CN101562409B - Piezoelectric structure damping control object compensation method - Google Patents

Abstract

The invention discloses a piezoelectric structure damping control object compensation method, which comprises the following: step 1, arranging a substrate; step 2, arranging an actuating piece; step 3, arranging a sensing vane; and step 4, adjusting gain g<c>. The damping control method provided by the invention overcomes the defects in the prior art, eliminates the feedback of partial excitation strain of the piezoelectric actuating piece so as to make a mathematic model of a piezoelectric structure return to a theoretical model, has skillful design and simple operation, and can be widely applied in the technical field of structural vibration active control.

Description

Piezoelectric structure damping control object compensation method

(1) technical field

The present invention relates to a kind of piezoelectric structure damping control method, relate in particular to a kind of piezoelectric structure damping control object compensation method, belong to the active control in structural vibration technical field.

(2) background technology

What the piezoelectric structure damping control of putting down in writing in numerous documents at present, was adopted is typical control model---the closed-loop system that negative velocity feedback constitutes.Explain typical control model principle and control method of the present invention with piezoelectric beam as typical structure among the present invention, but this method also is applicable to various other structures.

Fig. 1 is the typical control model sketch map that numerous documents adopt, and is visible from scheming:

1, the lower surface at beam 1 posts a piezoelectric actuating sheet 2, the upper surface same position post same size piezo-electric measurement sheet 3 and after connect operational amplifier 5 and constitute strain rate sensors with resistance 4; This actuator and transducer " coordination " configuration can guarantee to be connected into

2, the stability of the system after the negative velocity feedback.

2, piezoelectric strain rate transducer output u _sThrough gain g _sBack and external excitation voltage u _eSubtract each other, through power amplifier gain g _aBack excitation piezoelectric actuating sheet constitutes closed loop.

The shortcoming and defect that the Typical control method is brought has:

Damping ratio can be along with loop gain g in theory _sg _aAnd increase.But experimental result is really not so satisfactory.Along with g _sg _aIncrease, system but trends towards instability, produces high frequency or the very self-excited vibration of low frequency, and before this modal damping also do not reach expectation than increment requirement as 0.1.

The strain open loop frequency response that observation is surveyed, finding has significantly different with theoretical model:

1. phase-frequency characteristic: behind the pi/2 of resonance region whereabouts, but return to soon and approach zero.

2. amplitude-frequency characteristic: after crossing resonance region is not to decay down with the 40db/oct slope, but returns to an approximate constant always.

(3) summary of the invention

The purpose of this invention is to provide a kind of piezoelectric structure damping control object compensation method, it has overcome deficiency of the prior art, is ingenious, the simple to operate damping control method of a kind of design.

Existing that inventive principle is as described below:

1. foreword

Changing structural damping, always is one of basic assignment of vibration control, the topmost means of vibration suppression especially---increase damping.From traditional strigil and the Passive Control means such as distributed damping material of centralized damper to recent two decades, each means all are to utilize the energy dissipation behavior relevant with the basal body structure deformation velocity of accessory structure to reach the target that increases structural damping.Typical case's representative of classical ACTIVE CONTROL damping is the closed-loop system that constitutes with negative velocity feedback; In single-mode system; Extremely successful in theory and practice, to many-degrees of freedom system, the puzzlement of overflowing and controlling problems such as overflowing can appear observing; Possibly cause controlling deleterious, even loss of stability.

Another central issue of negative velocity feedback damping control is the equipment that what right sensors and actuator is arranged and match.For the large-scale flexible structure, more need large quantities of distributed transducers and actuator.The development of piezoelectric; People have just in time been adapted to for a long time to the requirement of this transducer and actuator hope; Thereby over nearly 20 years, control about negative velocity feedback structure active damping with piezoelectric patches actuator and transducer---the research mushroom development of so-called " electronic damping " is got up.

At first, on the basis of 2 joint piezoelectric structure modelings,, find that the result can not show a candle to the so good of expection so that the local excitation of piezoelectric cantilever---the damping of sensing negative velocity feedback is controlled to be example and launches to discuss.Particularly piezoelectric actuator---the Frequency Response Analysis and the computer simulation experiment of transducer are probed into its reason to experimental phenomena, are " partial excitation strain " interference that this special piezoelectricity " strain excitation---strain-responsive " of piezoelectric structure brings.This has caused our self-examination to 2 joint piezoelectric structure modelings, has proposed qualitatively but enough corrections of practicality at 3.2 joints.Then, 3.3 the joint, the partial excitation strain compensation scheme has been proposed---let the piezoelectric structure Mathematical Modeling revert to 2 the joint theoretical model in go, the damping that the result controls in experiment is greatly improved.

2. the transfer function model of piezoelectric structure

On a structure, paste some piezoelectric patches, utilize the vibrational state of their direct piezoelectric effect measurement structure, call " piezoelectric transducer " to these piezoelectric patches and auxiliary equipment thereof; Paste some piezoelectric patches in addition again and use piezoelectric excitation, its reversed piezoelcetric effect will evoke structural vibration, calls " piezoelectric actuator " to these piezoelectric patches and auxiliary equipment thereof.The mechanical-electric coupling structure that basal body structure, piezoelectric actuator and piezoelectric transducer lump together is called " piezoelectric structure ".

2.1 four types of piezoelectric equations of piezoelectric ceramic piece

The machine of piezoelectrics---electric constitutive relation also is that piezoelectric equations is described the coupled relation between its mechanical quantity (stress T and strain S) and electrical quantities (electric field strength E and electric displacement D).This joint will be derived four types of piezoelectric equations of the piezoelectric ceramic piece of using in theoretical and the experimental study (belonging to 6mm point group crystal).

If piezoelectric sheet plane internal coordinate is x, y, normal direction also is that polarised direction is z.To be main with the symbol of habitually practising in the mechanical analysis herein, but analyze in the argumentation that piezoelectric patches is the master at Ben Jie and later on relevant chapters and sections, be the original appearance that keeps the piezoelectrics analysis, analyzes the general symbol in the document with continuing to use piezoelectrics, and the two table of comparisons is following:

	Axle	Stress	Strain
				From the mechanics angle	x?y?z	σ x?σ y?σ z?τ yz?τ zx?τ xy	ε x?ε y?ε z?γ yz?γ zx?γ xy
From the piezoelectricity angle	1?2?3	T 1?T 2?T 3?T 4?T 5?T 6	S 1?S 2?S 3?S 4?S 5?S 6

Piezoelectric ceramic has 2 kinds of piezoelectric effect equations the most basic as 6mm point group crystal; One of which, electrical short (E ₁=E ₂=E ₃=0) direct piezoelectric effect under the condition

