CN104503244A - Nonrepetitiveness disturbance observer based precision positioning selective ILC (iteration learning control) system and method - Google Patents

Abstract

The invention discloses a nonrepetitiveness disturbance observer based precision positioning selective ILC (iteration learning control) system and method. The system comprises a selective iteration learning control law module (1) and a PID (proportion integration differentiation) feedback control module (3). Storages are used for storing magnitude of error ej(k) and a learning control variable rj(k); a learning filter (12) and a time-varying filter (14) are adopted to realize complete inhibition of repetitive disturbance. A nonrepetitiveness disturbance observer module (2) comprising a nonrepetitiveness disturbance filter (21) is adopted to inhibit nonrepetitiveness disturbance with the frequency range within the bandwidth range of the nonrepetitiveness disturbance filter (21). The nonrepetitiveness disturbance with the frequency range beyond the bandwidth range of the nonrepetitiveness disturbance filter (21) is selectively inhibited through the time-varying filter (14) so as to enter the iteration process. Good effect on both repeatability error and nonrepetitiveness error is achieved, positioning and tracking performance is improved, and the system and method is particularly suitable for ultraprecision positioning during grating ruling.

Description

Based on the precision positioning selectivity ILC system and method for non-repeatability disturbance observer

Technical field

The present invention relates to a kind of automatic control technology field, be specifically related to precision positioning selectivity ILC (iteration Learning Control, the iterative learning controls) method based on non-repeatability disturbance observer.The present invention can be applied in the accurate control technique such as ruling grating.

Background technology

Iterative learning controls the Best available control technology that (ILC, iteration Learning Control) is a kind of generally acknowledged execution repetitive operation system.In learning process, the tracking error of past iteration can merge the new feed-forward control signals of generation one to improve the performance of next iteration, effectively can suppress the reproducibility error independent of iterative learning number of times.Principle of work and the delineation data of optical grating graduating machine positioning system all show, this positioning system, in resetting process, has a lot of repeatable errors.So this position fixing process can utilize PID controller design ILC feedforward controller, with the repeatable error signal existed in suppression system.But in actual scoring process, non-repeatability disturbance also can exist simultaneously, and all can change in iterative process each time.Standard I LC can only unceasing study weaken repeated disturbance, and non-repeatability disturbance enters study circulation and can limit and even worsen accessible ILC performance originally, causes error to amplify.

In order to improve the antijamming capability of ILC to non-repeatability disturbance, each research institution has carried out a large amount of research work.A kind of method is carried out pre-filtering to the error signal of disturbance input and is decomposed into repeatability part and non-repeatability part.The repeatability part of error is only had just to allow to enter the study circulation of ILC.As list of references (Lee, J.H., Lee, K.S., and Kim, W.C., 2000, Model-based iterative learning control witha quadratic criterion fortime-varying linear systems, Automatica, 36, pp.641657.) described application process, shift out the part independent of iteration by Kalman filter, improve the validity of study.And list of references (Merry, R., van de Molengraft, R., and Steinbuch, M., 2008, Iterativelearning control with wavelet filtering, Int.J.Robust Nonlin.Control, 18, pp.1052-1071.) described application process then uses wavelet filter to filter out non-repeatability disturbance.Other method then concentrates on the adjustment of ILC scheme self, the robustness of enhanced scheme.These class methods comprise high-order ILC, segmentation ILC and are with the ILC sometimes becoming robust filter (Q wave filter).List of references (Chen, Y.and Moore, K.L., 2002, Harnessing the nonrepetitiveness initerative learning control, Proc.41 st IEEE Conference on Decision and Control, 3, pp.3350-3355.) by supposing that the pattern of non-repeatable errors is known, devising iteration territory disturbance observer (a kind of special high-order observer) and filtering for non-repeatability interference.List of references (Sandipan, M., Joshua, C., and Tomizuka, M., 2007, Precision Positioning ofWafer Scanners Segmented Iterative Learning Control for NonrepetitiveDisturbances, IEEE Control Syst.Mag., 27 (4), pp.20-25.) Time Domain Piecewise ILC strategy is used for the precise flange of wafer scanner, the opening and closing of its learning process are the amplitudes based on iteration repeatability and non-repeatability disturbance each time.Further popularization becomes Q wave filter when being and adding cutoff frequency iteration adjustment online according to positioning error time frequency analysis in ILC.When repeated disturbance mainly concentrates on low-frequency range, in time, becomes Q filter bandwidht and reduces with the impact reducing non-repeatability disturbance; Otherwise time become Q wave filter bandwidth increase to obtain maximum learning ability and better performance.The such ILC scheme of many research and establishments, as list of references (Zhang, B., Wang, D., andYe, Y., 2005, Wavelet transform-based frequency tuning ILC, IEEE Trans.Syst.Man Cyb.Part B, 35 (1), pp.107-114.) wavelet transformation is employed for Time-Frequency Analysis, list of references (Rotariu, I., Steinbuch, M., and Ellenbroek, R., 2008, AdaptiveIterative Learning Control for High Precision Motion Systems, IEEE Trans.Control Syst.Techn, 16 (5), 1075-1082.) have employed Wigner distribution algorithm.Above-mentioned enhancing robustness ILC algorithm can effectively avoid the error caused by non-repeatability disturbance to amplify, but the suppression of non-repeatability disturbance itself does not obtain essence to solve.

Summary of the invention

(1) technical matters that will solve

The present invention is intended to solve existing ILC method can not possess excellent rejection ability simultaneously problem to the repeated disturbance in the Precision Positioning such as ruling grating and non-repeatability disturbance.

