CN106940524A - A kind of vibration of piezoelectric positioning device and non-linear inhibition method - Google Patents

A kind of vibration of piezoelectric positioning device and non-linear inhibition method Download PDF

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Publication number
CN106940524A
CN106940524A CN201710129360.5A CN201710129360A CN106940524A CN 106940524 A CN106940524 A CN 106940524A CN 201710129360 A CN201710129360 A CN 201710129360A CN 106940524 A CN106940524 A CN 106940524A
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positioning device
piezoelectric
vibration
piezoelectric positioning
inhibition method
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CN106940524B (en
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刘志刚
张萌
步明繁
朱裕
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Xian Jiaotong University
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Xian Jiaotong University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B11/00—Automatic controllers
    • G05B11/01—Automatic controllers electric
    • G05B11/36—Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential
    • G05B11/42—Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential for obtaining a characteristic which is both proportional and time-dependent, e.g. P.I., P.I.D.
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D19/00—Control of mechanical oscillations, e.g. of amplitude, of frequency, of phase
    • G05D19/02—Control of mechanical oscillations, e.g. of amplitude, of frequency, of phase characterised by the use of electric means

Abstract

The present invention discloses vibration and the non-linear inhibition method of a kind of piezoelectric positioning device, including：(1) voltage signal of the piezoelectric ceramics to inputting piezoelectric positioning device is pre-processed；(2) Dynamic Modeling is carried out to piezoelectric positioning device, draws the open-loop transfer function between piezoelectric positioning device key parameter and input voltage and output displacement；(3) closed-loop control is carried out to piezoelectric positioning device using integral feedback method；(4) with the measured value for the force snesor being arranged between piezoelectric ceramics and flexible hinge as feedback quantity, feedback control is carried out to piezoelectric positioning device, the output displacement of flexible hinge is measured by displacement transducer, piezoelectric positioning device vibration and nonlinear suppression is realized.Modeling accuracy of the present invention independent of model, can suppress to vibration with non-linear simultaneously；Modern precision manufacture is met to piezoelectric positioning device high accuracy, the requirement of high tracking performance, operating efficiency is improved.