$\left[\begin{array}{c}{D}_1\\ D_2\\ D_3\end{array}\right]=\left[\begin{array}{cccccc}0& 0& 0& 0& {\mathrm{<figure-callout\; id="15"\; label="d"\; filenames="H2009100840041E00023.png"\; state="\{\{state\}\}">d</figure-callout>}}_{15}& 0\\ 0& 0& 0& d_{25}& 0& 0\\ d_{31}& d_{32}& d_{33}& 0& 0& 0\end{array}\right]\left[\begin{array}{c}{T}_1\\ T_2\\ T_3\\ T_4\\ T_5\\ {\mathrm{<figure-callout\; id="6"\; label="T"\; filenames="H2009100840041E00012.png"\; state="\{\{state\}\}">T</figure-callout>}}_6\end{array}\right],({\mathrm{<figure-callout\; id="1"\; label="E"\; filenames="H2009100840041E00011.png"\; state="\{\{state\}\}">E</figure-callout>}}_1=E_2=E_3=0)---(2-1)$

Its two, the free (T of mechanics _i=0, the i=1-6) inverse piezoelectric effect under the condition

$\left[\begin{array}{c}{S}_1\\ S_2\\ S_3\\ S_4\\ S_5\\ {\mathrm{<figure-callout\; id="6"\; label="S"\; filenames="H2009100840041E00012.png"\; state="\{\{state\}\}">S</figure-callout>}}_6\end{array}\right]=\left[\begin{array}{ccc}0& 0& d_{31}\\ 0& 0& d_{32}\\ 0& 0& d_{33}\\ 0& d_{25}& 0\\ {\mathrm{<figure-callout\; id="15"\; label="d"\; filenames="H2009100840041E00023.png"\; state="\{\{state\}\}">d</figure-callout>}}_{15}& 0& 0\\ 0& 0& 0\end{array}\right]\left[\begin{array}{c}{E}_1\\ E_2\\ E_3\end{array}\right],(T_i=0,i=1-6)---(2-2)$

E wherein _iAnd D _iBe respectively inside field intensity and the pole-face electric displacement of piezoelectrics, d along the i axle _IjPiezoelectric constant for relevant i and j axle has

d _p＝d ₃₁＝d ₃₂ (2-3)

Wherein subscript p indicates " piezoelectric patches ", and this paper will continue to use this subscript later always.

2 dimension piezoelectric patches for we are concerned about have

T ₃=0 and E ₁=E ₂=0 (2-4)

And we also only are concerned about D ₃, S ₁And S ₂, equation (2-1) (2-2) becomes

D ₃＝d ₃₁T ₁+d ₃₂T ₂＝d _p(T ₁+T ₂)(E ₃＝0) (2-5)

$\left[\begin{array}{c}{S}_1\\ S_2\end{array}\right]=\left[\begin{array}{c}{d}_{31}\\ d_{32}\end{array}\right]E_3=\left[\begin{array}{c}{d}_p\\ d_p\end{array}\right]E_3,({\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="H2009100840041E00011.png"\; state="\{\{state\}\}">T</figure-callout>}}_1=T_2=0)---(2-6)$

At the free (T of mechanics ₁=T ₂=0) under the condition, piezoelectric sheet also has the dielectric equation as a common electric capacity

$D_3={\mathrm{\&epsiv;}}_p^T{E}_3,({\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="H2009100840041E00011.png"\; state="\{\{state\}\}">T</figure-callout>}}_1=T_2=0)---(2-7)$

ε wherein _p ^TBe the free (T of mechanics ₁=T ₂=0, by subscript T sign) dielectric coefficient under the condition

As elastomeric piezoelectric sheet, electrical short (E is arranged ₃=0) elastic constitutive relation under the condition

$\left[\begin{array}{c}{S}_1\\ S_2\end{array}\right]=\frac{1}{E_p}\left[\begin{array}{cc}1& -{\mathrm{\&mu;}}_p\\ -{\mathrm{\&mu;}}_p& 1\end{array}\right]\left[\begin{array}{c}{T}_1\\ T_2\end{array}\right],(E_3=0)---(2-8)$

E wherein _pAnd μ _pBe respectively the modulus of elasticity and the Poisson's ratio of piezoelectric patches.

In conjunction with equation (2-5)---(2-8), obtain the machine of piezoelectric patches---the electric coupling constitutive equation

$\left[\begin{array}{c}{S}_1\\ S_2\\ D_3\end{array}\right]=\left[\begin{array}{ccc}\frac{1}{E_p}& \frac{-{\mathrm{\&mu;}}_p}{E_p}& d_p\\ \frac{-{\mathrm{\&mu;}}_p}{E_p}& \frac{1}{E_p}& d_p\\ d_p& d_p& {\mathrm{\&epsiv;}}_p^T\end{array}\right]\left[\begin{array}{c}{T}_1\\ T_2\\ E_3\end{array}\right]---(2-9)$

It has reflected 6 amount (4 mechanical quantity T of piezoelectric patches all sidedly ₁, T ₂, S ₁, S ₂With 2 electrical quantities D ₃And E ₃) between coupled relation, both comprised direct piezoelectric effect, comprised inverse piezoelectric effect again.

In different occasions, with different independents variable and dependent variable with more convenient.For this reason, call first kind piezoelectric equations to equation (2-9); Therefrom, can also lead with its other of equal value three types of piezoelectric equations.

Second type of piezoelectric equations

$\left[\begin{array}{c}{T}_1\\ T_2\\ D_3\end{array}\right]=\left[\begin{array}{ccc}\frac{E_p}{1-{\mathrm{\&mu;}}_p^2}& \frac{{\mathrm{\&mu;}}_p{E}_p}{1-{\mathrm{\&mu;}}_p^2}& -e_p\\ \frac{{\mathrm{\&mu;}}_p{E}_p}{1-{\mathrm{\&mu;}}_p^2}& \frac{E_p}{1-{\mathrm{\&mu;}}_p^2}& -e_p\\ e_p& e_p& {\mathrm{\&epsiv;}}_p^S\end{array}\right]\left[\begin{array}{c}{S}_1\\ S_2\\ E_3\end{array}\right]---(2-10)$

Piezoelectric modulus wherein

$e_p=\frac{E_p{d}_p}{1-{\mathrm{\&mu;}}_p}---(2-11)$

And

${\mathrm{\&epsiv;}}_p^S={\mathrm{\&epsiv;}}_p^T-2e_p{d}_p={\mathrm{\&epsiv;}}_p^T-\frac{2E_p{d}_p^2}{1-{\mathrm{\&mu;}}_p}---(2-12)$

For piezoelectric patches at clamping (S ₁=S ₂=0, with subscript S sign) dielectric constant under the condition.