(2) technical scheme

For solving the problems of the technologies described above, the present invention proposes a kind of precision positioning selectivity ILC system based on non-repeatability disturbance observer, for controlling control object, system comprises selectivity iterative learning control law module (1) and PID feedback control module (3), described selectivity iterative learning control law module (1) comprises first memory (11), learning filters (12), second memory (13) and time varying filter (14), wherein, the position reference control inputs amount y of described control object _d(k) and the previous location output quantity y of reality _jthe margin of error e of (k) _jk () inputs to described first memory (11); The positioning error amount e of described first memory (11) _jk () exports to described learning filters (12), the study control variable quantity that described learning filters (12) exports and the previous study control amount r that described second memory (13) stores _jk () is added and exports to described time varying filter (14) together, described time varying filter (14) exports new study control amount r _j+1(k), this new study control amount r _j+1k () feeds back to described second memory (13) and stores; New study control amount r _j+1(k) and previous positioning error amount e _jk () is added and inputs to described PID feedback control module (3), this PID feedback control module 3 exports initial control signal c _j+1(k); Described j is 0 or natural number, and represent iterative loop number of times, k is the time index of each iteration.Variable containing subscript j represents the quantity of information of the period of motion of a jth precision positioning, and the variable containing subscript j+1 represents the quantity of information of+1 period of motion of jth.

According to a kind of embodiment of the present invention, system also comprises non-repeatability disturbance observer module (2), described non-repeatability disturbance observer module (2) comprises system name model inversion model module (23) of non-repeatability disturbance wave filter (21), time factor module (22) and identification, wherein, previous effective control signal u _jk () inputs to described time factor module (22), this time factor module 22 exports k-m moment effective control signal u _j(k-m), m is the delay step of precision positioning closed-loop system complementary sensitivity function; The previous output signal y of described control object _jk () enters system name model inversion model module (23) of identification, the signal that described system name model inversion model module (23) exports and the signal u that described time factor module (22) exports _j(k-m) described non-repeatability disturbance wave filter (21) is entered after making difference; Described initial control signal c _j+1k () deducts signal that described non-repeatability disturbance wave filter (21) exports and to be effectively controlled signal u _j+1(k), this effective control signal and disturbing signal d _j+1k () is added and exports to described control object together.

According to a kind of embodiment of the present invention, described control object is ruling grating precisely locating platform.

According to a kind of embodiment of the present invention, to the ending-criterion of described control object be:

$e_{\∞}=\frac{1-Q_I}{1-Q_I(1-z^m\mathrm{LT})}[(1-T)Y_d+{\mathrm{PSD}}_r]+\frac{1}{1-Q_I(1-z^m\mathrm{LT})}\mathrm{PS}(D_{\mathrm{nj}+1}-Q_I{D}_{\mathrm{nj}})\→0$

Wherein, e represents ruling grating positioning system closed loop positioning error, Q _irepresent time varying filter, z ^mrepresent that the time delay factor is reciprocal, T represents supplementary sensitivity function, Y _drepresent that P represents ruling grating positioning system, and S represents sensitivity function, D with reference to control inputs amount z territory expression-form _rrepresent the z territory expression-form of repeated disturbance, D _njrepresent the non-repeatability disturbance z territory expression-form of jth time iteration, D _nj+1represent the non-repeatability disturbance z territory expression-form of jth+1 iteration.

According to a kind of embodiment of the present invention, described learning filters (12) supplements the inverse of sensitivity function for closed loop.

According to a kind of embodiment of the present invention, described time varying filter (14) is one and has wide bandwidth at boost phase, and the constant speed stage comprises the time varying filter of multiple notch.

According to a kind of embodiment of the present invention, described non-repeatability disturbance wave filter (21) meets following constraint condition:

$\left\{\begin{array}{c}\left|Q_D\left(e^{\mathrm{j\&omega;}}\right)\right|<\frac{1}{\left|\mathrm{\&Delta;T}\left(e^{\mathrm{j\&omega;}}\right)\right|},\&ForAll;\mathrm{\&omega;}\\ |1-z^{-m}{Q}_D|z=e^{{\mathrm{j\&omega;n}}_j}<<1{\mathrm{\&omega;}}_{\mathrm{nj}}\&le;{\mathrm{\&omega;}}_{\mathrm{cd}}\left(Q_D\right)\end{array}\right.$

Wherein, Δ T (e ^{j ω}) be multiplication indeterminate, ω _njnon-repeatability forcing frequency, z ^-mrepresent the time delay factor, Q _drepresent non-repeatability disturbance wave filter, ω _cdit is the cutoff frequency of this non-repeatability disturbance wave filter (21).

The present invention also proposes a kind of precision positioning selectivity ILC method based on non-repeatability disturbance observer, and for controlling control object, the method comprises the steps: to adopt storer to store the margin of error e in iterative process _j(k) and study control amount r _j(k); By disturbance d _jk () is decomposed into repeated disturbance d _r(k) and non-repeatability disturbance d _nj(k); Learning filters (12) and time varying filter (14) is adopted to realize the suppression completely of repeated disturbance.

According to a kind of embodiment of the present invention, described method also comprises the steps: that employing comprises the non-repeatability disturbance of non-repeatability disturbance observer module (2) blanketing frequency scope in this non-repeatability disturbance wave filter (21) bandwidth range of non-repeatability disturbance wave filter (21).

According to a kind of embodiment of the present invention, enter iterative process by described time varying filter (14) the non-repeatability disturbance that optionally blanketing frequency scope exceeds non-repeatability disturbance wave filter (21) bandwidth.

According to a kind of embodiment of the present invention, to the ending-criterion of described control object be:

$e_{\&infin;}=\frac{1-Q_I}{1-Q_I(1-z^m\mathrm{LT})}[(1-T)Y_d+{\mathrm{PSD}}_r]+\frac{1}{1-Q_I(1-z^m\mathrm{LT})}\mathrm{PS}(D_{\mathrm{nj}+1}-Q_I{D}_{\mathrm{nj}})\&RightArrow;0$

Wherein, e represents ruling grating positioning system closed loop positioning error, Q _irepresent time varying filter, z ^mrepresent that the time delay factor is reciprocal, T represents supplementary sensitivity function, Y _drepresent that P represents ruling grating positioning system, and S represents sensitivity function, D with reference to control inputs amount z territory expression-form _rrepresent the z territory expression-form of repeated disturbance, D _njrepresent the non-repeatability disturbance z territory expression-form of jth time iteration, D _nj+1represent the non-repeatability disturbance z territory expression-form of jth+1 iteration.

