that can be designed. The present invention has been made based on this finding.

That is, the present invention
(1) A smart board in which a piezoelectric fiber with a metal core is embedded is controlled, a finite element model for the controlled object is derived, a reduced-order model for control system design is obtained, and the piezoelectric fiber is used as a sensor or actuator. Active vibration control method of smart board, characterized by being used as
(2) Further, the reduced-order model is converted into a linear fractional transformation (LFT) expression that considers the non-uniformity of the actuator coefficient as a perturbation, and a generalized plant including the obtained LFT expression is constructed, and μ design A control system is designed by the active vibration control method for a smart board according to item (1),
(3) The active vibration control method for a smart board according to (1) or (2), wherein a plurality of piezoelectric fibers with metal cores are used as actuators and driven by a single piezo amplifier, and
(4) The smart board active vibration control method according to any one of (1) to (3), wherein the smart board is formed by embedding a carbon fiber reinforced plastic with a metal core-filled piezoelectric fiber. It is to provide.

According to the method of the present invention, a great vibration damping effect can be obtained by performing active vibration control on a smart board made of a CFRP plate in which a piezoelectric fiber with a metal core is embedded.
In addition, vibration control with good performance can be performed even when a plurality of piezoelectric fibers are simultaneously driven by a single piezo amplifier by a control system design method using a model in which the non-uniformity of the actuator is expressed as LFT.
Furthermore, resonance breakdown due to resonance frequency disturbance can be prevented, and the reliability of the structure can be improved.

  In the present invention, a smart board in which a piezoelectric fiber with a metal core is embedded is controlled, and active vibration control of the smart board is performed using the piezoelectric fiber as a sensor or an actuator. This control system is designed using the following i) modeling.

i) Modeling A piezoelectric fiber is oscillated at the natural frequency of a beam, an actuator coefficient is identified from its input and output signals, and a finite element model is introduced. Next, a reduced-order model is obtained for control system design.
In the present invention, a “finite element model” means a model that accurately represents the characteristics of a smart board for use in numerical simulations up to higher-order vibrations.
Further, the “reduced dimension model” means a model that simply represents the main resonance of the smart board characteristics for use in control system design.

In the modeling of the control system design, it is further possible to express a model using a linear fractional transformation (LFT) expression that considers the non-uniformity of the actuator coefficient as a perturbation, and further ii) design the control system as follows. preferable. In the present invention, “perturbation” means a deviation from the average value of the actuator coefficient.

ii) Control system design A generalized plant is constructed using a model expressed in LFT and a weight function. By introducing a weighting function, it is robust against high-order vibrations of the beam and high-frequency noise from the outside environment, and a design that focuses only on the primary mode that is the main resonance can be performed.

  In the present invention, based on the above generalized plant, the controller is designed by μ synthesis, which is a robust control theory (μ design), so that the control system can be designed in consideration of the non-uniformity of the actuator coefficient. Preferably it is done. The outline of the control system design by μ design is explained concretely. Instead of considering the actuator coefficient non-uniformity as a model error and designing conservatively with low control performance, the information is actively incorporated into the control system. This is a technique for designing with high control performance.

  With the control system designed by the above method, even if a plurality of metal core-containing piezoelectric fibers are used as actuators and a single piezo amplifier is driven, vibration can be controlled appropriately and cost reduction can be achieved.

  In the present invention, the smart board is preferably formed by embedding a CFRP containing a metal core in CFRP.

  The piezoelectric fiber with a metal core used in the present invention is preferably a lead zirconate titanate fiber formed by coating or laminating a lead zirconate titanate crystal on the surface of a metal wire as a core wire. The metal wire is preferably a titanium wire or a heat-resistant metal wire. Moreover, it is preferable that the said heat resistant metal wire is comprised from platinum, stainless steel, or nickel. Moreover, it is preferable to carry out the hydrothermal synthesis method or the extrusion molding method to coat the surface of the metal wire with the lead zirconate titanate crystal.

は基礎部の加速度、ｖは回転方向座標である。はりのねじり振動は微小なものと考え無視すると、要素の剛性行列および質量行列は Next, the present invention will be described in more detail based on the following specific examples.
(Finite element model)
The CFRP plate 10 in which the metal core-containing piezoelectric fiber 1 was embedded was used as a cantilever as shown in FIG. Sixteen piezoelectric fibers were embedded, one of which was used as a sensor and the other 15 as an actuator. The symbols were defined as follows: l: length of beam, E: elastic modulus of beam, t _b : thickness of beam, w _b : width of beam. First, a full order model is derived by the finite element method. As shown in FIG. 1, the coordinates were taken and the number of divisions was 18. In FIG.