The 3rd type of piezoelectric equations

$\left[\begin{array}{c}{S}_1\\ S_2\\ E_3\end{array}\right]=\left[\begin{array}{ccc}\frac{1}{E_p}-\frac{d_p^2}{{\mathrm{\&epsiv;}}_p^T}& \frac{-{\mathrm{\&mu;}}_p}{E_p}-\frac{d_p^2}{{\mathrm{\&epsiv;}}_p^T}& g_p\\ \frac{-{\mathrm{\&mu;}}_p}{E_p}-\frac{d_p^2}{{\mathrm{\&epsiv;}}_p^T}& \frac{1}{E_p}-\frac{d_p^2}{{\mathrm{\&epsiv;}}_p^T}& g_p\\ -g_p& -{\mathrm{<figure-callout\; id="1"\; label="g\; p"\; filenames="H2009100840041E00011.png"\; state="\{\{state\}\}">g</figure-callout>}}_p& \frac{1}{{\mathrm{\&epsiv;}}_p^T}\end{array}\right]\left[\begin{array}{c}{T}_1\\ T_2\\ D_3\end{array}\right]---(2-13)$

Piezoelectric modulus wherein

$g_p=\frac{d_p}{{\mathrm{\&epsiv;}}_p^T}---(2-14)$

The 4th type of piezoelectric equations

$\left[\begin{array}{c}{T}_1\\ T_2\\ E_3\end{array}\right]=\left[\begin{array}{ccc}\frac{E_p}{1-{\mathrm{\&mu;}}_p^2}+\frac{e_p^2}{{\mathrm{\&epsiv;}}_p^S}& \frac{{\mathrm{\&mu;}}_p{E}_p}{1-{\mathrm{\&mu;}}_p^2}+\frac{e_p^2}{{\mathrm{\&epsiv;}}_p^S}& -h_p\\ \frac{{\mathrm{\&mu;}}_p{E}_p}{1-{\mathrm{\&mu;}}_p^2}+\frac{e_p^2}{{\mathrm{\&epsiv;}}_p^S}& \frac{E_p}{1-{\mathrm{\&mu;}}_p^2}+\frac{e_p^2}{{\mathrm{\&epsiv;}}_p^S}& -h_p\\ -h_p& -{\mathrm{<figure-callout\; id="1"\; label="h\; p"\; filenames="H2009100840041E00011.png"\; state="\{\{state\}\}">h</figure-callout>}}_p& \frac{1}{{\mathrm{\&epsiv;}}_p^S}\end{array}\right]\left[\begin{array}{c}{S}_1\\ S_2\\ D_3\end{array}\right]---(2-15)$

Piezoelectric modulus wherein

$h_p=\frac{e_p}{{\mathrm{\&epsiv;}}_p^S}=\frac{E_p{d}_p}{{\mathrm{\&epsiv;}}_p^S(1-{\mathrm{\&mu;}}_p)}---(2-16)$

Piezoelectric patches is usually used in the one-dimensional stress structure like beam and so on, T ₂≡ 0, and corresponding four types of piezoelectric equations become

$\left[\begin{array}{c}{S}_1\\ D_3\end{array}\right]=\left[\begin{array}{cc}\frac{1}{E_p}& d_p\\ d_p& {\mathrm{\&epsiv;}}_p^T\end{array}\right]\left[\begin{array}{c}{T}_1\\ E_3\end{array}\right]$ (first kind T ₂≡ 0) (2-17)

$\left[\begin{array}{c}{T}_1\\ D_3\end{array}\right]=\left[\begin{array}{cc}{E}_p& -e_p\\ e_p& {\mathrm{\&epsiv;}}_p^S\end{array}\right]\left[\begin{array}{c}{S}_1\\ E_3\end{array}\right]$ (second type of T ₂≡ 0) (2-18)

$\left[\begin{array}{c}{S}_1\\ E_3\end{array}\right]=\left[\begin{array}{cc}\frac{1}{E_p}\frac{{\mathrm{\&epsiv;}}_p^S}{{\mathrm{\&epsiv;}}_p^T}& g_p\\ -{\mathrm{<figure-callout\; id="1"\; label="g\; p"\; filenames="H2009100840041E00011.png"\; state="\{\{state\}\}">g</figure-callout>}}_p& \frac{1}{{\mathrm{\&epsiv;}}_p^T}\end{array}\right]\left[\begin{array}{c}{T}_1\\ D_3\end{array}\right]$ (the 3rd type of T ₂≡ 0) (2-19)

$\left[\begin{array}{c}{T}_1\\ E_3\end{array}\right]\left[\begin{array}{cc}\frac{1}{E_p}\frac{{\mathrm{\&epsiv;}}_p^T}{{\mathrm{\&epsiv;}}_p^S}& -h_p\\ -{\mathrm{<figure-callout\; id="1"\; label="h\; p"\; filenames="H2009100840041E00011.png"\; state="\{\{state\}\}">h</figure-callout>}}_p& \frac{1}{{\mathrm{\&epsiv;}}_p^S}\end{array}\right]\left[\begin{array}{c}{S}_1\\ D_3\end{array}\right]$ (the 4th type of T ₂≡ 0) (2-20)

Wherein

e _p＝E _pd _p (2-21)

$g_p=d_p/{\mathrm{\&epsiv;}}_p^T---(2-22)$

$h_p=e_p/{\mathrm{\&epsiv;}}_p^S=\frac{E_p{d}_p}{{\mathrm{\&epsiv;}}_p^S}---(2-23)$

${\mathrm{\&epsiv;}}_p^S={\mathrm{\&epsiv;}}_p^T-e_p{d}_p={\mathrm{\&epsiv;}}_p^T-E_p{d}_p^2---(2-24)$

2.2 two kinds of piezoelectric ceramic piece strain transducers

See Fig. 3 c, establish piezoelectric patches two interpolars and constitute the loop through resistance R.By the 4th type of piezoelectric equations (2-15), field intensity does in the piezoelectric patches

$E_3\left(t\right)=-h_p(S_1\left(t\right)+S_2\left(t\right))+D_3\left(t\right)/{\mathrm{\&epsiv;}}_p^S---(2-25)$

Output voltage does

$u_p\left(t\right)={\mathrm{\&delta;}}_p{E}_3\left(t\right)=-{\mathrm{\&delta;}}_p{h}_p(S_1\left(t\right)+S_2\left(t\right))+({\mathrm{\&delta;}}_p/{\mathrm{\&epsiv;}}_p^S)D_3\left(t\right)---(2-26)$

δ wherein _pBe piezoelectric patches thickness.The electric current that the unit are piezoelectric patches provides does

$i\left(t\right)=-{\stackrel{\&CenterDot;}{D}}_3\left(t\right)=\frac{u_p\left(t\right)}{R}=\frac{-{\mathrm{\&delta;}}_p{h}_p}{R}(S_1\left(t\right)+S_2\left(t\right))+\frac{{\mathrm{\&delta;}}_p}{{\mathrm{\&epsiv;}}_p^{S}R}{D}_3\left(t\right)---(2-27)$

Therefrom can be about electric displacement D ₃(t) differential equation of first order

