CN108278323A - A kind of zero stiffness vibration isolating method without tow platform towards electrostatic suspension formula twin-stage - Google Patents

A kind of zero stiffness vibration isolating method without tow platform towards electrostatic suspension formula twin-stage Download PDF

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Publication number
CN108278323A
CN108278323A CN201810019668.9A CN201810019668A CN108278323A CN 108278323 A CN108278323 A CN 108278323A CN 201810019668 A CN201810019668 A CN 201810019668A CN 108278323 A CN108278323 A CN 108278323A
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China
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electrostatic
suspension
stage
feedback voltage
zero stiffness
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CN201810019668.9A
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Chinese (zh)
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CN108278323B (en
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范达
贾海鹏
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中国空间技术研究院
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    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16FSPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F15/00Suppression of vibrations in systems; Means or arrangements for avoiding or reducing out-of-balance forces, e.g. due to motion
    • F16F15/02Suppression of vibrations of non-rotating, e.g. reciprocating systems; Suppression of vibrations of rotating systems by use of members not moving with the rotating systems

Abstract

A kind of zero stiffness vibration isolating method without tow platform towards electrostatic suspension formula twin-stage, by introducing the displacement of suspension payload platform, non-linear modulation is carried out to the output of suspension control algolithm, electrostatic force caused by displacement is compensated and changes, to eliminate electrostatic negative stiffness, the suspension vibration isolation of zero stiffness is realized.Absolute zero stiffness vibration isolation may be implemented in the method for the present invention, realizes to the vibrational energy in wideband segment limit and effectively inhibits, and due to the structure of zero stiffness, so that two-stage system is full decoupled, can be independent of each other with independent design between plateform system, stability is more preferable, and method flow is simple.

Description

A kind of zero stiffness vibration isolating method without tow platform towards electrostatic suspension formula twin-stage

Technical field

The present invention relates to a kind of towards the electrostatic suspension formula twin-stage zero stiffness vibration isolating method without tow platform, it is outstanding to belong to electrostatic Floating control and precision vibration damping technical field.

Background technology

High-precision spatial measurement, high-resolution remote sensing of the earth and the experiment of ultraprecise space science etc. are movable to be carried out in a deep going way, New demand is proposed to space-based vibration isolation and damping platform and is chosen a little.It is without towing space-based ultra quiet platform based on the twin-stage of electrostatic suspension A kind of novel vibration isolation and damping platform, system are divided into satellite parent, three independent parts of payload platform and reference mass block.System The space motion pattern of system is:Satellite parent realized by way of electrostatic suspension with payload platform it is contactless be isolated, the two it Between form differential capacitor, Electrostatic Control power can be generated according to the relative displacement of payload platform and reference mass block, driving load is flat Platform track reference mass block realizes the first order without towing, and wherein reference mass block is suspended in the vacuum chamber in payload platform, complete It is not interfered entirely by extraneous nonconservative force, operates in the track under pure terrestrial gravitation effect, be the quiet ginseng under no Condition Of Tow Examine source;And micro-thruster can generate reaction control power according to the relative displacement between satellite parent and payload platform, drive satellite Parent tracks payload platform, realizes the second level without towing.Total system, without towing framework, is realized using twin-stage using electrostatic suspension Zero stiffness vibration isolation realizes that active damping, integration realize the inhibition to vibration using electrostatic drive.

However, electrostatic suspension actually can form electrostatic negative stiffness between payload platform and satellite parent, not really The shift perturbation of zero stiffness vibration isolation, satellite parent can be transmitted to by this electrostatic negative stiffness on payload platform so that system shape At every and micro-vibration coupling path without cease, reduce the vibration isolating effect of system.

Zero stiffness vibration isolation thought originates from mechanical vibration damping field, since mechanical support structure is generally positive rigidity, vibration isolation system The zero stiffness of system is generally realized by being superimposed the negative stiffness of non-linear force.In the prior art it has been suggested that a kind of bent based on Euler The negative stiffness construction method of curved beam structure and a kind of utilization nonlinear negative stiffness production method of magnetic force.However, such method institute It is accomplished that a kind of quasi- zero stiffness vibrating isolation system, is only complete zero stiffness in functioning equalization point position, near matching point It is then quasi- zero stiffness, anti-vibration performance is related with the excitation size of vibration, it cannot be guaranteed that electrostatic negative stiffness is equal under all conditions It is zero.

Invention content

Present invention solves the technical problem that being:For problems of the prior art, it is proposed that a kind of outstanding towards electrostatic Zero stiffness vibration isolating method of the floating twin-stage without tow platform solves electrostatic suspension platform due to electrostatic negative stiffness not all zero Formed can not complete vibration isolation the problem of.

