CN106802565A - A kind of adaptive inverse control of piezoelectric actuator - Google Patents

A kind of adaptive inverse control of piezoelectric actuator Download PDF

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Publication number
CN106802565A
CN106802565A CN201710146154.5A CN201710146154A CN106802565A CN 106802565 A CN106802565 A CN 106802565A CN 201710146154 A CN201710146154 A CN 201710146154A CN 106802565 A CN106802565 A CN 106802565A
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piezoelectric actuator
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陈远晟
陈朝霞
郭家豪
罗丹
应展烽
张旭东
徐冰
董妍男
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Nanjing University of Science and Technology
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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
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance

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Abstract

The present invention relates to a kind of adaptive inverse control of piezoelectric actuator, the method includes：For the Hysteresis Nonlinear relation of piezoelectric actuator, the output displacement of piezoelectric actuator and the nonlinear mathematical model of input voltage are set up offline；According to the nonlinear mathematical model set up, the inversion model of piezoelectric actuator is calculated, piezoelectric actuator is driven as initial inverse controller；During piezoelectric actuator on-line operation, its actual output displacement and input voltage are measured；On-line identification is carried out to model parameter by adaptive algorithm, model when obtaining on-line operation simultaneously calculates its inversion model；According to gained inversion model parameter is calculated, original parameter carries out online updating in replacing the controller of piezoelectric actuator.The present invention effectively overcomes the influence that the reasons such as the parameter uncertainty and unknown disturbances of model are caused, and compared to simple inversion model, control accuracy is enhanced, it is adaptable to different model, the piezoelectric actuator of different size.