$\frac{R{\mathrm{\&epsiv;}}_p^S}{{\mathrm{\&delta;}}_p}{\stackrel{\&CenterDot;}{D}}_3\left(t\right)+D_3\left(t\right)={\mathrm{\&epsiv;}}_p^S{h}_p(S_1\left(t\right)+S_2\left(t\right))---(2-28)$

Separating in frequency domain is (in this article, a variable will adopt prosign at time domain t in frequency domain ω or the Laplace territory s)

$D_3\left(\mathrm{j\&omega;}\right)=\frac{h_p{\mathrm{\&epsiv;}}_{\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="H2009100840041E00011.png"\; state="\{\{state\}\}">p</figure-callout>}}^S}{1+\mathrm{j\&omega;}\frac{R{\mathrm{\&epsiv;}}_p^S}{{\mathrm{\&delta;}}_p}}(S_1\left(\mathrm{j\&omega;}\right)+S_2\left(\mathrm{j\&omega;}\right))---(2-29)$

In generation, returned (2-27), obtains in frequency domain

$i\left(\mathrm{j\&omega;}\right)=-\mathrm{j\&omega;}{D}_3\left(\mathrm{j\&omega;}\right)=\frac{-\mathrm{j\&omega;}{h}_p{\mathrm{\&epsiv;}}_{\mathrm{<figure-callout\; id="1"\; label="p\; S"\; filenames="H2009100840041E00011.png"\; state="\{\{state\}\}">p</figure-callout>}}^S}{1+\mathrm{j\&omega;}\frac{R{\mathrm{\&epsiv;}}_p^S}{{\mathrm{\&delta;}}_p}}(S_1\left(\mathrm{j\&omega;}\right)+S_2\left(\mathrm{j\&omega;}\right))---(2-30)$

Consider two kinds of special cases.One of which, R=0 has (noting equation 2-16)

i(jω)＝-jωe _p(S ₁(jω)+S ₂(jω)) (2-31)

$i\left(t\right)=-e_p({\stackrel{\&CenterDot;}{S}}_1\left(t\right)+{\stackrel{\&CenterDot;}{S}}_2\left(t\right))$

The electric current that piezoelectric patches provides is directly proportional with its strain rate sum along 1 and 2; Its two, R is very big, so that in frequency domain, have

$\mathrm{\&omega;}\frac{R{\mathrm{\&epsiv;}}_p^S}{{\mathrm{\&delta;}}_p}>>1---(2-32)$

Equation (2-30) is approximately

$i\left(\mathrm{j\&omega;}\right)\&ap;\frac{-{\mathrm{\&delta;}}_p{h}_p}{R}(S_1\left(\mathrm{j\&omega;}\right)+S_2\left(\mathrm{j\&omega;}\right))---(2-33)$

$i\left(t\right)\&ap;\frac{-{\mathrm{\&delta;}}_p{h}_p}{R}(S_1\left(t\right)+S_2\left(t\right))$

The electric current that piezoelectric patches provides is directly proportional with its normal strain sum along 1 and 2

Equation (2-30) or (2-31) with (2-33) constituted the basis of piezoelectric patches as structural strain rate or strain transducer.

If paste piezoelectric patches on the structure " ideal "---the local strain facies that so-called " the desirable stickup " is meant strain that piezoelectric patches pastes the face place and structure is together; It is very thin to establish piezoelectric patches again, can ignore the variation of its strain along thickness, like this, and the strain S in the piezoelectric patches plane domain ₁And S ₂Respectively with the local strain stress of structure _xAnd ε _yConsistent

S ₁(x，y，t)＝ε _x(x，y，t) S ₂(x，y，t)＝ε _y(x，y，t) (2-34)

2.2.1 piezoelectric strain rate transducer

Directly receive piezoelectric patches the negative input end of a linear operational amplifier and (see Fig. 3 a).Because negative input end is " virtual earth ", current potential is approximately zero, so the approximate establishment of equation (2-31), and the amplifier output voltage does

$u_s\left(t\right)=-R_f{\&Integral;\&Integral;}_{{\mathrm{\&Omega;}}_S}i(x,y,t)\mathrm{dxdy}=R_f{e}_p{\&Integral;\&Integral;}_{{\mathrm{\&Omega;}}_S}({\stackrel{\&CenterDot;}{\mathrm{\&epsiv;}}}_x(x,y,t)+{\stackrel{\&CenterDot;}{\mathrm{\&epsiv;}}}_y(x,y,t))\mathrm{dxdy}---(2-35)$

R wherein _fBe amplifier feedback resistance, Ω _sThe structural region that spreads all over for piezoelectric patches; It shows: piezoelectric patches---the amplifier combination is as " strain rate sensor " of structure; Output voltage is proportional to the integration of the local normal strain rate sum of structure; When enough hour of patch area, will be tending towards directly being proportional to structure when place normal strain rate sum.

2.2.2 piezoelectric strain transducer

The negative input end (see Fig. 3 b) of piezoelectric patches through a big resistance R access amplifier, the piezoelectric patches situation will be as Fig. 3 c, and under condition (2-32), the amplifier output voltage does

$u_s\left(t\right)=-R_f{\&Integral;\&Integral;}_{{\mathrm{\&Omega;}}_s}i(x,y,t)\mathrm{dxdy}$

$=\frac{{\mathrm{\&delta;}}_p{h}_p{R}_f}{R}{\&Integral;\&Integral;}_{{\mathrm{\&Omega;}}_s}({\mathrm{\&epsiv;}}_x(x,y,t)+{\mathrm{\&epsiv;}}_y(x,y,t))\mathrm{dxdy},(\frac{\mathrm{\&omega;R}{\mathrm{\&epsiv;}}_p^S}{{\mathrm{\&delta;}}_p}>>1)---(2-36)$

It shows: piezoelectric patches---amplifier combination is as " strain transducer " of structure, and output voltage is proportional to the integration of the local normal strain sum of structure, when enough hour of patch area, will be tending towards directly being proportional to when place normal strain sum.

Because the input impedance of amplifier positive input terminal is very big, therefore directly receive piezoelectric patches the positive input terminal (seeing Fig. 3 b) of amplifier, also will constitute strain transducer.

For one-dimensional stress structure (T ₂(x, t)=σ _y(x, t)=0), output is respectively with (2-36) strain transducer corresponding to the strain rate of equation (2-35)

$u_s\left(t\right)\&ap;b_p{R}_f{e}_p{\&Integral;}_{{\mathrm{\&Omega;}}_s}{\stackrel{\&CenterDot;}{\mathrm{\&epsiv;}}}_x(x,t)\mathrm{dx}---(2-37)$

$u_s\left(t\right)\&ap;\frac{b_p{\mathrm{\&delta;}}_p{h}_p{R}_f}{R}{\&Integral;}_{{\mathrm{\&Omega;}}_s}{\mathrm{\&epsiv;}}_x(x,t)\mathrm{dx}---(2-38)$

B wherein _pBe the piezoelectric patches width.Note piezoelectric constant e wherein _pAnd h _pConfirm by equation (21-24).

