Acceleration Feedback in a Stage Having Paired Reluctance Linear Actuator with Hysteresis. Qing-sheng CHEN, Xiao-feng YANG and Li-wei WU

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1 06 International Conference on Electrical Engineering and Autoation (ICEEA 06) ISBN: Acceleration eedback in a Stage Having Paired Reluctance Linear Actuator with Hyterei Qing-heng CHEN, Xiao-feng YANG and Li-wei WU Departent of Microelectronic, udan Univerity, Shanghai, China Keyword: Acceleration feedback, ine tage, Reluctance linear actuator, Hyterei. Abtract. The hyterei force in the reluctance linear actuator liit it application in the lithographic equipent for nanoeter poitioning. Acceleration feedback increae the a of a yte a eperienced by diturbance force. In thi paper, acceleration feedback i deigned for the fine tage having paired reluctance linear actuator with hyterei. The feature of thi ethod lie in that by treating the hyterei force a a diturbance force, we can deign the acceleration feedback loop to reduce the influence of the hyterei force. The propoed ethod can iprove the proce enitivity at low frequency. Acceleration feedback ipleentation in digital controller and control for a fine tage ounted on a coare tage are dicued. Siulation reult how that the propoed ethod i effective in overcoing the hyterei force and proiing in preciion tage control. Introduction In integrated circuit (IC) anufacturing, lithographic canner uually ue the fine tage to achieve high velocity and high preciion poitioning during quick ynchronou canning []. The ore functionality i packed into each IC, the aller the feature ie (indicative of the allet coponent that can be anufactured in one IC) i required. Today, the iniu feature ie i about 5 n []. Thee requireent ake the fine tage in the lithographic canner challenging fro a poition control perpective. The net generation fine tage actuator hould provide a larger force denity and higher force accuracy. Due to it low efficiency and high power diipation, the voice coil actuator i no longer the bet choice a the ain driving actuator for the net-generation fine tage [3]. Since the reluctance force i proportional to the quare of the ecitation current, the reluctance linear actuator ha a unique property of all volue, low current and high power, it can provide a olution for driving the fine tage [4]. However, the reluctance linear actuator ha non-negligible hyterei [5] between the input current and output force, which ay introduce an epected force error in the nanoeter poitioning. So we need to tudy the control ethod to obtain a predictable reluctance force for the high accuracy requireent. Conventionally, the poitioning control deign of a tage fall into two part: () the actuator dynaic i oitted and the force i deigned, () the current reference i coputed fro the deigned force baed on their tatic nonlinear relation [6]. But it doe not conider the effect of hyterei and paraeter uncertainty on the force accuracy. or the hyterei copenation, uing the invere hyterei odel [7] i the ot noticeable approach. Reference [8] propoed an invere hyterei odel and obtained a good perforance for the reluctance linear actuator. However, the above ethod both need precie hyterei odel, which i generally cople and hardly to obtain. Owing to it online elf-learning ability, the adaptive neural network [9] i ued to copenate the hyterei. Due to the fact that neural network ha a cople algorith; it i not eay to apply in the real-tie digital controller. Meanwhile acceleration feedback increae the virtual a of a yte a eperienced by diturbance force. Acceleration feedback ha been applied to land gear [0] and the voice coil actuator [] a an auiliary to poition control. The acceleration feedback added in an eiting poition controller for a wafer tage control ha been propoed in [], which plit the acceleration

2 controller into a forward and backward path to create the original proce behavior for poition controller, and reoving the high-bandwidth requireent. The hyterei influence in reluctance linear actuator introduce i ainly in the low frequencie [3].In thi paper, we regard the hyterei force a a diturbance force and deign the acceleration feedback[] for the fine tage having paired reluctance linear actuator with hyterei. The propoed ethod can iprove the proce enitivity at low frequency and reove the high-bandwidth requireent. The propoed ethod doe not need the invere hyterei odel and can be eaily applied in the real tie digital controller. Siulation reult how that the propoed ethod i effective in overcoing the hyterei force and proiing in preciion tage control. Thi paper i organied a follow. In Section, reluctance actuator odel with and without hyterei are briefly reviewed. A fine tage having paired reluctance linear actuator control i preented in Section3. Acceleration feedback deigned for the fine tage having paired reluctance linear actuator i propoed in Section 4. inally, iulation reult are illutrated in Section 5. Reluctance Linear Actuator Reluctance linear actuator i a type of electric otor that induce non-peranent agnetic pole on the ferroagnetic rotor and produce teporary agnetic. The reluctance actuator i naed a uch becaue it ue agnetic reluctance to generate force, which can be called reluctance force. The E/I core actuator i a kind of ot baic linear reluctance linear actuator [4]. A hown in igure, the actuator include a generally Cobalt-Iron haped electroagnet and an I haped target. The electroagnet ha an electrical coil wound around the center ection. Current flowing through the coil generate a agnetic flu and thi flu create a reluctance force on the target. The aount of current deterine the aount of reluctance force. The reluctance force acting on the I target i decribed by: i () g where 0 N A i the electroagnetic contant, 0 i the pereability of air, N i the nuber of turn 4 in coil on the center leg of the E-core and A i the area of the air gap. It i a luped odel which diregard unodeled effect uch a hyterei leakage, fringing and aturation. However, the E-core coil ue oft agnetic aterial, which ha agnetic hyterei [5] between the agnetic field H and the bulk agnetic flu denity B. The hyterei can be defined a a loop in the input-output ap and it i hown that the hyteretic B H can be odeled [8] by a hyterei operator. Then igure. Sketche of the E-core Actuator.