According to a kind of embodiment of the present invention, described learning filters (12) supplements the inverse of sensitivity function for closed loop.

According to a kind of embodiment of the present invention, described time varying filter (14) is one and has wide bandwidth at boost phase, and the constant speed stage comprises the time varying filter of multiple notch.

According to a kind of embodiment of the present invention, described non-repeatability disturbance wave filter (21) meets following constraint condition:

$\left\{\begin{array}{c}\left|Q_D\left(e^{\mathrm{j\&omega;}}\right)\right|<\frac{1}{\left|\mathrm{\&Delta;T}\left(e^{\mathrm{j\&omega;}}\right)\right|},\&ForAll;\mathrm{\&omega;}\\ |1-z^{-m}{Q}_D|z=e^{{\mathrm{j\&omega;n}}_j}<<1{\mathrm{\&omega;}}_{\mathrm{nj}}\&le;{\mathrm{\&omega;}}_{\mathrm{cd}}\left(Q_D\right)\end{array}\right.$

Wherein, Δ T (e ^{j ω}) be multiplication indeterminate, ω _njnon-repeatability forcing frequency, z ^-mrepresent the time delay factor, Q _drepresent non-repeatability disturbance wave filter, ω _cdit is the cutoff frequency of this non-repeatability disturbance wave filter (21).

(3) beneficial effect

The present invention adopts the learning filters comprising time factor to carry out preliminary shaping to selectivity iterative learning control module, and according to the bandwidth determination time parameter of the feedback system be made up of control object, feedback control module and state observer module.For the feature of the agitation error comprised in Precision Positioning, the shaping of HFS is carried out by study control rule module and time varying filter, the reproducibility error on the one hand suppressing repeated disturbance to cause completely, the on the other hand non-repeatable errors that causes higher than the non-repeatability disturbance of non-repeatability disturbance filter bandwidht of Selective depression frequency range; By the non-repeatable errors that the non-repeatability disturbance wave filter in disturbance observer module inhibits frequency range to cause lower than the non-repeatability disturbance of non-repeatability disturbance filter bandwidht.Therefore, the present invention can ensure the positioning precision of ruling grating platform stable working stage.

Invention increases the locating and tracking performance of ruling grating, start with from positioning precision index, combine learning filters, time varying filter and non-repeatability disturbance wave filter, time factor module, constitute a ruling grating precision positioning selectivity iterative learning control method based on non-repeatability disturbance observer.It is for the requirement of high precision delineation, can the repeatability in the effective attenuation external world and non-repeatability disturbance, add the bandwidth of ruling grating Precision Positioning in the repeated disturbance decay of out of phase to greatest extent, do not cause the amplification of non-repeatability disturbance, enhance the ability that iterative learning controls.

The invention process is simple, the basis of conventional iterative study control is easily transformed, for the fine positioning system of ruling grating, there is good applicability, reference location control inputs amount can change according to the difference of grating spacing, even may be used for the delineation of Variable line-space gratings.

Filter design method, improves non-repeatability Disturbance Rejection ability, especially for the discrete-time system with time delay.Another advantage is compared with the existing ILC scheme using DQB, becomes Q during by introducing in iterative learning circulation _iwave filter, reaches frequency can be filtered out study circulation object higher than the non-repeatability disturbance of DQB bandwidth.The present invention program adds the bandwidth of ruling grating Precision Positioning in the repeated disturbance decay of out of phase to greatest extent, and does not cause the amplification of non-repeatability disturbance.

Accompanying drawing explanation

Fig. 1 is the control block diagram of precision positioning selectivity ILC system of the present invention;

Fig. 2 is the result curve that ruling grating location adopts basic PID to control;

Fig. 3 is the positioning error comparison diagram after ruling grating locating platform adopts the present invention and different Iterative Learning Control Algorithm;

Fig. 4 is the grating positioning error spectrum figure using the present invention and the 5th iteration during different Iterative Learning Control Algorithm.

Embodiment

The present invention proposes a kind of precision positioning selectivity ILC system and method based on non-repeatability disturbance observer.Generally, the present invention passes through in precise Positioning Control circulation in conjunction with disturbance observer (DQB) and a time varying filter, improve ruling grating be positioned in the face of non-repeatability disturbance time rejection, particularly when the frequency of non-repeatability disturbance and repeated disturbance occurs overlapping, ruling grating positioning system has good Disturbance Rejection ability.

Specifically, the present invention adopts storer to store the margin of error e in iterative process _j(k) and study control amount r _jk (), by disturbance d _jk () is decomposed into repeated disturbance d _r(k) and non-repeatability disturbance d _nj(k); Learning filters and time varying filter is adopted to realize the suppression completely of repeated disturbance.

The present invention also adopts the non-repeatability disturbance of non-repeatability disturbance observer module blanketing frequency scope in this non-repeatability disturbance filter band wide region comprising non-repeatability disturbance wave filter.And enter iterative process by the non-repeatability disturbance that optionally blanketing frequency scope exceeds non-repeatability disturbance filter bandwidht of described time varying filter.

For making the object, technical solutions and advantages of the present invention clearly understand, below in conjunction with specific embodiment, and with reference to accompanying drawing, the present invention is described in further detail.

Fig. 1 is the control block diagram based on non-repeatability disturbance observer precision positioning selectivity ILC system of the present invention.As shown in Figure 1, ILC system of the present invention is used for controlling control object P, and this control object P is being such as the precisely locating platforms such as ruling grating precisely locating platform.Control system comprises selectivity iterative learning control law module 1, non-repeatability disturbance observer module 2 and PID feedback control module 3.

Selectivity iterative learning control law module 1 comprises first memory 11, learning filters 12, second memory 13 and time varying filter 14 module.

Non-repeatability disturbance observer module 2 comprises the system name model inversion model module 23 of non-repeatability disturbance wave filter 21, time factor module 22 and identification.