2.3 the transfer function model of piezoelectric beam

We will paste some piezoelectric patches on structure to be controlled, utilize its direct piezoelectric effect to make structural strain or strain rate sensor (" piezoelectric transducer "); Simultaneously, paste some piezoelectric patches again in addition and receive voltage drive, utilize its inverse piezoelectric effect as actuator (" piezoelectric actuator ").In this article, call " piezoelectric structure " to this structure that has piezoelectric transducer and actuator simultaneously, like " piezoelectric beam ", " piezoelectric board " etc.

Beam because of its mechanical model is simple, has the analytic solutions of succinct explicit physical meaning as the most basic a kind of continuous structure, usually selected basic research object as the development of novel vibrating control technology; In addition, have a large amount of flexible structures also can be classified as the category of beam really in the actual engineering, therefore, the modeling of piezoelectric beam and vibration control become one of research topic that people pay close attention to the most, development is also comparatively ripe.But be noted that the present invention discusses with beam as an example, the method for this invention is applicable to other various structures, and just the theoretical modeling of structure has difference.

2.3.1 the piezoelectric actuator analysis on the beam

Consult Fig. 4, length and width and the height of establishing beam are respectively L, and b and h correspond respectively to x, y and z axle.Be located at the latitude of emulsion (x of beam ₁, x ₂) respectively to post a width be b to interior upper and lower surfaces _p, thickness is δ _pPiezoelectric ceramic piece, polarised direction is all along positive z axle, simultaneously extrinsic motivated voltage u _a(t).

If beam is the Bernoulli-Euller beam.Because beam is one-dimensional stress structure (σ _y(t) ≡ 0 for x, z), so piezoelectric patches is also located one-dimensional stress state (T ₂(x, t) ≡ 0), according to second type of piezoelectric equations (2-18), upper surface piezoelectric patches section stress does

T ₁＝E _pS ₁-e _pE ₃(e _p＝E _pd _p) (2-39)

Field intensity in the piezoelectric patches wherein

E ₃＝u _a/δ _p (2-40)

If (the consulting condition 2-34) that piezoelectric patches is pasted at Liang Shangshi " ideal ", the upper surface strain of beam does

ε _x0＝ε _x| _z＝h/2＝S ₁ (2-41)

It with (2-40) together for returning (2-39), have

${\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="H2009100840041E00011.png"\; state="\{\{state\}\}">T</figure-callout>}}_1=E_p{\mathrm{\&epsiv;}}_{x0}-\frac{E_p{d}_p}{{\mathrm{\&delta;}}_p}{u}_a---(2-42)$

Can know that by symmetry lower surface piezoelectric patches section stress is-T ₁Thereby piezoelectric patches to the excitation moment of flexure of beam does

$M=-\left(T_1{b}_p{\mathrm{\&delta;}}_p\right)h=-E_p{b}_p{\mathrm{\&delta;}}_{p}h{\mathrm{\&epsiv;}}_{x0}+\frac{h{b}_p{E}_p{d}_p}{{\mathrm{\&delta;}}_p}{u}_a---(2-43)$

Above-mentioned excitation moment is converted the cross section moment of flexure of beam

$M=\frac{2\mathrm{EI}{\mathrm{\&epsiv;}}_{x0}}{h},(I=\frac{1}{12}b{h}^3)---(2-44)$

Wherein E and I are respectively the modulus of elasticity and the cross section moments of inertia of beam.Couplet is solved an equation (2-43) and (2-44) is had

$M\left(t\right)=\frac{h{b}_p{E}_{\mathrm{<figure-callout\; id="1"\; label="p\; d\; p"\; filenames="H2009100840041E00011.png"\; state="\{\{state\}\}">p</figure-callout>}}{d}_p{}_{}}{1+6\frac{E_p{\mathrm{\&delta;}}_p{b}_p}{\mathrm{Ehb}}}{u}_a\left(t\right)---(2-45)$

Equation (2-45) shows

(1) because u _a(t) do not become, so the cross section of piezoelectric actuator excitation moment M (t) do not become with x yet, be the beam latitude of emulsion (x that spreads all at piezoelectric patches with coordinate x ₁, x ₂) interior even moment; Perhaps, also can be regarded as x at the piezoelectric patches two ends ₁And x ₂The place has applied a pair of reverse moment M (t) (see figure 4).

(2) fillip of piezoelectric actuator size is removed its piezoelectric constant of direct direct ratio d _pDepend on that also section rigidity between piezoelectric patches and beam is than (Rigidity Matching) outward.Elastic modulus E _pBigger piezoelectric ceramic piece is much littler that piezoelectric membrane (PVDF) has bigger driving force than modulus of elasticity, this just we to select piezoelectric ceramic piece for use be one of fundamental cause of actuator.

2.3.2 the infinitesimal piezoelectric actuator is to the transfer function of transducer

According to the modal theory of beam, the amount of deflection of beam expands into by its natural mode of vibration

$w(x,t)=\underset{r=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{\mathrm{\&Phi;}}_r\left(x\right)q_r\left(t\right)---(2-46)$

Φ wherein _r(x) and q _r(t) be respectively r rank natural mode of vibration and corresponding modal coordinate, its equation of motion in Laplace territory (s) does

$q_r\left(s\right)=\frac{f_r\left(s\right)}{m_r{s}^2+k_r}---(2-47)$

M wherein _r, k _r, f _r(s) be respectively r rank modal mass, rigidity and mode generalized force.

Impose on x=x _aAnd x=x _a+ dx _aThe mode generalized force that a pair of opposing torque M (t) at place produces

$f_r(x_a,t)=M\left(t\right)({\mathrm{\&Phi;}}_r^x(x_a+d{x}_a)-{\mathrm{\&Phi;}}_r^x\left(x_a\right))=M\left(t\right){\mathrm{\&Phi;}}_r^{\mathrm{xx}}\left(x_a\right)d{x}_a---(2-48)$

Wherein subscript x representative is to the x differentiate; In generation, returned (2-47) and (2-46), and the response of beam in the Laplace territory does

$w(x,x_a,s)=\underset{r=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&Phi;}}_r\left(x\right)f_r(x_a,t)}{m_r{s}^2+k_r}=M\left(s\right)d{x}_a\underset{r=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&Phi;}}_r\left(x\right){\mathrm{\&Phi;}}_r^{\mathrm{xx}}\left(x_a\right)}{m_r{s}^2+k_r}---(2-49)$

Be located at x=x at present _aThe a pair of wide b that is is posted at the place _p, long is dx _aPiezoelectric actuator, according to the analysis of 2.3.1 joint,, just can obtain the response of beam to piezoelectric actuator as long as equation (2-45) substitution (2-49)