Is the acceleration of the foundation, and v is the rotation direction coordinate. If the torsional vibration of a beam is considered to be minute, the stiffness matrix and mass matrix of the element are

It becomes.
The piezoelectric fiber expands and contracts in the longitudinal direction when an electric field is generated between the metal core and the fiber surface. Therefore, it is assumed that a bending moment M _ai is generated at the tip of the beam by applying the voltage V _i to the _i-th piezoelectric fiber.

Here, C _ai is an actuator coefficient, and can be obtained experimentally by a resonance experiment in the primary resonance mode and system identification by the subspace method. A typical example of the actuator coefficient of each piezoelectric fiber is shown in FIG.
Here, since the piezoelectric fiber is embedded from the element 1 to the element 18, it is considered that a bending moment is applied to the tip of the beam, and the equation of motion is

It becomes. When a piezoelectric fiber is used as a sensor, a voltage is generated in proportion to the deflection angle of the beam tip. As a result, the equation of state becomes

It becomes. Here, Ks is a sensor coefficient, and the voltage generated in the piezoelectric fiber due to the deflection of the CFRP plate is Vs.

である。センサ係数はアクチュエータ係数と同様に実験的に求めることができる。

It is. The sensor coefficient can be obtained experimentally in the same manner as the actuator coefficient.

(Low-dimensional model for control system design)
Here, in order to consider the damping of only the primary mode, a model in the mode space is used for the design of the control system. The displacement y (x, t) is calculated using the shape function φ _i (x) and the generalized coordinates q _i (t).

となる。ここで、境界条件により形状関数は

It becomes. Here, the shape function depends on the boundary condition.

となる、１次モードまでを考慮すると状態空間表現は

Considering up to the first-order mode, the state space representation is

ここでω_ｎ、ζ_ｎをｎ次モード固有振動数、減衰係数、ｘ_１、ｌ_ｐを圧電ファイバの左端の座標、長さとすると

Here, ω _n and ζ _n are the n-th mode natural frequency and damping coefficient, and x ₁ and l _p are the coordinates and length of the left end of the piezoelectric fiber.

となる。観測量ははり先端のたわみ角であるため出力方程式は、

It becomes. Since the observed quantity is the deflection angle of the beam tip, the output equation is

となる。

It becomes.

(Derivation of linear fractional transformation (LFT) expression)
Next, a linear fractional transformation (LFT) expression that considers the non-uniformity of the actuator coefficient as a perturbation was derived. Equation (16) is

となる。ここで、

It becomes. here,

である。式（１３）は、

It is. Equation (13) is

と表すことができ、ヒラタらの文献(M. Hirata, K. Z. Liu and T. Mita, Control
Eng. Practice, Vol.4, No.4, pp.545-552, 1996)の記載に従い、

Hirata et al. (M. Hirata, KZ Liu and T. Mita, Control
Eng. Practice , Vol.4, No.4, pp.545-552, 1996)

として、

As

と分解し、

And decompose

とおくと、以下のようなＬＥＴ表現が得られる。

Then, the following LET expression is obtained.

ただし、

However,

である。

It is.

(Control design)
As shown in the generalized plant shown in FIG. 3, external inputs w ₁₁ and w ₁₂ and control inputs z ₁₁ and z ₁₂ are added to the LFT expression obtained by Expression (26), and weight functions W ₁ and W ₁₂ are added. Multiply ₂ to ensure stability against truncated higher order modes and high frequency noise. Furthermore, by introducing a virtual perturbation Δw between z ₁₁ , z ₁₂ to w ₁₁ , w ₁₂ , the robust control performance problem in the μ design method can be reduced to a robust stabilization problem, and a controller can be designed. it can. In FIG. 3, u is a control input, y is an observation output, P is a control target, and δ is a structured perturbation.
(Test example)

(Active vibration control test)
A PZT fiber molded body containing a metal core is extruded from a nozzle attached to an extrusion molding machine at the same time from a nozzle outlet together with a platinum fine wire having a diameter of 50 μm guided from a wire guide and kneaded by adding an appropriate amount of binder and water to the PZT powder. It was prepared by. The extruded fiber was thoroughly dried at room temperature, and then fixed so as not to bend, and sintered in a sintering furnace to produce a piezoelectric fiber having a diameter of about 220 μm. Next, 6-ply with a hot press _{[0 2/90 2/0} 2] (two 0-degree direction unidirectional fiber prepreg (Toray T700S), two 90-degree direction, the two 0-degree direction Laminated piezoelectric fiber is placed on the surface of the CFRP prepreg, and the pressure is 185 ° C. and 0.3 MPa is applied for 2 hours using a hot press, and the piezoelectric fiber placed on the surface is embedded in the CFRP prepreg. Was made.