The position reference control inputs amount y of control object P _d(k) and the previous location output quantity y of reality _jthe margin of error e of (k) _jk () inputs to first memory 11. j represents iterative loop number of times, and k is the time index of each iteration.The positioning error amount e of first memory 11 _jk () exports to learning filters 12, the study control variable quantity that learning filters 12 exports and the previous study control amount r that second memory 13 stores _jk () is added and exports to time varying filter 14 together, time varying filter 14 exports new study control amount r _j+1(k), new study control amount r _j+1k () feeds back to second memory 13 and stores.

New study control amount r _j+1(k) and previous positioning error amount e _jk () addition inputs to PID feedback control module 3, PID feedback control module 3 and exports initial control signal c _j+1(k).

On the one hand, previous effective control signal u _jk () inputs to time factor module 22, time factor module 22 exports k-m moment effective control signal u _j(k-m), m is the delay step of precision positioning closed-loop system complementary sensitivity function.

On the other hand, with disturbing signal d _jk () is added the previous output signal y exporting to control object P together _jk () enters the system name model inversion model module 23 of identification, inversion model module 23 outputs signal the signal u exported with time factor module 22 _j(k-m) non-repeatability disturbance wave filter 21 is entered after making difference.Initial control signal c _j+1k () deducts the signal that non-repeatability disturbance wave filter 21 exports and to be effectively controlled signal u _j+1(k), this effective control signal and disturbing signal d _j+1k () is added and exports to control object P together.

The control method of the precision positioning selectivity ILC system based on non-repeatability disturbance observer of the present invention adopts first memory 11 and second memory 13 to store the margin of error e of iterative process _j(k) and study control amount r _j(k).By disturbance d _jk () is decomposed into a repeated disturbance d _r(k) and a non-repeatability disturbance d _nj(k), learning filters 12 and time varying filter 14 is then adopted to realize the suppression completely of repeated disturbance, adopt and comprise the non-repeatability disturbance of non-repeatability disturbance observer module 2 blanketing frequency scope in non-repeatability disturbance wave filter 21 bandwidth range of non-repeatability disturbance wave filter 21, enter iterative process by the time varying filter 14 non-repeatability disturbance that optionally blanketing frequency scope exceeds non-repeatability disturbance wave filter 21 bandwidth.

In foregoing description, wherein, j is 0 or natural number, and represent iterative loop number of times, k is the time index of each iteration.Variable containing subscript j represents the quantity of information of the period of motion of a jth precision positioning, and the variable containing subscript j+1 represents the quantity of information of+1 period of motion of jth.

When the period of motion of j=0, effective controlled quentity controlled variable u (k)=0, margin of error e (k)=0.

In a jth period of motion, position reference control inputs amount y _dk () deducts previous actual output quantity y _jk () obtains margin of error e _j(k), and stored in first memory 11.This margin of error includes reproducibility error d _rk () and frequency range exceed the non-repeatable errors of non-repeatability disturbance wave filter 21 bandwidth.The margin of error e stored in first memory 11 _jk () enters the learning filters 12 in selectivity iterative learning control law module 1, first obtain the margin of error in k-m moment, then obtain the variable quantity of study control by the margin of error in k-m moment, the controlled quentity controlled variable r stored simultaneously in second memory 13 _jk () is added with the variable quantity of this study control and enters time varying filter 14, obtain new study control amount r after inhibit repeated disturbance and the non-repeatability disturbance of frequency higher than non-repeatability disturbance wave filter 21 bandwidth _j+1k () is stored in second memory 13, enter+1 period of motion of jth.

Its process can describe with following formula: r _j+1(k)=Q _i(q) [r _j(k)+L (q) e _j(k+m)], wherein Q _iq () represents time varying filter, L (q) represents learning filters, and q represents leading time translation operator.

In+1 period of motion of jth, effective study control amount r _j+1(k) and margin of error e _jk () acts on PID feedback control module 3 after being added and obtains initial control signal c _j+1k (), the output then deducting non-repeatability disturbance observer module is effectively controlled signal u _j+1(k), then with external disturbance d _j+1k () reacts on control object, obtain the actual output quantity y of j+1 the period of motion _j+1(k).

The output of the above non-repeatability disturbance observer module 2 is by effective steering order u of jth time iteration _jy is exported with system _jk () enters disturbance observer module and obtains: effective steering order u on the one hand _jk () inputs to time factor module 22, obtain effective steering order u in k-m moment _j(k-m), another aspect effectively steering order u _j(k-m) extraneous repeated disturbance d is added _r(k) and non-repeatability disturbance d _njk () remakes and obtains system output y for control object P _jk (), system exports y _jk system name model inversion model module 23 that () enters identification obtains the actual input quantity of system based on model.This actual input quantity deducts effective steering order u _j(k-m) enter the output that non-repeatability disturbance wave filter 21 obtains non-repeatability disturbance disturbance observer 2 again, inhibit frequency range at wave filter Q _dnon-repeatability disturbance in bandwidth range.

According to above process successively reciprocation cycle, until control object P motion terminates.Ending-criterion is:

$e_{\&infin;}=\frac{1-Q_I}{1-Q_I(1-z^m\mathrm{LT})}[(1-T)Y_d+{\mathrm{PSD}}_r]+\frac{1}{1-Q_I(1-z^m\mathrm{LT})}\mathrm{PS}(D_{\mathrm{nj}+1}-Q_I{D}_{\mathrm{nj}})\&RightArrow;0$

Wherein, e ruling grating positioning system closed loop positioning error, Q _irepresent time varying filter, z ^mrepresent that the time delay factor is reciprocal, T represents supplementary sensitivity function, Y _drepresent that P represents ruling grating positioning system, and S represents sensitivity function, D with reference to control inputs amount z territory expression-form _rrepresent the z territory expression-form of repeated disturbance, D _njrepresent the non-repeatability disturbance z territory expression-form of jth time iteration, D _nj+1represent the non-repeatability disturbance z territory expression-form of jth+1 iteration.Above-mentioned iterative process is along with the repeatable motion process of whole control object P, as long as precision positioning motion continues always, study control and disturbance observation would not stop, and non-repeatability disturbance wave filter 21, time varying filter 14 continuous disturbance suppression together with learning filters 12 reduces positioning error.Its learning process is the process that system performance constantly promotes, final error amount e _jk () reduces gradually, and tend towards stability.