$w(x,x_a,s)=\frac{h{E}_{\mathrm{<figure-callout\; id="1"\; label="p\; d\; p"\; filenames="H2009100840041E00011.png"\; state="\{\{state\}\}">p</figure-callout>}}{d}_p{}_{}}{1+6\frac{E_p{\mathrm{\&delta;}}_p{b}_p}{\mathrm{Ehb}}}\left(b_{p}d{x}_a\right)u_a\left(s\right)\underset{r=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&Phi;}}_r\left(x\right){\mathrm{\&Phi;}}_r^{\mathrm{xx}}\left(x_a\right)}{m_r{s}^2+k_r}---(2-50)$

Accordingly, the surface strain of beam does

${\mathrm{\&epsiv;}}_{x0}(x,x_a,s)=\frac{h}{2}{w}^{\mathrm{xx}}(x,x_a,s)---(2-51)$

Be located at x=x at present _sA wide b of being is posted at the place _Ps, thick is δ _Ps, long is dx _s(δ wherein _Ps, h _PsDeng the subscript s in variable sign " piezoelectric transducer ", with the respective amount difference of piezoelectric actuator) the infinitesimal piezoelectric patches and after connect amplifier and constitute piezoelectric strain transducer (Fig. 3 b), according to equation (2-38), (2-51) with sensor output voltage (2-50) is arranged

$u_s\left(s\right)=\frac{{\mathrm{\&delta;}}_{\mathrm{ps}}{h}_{\mathrm{ps}}{R}_f}{R}{\mathrm{\&epsiv;}}_{x0}(x_s,x_a,s)b_{\mathrm{ps}}d{x}_s$

$=\mathrm{\&alpha;}{u}_a\left(s\right)\underset{r=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&Phi;}}_r^{\mathrm{xx}}\left(x_s\right){\mathrm{\&Phi;}}_r^{\mathrm{xx}}\left(x_a\right)}{m_r{s}^2+k_r}\left(b_{\mathrm{ps}}d{x}_s\right)\left(b_{p}d{x}_a\right)---(2-52)$

Wherein

$\mathrm{\&alpha;}=\frac{h{\mathrm{\&delta;}}_{\mathrm{ps}}{h}_{\mathrm{ps}}{R}_f}{2R}\frac{h{E}_{\mathrm{<figure-callout\; id="1"\; label="p\; d\; p"\; filenames="H2009100840041E00011.png"\; state="\{\{state\}\}">p</figure-callout>}}{d}_p{}_{}}{1+6\frac{E_p{b}_p{h}_p}{\mathrm{Ehb}}}---(2-53)$

Hence one can see that, from unit are (b _pDx _a=1) the driving voltage u of piezoelectric actuator _aTo unit are (b _PsDx _s=1) the output voltage u of piezoelectric transducer _sTransfer function do

$H(x_s,x_a,s)=\frac{u_s\left(s\right)}{u_a\left(s\right)}=\mathrm{\&alpha;}\underset{r=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&Phi;}}_r^{\mathrm{xx}}\left(x_s\right){\mathrm{\&Phi;}}_r^{\mathrm{xx}}\left(x_a\right)}{m_r{s}^2+k_r}---(2-54)$

In like manner, if usefulness be that (Fig. 3 a) will have piezoelectric strain rate transducer

$H(x_s,x_a,s)=\frac{u_s\left(s\right)}{u_a\left(s\right)}={\mathrm{\&alpha;}}_v\underset{r=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&Phi;}}_r^{\mathrm{xx}}\left(x_s\right){\mathrm{\&Phi;}}_r^{\mathrm{xx}}\left(x_a\right)}{m_r{s}^2+k_r}---(2-55)$

Wherein

${\mathrm{\&alpha;}}_v=\frac{-h{R}_f{e}_{\mathrm{ps}}}{2}\frac{h{E}_{\mathrm{<figure-callout\; id="1"\; label="p\; d\; p"\; filenames="H2009100840041E00011.png"\; state="\{\{state\}\}">p</figure-callout>}}{d}_p{}_{}}{1+6\frac{E_p{b}_p{\mathrm{\&delta;}}_p}{\mathrm{Ehb}}}---(2-56)$

2.3.3 the finite size piezoelectric actuator is to the transfer function of transducer

Establish piezoelectric actuating sheet and vane all is finite size at present, parameter d _p, b _p, d _Ps, b _PsDeng not becoming with beam coordinate x.According to equation (2-54), the transfer function from finite size piezoelectric patches actuator to finite size piezoelectric patches strain transducer does

$H({\mathrm{\&Omega;}}_s,{\mathrm{\&Omega;}}_a,s)=\frac{u_s\left(s\right)}{u_a\left(s\right)}=\mathrm{\&alpha;}{b}_{\mathrm{ps}}{b}_p{\&Integral;}_{{\mathrm{\&Omega;}}_s}d{x}_s{\&Integral;}_{{\mathrm{\&Omega;}}_a}H(x_s,x_a,s)d{x}_a$

Wherein

Ω _s, Ω _aRepresent the zone of piezoelectric sensing sheet and the beam that spreads all over as moving plate respectively.If usefulness is strain rate sensor, have accordingly

3 piezoelectric structure damping controls and partial excitation strain compensation

3.1 the local negative velocity feedback damping control of piezoelectric beam experimental exploring

Fig. 5 is the typical control model that numerous documents adopt, and has also provided detailed diagram in the background technology part, will do quantitative explanation here, so that better understand the argumentation in the background technology part.

Modeling according to 2 joint beams has open-loop transfer function equation (equation 2-59)

square journey (2-58) wherein.A is the beam zone that piezoelectric actuating sheet and vane spread all over.Being that the upper and lower surfaces of beam respectively pastes one and makes moving plate when noting 2 joint modelings, is only to paste a slice at lower surface here, but from the overall bending response of beam, is equivalent to the alpha of equation (3-1) _vReduce by half.

Press the control block diagram on Fig. 5 the right, can be in the hope of doing to closed loop transfer function,

${\stackrel{\&OverBar;}{H}}_v\left(s\right)=\frac{u_s\left(s\right)}{u_e\left(s\right)}=\frac{g_a{H}_v\left(s\right)}{1+H_v\left(s\right)g_a{g}_s}---(3-2)$

If each rank mode natural frequency of beam disperses the natural frequency Ω on the r rank _rContiguous, the response of all the other each rank mode can be ignored, thereby has

Generation is returned (3-2) to be had

This shows that r rank mode has increased damping coefficient

Or damping ratio

Along with loop gain g _sg _aAnd increase, it seems it is very desirable.

But experimental result is really not so satisfactory.Along with g _sg _aIncrease, system but trends towards instability, produces high frequency or the very self-excited vibration of low frequency, and before this modal damping also do not reach expectation than increment requirement as 0.1.