The present invention solves above-mentioned technical problem and is achieved by following technical solution:

A kind of zero stiffness vibration isolating method without tow platform towards electrostatic suspension formula twin-stage, includes the following steps:

(1) linearization process is carried out to the relationship of electrostatic suspension plateform system feedback voltage and electrode electrostatic force so that strong Electrostatic negative stiffness processed is 0;

(2) it on the basis of step (1) is completed, for electrostatic suspension formula twin-stage without tow platform, independently carries out quiet Electric drive and micro- control algorithm design for pushing away drive control;

(3) non-linear modulation is carried out to the control algolithm output of electrostatic drive controller obtained by step (2), and will be non-linear Modulated control algolithm exports the reality output as electrostatic drive controller.

In the step (1), to electrostatic suspension plateform system linearized the specific steps are:

(1a) ignores electrode electrostatic force F in differential capacitance modeleMiddle displacement high-order is a small amount of, by electricity among real system Pole electrostatic force FeCalculation formula be expressed as:

In formula, εrFor relative dielectric constant, ε0For permittivity of vacuum, A is one piece of capacitor plate effective area, Vs_effFor High-frequency ac driving voltage virtual value, VrFor pre-load voltage (bias direct current voltage), VbFor feedback voltage, d0For nominal gap, x Deviate the displacement of center for suspended substance;

(1b) detaches electrostatic negative stiffness;The calculation formula of the electrostatic negative stiffness is:

It is 0 that (1c), which forces electrostatic negative stiffness, completes feedback voltage and is linearized with electrode electrostatic force.

In the step (3), the modulated feedback voltage of differential capacitance both sides load includes upper feedback voltage and lower anti- Feedthrough voltage, wherein upper feedback voltage Vb_up, lower feedback voltage Vb_downComputational methods be respectively:

Wherein, payload platform relative displacementCalculation formula it is as follows:

In formula, VcAlgorithm output voltage in order to control.

The advantages of the present invention over the prior art are that:

(1) the present invention provides a kind of towards the electrostatic suspension formula twin-stage zero stiffness vibration isolating method without tow platform, passes through It is zero that non-linear modulation, which controls electrostatic negative stiffness, reaches the limitation for overcoming quiescent point in zero stiffness, can be in large amplitude Under the conditions of form zero stiffness, can give bandwidth higher linear modulation, realize to the vibration isolation of wideband segment limit;

(2) use the electrostatic suspension formula twin-stage of the method for the present invention without tow platform system, it is non-thread under conditions of zero stiffness Property modulation after the two poles of the earth system can be made full decoupled, each system easy to implement is independent of each other, control environment independently, surely It is fixed more preferable.

Description of the drawings

Fig. 1 is the plateform system structure chart that invention provides;

Fig. 2 is the vibration isolating method flow chart that invention provides;

Fig. 3 is the equivalent differential capacitor illustraton of model of electrostatic force generating means;

Fig. 4 is the twin-stage suspension system control block diagram after linearisation;

Fig. 5 is that electrostatic negative stiffness Ke is considered as the twin-stage suspension system control block diagram after zero;

Fig. 6 is the real system control block diagram after constructing zero stiffness;

Fig. 7 is the simulation results figure of the method for the present invention;

Specific implementation mode

In the patent of Publication No. CN104158431A, it is proposed that a kind of electrostatic suspension formula space-based ultra quiet platform system, Including quiet frame of reference, payload platform, star top electrode chamber, capacitive detection circuit, numerical control system, driving circuit and micro- Propeller, it realizes a kind of using the progress Low rigidity vibration isolation of weak electrostatic negative stiffness and by the progress active of controlled feedback electrostatic force For the twin-stage of vibration damping without towing system, zero stiffness vibration isolating method provided by the invention is to implement in this plateform system, is passed through Displacement of the suspension payload platform relative to satellite parent is introduced, non-linear modulation is carried out to the output of suspension controller, compensates position Electrostatic force variation, to realize zero stiffness, ensures modulated system electrostatic force platform relative satellite not loaded caused by moving Parent Influence of Displacement.

As shown in Figure 1, space motion pattern of the electrostatic suspension formula twin-stage without towing space-based ultra quiet platform system is:Satellite is female Body realized by way of electrostatic suspension with payload platform it is contactless be isolated, form differential capacitor therebetween, can be according to load The relative displacement of platform and reference mass block generates Electrostatic Control power, drives payload platform track reference mass block, realizes first Without towing, wherein reference mass block is suspended in the vacuum chamber in payload platform, is not interfered completely by extraneous nonconservative force grade, The track under pure terrestrial gravitation effect is operated in, is the quiet reference source under no Condition Of Tow;And micro-thruster can be according to satellite Relative displacement between parent and payload platform generates reaction control power, and driving satellite parent tracks payload platform, realizes second Grade is without towing.Total system, without towing framework, zero stiffness vibration isolation is realized using electrostatic suspension using twin-stage, utilizes electrostatic drive reality The inhibition to micro-vibration is realized in existing active damping, integration.