  The produced smart board 2 was applied to a control test apparatus as shown in FIG. When the bending deformation occurs in the CFRP composite material, the embedded piezoelectric fiber 3 is stretched and deformed, and an electric charge is generated between the CFRP material and the metal core. In the present embodiment, the AD / DA converter 5 performs AD conversion via the voltage follower 4 to take in the personal computer 6. The controller designed as described above was discretized and mounted in 1 ms. A feedback signal for suppressing vibration is calculated using this signal in the personal computer 6. This signal is D / A converted by the AD / DA converter 7, amplified by a single piezo amplifier 8, and applied to all voltage fibers. Thereby, the voltage fiber was used as an actuator. In the present embodiment, AD / DA converters 5 and 7 are ADA16-32 / 2 (PCI) F manufactured by Contec. As the piezo amplifier 5, a piezo driver 4005 manufactured by NF ELECTRONIC INSTRUMENT was used. Further, a laser displacement meter LK-2000 manufactured by Keyence Corporation was used as the laser sensor 9 for measuring displacement data at the tip of the beam.

  5 and 6 show response results in a smart board control test based on the above formulas (1) to (27) using a piezoelectric fiber as a sensor and an actuator. Table 1 shows the parameters of the model in this test example.

  The disturbance is given by applying a voltage of ± 50 V at the primary mode natural frequency for 1 second before starting the control to oscillate. The response at the time of control is indicated by a solid line, and the response at the time of non-control is indicated by a broken line as a comparison. FIG. 5 is a graph showing the displacement of the beam tip. The horizontal axis indicates time (seconds), and the vertical axis indicates displacement (m). What is indicated by the solid line has a smaller displacement width in a shorter time than that indicated by the broken line, and it can be seen that the vibration of the beam is quickly suppressed by the operation of this control system design method. FIG. 6 is a graph showing the sensor output of the piezoelectric fiber. The horizontal axis represents time (seconds), and the vertical axis represents sensor output (V). FIG. 6 shows that although some noise is mixed due to the influence of external high-frequency noise, control can be performed on the controlled input without the control system becoming unstable.

It is explanatory drawing of an example of the coordinate for finite element model introduction | transduction of the piezoelectric fiber containing a metal core. It is data which shows an example of the identification result of each actuator coefficient of the piezoelectric fiber with a non-uniform characteristic. It is process drawing which shows an example of the generalized plant containing LFT and the weight function which considered the non-uniformity of the piezoelectric fiber. It is explanatory drawing of the vibration control test apparatus in a test example. It is a graph which shows the response of the beam tip in the vibration control test of a test example. It is a graph which shows the sensor output response in the vibration control test of a test example.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Piezoelectric fiber 2 Smart board 3 Piezoelectric fiber 4 Voltage follower 5 AD / DA converter 6 Personal computer 7 AD / DA converter 8 Piezo amplifier 9 Laser sensor 10 CFRP board

Claims (4)

  Using a smart board with a metal core embedded piezoelectric fiber as a control target, deriving a finite element model of the control target, obtaining a reduced-order model for control system design, and using the piezoelectric fiber as a sensor or actuator A smart board active vibration control method.   Furthermore, the reduced-order model is converted into a linear fractional transformation (LFT) expression that considers the non-uniformity of the actuator coefficient as a perturbation, and a generalized plant including the obtained LFT expression is configured, and the control system is configured by μ design. The active vibration control method for a smart board according to claim 1, wherein:   3. The smart board active vibration control method according to claim 1, wherein a plurality of metal core-containing piezoelectric fibers are used as actuators and driven by a single piezo amplifier.   4. The smart board active vibration control method according to claim 1, wherein the smart board is formed by embedding a piezoelectric fiber containing a metal core in a carbon fiber reinforced plastic.

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