Description

A kind of vibration of piezoelectric positioning device and non-linear inhibition method
Technical field
The present invention relates to micro electro mechanical system field, the vibration of more particularly to a kind of Piezoelectric Driving displacement platform and non-linear Suppressing method.
Background technology
Piezoelectric positioning device is the machinery positioning that can the provide nanometer resolution dress driven by piezoelectric ceramics (PZT) Put.Piezoelectric positioning device has rigidity high, compact dimensions, and displacement resolution is high, the advantage of quick response and low-power consumption, by It is widely used in the fields such as precision positioning, nano manufacturing system, afm scan and optic test.
However, the positioning precision of piezoelectric positioning device can be by PZT is non-linear and mechanical oscillation are influenceed.It is non-linear including Sluggish (occurring in the case of big displacement) and creep effect (occurring in low-frequency sweep).And mechanical oscillation are due to scanning signal High order component near or above positioner first natural frequency so that trigger resonate and cause.Currently for non-linear and The control method of vibration, mainly there is feed-forward regulation or feedback regulation.The degree of accuracy heavy dependence modeling accuracy of feed-forward regulation method, And feedback regulation can only provide limited compensating action.
The content of the invention
It is an object of the invention to provide a kind of vibration of piezoelectric positioning device and non-linear inhibition method, piezoelectricity is positioned Device is sluggish, creep and mechanical oscillation control effectively, to solve the problem of prior art is present.The present invention is by based on most The input signal trajectory planning and integration force-feedback control method of small acceleration criterion realize piezoelectric positioning device vibration and non- Linear double control.
In order to solve the above-mentioned technical problem, present invention employs following technical scheme：
A kind of vibration of piezoelectric positioning device and non-linear inhibition method, comprise the following steps：
(1) voltage signal of the piezoelectric ceramics to inputting piezoelectric positioning device is pre-processed；
(2) Dynamic Modeling is carried out to piezoelectric positioning device, draws piezoelectricity locating stiffness, damping, intrinsic frequency and defeated Enter the open-loop transfer function between voltage and output displacement；
(3) closed-loop control is carried out to piezoelectric positioning device using integral feedback method；
(4) with the measured value for the force snesor being arranged between piezoelectric ceramics and flexible hinge as feedback quantity, to piezoelectricity Positioner carries out feedback control, and the output displacement of flexible hinge is measured by displacement transducer, realizes that piezoelectricity is positioned Device vibrates and nonlinear suppression.
Further, step (1) includes carrying out subsection optimization to the triangular wave track for inputting piezoelectric ceramics：The range of linearity is protected Hold constant, waveform smoothing processing is carried out to signal waveform cusp region using minimum acceleration criterion.
Further, cusp is carried out to the triangular wave for inputting piezoelectric ceramics in step (1) and seamlessly transits processing：
The time cycle for seamlessly transitting curve in a cycle at crest and trough is made to account for signal period altogether P%, then crest seamlessly transits the left and right terminal A of curve and C abscissa absolute value representation is：
tc=TP%/4
Set up with quintic algebra curve and seamlessly transit curve AB, its function expression is expressed as：
yAB=f (t)=a1t5+a2t4+a3t3+a4t2+a5t+a6,(-tc≤t≤0)
In formula：a1~a6For multinomial coefficient；Calculated using Matlab softwares and meet institute's Prescribed Properties and object function Parameter；
The drive signal of one complete cycle is always divided into six sections：BC, CG, GH, HJ, JQ and QU, a cycle 0 The final piecewise function expression formula of drive signal is expressed as in~T：
Wherein, AmFor amplitude, T is the cycle.
Further, in step (3), the yield value of integral element passes throughObtain；Wherein ωpFor limit Intrinsic frequency, ωzFor zero point intrinsic frequency, ga、gsFor coefficient.
Further, in step (2), input voltage is VaOutput displacement is d, obtains opening for input voltage and output displacement Ring transmission function is：
Further, force snesor (3) is arranged between piezoelectric ceramics (2) and flexible hinge (1), for measuring piezoelectricity pottery Porcelain and flexible hinge interaction force Fs；Utilize FsIt is integrated force feedback；By introducing integral element in step (3)Carry out force-feedback control；α represents yield value,Represent integral element.
Compared with prior art, the invention has the advantages that：Input signal preprocess method and integration power is anti- Feedback method integration is applied in the vibration and nonlinear Control of piezoelectric positioning device, and this method has：It is simple in construction, robustness It is good, the advantage independent of modeling accuracy.Modern precision manufacture is being met to piezoelectric positioning device high accuracy, high tracking performance need On the basis of asking, realize to vibration and nonlinear integrated control.