A kind of zero stiffness vibration isolating method without tow platform towards electrostatic suspension formula twin-stage, as shown in Fig. 2, specific steps are such as Under:

(1) linearization process is carried out to the conversion link of electrostatic suspension plateform system voltage and electrostatic force;The specific steps are:

(1a) in differential capacitance model, real system target electrostatic force FeCalculation formula be:

In formula, εrFor relative dielectric constant, ε0For permittivity of vacuum, A is one piece of capacitor plate effective area, Vs_effFor High-frequency ac driving voltage virtual value, VrFor pre-load voltage (bias direct current voltage), VbFor feedback voltage, d0For nominal gap, x Deviate the displacement of center for suspended substance;

(1b) ignores electrode electrostatic force FeMiddle displacement high-order is a small amount of, at this time electrode electrostatic force FeCalculation formula be:

(1c) detaches electrostatic negative stiffness, and the calculation formula of the electrostatic negative stiffness is:

It is 0 that (1d), which forces electrostatic negative stiffness, completes feedback voltage and is linearized with electrode electrostatic force.

In above-mentioned formula, electrode electrostatic force FeIt is related with the suspended substance deviation displacement x of center, it is not carrying out linearly When change, the electrostatic negative stiffness K of electrostatic suspension systemeFor electrode electrostatic force FeThe displacement x for deviateing suspended substance center asks inclined It leads.

It, can be by K after carrying out the Linearization Design to electrostatic suspension systemeIt is considered as 0.

(2) electrostatic suspension formula twin-stage is directed to without tow platform, carries out electrostatic drive and micro- drive control algorithm that pushes away designs;

Control algorithm design mentioned here, due to the control algolithm of design be towards electrostatic negative stiffness eliminate after be System, i.e., the relative displacement variation between payload platform and satellite body not will produce the variation of electrostatic force, to make in ultra quiet platform Two-stage it is full decoupled without towing system, therefore the prior art (second-order optimum Controlling model or conventional PID controller may be used Etc. design methods) mode that independently designs realizes excellent controller.

(3) control algolithm is exported according to control algolithm obtained by step (2) and carries out non-linear modulation, and utilized modulated Control algolithm output substitutes former algorithm output.

Non-linear modulation, the upper feedback voltage exported after being modulated are carried out to the feedback voltage of differential capacitance both ends load And lower feedback voltage, wherein upper feedback voltage Vb_up, lower feedback voltage Vb_downComputational methods be respectively:

Wherein, payload platform relative displacementCalculation formula it is as follows:

The modulated feedback voltage that feedback voltage obtained by non-linear modulation is loaded as differential capacitance both sides, at this time Virtual electrode electrostatic force Fe' calculation formula be:

Gained virtual electrode electrostatic force Fe' calculation formula not by local linearisation as a result, but the reality realized after modulating Border electrode electrostatic force size, by formula it is found that under conditions of zero stiffness, during virtual electrode electrostatic force size deviates with suspended substance The displacement x of heart position is unrelated, to ensure that plateform system is not influenced by large amplitude, has reached better vibration isolating effect, such as Fig. 3 It is shown.

As shown in figure 4, after carrying out the Linearization Design, the system block diagram after being linearized.Wherein, m is payload platform Quality, Fn1To act on the nonconservative force on payload platform, x1Displacement for payload platform with respect to reference mass block;M is to defend The quality of star parent, Fn2For the nonconservative force for acting on satellite parent, x2Displacement for satellite parent with respect to reference mass block, K1The detection gain for being displaced to voltage for payload platform with respect to reference mass block, G1For electrostatic drive control algolithm, H1For feedback Voltage to electrostatic force driving gain linear segment, K2Increase for the detection for being displaced to voltage of satellite parent relative load platform Benefit, G2For the control algolithm of micro-thruster, H2For electricity/power conversion gain of micro-thruster.

Due to finally by controller application in zero stiffness system, to make controller parameter performance under zero stiffness system It is optimal, it forces electrostatic negative stiffness being considered as zero, obtains zero stiffness linear system control block diagram as shown in Figure 5.

In real system control method after construction zero stiffness as shown in FIG. 6, the simulink emulation moulds of system are established Type, simulation parameter are as shown in table 1.