Learning filters 12 and time varying filter 14 can ensure the learning performance of whole system, guarantee repeated disturbance and the frequency non-repeatability Disturbance Rejection higher than non-repeatability disturbance wave filter 21 bandwidth, non-repeatability disturbance wave filter 21 ensure that the non-repeatability Disturbance Rejection of frequency within non-repeatability disturbance wave filter 21 bandwidth.Time factor module 22 plays control signal and initially to adjust effect, time parameter m determines according to the Bandwidth adjustment of the feedback system that control object P, PID Feedback Control Laws module 3 and non-repeatability disturbance observer module 2 are formed, and can adjust to the disturbance observation closed-loop system comprising control object P.

In the present invention, the Precision Position Location System closed loop positioning error of jth time iteration is:

$\begin{array}{c}{e}_j=y_d\left(k\right)-y_j\left(k\right)\\ =\frac{1-Q_D(q^{-m}-{\mathrm{PP}}_m^{-1})}{1+\mathrm{PC}-Q_D(q^{-m}-{\mathrm{PP}}_m^{-1})}{y}_d\left(k\right)-\frac{(1-q^{-m}{Q}_D)P}{1+\mathrm{PC}-Q_D(q^{-m}-{\mathrm{PP}}_m^{-1})}[d_r\left(k\right)-d_{\mathrm{nj}}\left(k\right)]\end{array}$

Then can obtain sensitivity function S (z ^-1) and supplementary sensitivity function T (z ^-1) be respectively

$S=\frac{1-Q_D(q^{-m}-{\mathrm{PP}}_m^{-1})}{1+\mathrm{PC}-Q_D(q^{-m}-{\mathrm{PP}}_m^{-1})}$

$T=\frac{\mathrm{PC}+Q_D{\mathrm{PP}}_m^{-1}}{1+\mathrm{PC}-Q_D(q^{-m}-{\mathrm{PP}}_m^{-1})}$

Z ^-1the z conversion representing discrete time function is expressed, z=e ^{σ+j ω}, then z is amplitude is e ^σ, phase place is the complex variable of ω, and then obtains the iterative territory ILC kinetics equation of location:

R _j+1＝Q _I(1-z ^mLT)R _j+Q _Iz ^mL[(1-T)Y _d-PS(Dr+D _nj)]

E _J+1＝Q _I(1-z ^mLT)E _j+(1-Q _I)[(1-T)Y _d-PSDr]+PS(D _nj+1-Q _ID _nj)

The adequate condition that this iterative process is stable is Q _i(1-z ^mlT) must meet | Q _i(1-z ^mlT) || _∞< 1, wherein, the performance that can be controlled by following progressive error criterion iterative learning after this adequate condition meets:

$e_{\&infin;}=\frac{1-Q_I}{1-Q_I(1-z^m\mathrm{LT})}[(1-T)Y_d+{\mathrm{PSD}}_r]+\frac{1}{1-Q_I(1-z^m\mathrm{LT})}\mathrm{PS}(D_{\mathrm{nj}+1}-Q_I{D}_{\mathrm{nj}})\&RightArrow;0$

The optimal selection that can obtain learning filters 12 (being expressed as L in formula) from adequate condition is the inverse that closed loop supplements sensitivity function, namely $L=z^{-m}{T_n}^{-1}=z^{-m}\frac{1+P_{n}C-Q_D(q^{-m}-P_n{P}_m^{-1})}{P_{n}C+Q_D{P}_n{P}_m^{-1}}.$ Z herein ^-mensure that learning filters 12 is attainable.

But determine due to the uncertainty of system model, actual Precision Position Location System can be expressed as: P (z ^-1)=P _n(z ^-1) (1+ Δ (z ^-1)), wherein P _n(z ^-1) be the Precision Position Location System nominal plant model of identification, Δ (z ^-1) be uncertain item.Then T (z ^-1)=T _n(z ^-1) (1+ Δ T (z ^-1)), learning filters is actual is $L=z^{-m}{T_n}^{-1}=z^{-m}\frac{1+P_{n}C-Q_D(q^{-m}-P_n{P}_m^{-1})}{P_{n}C+Q_D{P}_n{P}_m^{-1}}.$

In a particular embodiment, non-repeatability disturbance observer module 2 needs blanketing frequency (to be expressed as Q in formula at non-repeatability disturbance wave filter 21 _d) non-repeatability disturbance in bandwidth, so can show that non-repeatability disturbance wave filter 21 must meet following constraint condition by formula:

$\left\{\begin{array}{c}\left|Q_D\left(e^{\mathrm{j\&omega;}}\right)\right|<\frac{1}{\left|\mathrm{\&Delta;T}\left(e^{\mathrm{j\&omega;}}\right)\right|},\&ForAll;\mathrm{\&omega;}\\ |1-z^{-m}{Q}_D|z=e^{{\mathrm{j\&omega;}}_{\mathrm{nj}}}<<1{\mathrm{\&omega;}}_{\mathrm{nj}}\&le;{\mathrm{\&omega;}}_{\mathrm{cd}}\left(Q_D\right)\end{array}\right.$

Wherein, Δ _t(e ^{j ω}) be multiplication indeterminate, ω _njnon-repeatability forcing frequency, z ^-mrepresent the time delay factor, Q _drepresent non-repeatability disturbance wave filter, ω _cdbe this non-repeatability disturbance wave filter (21) be wave filter Q _dcutoff frequency.Constraint condition ensure that the closed loop stability of disturbance observer module, and because Δ _t(e ^{j ω}) can be very large in high frequency duration, ensure that non-repeatability disturbance wave filter 21 is low-pass filters.