3 igure. Shape of an input current and the correponding output force baed on the reluctance actuator odel with hyterei. We get a reluctance linear actuator odel with hyterei a: Hhy i,, () g where H hy (i,, ) i the paraetric hyterei operator and defined a follow: Let r(k), y(k) be bounded,, > 0. Then the paraetric hyterei operator y(k) Hhy r(k),, (3) ( pq) M, i defined a follow: when y r W ( r(k) r 0 (k) r(k) y ) o 0 ( e ) When r(k) r(k) 0, (4) y r n W n (n r(k) r 0 (k) r(k) y ) o 0 ( e ) where r0 y o and n r0 y o, r 0 r(k ) and y0 y(k ).The indicator k denote the lat tie intant before k when the difference of r changed ign, i.e. an etreu occurred, which correpond to a corner point of the y rcurve. The paraeter repreent the aount of hyterei around the traight line r(k) y(k) and define the ayptote, while the paraeter define the oothne of the hyterei loop, i.e. the rate of convergence toward the left or right ayptote. W i the principal branch of the Labert W function [5]. Thi odel contain both the hyterei and obviou quare linearity between the input current i and output force. Since the gap ditance i related to the hyterei in the reluctance linear actuator, the paraeter in Equation () can be elected a with 0. If the reluctance g actuator i odeled by Equation (), the curve of input current and the correponding output force are obtained a hown in igure. It can be een that the hyterei odel Equation () provide a good approiation for the hyterei phenoenon between the input current i and output force. E core E core (5) i ine tage i g g igure 3. Paried E/I core actuator.

4 Control for a ine Stage Having Paired Reluctance Linear Actuator ine Stage Having Paired Reluctance Linear Actuator Uually, fine tage in a lithographic tool ha i degree of otion [] and i ingle-input ingle output controller are ued to control each otion. In thi article, only one otion i conidered, uch a the canning direction. Due to the nature of reluctance force, an E/I core actuator can only generate a unidirectional attractive force. To generate an active force in the oppoite direction, a econd actuator need to be placed on the oppoite ide. igure 3 illutrate a iplified one otion fine tage [4] having paired reluctance actuator E-core and E-core. The gap between the E-core, and the tage are g and g, which can be eaured by uitable enor uch a capacitor enor. The force and are nonnegative, while the difference between and can take any value and direction. In the initial tate, the gap are g g 0and g g0, where g 0 i the initial gap. In igure 3, we define the right a the poitive direction. urtherore, when the tage ove to the poitive direction, the gap becoe g g0 and g g0 repectively where i the global placeent and can be eaured by poition enor uch a a laer interferoeter [4]. Control of Paired Reluctance Linear Actuator A conventional control chee i depicted in igure 4, in which the controller C() i fored by a proportional integral-derivative (PID) controller, a low-pa filter and a lead copenator. In the feedback loop, the controller ue the poition of the tage to generate the force. The filter Q() generate a feedforward force baed on the et-point poition. When P() can be properly decribed by, Q(), generating a force that i proportional to the et-point acceleration. The final poition accuracy i deterined by the eaureent error, diturbance force including the nonlinearity force caued by the hyterei which ha an effect on the cloed loop perforance. Rejection of output (eaureent) diturbance and input (force) diturbance i judged by, repectively, the output enitivity G o P () C() and the proce enitivity (6) P() Gp (7) P ()C() Baed on the conventional controller hown in igure 4, the propoed control loop for the fine tage having paired E/I core actuator i hown in igure 5. C () denote the poition controller, Q () denote the feedforward controller, P () denote the fine tage proce, EI and EI denote the E-core and E-core, NC and NC denote nonlinear current copenator and D denote the force ditributor. Q C P igure 4. Baic control chee.