Description

A kind of adaptive inverse control of piezoelectric actuator
Technical field
The invention belongs to automation field, and in particular to a kind of adaptive inverse control of piezoelectric actuator.
Background technology
With the rise and development of the frontier science and technology-nanometer technology of new century, the mankind open in terms of understanding and nature remodeling A unprecedented new situation is created.It is to information technology, advanced manufacturing technology, medical science, the energy, space flight and aviation and national defence etc. Multiple fields bring major transformation.Precision actuation technology as nanosecond science and technology one of key technology, in micro-electronic manufacturing, light The fields such as electronic technology, space technology, Ultra-precision Turning, biomedical engineering, AFM, all play very important Effect.Various industries in the whole world just gradually using micron, nanometer as accuracy standard, such as in micro-lithography is operated, it is desirable to which stepping is fixed The error of position system is within 20nm.Precision actuation technology has turned into many modern industry fields and front line science technical research Common base, its breakthrough each time can all make many correlation techniques, such as integrated level of electronic product, the capacity of CD, machinery The accuracy class of product, miniaturization degree of instrument and equipment etc. obtain raising by a relatively large margin.
Piezoelectric actuator has the advantages that rigidity high, small volume, response is fast, displacement resolution is high, in being micro- precision actuation Preferable driving element, so piezoelectric actuator is most widely used driving element in micro-, nanoscale precision actuation.But as A kind of ferroelectric polycrystalline material, piezoelectric actuator can produce the nonlinear characteristics such as sluggishness, creep under electric field action, greatly limit The raising of response speed and positioning precision.
Therefore the research to piezoelectric actuator Hysteresis Nonlinear model and control algolithm has important practice significance.Mesh Before, piezoelectric ceramics hysteresis is modeled, using the thought of Adverse control on the basis of Hysteresis Model, carry out feedforward control Technology is more ripe.Although this method can be effectively reduced the influence that piezoelectric ceramics lagging characteristics bring, but preceding The model error that Parameters variation causes can not be eliminated in feedback Adverse control, simultaneously for different size, the piezoelectric actuator of model, Different inverse model control devices are needed, the scope of application is single.
The content of the invention
It is an object of the invention to provide a kind of adaptive inverse control of piezoelectric actuator, by on-line measurement reality Input voltage and output displacement, are modeled and invert to actual sluggishness relation, and with adaptive control algorithm to PI against mould The weights and threshold value of type carry out on-line tuning, can effectively eliminate influence of the model parameter change to tracking effect.
The technical scheme for realizing the object of the invention is：A kind of adaptive inverse control of piezoelectric actuator, including it is following Step：
Step 1, the Hysteresis Nonlinear relation for piezoelectric actuator, set up offline the output displacement of piezoelectric actuator with it is defeated Enter the nonlinear mathematical model of voltage；
Step 2, the nonlinear mathematical model according to foundation, calculate the inversion model of piezoelectric actuator, used as initial inverse control Device processed drives piezoelectric actuator；
When step 3, piezoelectric actuator on-line operation, its actual output displacement and input voltage are measured；
Step 4, on-line identification is carried out to model parameter by adaptive algorithm, model when obtaining on-line operation is simultaneously calculated Its inversion model；
Step 5, the inversion model parameter according to obtained by calculating, original parameter is carried out online in replacing the controller of piezoelectric actuator Update.
Compared with prior art, beneficial effects of the present invention are：
(1) the adjustable inverse controller of on-line parameter proposed by the present invention, it is online with output displacement according to voltage is actually entered Adjusting parameter, improves output accuracy；(2) when the present invention can run efficiently against piezoelectric actuator, due to input signal The reasons such as change and the error caused by the Hysteresis Model Parameters variation that causes；(3) Adaptive inverse control side proposed by the present invention Method, can simultaneously be applied to different size, the piezoelectric actuator of model.
Brief description of the drawings
Fig. 1 is the flow chart of the adaptive inverse control of piezoelectric actuator of the present invention.
Fig. 2 is basic Play operators schematic diagram.
Fig. 3 is piezoelectric actuator hesitation schematic diagram.
Fig. 4 is present system block diagram.
Fig. 5 is example input waveform figure.
Fig. 6 is model adaptation identification result figure.
Specific embodiment
With reference to Fig. 1, a kind of adaptive inverse control of piezoelectric actuator of the invention is comprised the following steps：
Step 1, the Hysteresis Nonlinear relation for piezoelectric actuator, set up offline the output displacement of piezoelectric actuator with it is defeated Enter the nonlinear mathematical model of voltage；
Step 2, the nonlinear mathematical model according to foundation, calculate the inversion model of piezoelectric actuator, used as initial inverse control Device processed drives piezoelectric actuator；
When step 3, piezoelectric actuator on-line operation, its actual output displacement and input voltage are measured；
Step 4, on-line identification is carried out to model parameter by adaptive algorithm, model when obtaining on-line operation is simultaneously calculated Its inversion model；