In the present embodiment, one of object of selectivity iterative learning control module 1 eliminates all repeated disturbances, and the error of the adequate condition stable according to iterative process and identification system model, when learning filters 12 is expressed as L=z ^-mt _n ^-1, then wave filter Q _ia low-pass filter can be designed to, its cutoff frequency ω _icsatisfy condition: as can be seen from iterative territory ILC error dynamics equation: if as ω < ω _citime, 1-Q _i(e ^{j ω}) ≈ 0, ω _ciwave filter Q _icutoff frequency, low frequency reproducibility error can an iteration elimination.But the e produced by non-repeatability disturbance _j+1middle non-repeatable errors part is then:

$e_{\mathrm{nj}+1}\left(k\right)=P\frac{1-q^{-m}{Q}_D}{1+\mathrm{PC}-Q_D(q^{-m}-{\mathrm{PP}}_m^{-1})}{n}_j\left(k\right)$

Wherein, n _j=d _nj+1(k)-Q _id _nj(k).As non-repeatability disturbance d _njk () concentrates on specific frequency band, and when amplitude is relevant with iteration with phase place, if Q _i≈ 1 will cause error to amplify, so Q _ibe designed to a time varying filter.

The non-repeatability disturbance higher than bandwidth of all repeated disturbances and frequency eliminated by time varying filter 14.The positioning track of Precision Position Location System comprises the different stages.At location boost phase, error is mainly derived from track following, and comprises abundant frequency content, this demands wave filter Q _i(ω _ci) bandwidth is higher; At constant rate period, the error caused by non-repeatability disturbance occupies primary component of error, and iterative learning module 1 needs this fractional error of optionally filtering, then the Q in this stage _iwave filter needs to comprise notch function.Therefore, Q _iwave filter 14 is one and has wide bandwidth at boost phase, and the constant speed stage comprises the time varying filter of multiple notch, and its handoff procedure is as follows:

$Q_I=\left\{\begin{array}{cc}{Q}_{I0}& t<t_{\mathrm{ae}}\\ (1-\mathrm{\&alpha;}\left(t\right))Q_{I0}+\mathrm{\&alpha;}\left(t\right)Q_{I1}& t_{\mathrm{ae}}<t<t_{\mathrm{ae}}+\mathrm{\&Delta;t}\\ Q_{I1}& t\&GreaterEqual;t_{\mathrm{ae}}+\mathrm{\&Delta;t}\end{array}\right.$

Wherein, t _aerepresent the location accelerating sections end time, Δ t is switching cycle, and α (t) gradually changes from 0 to 1: α (t)=(t-t _ae)/Δ t, Q _i0q _iwave filter accelerating sections filter form, Q _i1q _iwave filter constant speed section wave filter, $Q_I\left(q\right)=Q_{I0}\left(q\right)\frac{1-2\cos \left(2\mathrm{\&pi;}{\mathrm{\&omega;}}_0\right)q^{-1}+q^{-2}}{1-2\mathrm{\&alpha;}\cos \left(2\mathrm{\&pi;}{\mathrm{\&omega;}}_0\right)q^{-1}+{\mathrm{\&alpha;}}^2{q}^{-2}},$ ω ₀that frequency is higher than wave filter Q _dthe frequency of the non-repeatability disturbance of bandwidth.

The present invention is applicable to the precise flange system comprising ruling grating Precision Position Location System.

Embodiment

Be that the present invention will be described for an embodiment with the accurate straight line setting movement of the grating blank of ruling grating system below.

The mechanical scratching principle of ruling grating is extruded the coat of metal (aluminium film) on grating substrate by the diamond graver blade of mechanical type optical grating graduating machine, makes it deformation occur and form the cutting of stairstepping.Delineation mode mainly adopts rowland type working method, and namely worktable carries grating blank to be etched and does precision positioning motion, and diamond graver moves reciprocatingly, and direction of motion is vertical with orientation.Often run one-period and delineate a cutting.Very high to the requirement of repetitive positioning accuracy in the precision positioning motion process of grating blank, so all there is a large amount of repeatable errors in its reference locus and undesired signal.Simultaneously due to factor impacts such as thrust calculation and external environment condition (as temperature, foundation vibration, atmospheric pressure etc.) changes, ruling grating Precision Positioning also can be subject to the interference of non-repeatable errors.

With in this embodiment, control object P is the fine positioning platform of carrying grating blank, and it includes fine positioning worktable, grating blank and Piexoelectric actuator, and the expression-form of the P obtained by identification algorithm is: $P\left(z^{-1}\right)=3.3526\&times;{10}^{-7}{z}^{-2}\frac{1+0.813z^{-1}}{1-2.331z^{-1}+2.539z^{-2}},$ The measurement of stop position is completed by two-frequency laser interferometer, and sample frequency is f _s=2.5kHz, sampling period T _sthree controling parameters of=0.0004s, basic PID are respectively: k _p=0.01, k _i=0.01, k _d=0.01.

Fig. 2 is that grating positioning adopts basic PID to control positioning result.Can find that its positioning error comprises repeatability and non-repeatable errors, reproducibility error is distributed in very wide frequency range 0 ~ 100Hz; Non-repeatable errors mainly concentrates on some specific Frequency points, and as 18.32Hz and 50Hz, each iteration initial phase all can change.

Adopt control system of the present invention and method, non-repeatability disturbance wave filter 21 (Q _d) and time varying filter 14 (Q _i) be designed to cutoff frequency ω respectively _cthe wave filter of=60 π rad/s and time varying filter, wherein Δ t=100T _s=0.04s, then Q _d(z ^-1), Q _i0(z ^-1) and Q _i1(z ^-1) be respectively:

$Q_D\left(z^{-1}\right)=\frac{0.1128-0.1074z^{-1}}{1-1.874z^{-1}+{0.889z}^{-2}}$

$Q_{I0}=\frac{0.02691+0.05482z^{-1}+0.02893z^{-2}}{1-1.485z^{-1}+0.5866z^{-2}}$

$\begin{array}{c}{Q}_{I1}=Q_{I0}\left(z^{-1}\right)\frac{1.0372(1-2\cos (2\mathrm{\&pi;}{T}_s*18.32)z^{-1}+z^{-2})}{1-1.98\cos (2\mathrm{\&pi;}{T}_s*18.32)z^{-1}+0.9801*z^{-2}}\\ *\frac{0.9963(1-2\cos (2\mathrm{\&pi;}{T}_s*50)z^{-1}+z^{-2})}{1-1.98\cos (2\mathrm{\&pi;}{T}_s*50)z^{-1}+0.9801z^{-2}}\end{array}$