5 P g e Q C d d d i i M g igure 5. Paired E/I core actuator control. In igure 5, D ditribute the deired force to each E/I core actuator a follow: d 0 d, (8) d 0 d where 0 i the bia force generated by paired E/I core actuator repectively in the oppoite direction, which provide a ero net force on the tage, thu aintaining the poition of the tage. In thi paper, 0 i deterined a 0 a, in which a i the aiu force correponding the aiu acceleration. More detail about how to elect the bia force 0 can be found in patent [6]. Since there eit trong linearity between the input current i and output force, fro Equation (), direct nonlinear current copenator NC and NC can be obtained a: i i d d g, d g d where d i the etiate of real contant. However, the reluctance actuator ue oft agnet aterial, there eit a hyterei between the input current i and output force in reluctance actuator EI and EI a hown in igure 5. Since the nonlinear current copenator NC and NC cannot copenate the hyterei between the input current i and output force in each E/I actuator, a hyterei force reult in between the poition controller force coand d and the real output force. However, the hyterei influence ut be conidered in the high-preciion poitioning [8]. So, it i neceary to find the hyterei copenation ethod for the reluctance linear actuator. In the following, the acceleration feedback control will be introduced to reduce the hyterei influence. (9) Acceleration eedback Control Baic Idea Conider the relationhip between the force coand d (d) and output force and define the hyterei force error hy a hy d.then fro igure 5, a iplified control chee i hown in igure 6, in which the tage tranfer function M () i iplified into two integrator and the fine tage a, ignoring etra dynaic in M () and the other diturbance force. ro Equation (7), if the a of the fine tage i increaed while keeping the poition control band width equal, we can get the ae output enitivity but iproved proce enitivity. Since a larger a i generally not epected for high acceleration control in the fine tage, increaing the virtual a intead by the feedback of the acceleration in addition to the poition, and ay hence iprove the proce enitivity by reducing the influence of the hyterei force.

6 hy e C d igure 6. Siplified virtual control chee. hy e C H () d H () igure 7. Uing H () and H () in the acceleration feedback loop. Deign of Acceleration eedback in requency Doain A control tructure a hown in igure 7 uing the acceleration feedback ethod [] i applied to reduce the influence of the hyterei in paired reluctance linear actuator. It i better that the acceleration feedback loop introduced doe not caue any change in the proce behavior. So the acceleration loop filter H () and H () are deigned a uch that the tranfer function fro the poition controller output to tage acceleration P e C H M d d d i i M H a T reain the ae, naely igure 8. inal Dicrete for of acceleration feedback. : H() H () H () It follow that g (0) H() H () () g H () H () H () g ()

7 Satify uch requireent, where H () H() H(). The hyterei force rejection only depend on H (), which can be deigned a a econd-order low-pa filter or an integrator. Acceleration eedback Ipleentation for Dicretiation So far, the acceleration feedback ued in paired reluctance actuator i conidered in continuou-tie. In thi ection, the dicretiation ethod [] i ued in the acceleration feedback for the reluctance linear actuator a hown in igure 9. Since the apling effect ut be taken into account when the digital controller i applied in reality. Uually, there eit a p-aple delay in the proce tranfer function and a q-aple delay caued by the acceleration eaureent. ro Equation (0), we have p H () ( pq) H H () () p The dicrete acceleration feedback filter H() and H() correponding to the delay p and q can be obtained (3) ( pq) H () Ha () (4) H a () H () (5) ( pq) H a () The feedback acceleration a i coputed fro the eaured poition by a digital double different ( ) a T (6) () T el Cl P l l l T e a C H M d P d d i i M H a T igure 9. Total feedback chee for coare tage and fine tage uing acceleration feedback. where TS i the aple tie. A diadvantage of double differentiation i it enitivity to noie. But the cloed acceleration loop ha a low-pa characteritic, o it can reduce the noie. In addition, the leat-quared filter ued a filter ay reduce the noie ipact [6]. A hown in igure 8, in order to reduce the increaed poition ettling error, a relative acceleration i ued by the deviation between the acceleration feedforward and the acceleration feedback [] by hifting the feedforward entry point can reduce the increaed poition ettling error caued by H () and H (). A delay of p qaple ut be ued to atch the acceleration feedback delay ( pq) fro the acceleration feedforward, o M.