Step 5, the inversion model parameter according to obtained by calculating, original parameter is carried out online in replacing the controller of piezoelectric actuator Update.
Further, Hysteresis Nonlinear shows as the circular relation between input voltage and output displacement in step 1；Due to Prandtl-Ishlinskii models possess the inversion model of parsing, therefore the present invention takes PI models slow to describe piezoelectric actuator Stagnant nonlinear characteristic.Hysteresis Nonlinear is regarded as what a series of basic Play operators linear weighted functions were formed by stacking by PI models, knot Structure is simple, and can obtain the inversion model of analytical form.
As shown in Fig. 2 the operator between input signal v and output signal y is referred to as Play operators, recurrence mathematic(al) representation For：
In formula, v [k] and y [k] represents the input and output at Play operator k moment respectively, and r is the threshold values of Play operators；
Play operators for multiple difference threshold values carry out linear weighted function superposition, obtain PI Hysteresis Models output formula and are：
In formula, H represents piezoelectric actuator sluggishness PI models, and n is the Play operator quantity chosen, and weight coefficient vector isThreshold values vector rT=(r1,…,rn), 0=r1＜ ... ＜ rn＜ ∞；The initial shape of Play operators State vector y [0]T=(y1[0],…,yn[0])。
Further, in step 2 inversion model as controller, according to given expected displacement input instruction, by inversion model Controller drives piezoelectric actuator to export corresponding voltage.
PI inversion model expression formulas are as follows：
In formula： H represents that piezoelectric actuator is sluggish PI models,For sluggish PI inversion models are estimated.
Further, traditionally PI model parameter identification methods mostly using least square method or the Norm minimum of error two come Realize, parameter is obtained under offline mode, the model error that Parameters variation causes can not be eliminated in the Adverse control that feedovers.
On-line identification is carried out to PI models weight vector using adaptive statistical filtering in step 4, detailed process is：
It is [v to set piezoelectric actuator input voltage range firstmin,vmax], output displacement scope is [ymin,ymax]；Input Voltage uses digital control, and k-1 moment input voltages v [k-1] and k moment input voltages v [k] is monotone variation, therefore k moment PI Model output is expressed as：
In formula,It is n Play operator output vector of k moment, w*It is the weight coefficient vector of PI models,It is k moment w*Estimation,
For the prediction of k moment PI models is exported.
Parameter updates rule：
0 ＜ γ ＜ 2 are adjustable constant in formula, to ensure the nonnegative weights of PI models, ifIn i-thFor It is negative, order
Below in conjunction with drawings and Examples, the invention will be further described.
Embodiment
With reference to Fig. 3, there is the non-linear deficiencies such as sluggishness, creep in piezoelectric ceramics, traditional method is to utilize high-precision sensing Device and PID controller realize closed-loop control to reach control purpose.But this method assumes that the linear model of driving implement, Make system that there is preferable dynamic characteristic by setting parameter.Actually because driver has lagging characteristics, above-mentioned side is taken Method can only for certain point and determine condition setting parameter reach Optimal Control effect, when control signal on a large scale it is interior change or Control performance will decline and be difficult to setting parameter when service condition changes.
Present invention application basic Hysteresis Model (PI) lagging characteristics of piezoelectric ceramics are analyzed model and calculate it is inverse Model, carrying out closed-loop control based on this inverse model control device can obtain more satisfied control effect in theory.
With reference to Fig. 1, piezoelectric actuator shows as a kind of many-valued corresponding Non-smooth surface, nonlinear lagging characteristics, and When input signal changes, lagging characteristics can also change, i.e., piezoelectric actuator shows as a kind of special Dynamic Hysteresis Nonlinear characteristic.For the model error for preventing model parameter from causing when changing, the present invention is actual when piezoelectric actuator runs The input voltage and output displacement at its two ends are measured, and on-line identification is carried out to model parameter, then derive corresponding inverse mould Type.
Then according to real income inversion model parameter, original controller parameter is adjusted, specific control block diagram is shown in figure 4。
Fig. 5 and Fig. 6 illustrate the parameter identification based on adaptive algorithm.The triangle shown in Fig. 5 is input into piezoelectric actuator Wave voltage, take parameter to update rule formula (5) carries out on-line identification to PI models, takes γ=0.5, and Play operator quantity n takes 10, The selection of threshold values according toFig. 6 is simulation output and driver reality output displacement.
Can show that adaptive algorithm recognizes PI model mean absolute errorsRoot mean square is missed DifferenceError is minimum.
The foregoing describe general principle of the invention, principal character and advantage.One's own profession technical staff is it should be appreciated that the present invention It is not restricted to the described embodiments, merely illustrating the principles of the invention described in above-described embodiment and specification is not departing from On the premise of spirit and scope of the invention, various changes and modifications of the present invention are possible, and these changes and improvements both fall within requirement In the scope of the invention of protection.Claimed thunderbolt is by appending claims and its equivalent thereof.