Brief description of the drawings
Fig. 1 seamlessly transits curve for symmetric triangular ripple cusp；
Fig. 2 is piezoelectric positioning device structure chart；
Fig. 3 is integration force feedback block diagram；
Fig. 4 is that system hardware indicates figure；
Fig. 5 (a) and Fig. 5 (b) are respectively vibration and non-linear inhibition figure.
Embodiment
Illustrate the preferred embodiments of the present invention below in conjunction with the accompanying drawings.
Refer to shown in Fig. 1 to Fig. 4, a kind of vibration of piezoelectric positioning device of the invention and non-linear inhibition method, including Following steps：
(1) voltage signal for inputting piezoelectric ceramics is pre-processed：Subsection optimization is carried out to input triangular wave track.Line Property region keep it is constant, using minimum acceleration criterion to signal waveform cusp region carry out waveform smoothing processing.Do not changing On the basis of signal key characteristic, the suppression to signal frequency domain high order component is realized.
(2) Dynamic Modeling is carried out to piezoelectric positioning device and draws system stiffness, damping, intrinsic frequency and input voltage Open-loop transfer function between output displacement.
(3) closed-loop control is carried out to piezoelectric positioning device using integral feedback method, the yield value of integral element passes throughObtain.
(4) with the measured value for the force snesor being arranged between piezoelectric ceramics and flexible hinge as feedback quantity, to piezoelectricity Positioner carries out feedback control, and the hardware of feedback control indicates that figure is as shown in Figure 4.By displacement transducer to flexible hinge Output displacement is measured, and realizes piezoelectric positioning device vibration and nonlinear suppression.
As shown in figure 1, carrying out cusp to input triangular wave seamlessly transits processing.Fine dotted line represents that symmetric triangular ripple is believed in figure Number cusp waveform.Heavy line is the signal waveform after cusp seamlessly transits finishing, and its medium wave peak and trough sentence smooth song Line replaces curve ABC, EF and GHJ in symmetric triangular waveform cusp, such as figure.
The time cycle for seamlessly transitting curve in a cycle at crest and trough is made to account for signal period altogether P%, then crest seamlessly transits the left and right terminal A of curve and C abscissa absolute value is represented by：
tc=TP%/4
Set up with quintic algebra curve and seamlessly transit curve AB, its function expression is represented by：
yAB=f (t)=a1t5+a2t4+a3t3+a4t2+a5t+a6,(-tc≤t≤0)
In formula：a1~a6--- it is multinomial coefficient.And seamlessly transitting curve AB has six location parameters, so when B points position Put a6When determining, so that it may calculate remaining unknown parameter a according to five equality constraints1~a5.Therefore above mentioned problem is converted into one Individual linear programming problem, the parameter for meeting institute's Prescribed Properties and object function is calculated using Matlab softwares.
Always being divided into six sections according to the drive signal of mono- complete cycle of Fig. 1 is respectively：BC, CG, GH, HJ, JQ and QU, institute It is represented by with the final piecewise function expression formula of drive signal in 0~T of a cycle：
Be made up of flexible hinge 1, piezoelectric ceramics (PZT) 2 and level crossing is that piezoelectric positioning device is as shown in Figure 2.Input Voltage is VaOutput displacement is d.The open-loop transfer function that input voltage and output displacement can be obtained is：
Force snesor 3 is arranged between PZT2 and flexible hinge 1, for measuring PZT and flexible hinge interaction force Fs。 Utilize FsIt is integrated force feedback.Feedback control block diagram is as shown in Figure 4.By introducing integral elementCarry out force feedback Control.
The hardware system 1 of feedback control is flexible hinge structure, 2 is PZT actuator, 3 is force snesor, 4 is displacement sensing Device.Main working process：1. being pre-processed in Signal Pretreatment link to input signal, 2. are made using force sensor measuring value For feedback quantity carry out closed-loop system integration force-feedback control, 3. in feedback control simultaneously, pass through displacement sensor flexible hinge Last-in-chain(LIC) end movement verifies complex controll effect.Instrument equipment has：Sent out using the AFG3052C binary channels arbitrary function of Tyke Raw device is used as signal generation apparatus；Using the PZS001 type stacking-types piezoelectric ceramics 2 of Thorlabs companies of the U.S., its controller is adopted With MDT693A single channel open-cycle controllers；Measured using the capaNCDT6500 non-contact displacement sensors 4 of German meter Yi companies Change in displacement, the dynamic for carrying out contact force using German HBM micro-force sensors 3 is measured；Using Stamford company SIM960PID controllers and SIM980 adders carry out feedback control；Data acquisition module has capture card NI-PXI 6133PXI and main frame NI-PXI 1031 are constituted.
Experimental result is as shown in Figure 5：After being controlled to piezoelectric positioning device, during 50Hz triangular wave swept frequencies, Because sluggish 1.47 μm (18.47%) with before maximum displacement error is by controlling caused by mechanical oscillation are reduced to after control 161nm (2.03%).And vibrate and also reduce 48.5dB.