It and theoretical model are found in the strain open loop frequency response (Fig. 6 b) that observation is surveyed

H(jω)＝H _v(jω)/jω (3-7)

(see that Fig. 6 a) has a remarkable difference:

(1) phase-frequency characteristic: behind the pi/2 of resonance region whereabouts, but return to soon and approach zero.

(2) amplitude-frequency characteristic: after crossing resonance region is not to decay down with the 40db/oct slope, but returns to an approximate constant always.

To piezoelectric actuator particularly the modeling of transducer analyze again and computer simulation experiment; Show that this difference derives from the interference of actuator partial excitation strain to the strain of piezo-electric measurement sheet, and this of retraining just that the closed-loop system feedback oscillator can not improve important reasons very.

3.2 self-examination and correction to the piezoelectric structure modeling

When 2 joint piezoelectric structure modelings, we have continued to use traditional excitation in fact---and a kind of acquiescence of sensing pattern: actuator encourages the local deformation that only produces the structural strain's of structure and ignore application of force place; Transducer is only experienced the structural strain's of structure and is ignored the influence that the coordination actuator encourages the local deformation that produces.For traditional power or basic excitation---accelerometer response and so on, this hypothesis are enough reasonably really,---piezoelectric sensing sheet this " strain excitation---strain sensing now at the piezoelectric actuating sheet " new situation under, just possibly become problem.

With the piezoelectric beam is example, piezoelectric actuating sheet strain stress _aIn comprise two parts

ε _a＝-ε _m+ε _ta (3-8)

ε wherein _mBe the overall bending strain response of beam, and ε _TaIt is the partial excitation strain component that produces as driving source because of it.The strain stress of piezoelectric sensing sheet _sAlso comprise corresponding two parts

ε _s＝ε _m+ε _ts (3-9)

ε wherein _TsBe that it is to piezoelectric actuating sheet partial excitation strain ε _TaThe response that comes through structure-borne.Like this, from voltage for piezoelectric actuation u _aTo strain transducer ε _sTransfer function do

$H_{\mathrm{\&epsiv;}}\left(s\right)=\frac{{\mathrm{\&epsiv;}}_s\left(s\right)}{u_a\left(s\right)}=\frac{{\mathrm{\&epsiv;}}_m\left(s\right)}{u_a\left(s\right)}+\frac{{\mathrm{\&epsiv;}}_{\mathrm{ts}}\left(s\right)}{u_a\left(s\right)}=\frac{{\mathrm{\&epsiv;}}_m\left(s\right)}{u_a\left(s\right)}+\frac{{\mathrm{\&epsiv;}}_{\mathrm{ts}}\left(s\right)}{{\mathrm{\&epsiv;}}_{\mathrm{ta}}\left(s\right)}\frac{{\mathrm{\&epsiv;}}_{\mathrm{ta}}\left(s\right)}{u_a\left(s\right)}---(3-10)$

First wherein is equivalent to save the transfer function that obtains in the modelings 2; Factor ε in the second portion _Ta(s)/u _a(s) depend on the drive characteristic of piezoelectric actuating sheet, can be considered constant; And another factor ε _Ts(s)/ε _Ta(s) then depend on the propagation characteristic of stress wave in structure, relevant with vane with the relative position of making moving plate, when two coordination configurations, because the two at a distance of recently, will reach maximum.

Like this, to the piezoelectricity modeling of 2 joints, at least at vane from making moving plate when very near, must introduce one and represent the correction term of making moving plate partial excitation strain transmission characteristic in structure.For example equation (3-1) should change into

To this correction term H _t(s) quantitative analysis will be a problem that is worth research, when having a plurality of piezoelectric patches to encourage, can seem more complicated.It was gratifying that it is not difficult to discern through experiment parameter and estimates and go to eliminate or " compensation " through some simple strategies, go that this will be 3.3 to save the problem that will study thereby the piezoelectric structure Mathematical Modeling is revert to again in " routine ".

We have introduced normal correction term H in computer simulation experiment _t(s)=Const, when it when 0 increases, can see that frequency response curve will (Fig. 6 a) turns to " piezoelectricity pattern " (Fig. 6 b) gradually from the pattern of routine.In experiment, we add survey from making the moving plate frequency response curve u of the piezoelectric sensing sheet in (" strange land ") nearby _St(j ω)/u _a(j ω)/(j ω) be illustrated among Fig. 6 c, and it approaches conventional frequency response pattern very much, and (Fig. 6 a); This is because make the cause (Saint Venant's principle) that the propagation of moving plate partial excitation strain decays rapidly with distance.

At 2 joints, we post piezoelectric patches with two sides up and down and constitute piezoelectric actuator together, as if with present analysis have only the different of a piezoelectric patches, actually this is not so.In fact, moving plate excitation strain component, ε are made in the direct impression of piezoelectric sensing sheet at this moment _Ts(s)/ε _Ta(s)=1, thus make the response of partial excitation strain become bigger.

3.3 the compensation of piezoelectric actuator partial excitation strain

Note

Open loop frequency response (3-11) becomes

$H_v\left(s\right)=\frac{u_s\left(s\right)}{u_a\left(s\right)}=b_{\mathrm{ps}}{b}_p{\mathrm{\&alpha;}}_{v}s(H_m\left(s\right)+H_t\left(s\right))---(3-13)$

The control block diagram of Fig. 5 becomes Fig. 7 (not having Δ H (s) branch road for the time being).The closed loop frequency response does

${\stackrel{\&OverBar;}{H}}_v\left(s\right)=\frac{u_s\left(s\right)}{u_e\left(s\right)}\&ap;\frac{g_a{b}_{\mathrm{ps}}{b}_p{\mathrm{\&alpha;}}_{v}s(H_m\left(s\right)+H_t\left(s\right))}{1+g_s{g}_a{b}_{\mathrm{ps}}{b}_p{\mathrm{\&alpha;}}_{v}s(H_m\left(s\right)+H_t\left(s\right))}---(3-14)$

Corresponding to the approximate equation in the arrowband (3-3) and (3-4)

Become quite complicated, no longer include succinct damping incremental solution (3-5) or (3-6).

In fact, just because of H _t(s) objective reality after constituting closed-loop system, has been damaged the controlling performance of flexural vibrations.Manage to eliminate H _t(s) influence becomes a major issue that improves the piezoelectric structure control of quality.

See Fig. 7, in theory, do not have too big difficulty: increase a bypass correction link

ΔH(s)＝-H _t(s) (3-17)

That's all.In other words, the compensation of this link will revert to the transfer function model of piezoelectric structure among the result that 2 joints derive and go.

Comprehensive the above; The present invention realizes through following technical scheme: with piezoelectric beam on moving plate two piezoelectric patches identical of doing with vane be attached on a material little substrate identical with the beam matrix and constituted " piezoelectricity compensating plate " with thickness; It do receive same excitation as moving plate on moving plate and the beam; And connect amplifier behind the vane, its arrange also with beam on transducer the same.