Claims (4)

1. a kind of adaptive inverse control of piezoelectric actuator, it is characterised in that comprise the following steps：
Step 1, the Hysteresis Nonlinear relation for piezoelectric actuator, set up the output displacement and input electricity of piezoelectric actuator offline The nonlinear mathematical model of pressure；
Step 2, the nonlinear mathematical model according to foundation, calculate the inversion model of piezoelectric actuator, as initial inverse controller To drive piezoelectric actuator；
When step 3, piezoelectric actuator on-line operation, its actual output displacement and input voltage are measured；
Step 4, on-line identification is carried out to model parameter by adaptive algorithm, model when obtaining on-line operation and to calculate its inverse Model；
Step 5, the inversion model parameter according to obtained by calculating, original parameter is carried out online more in replacing the controller of piezoelectric actuator Newly.
2. the adaptive inverse control of piezoelectric actuator according to claim 1, it is characterised in that used in step 1 PI models describe piezoelectric actuator Hysteresis Nonlinear characteristic；
Operator between input signal v and output signal y is referred to as Play operators, and recurrence mathematic(al) representation is：
y [ k ] = max { v [ k ] - r , min { v [ k ] + r , y [ k - 1 ] } } y [ 0 ] = max { v [ 0 ] - r , min { v [ 0 ] + r , y [ 0 ] } } - - - ( 1 )
In formula, v [k] and y [k] represents the input and output at Play operator k moment respectively, and r is the threshold values of Play operators；
Play operators for multiple difference threshold values carry out linear weighted function superposition, obtain PI Hysteresis Models output formula and are：
y [ k ] = H [ v [ k ] , y [ k - 1 ] ] = Σ i = 1 n w i * [ k ] { m a x { v [ k ] - r i , min { v [ k ] + r i , y [ k - 1 ] } } - - - ( 2 )
In formula, H represents piezoelectric actuator sluggishness PI models, and n is the Play operator quantity chosen, and weight coefficient vector isThreshold values vector rT=(r1,…,rn), 0=r1＜ ... ＜ rn＜ ∞；The initial shape of Play operators State vector y [0]T=(y1[0],…,yn[0])。
3. the adaptive inverse control of piezoelectric actuator according to claim 1, it is characterised in that PI is inverse in step 2 Model expression is as follows：
v [ k ] = H - 1 [ y [ k ] , v [ k - 1 ] ] = Σ i = 1 n w i ′ [ k ] { m a x { y [ k ] - r i ′ , min { y [ k ] + r i ′ , v [ k - 1 ] } } - - - ( 3 )
In formula, H represents that piezoelectric actuator is sluggish PI models,For sluggish PI inversion models are estimated.
4. the adaptive inverse control of piezoelectric actuator according to claim 1, it is characterised in that used in step 4 Adaptive statistical filtering carries out on-line identification to PI models weight vector, and detailed process is：
If piezoelectric actuator input voltage range is [vmin,vmax], output displacement scope is [ymin,ymax]；Input voltage is used Digital control, k-1 moment input voltages v [k-1] and k moment input voltages v [k] is monotone variation, therefore k moment PI model is exported It is expressed as：
In formula,It is n Play operator output vector of k moment, w*It is the weight coefficient vector of PI models,It is k moment w*Estimation,It is k moment PI The prediction output of model.
Parameter updates rule：
0 ＜ γ ＜ 2 are adjustable constant in formula, to ensure the nonnegative weights of PI models, ifIn i-thBe it is negative, Order
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CN107544241A (en) * 2017-09-25 2018-01-05 广州佳越实业有限公司 The sluggish non-linearity PID of piezoelectric ceramic actuator is against compensating control method
CN107688292A (en) * 2017-08-28 2018-02-13 广东工业大学 A kind of flexible nano localization method, apparatus and system based on piezoelectric ceramics
CN107807531A (en) * 2017-11-30 2018-03-16 北京航空航天大学 A kind of adaptive inversion tracking and controlling method for ultra-magnetic telescopic tracking platform
CN107807532A (en) * 2017-11-30 2018-03-16 北京航空航天大学 A kind of adaptive inversion vibration isolation control method for ultra-magnetic telescopic vibration-isolating platform
CN108877843A (en) * 2018-09-11 2018-11-23 中科院合肥技术创新工程院 A kind of threshold decision anti-saturation method for piezo actuator in hard disk
CN109557816A (en) * 2018-12-28 2019-04-02 武汉工程大学 A kind of suppressing method, system and the medium of piezoelectric ceramic actuator lagging characteristics
CN110632845A (en) * 2019-09-16 2019-12-31 杭州电子科技大学 Piezoelectric driver hysteresis modeling and feedforward control method based on improved PI model

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CN107688292A (en) * 2017-08-28 2018-02-13 广东工业大学 A kind of flexible nano localization method, apparatus and system based on piezoelectric ceramics
CN107688292B (en) * 2017-08-28 2020-11-13 广东工业大学 Flexible nano positioning method, device and system based on piezoelectric ceramics
CN107544241B (en) * 2017-09-25 2020-10-02 江西赛鹰智能科技有限公司 Nonlinear PID inverse compensation control method for piezoelectric ceramic actuator hysteresis
CN107544241A (en) * 2017-09-25 2018-01-05 广州佳越实业有限公司 The sluggish non-linearity PID of piezoelectric ceramic actuator is against compensating control method
CN107807532A (en) * 2017-11-30 2018-03-16 北京航空航天大学 A kind of adaptive inversion vibration isolation control method for ultra-magnetic telescopic vibration-isolating platform
CN107807532B (en) * 2017-11-30 2020-02-18 北京航空航天大学 Self-adaptive reverse vibration isolation control method for giant magnetostrictive vibration isolation platform
CN107807531B (en) * 2017-11-30 2020-02-18 北京航空航天大学 Self-adaptive inverse tracking control method for giant magnetostrictive tracking platform
CN107807531A (en) * 2017-11-30 2018-03-16 北京航空航天大学 A kind of adaptive inversion tracking and controlling method for ultra-magnetic telescopic tracking platform
CN108877843A (en) * 2018-09-11 2018-11-23 中科院合肥技术创新工程院 A kind of threshold decision anti-saturation method for piezo actuator in hard disk
CN109557816A (en) * 2018-12-28 2019-04-02 武汉工程大学 A kind of suppressing method, system and the medium of piezoelectric ceramic actuator lagging characteristics
CN109557816B (en) * 2018-12-28 2021-06-29 武汉工程大学 Method, system and medium for inhibiting hysteresis characteristic of piezoelectric ceramic actuator
CN110632845A (en) * 2019-09-16 2019-12-31 杭州电子科技大学 Piezoelectric driver hysteresis modeling and feedforward control method based on improved PI model
CN110632845B (en) * 2019-09-16 2022-05-31 杭州电子科技大学 Piezoelectric driver hysteresis modeling and feedforward control method based on improved PI model

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