Claims (6)

1. vibration and the non-linear inhibition method of a kind of piezoelectric positioning device, it is characterised in that comprise the following steps：
(1) voltage signal of the piezoelectric ceramics to inputting piezoelectric positioning device is pre-processed；
(2) Dynamic Modeling is carried out to piezoelectric positioning device, draws piezoelectricity locating stiffness, damping, intrinsic frequency and input electricity Open-loop transfer function between pressure and output displacement；
(3) closed-loop control is carried out to piezoelectric positioning device using integral feedback method；
(4) piezoelectricity is positioned as feedback quantity with the measured value for the force snesor being arranged between piezoelectric ceramics and flexible hinge Device carries out feedback control, and the output displacement of flexible hinge is measured by displacement transducer, piezoelectric positioning device is realized Vibration and nonlinear suppression.
2. vibration and the non-linear inhibition method of a kind of piezoelectric positioning device according to claim 1, it is characterised in that step Suddenly (1) includes carrying out subsection optimization to the triangular wave track for inputting piezoelectric ceramics：The range of linearity keeps constant, utilizes minimum acceleration Spend criterion and waveform smoothing processing is carried out to signal waveform cusp region.
3. vibration and the non-linear inhibition method of a kind of piezoelectric positioning device according to claim 2, it is characterised in that step Suddenly cusp is carried out to the triangular wave for inputting piezoelectric ceramics in (1) and seamlessly transits processing：
The time cycle for seamlessly transitting curve in a cycle at crest and trough is made to account for the P% of a signal period altogether, then Crest seamlessly transits the left and right terminal A of curve and C abscissa absolute value representation is：
tc=TP%/4
Set up with quintic algebra curve and seamlessly transit curve AB, its function expression is expressed as：
yAB=f (t)=a1t5+a2t4+a3t3+a4t2+a5t+a6,(-tc≤t≤0)
In formula：a1~a6For multinomial coefficient；The ginseng for meeting institute's Prescribed Properties and object function is calculated using Matlab softwares Number；
The drive signal of one complete cycle is always divided into six sections：BC, CG, GH, HJ, JQ and QU, 0~T of a cycle The final piecewise function expression formula of interior drive signal is expressed as：
f ( - t ) , , 0 &le; t &le; t c - 2 A m t / T + A m / 2 , t c < t &le; 0.5 T - t c - f ( t - 0.5 T ) , 0.5 T - t c < t &le; 0.5 T - f ( - t + 0.5 T ) , 0.5 T < t &le; 0.5 T + t c 2 A m t / T - A m , 0.5 T + t c < t &le; T - t c f ( t - T ) , T - t c < t &le; T ,
Wherein, AmFor amplitude, T is the cycle.
4. vibration and the non-linear inhibition method of a kind of piezoelectric positioning device according to claim 1, it is characterised in that step Suddenly in (3), the yield value of integral element passes throughObtain；Wherein ωpFor limit intrinsic frequency, ωzFor zero point Intrinsic frequency, ga、gsFor coefficient.
5. vibration and the non-linear inhibition method of a kind of piezoelectric positioning device according to claim 1, it is characterised in that step Suddenly in (2), input voltage is VaOutput displacement is d, and the open-loop transfer function for obtaining input voltage and output displacement is：
G dV a = d V a = g a l 2 Is 2 + c f s + ( k b + k a l 2 )
6. vibration and the non-linear inhibition method of a kind of piezoelectric positioning device according to claim 1, it is characterised in that power Sensor (3) is arranged between piezoelectric ceramics (2) and flexible hinge (1), for measuring piezoelectric ceramics and flexible hinge phase interaction Firmly Fs；Utilize FsIt is integrated force feedback；By introducing integral element in step (3)Carry out force-feedback control；α Represent yield value,Represent integral element.
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CN114035627A (en) * 2021-11-17 2022-02-11 上海大学 Active compound control system and method based on single-degree-of-freedom vibration isolation platform
CN116859711A (en) * 2023-06-27 2023-10-10 中科沃业江苏生物有限公司 IABC (advanced integrated circuit controller) -based fuzzy PID (proportion integration differentiation) optimized constant flow pump control system

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CN114035627A (en) * 2021-11-17 2022-02-11 上海大学 Active compound control system and method based on single-degree-of-freedom vibration isolation platform
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CN116859711A (en) * 2023-06-27 2023-10-10 中科沃业江苏生物有限公司 IABC (advanced integrated circuit controller) -based fuzzy PID (proportion integration differentiation) optimized constant flow pump control system
CN116859711B (en) * 2023-06-27 2024-04-12 中科沃业江苏生物有限公司 IABC (advanced integrated circuit controller) -based fuzzy PID (proportion integration differentiation) optimized constant flow pump control system

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