Fig. 3 is the positioning error comparison diagram after the ruling grating locating platform of this embodiment adopts different Iterative Learning Control Algorithm.As shown in Figure 3, due to the amplification of non-repeatability disturbance, adopt standard I LC method ruling grating precisely locating platform positioning error alter a great deal at different iteration steps; The method adopting standard I LC and DOB to combine can reduce positioning error significantly, but still not ideal enough relative to the robustness of non-repeatability periodic perturbation, this is because disturbance observer DOB can only reach blanketing frequency lower than Q _dthe non-repeatable errors part of filter cutoff frequency, does not have inhibiting effect for the part higher than cutoff frequency, also inevitably can produce amplification; The wave filter 14 become during by introducing one, ILC scheme of the present invention, through 16 iteration cycles, improves dynamic adjustment process well, and namely the positioning performance of ruling grating Precision Position Location System improves.

Fig. 4 is the grating positioning error spectrum figure using the present invention and the 5th iteration during different Iterative Learning Control Algorithm.As can be seen from Figure 4 at the 50Hz place higher than non-repeatability disturbance filter filtering device 21 cutoff frequency, adopt system and method for the present invention not have non-repeatability disturbance to amplify and occur.

Visible, the present invention not only can effectively blanketing frequency lower than the disturbance of non-repeatability disturbance filter filtering device 21 cutoff frequency, remaining non-repeatable errors can also be controlled flexibly by the study circulation of ILC, effectively suppress the amplification of non-repeatability disturbance, improve the positioning performance of ruling grating.

The 50Hz place of cutoff frequency, adopts present system method not have non-repeatability disturbance to amplify and occurs.

In sum, the present invention is directed to the control objects such as ruling grating Precision Positioning, need that excellent rejection ability is possessed to repeated disturbance and non-repeatability disturbance simultaneously, propose a kind of precision positioning selectivity iterative learning control systems based on non-repeatability disturbance observer and method.The present invention passes through in precise Positioning Control circulation in conjunction with disturbance observer (DOB) module and a time varying filter, improve the rejection when in the face of non-repeatability disturbance, particularly when the frequency of non-repeatability disturbance and repeated disturbance occurs overlapping, system has good Disturbance Rejection ability.

The present invention is compared with existing ILC scheme, and first advantage improves non-repeatability Disturbance Rejection ability, especially for the discrete-time system with time delay.Another advantage be reach frequency higher than DOB bandwidth non-repeatability disturbance can by selectivity filter out study circulation object.The present invention program adds the bandwidth of the Precision Positioning such as ruling grating in the repeated disturbance decay of out of phase to greatest extent, and does not cause the amplification of non-repeatability disturbance.

Above-described specific embodiment; object of the present invention, technical scheme and beneficial effect are further described; be understood that; the foregoing is only specific embodiments of the invention; be not limited to the present invention; within the spirit and principles in the present invention all, any amendment made, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (14)

1. the precision positioning selectivity ILC system based on non-repeatability disturbance observer, for controlling control object, it is characterized in that, comprise selectivity iterative learning control law module (1) and PID feedback control module (3), described selectivity iterative learning control law module (1) comprises first memory (11), learning filters (12), second memory (13) and time varying filter (14), wherein

The position reference control inputs amount y of described control object _d(k) and the previous location output quantity y of reality _jthe margin of error e of (k) _jk () inputs to described first memory (11);

The positioning error amount e of described first memory (11) _jk () exports to described learning filters (12), the study control variable quantity that described learning filters (12) exports and the previous study control amount r that described second memory (13) stores _jk () is added and exports to described time varying filter (14) together, described time varying filter (14) exports new study control amount r _j+1(k), this new study control amount r _j+1k () feeds back to described second memory (13) and stores;

New study control amount r _j+1(k) and previous positioning error amount e _jk () is added and inputs to described PID feedback control module (3), this PID feedback control module 3 exports initial control signal c _j+1(k);

Described j is 0 or natural number, and represent iterative loop number of times, k is the time index of each iteration.Variable containing subscript j represents the quantity of information of the period of motion of a jth precision positioning, and the variable containing subscript j+1 represents the quantity of information of+1 period of motion of jth.

2. as claimed in claim 1 based on the precision positioning selectivity ILC system of non-repeatability disturbance observer, it is characterized in that, also comprise non-repeatability disturbance observer module (2), described non-repeatability disturbance observer module (2) comprises system name model inversion model module (23) of non-repeatability disturbance wave filter (21), time factor module (22) and identification, wherein

Previous effective control signal u _jk () inputs to described time factor module (22), this time factor module 22 exports k-m moment effective control signal u _j(k-m), m is the delay step of precision positioning closed-loop system complementary sensitivity function;

The previous output signal y of described control object _jk () enters system name model inversion model module (23) of identification, the signal that described system name model inversion model module (23) exports and the signal u that described time factor module (22) exports _j(k-m) described non-repeatability disturbance wave filter (21) is entered after making difference;

Described initial control signal c _j+1k () deducts signal that described non-repeatability disturbance wave filter (21) exports and to be effectively controlled signal u _j+1(k), this effective control signal and disturbing signal d _j+1k () is added and exports to described control object together.

3., as claimed in claim 1 or 2 based on the precision positioning selectivity ILC system of non-repeatability disturbance observer, it is characterized in that, described control object is ruling grating precisely locating platform.