Because adopt technique scheme, damping control method provided by the invention has been eliminated the feedback of piezoelectric actuating sheet partial excitation strain,, the Mathematical Modeling of piezoelectric structure goes thereby being revert in the theoretical model again.

See shown in Figure 2ly, a kind of piezoelectric structure damping control object compensation method is that as an exampleBSEMGVR takeN-PSVSEMOBJ is bright with the beam, and these method concrete steps are following:

Step 1: matrix is set.Get a little substrate 8, the material of this substrate is all identical with beam 1 with thickness.

Step 2: be provided with and make moving plate.With beam 1 on the moving plate 2 identical moving plates 9 of doing of doing be attached on the little substrate 8, make moving plate 9 and receive same excitation with the moving plate 2 of doing on the beam 1.

Step 3: vane is set.With beam 1 on measured sheet 3 identical measured sheet 10 be attached to the another side of little substrate 8, with original do moving plate 9 over against.Connect operational amplifier 12 and resistance 11 after the measured sheet 10; The same with measured sheet 3 resistance 4 at the back on the beam 1 with operational amplifier 5; And measured sheet 10, the annexation of operational amplifier 12 and resistance 11 also with measured sheet 3, resistance 4 is the same with the annexation of operational amplifier 5.

Step 4: regulate gain g _cBecause chip area is very little; In the non-high frequency mode frequency band of beam; The bending strain of substrate can be ignored, and has only the tension and compression strain, thus it can do the propagation of the local excitation of moving plate tension and compression strain by the direct modeling beam from doing the moving plate strain to the propagation of vane to vane; In other words, the tension and compression strain transfer function ε of the two _Ts(s)/ε _Ta(s) identical or proportional.Like this, as long as regulate gain g _cJust can reach " compensation " condition (3-17)

$\mathrm{\&Delta;H}(s,g_c)=\frac{\mathrm{\&Delta;}{u}_s(s,g_c)}{u_a\left(s\right)}=-H_t\left(s\right)---(3-18)$

g _cShould approach-1.

The advantage and the effect of this method are: it has eliminated the feedback of piezoelectric actuating sheet partial excitation strain, goes thereby the Mathematical Modeling of piezoelectric structure is revert in the theoretical model again.So it is ingenious, the simple to operate damping control method of a kind of design.

(4) description of drawings

The local negative velocity feedback damping control of Fig. 1 piezoelectric beam sketch map

Damping control sketch map under the compensation of Fig. 2 partial excitation strain

Fig. 3 piezoelectric patches transducer sketch map (a strain rate sensor b strain transducer c basic circuit)

Piezoelectric actuator is analyzed sketch map on Fig. 4 beam

The local negative velocity feedback damping control of Fig. 5 piezoelectric beam sketch map

Fig. 6 strain open loop frequency response sketch map (a theoretical model b actual measurement---local c actual measurement---strange land)

The influence of Fig. 7 partial excitation strain and compensation sketch map

Wherein symbol description is following among the figure:

1 beam, 2 make moving plate, 3 measured sheet, 4 resistance R _ f, 5 operational amplifiers, 6 gain g _s, 7 gain g _a,

8 little substrates, 9 make moving plate, 10 measured sheet, 11 resistance, 12 operational amplifiers, 13 gain g _c

(5) embodiment

See shown in Figure 2ly, the present invention is a kind of piezoelectric structure damping control object compensation method, is that as an exampleBSEMGVR takeN-PSVSEMOBJ is bright with the beam, and these method concrete steps are following:

Step 1: matrix is set.Get a little substrate 8, the material of this substrate is all identical with beam 1 with thickness.

Step 2: be provided with and make moving plate.With beam 1 on the moving plate 2 identical moving plates 9 of doing of doing be attached on the little substrate 8, make moving plate 9 and receive same excitation with the moving plate 2 of doing on the beam.

Step 3: vane is set.With beam 1 on measured sheet 3 identical measured sheet 10 be attached to the another side of little substrate 8, with original do moving plate 9 over against.Connect operational amplifier 12 and resistance 11 after the measured sheet 10; The same with measured sheet 3 resistance 4 at the back on the beam 1 with operational amplifier 5; And measured sheet 10, the annexation of operational amplifier 12 and resistance 11 also with measured sheet 3, resistance 4 is the same with the annexation of operational amplifier 5.

Step 4: regulate gain g _cBecause chip area is very little; In the non-high frequency mode frequency band of beam; The bending strain of substrate can be ignored, and has only the tension and compression strain, thus it can do the propagation of the local excitation of moving plate tension and compression strain by the direct modeling beam from doing the moving plate strain to the propagation of vane to vane; In other words, the tension and compression strain transfer function ε of the two _Ts(s)/ε _Ta(s) identical or proportional.Like this, as long as regulate gain g _cJust can reach " compensation " condition (3-17)

$\mathrm{\&Delta;H}(s,g_c)=\frac{\mathrm{\&Delta;}{u}_s(s,g_c)}{u_a\left(s\right)}=-H_t\left(s\right)---(3-18)$

g _cShould approach-1.

Claims (1)

1. piezoelectric structure damping control object compensation method, it is characterized in that: these method concrete steps are following:

Step 1: matrix is set; Get a little substrate (8), the material of this substrate is all identical with beam (1) with thickness;

Step 2: be provided with and make moving plate; With beam (1) on first do identical second the making moving plate (9) and be attached on the little substrate (8) of moving plate (2), second makes first on moving plate (9) and the beam makes moving plate (2) and receives same excitation;

Step 3: vane is set; With beam (1) on identical second measured sheet (10) of first measured sheet (3) be attached to the another side of little substrate (8), with original second do moving plate (9) over against; Connect operational amplifier (12) and resistance (11) after second measured sheet (10); The same with first measured sheet (3) resistance (4) at the back on the beam (1) with operational amplifier (5); And second measured sheet (10); The annexation of operational amplifier (12) and resistance (11) also with first measured sheet (3), resistance (4) is the same with the annexation of operational amplifier (5);

Step 4: regulate gain g _cBecause chip area is very little; In the non-high frequency mode frequency band of beam; The bending strain of substrate can be ignored; Have only the tension and compression strain, thus it can make the propagation of the local excitation of moving plate tension and compression strain to vane, i.e. the tension and compression strain transfer function ε of the two by the direct modeling beam from doing the moving plate strain to the propagation of vane _Ts(s)/ε _Ta(s) identical, promptly proportional, like this, as long as regulate gain g _cJust can reach " compensation " condition,

$\mathrm{\&Delta;H}(s,g_c)=\frac{{\mathrm{\&Delta;u}}_s(s,g_c)}{u_a\left(s\right)}=-H_t\left(s\right)$

g _cShould approach-1.

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