8 Acceleration eedback in a ine Stage Mounted on a Coare Stage The true reluctance linear actuator ha a oving rang of only about, which i inufficient for the tage in the lithographic equipent. Thi proble i olved by introducing a coare tage actuated by the linear otor [], which can travel over large ditance with oderate icroeter-rang accuracy, and ove the fine tage actuated by the reluctance linear actuator [6]. Uually the E/I core part i ounted on the coare tage to avoid croover of cable and cooling hoe to the accurate fine tage. A total baic control chee, which cobine the fine tage and coare tage controller with acceleration feedback loop, i hown in igure 9. Since the fine tage ha a key roll in the final poition accuracy, the acceleration feedback i added into the fine tage control loop. In igure 9, Pl () repreent the coare tage proce yte. The coare tage i required to track the fine tage to keep the E/I core and fine tage cloe together. To thi end, the gap enor eaure the gap ditance between the coare tage and fine tage by the gd ignal. Since the fine tage i decoupled fro the coare tage by tracking the interferoeter, the coare tage controller Cl () i deigned baed on the dynaic of the coare tage without taking the fine tage into account. In the feedforward path, ince a reaction force i added to the coare tage while the fine tage i accelerated, the a of the fine tage ut be included to accelerate the coare tage. Siulation In order to verify whether the propoed acceleration feedback configuration can be applied in high-preciion yte, we do the following iulation. or coparion the no acceleration feedback cae i ued. The reluctance linear actuator with hyterei i odeled by Equation (), whoe paraeter are choen a in the patent [4]: the aiu force i about 00 N, the aiu gap g between the 6 E-core and I-target i 0:4 and the contant k Here, the hyterei operator paraeter are choen 0.0 and 0. The fine tage a i 0 kg and the bia force i 0 = 50 N, which i applied on both E/I core actuator. The gap g and g between the E-core, and the tage are in the range of 0 to 400 and the initial gap i g The coare tage a i 0 kg. A typical et point poition profile [], which i ued during epoing in lithographic equipent, i deterined by the 3rd order trajectory planning ethod [7]. The poition and velocity are hown in igure 0. urther, we define the canning velocity ettling tie a the tie intant after which the poition tracking error i le than 0 n. The canning velocity i 0.5, the acceleration i0. In the practical application, the poition controller i deigned a a PI controller and a lead copenator, which ake the poition-controlled fine tage yte having about a 00 H bandwidth correponding the echanical tructure. The acceleration feedback filter H ( ) and H ( ) are deigned a follow. H a ( ) i choen a an integrator with a gain that create a cloed acceleration loop bandwidth of f 30H abw fabwt Ha ( ) (7) By auing that the proce delay i p and the acceleration eaureent delay i q, we obtain M. ro Equation (4) and (5), it follow that fabwt H( ) fabwt H ( ) fabwt (8) (9)

9 The control objective i to ake the tage poition follow the reference poition and ha a quickly canning velocity ettling tie. igure how the poition tracking error with and without acceleration feedback. The canning velocity ettling tie i about 56 without acceleration feedback which i lower than 46 of acceleration feedback. igure how the fine tage poition loop proce enitivity, defined by Equation (7) which indicate the influence of the hyterei force to the poition. ro igure, the fine tage poition loop proce enitivity without acceleration feedback i about 70 db and with acceleration feedback decreae to about 30 db at low frequency. It can be een that, the acceleration feedback provide a low proce enitivity for the hyterei force. The cloed control loop bode plot of the fine tage with and without acceleration feedback i hown in igure 3 (a). It can be een that, the acceleration feedback loop added into the yte loop doe not change the fine tage cloe loop for low frequencie, the agnitude increae a little for high frequencie. The cloed control loop bode plot of the coare tage with and without acceleration feedback i hown in igure 3 (b) and the coare tage cloe loop. Concluion Thi paper ha propoed a new acceleration feedback control ethod for the fine tage having paired reluctance linear actuator with hyterei. Noting that we treat the hyterei in the reluctance linear actuator a a diturbance force to deign the acceleration feedback loop. The practical ipleentation ha been dicued for the digital controller. The iulation reult how that by properly chooing H and H, the acceleration feedback can provide a low proce enitivity and a hort canning velocity ettling tie. The propoed ethod i effective in overcoing the reluctance linear actuator with hyterei and proiing in high-preciion control application. igure 0. Reference poition and velocity. igure. Poition tracking error.

10 igure. Poition loop proce enitivity of the fine tage. igure 3. ine tage cloe control loop bode plot. Acknowledgeent Thi work i upported by National Natural Science oundation (NNS) of China under Grant Reference [] Butler, H. Poition control in lithographic equipent. IEEE Control Syte Magaine, 3(5), 8-47, 0. [] Intel technology-new. Tohiba tart a production of world firt 5n NAND flah eorie. -world -5n.htl, 04. [3] Vrijen, N.H., Janen, J.W. Coparion of linear voice coil and reluctance actuator for high-preciion application.4th International Power Electronic and Motion Control Conference, S3-9, 00. [4] Teng, T. C., Yuan, B. Magnetic actuator producing large acceleration on fine tage and low RMS powergain. US Patent, No. 6,30,57, 000. [5] Bertotti, G. Hyterei in agneti: for phyicit, aterial cientit, and engineer. Acadeic pre, 998.

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