1 system emulation parameter of table

Parameter Value Payload platform quality m/kg 100 Satellite body mass M/kg 500 Displacement detecting circuit gain K between payload platform-mass block1/(V/m) 500000 Displacement detecting circuit gain K between payload platform-satellite body2/(V/m) 30000 Capacitor plate effective area A/m2 1 Pre-load voltage Vr/V 1000 Nominal gap d between payload platform-satellite body0/m 0.001 Micro-thruster power electricity conversion gain H2/(V/N) 1

Wherein, f1f2The resultant effect of two links is the H being equivalent in Fig. 51Link;

The controller parameter of design is:

The perturbed force F acted on satellite parent is setn2Amplitude be 50N, frequency 50Hz, it is flat that setting acts on load Perturbed force F on platformn1It is zero, emulation can obtain the displacement of suspension payload platform to acting on the perturbed force F on satellite parentn2 Time domain response, be also response to satellite parent shift perturbation, the results are shown in Figure 7.Undulating value is almost as shown in Figure 7 Zero, burr is error caused by numerical computations.As it can be seen that this method has reached the vibration isolating effect of absolute zero stiffness.

The content that description in the present invention is not described in detail belongs to the known technology of those skilled in the art.

Claims (3)

1. a kind of zero stiffness vibration isolating method without tow platform towards electrostatic suspension formula twin-stage, it is characterised in that including walking as follows Suddenly:
(1) linearization process is carried out to the relationship of electrostatic suspension plateform system feedback voltage and electrode electrostatic force so that force quiet Electric negative stiffness is 0;
(2) on the basis of step (1) is completed, for electrostatic suspension formula twin-stage without tow platform, electrostatic drive is independently carried out Dynamic and micro- control algorithm design for pushing away drive control;
(3) non-linear modulation carried out to the control algolithm output of electrostatic drive controller obtained by step (2), and by non-linear modulation Control algolithm afterwards exports the reality output as electrostatic drive controller.
2. a kind of zero stiffness vibration isolating method without tow platform towards electrostatic suspension formula twin-stage according to claim 1, It is characterized in that:In the step (1), to electrostatic suspension plateform system linearized the specific steps are:
(1a) ignores electrode electrostatic force F in differential capacitance modeleMiddle displacement high-order is a small amount of, by real system target electrostatic Power FeCalculation formula be expressed as:
In formula, εrFor relative dielectric constant, ε0For permittivity of vacuum, A is one piece of capacitor plate effective area, Vs_effFor high frequency Ac-excited voltage effective value, VrFor pre-load voltage, VbFor feedback voltage, d0For nominal gap, x is that suspended substance deviates centre bit The displacement set;
(1b) detaches electrostatic negative stiffness;The calculation formula of the electrostatic negative stiffness is:
It is 0 that (1c), which forces electrostatic negative stiffness, completes feedback voltage and is linearized with electrode electrostatic force.
3. a kind of zero stiffness vibration isolating method without tow platform towards electrostatic suspension formula twin-stage according to claim 1 or 2, It is characterized in that:In the step (3), differential capacitance both sides load modulated feedback voltage include upper feedback voltage and under Feedback voltage, wherein upper feedback voltage Vb_up, lower feedback voltage Vb_downComputational methods be respectively:
Wherein, payload platform relative displacementCalculation formula it is as follows:
In formula, VcAlgorithm output voltage in order to control.
CN201810019668.9A 2018-01-09 2018-01-09 A kind of zero stiffness vibration isolating method towards electrostatic suspension formula twin-stage without tow platform CN108278323B (en)

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Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
GB2288277B (en) * 1994-04-01 1998-02-25 Nikon Precision Inc Guideless stage with isolated reaction stage
US6196514B1 (en) * 1998-09-18 2001-03-06 Csa Engineering, Inc. Large airborne stabilization/vibration isolation system
CN102606673A (en) * 2012-03-26 2012-07-25 湖南大学 Load-bearing adjustable zero-stiffness electromagnetic vibration isolator and control method thereof
CN106508087B (en) * 2011-04-12 2013-06-19 西北工业大学 A kind of floating microgravity effect ground simulation method is mixed based on magnetic liquid
CN106594172B (en) * 2017-01-12 2019-02-26 北京理工大学 Semi- active control type vertical vibration isolation device with quasi- zero stiffness

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
GB2288277B (en) * 1994-04-01 1998-02-25 Nikon Precision Inc Guideless stage with isolated reaction stage
US6196514B1 (en) * 1998-09-18 2001-03-06 Csa Engineering, Inc. Large airborne stabilization/vibration isolation system
CN106508087B (en) * 2011-04-12 2013-06-19 西北工业大学 A kind of floating microgravity effect ground simulation method is mixed based on magnetic liquid
CN102606673A (en) * 2012-03-26 2012-07-25 湖南大学 Load-bearing adjustable zero-stiffness electromagnetic vibration isolator and control method thereof
CN106594172B (en) * 2017-01-12 2019-02-26 北京理工大学 Semi- active control type vertical vibration isolation device with quasi- zero stiffness

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