4., as claimed in claim 1 or 2 based on the precision positioning selectivity ILC system of non-repeatability disturbance observer, it is characterized in that, to the ending-criterion of described control object be:

$e_{\&infin;}=\frac{1-Q_I}{1-Q_I(1-z^m\mathrm{LT})}[(1-T)Y_d+{\mathrm{PSD}}_r]+\frac{1}{1-Q_I(1-z^m\mathrm{LT})}\mathrm{PS}(D_{\mathrm{nj}+1}-Q_I{D}_{\mathrm{nj}})\&RightArrow;0$

Wherein, e represents ruling grating positioning system closed loop positioning error, Q _irepresent time varying filter, z ^mrepresent that the time delay factor is reciprocal, T represents supplementary sensitivity function, Y _drepresent that P represents ruling grating positioning system, and S represents sensitivity function, D with reference to control inputs amount z territory expression-form _rrepresent the z territory expression-form of repeated disturbance, D _njrepresent the non-repeatability disturbance z territory expression-form of jth time iteration, D _nj+1represent the non-repeatability disturbance z territory expression-form of jth+1 iteration.

5. as claimed in claim 1 or 2 based on the precision positioning selectivity ILC system of non-repeatability disturbance observer, it is characterized in that, described learning filters (12) supplements the inverse of sensitivity function for closed loop.

6. as claimed in claim 1 or 2 based on the precision positioning selectivity ILC system of non-repeatability disturbance observer, it is characterized in that, described time varying filter (14) is one and has wide bandwidth at boost phase, and the constant speed stage comprises the time varying filter of multiple notch.

7., as claimed in claim 2 based on the precision positioning selectivity ILC system of non-repeatability disturbance observer, it is characterized in that, described non-repeatability disturbance wave filter (21) meets following constraint condition:

$\left\{\begin{array}{c}\left|Q_D\left(e^{\mathrm{j\&omega;}}\right)\right|<\frac{1}{\left|{\mathrm{\&Delta;}}_T\left(e^{\mathrm{j\&omega;}}\right)\right|},\&ForAll;\mathrm{\&omega;}\\ {{|1-z^{-m}{Q}_D|}_{z=e}}^{{\mathrm{j\&omega;n}}_j}<<1{\mathrm{\&omega;}}_{\mathrm{nj}}\&le;{\mathrm{\&omega;}}_{\mathrm{cd}}\left(Q_D\right)\end{array}\right.$

Wherein, T _t(e ^{j ω}) be multiplication indeterminate, ω _njnon-repeatability forcing frequency, z ^-mrepresent the time delay factor, Q _drepresent non-repeatability disturbance wave filter, ω _cdit is the cutoff frequency of this non-repeatability disturbance wave filter (21).

8., based on a precision positioning selectivity ILC method for non-repeatability disturbance observer, for controlling control object, it is characterized in that, comprising the steps:

Storer is adopted to store margin of error ej (k) in iterative process and study control amount r _j(k);

By disturbance d _jk () is decomposed into repeated disturbance d _r(k) and non-repeatability disturbance d _nj(k);

Learning filters (12) and time varying filter (14) is adopted to realize the suppression completely of repeated disturbance.

9. the precision positioning selectivity ILC method of non-repeatability disturbance observer as claimed in claim 8, is characterized in that, also comprise the steps:

Employing comprises the non-repeatability disturbance of non-repeatability disturbance observer module (2) blanketing frequency scope in this non-repeatability disturbance wave filter (21) bandwidth range of non-repeatability disturbance wave filter (21).

10. the precision positioning selectivity ILC method of non-repeatability disturbance observer as claimed in claim 8, it is characterized in that, enter iterative process by described time varying filter (14) the non-repeatability disturbance that optionally blanketing frequency scope exceeds non-repeatability disturbance wave filter (21) bandwidth.

11. precision positioning selectivity ILC methods based on non-repeatability disturbance observer as described in claim 9 or 10, is characterized in that, to the ending-criterion of described control object be:

$e_{\&infin;}=\frac{1-Q_I}{1-Q_I(1-z^m\mathrm{LT})}[(1-T)Y_d+{\mathrm{PSD}}_r]+\frac{1}{1-Q_I(1-z^m\mathrm{LT})}\mathrm{PS}(D_{\mathrm{nj}+1}-Q_I{D}_{\mathrm{nj}})\&RightArrow;0$

Wherein, e represents ruling grating positioning system closed loop positioning error, Q _irepresent time varying filter, z ^mrepresent that the time delay factor is reciprocal, T represents supplementary sensitivity function, Y _drepresent that P represents ruling grating positioning system, and S represents sensitivity function, D with reference to control inputs amount z territory expression-form _rrepresent the z territory expression-form of repeated disturbance, D _njrepresent the non-repeatability disturbance z territory expression-form of jth time iteration, D _nj+1represent the non-repeatability disturbance z territory expression-form of jth+1 iteration.

12. precision positioning selectivity ILC methods based on non-repeatability disturbance observer as described in claim 9 or 10, is characterized in that, described learning filters (12) supplements the inverse of sensitivity function for closed loop.

13. precision positioning selectivity ILC methods based on non-repeatability disturbance observer as described in claim 9 or 10, it is characterized in that, described time varying filter (14) is one and has wide bandwidth at boost phase, and the constant speed stage comprises the time varying filter of multiple notch.

14. precision positioning selectivity ILC methods based on non-repeatability disturbance observer as described in claim 9 or 10, it is characterized in that, described non-repeatability disturbance wave filter (21) meets following constraint condition:

$\left\{\begin{array}{c}\left|Q_D\left(e^{\mathrm{j\&omega;}}\right)\right|<\frac{1}{\left|{\mathrm{\&Delta;}}_T\left(e^{\mathrm{j\&omega;}}\right)\right|},\&ForAll;\mathrm{\&omega;}\\ {{|1-z^{-m}{Q}_D|}_{z=e}}^{{\mathrm{j\&omega;n}}_j}<<1{\mathrm{\&omega;}}_{\mathrm{nj}}\&le;{\mathrm{\&omega;}}_{\mathrm{cd}}\left(Q_D\right)\end{array}\right.$

Wherein, Δ _t(e ^{j ω}) be multiplication indeterminate, ω _njnon-repeatability forcing frequency, z ^-mrepresent the time delay factor, Q _drepresent non-repeatability disturbance wave filter, ω _cdit is the cutoff frequency of this non-repeatability disturbance wave filter (21).