Model-Based Control of a High-Precision Imprinting Actuator for Micro-Channel Fabrications

Transcription

1 Model-Based Control of a Hgh-Precson Imprntng Actuator for Mcro-Channel Fabrcatons Tat Joo Teo, Member; IEEE, I-Mng Chen, Senor Member; IEEE, Choon Meng Kew, Member; IEEE, Guln Yang, Member; IEEE and We Ln, Member; IEEE Abstract Ths paper presents the modelng and control of a Flexure-Based Electromagnetc Lnear Actuator (FELA) that s employed as a hgh-precson mprntng actuator of a desktop hot-embossng mprnter. In ths work, a systematc approach of obtanng the unknown physcal parameters of FELA s presented. Subsequently, these parameters are used to desgn two model-based PID controllers that allow the FELA to perform hgh-precson postonng tasks and drectforce mprntng tasks respectvely. As the mprntng tasks requre the FELA to operate n both poston and drect-force control modes, two types of control strateges are explored and ther competency of enablng the FELA to perform such tasks are nvestgated. Lastly, the selected control strategy s mplemented on the FELA to assst the hot-embossng mprnter n fabrcatng mcro-channels on polymer substrates va a hotembossng process. I. INTRODUCTION The transfer of hgh-resoluton features through mechancal pressng has recently become a promsng approach n achevng hgh-throughput fabrcaton of polymer-based devces such as optcal components and mcro-fludc devces etc. Ths approach physcally mprnts the pre-fabrcated features from the molds (or templates) onto the polymer substrates and uses ether the thermal forgng (termed hotembossng process) or the Ultra-Volet (UV) curng (termed UV-embossng process) to complete the formaton of the mprnted features. To nvestgate the deformaton behavor of the polymer substrate durng hot-embossng, Kew et al [1] proposed a mathematcal model to smulate the behavor of a polymer materal,.e., PolyMethyl-MethAcryle (PMMA), durng a hot-embossng process. Unlke conventonal smulaton approaches, whch use the Mooney-Rvln model [2], ths approach allows the use of fundamental materal propertes drectly and acheves more realstc smulatons of those polymer behavoral. The promsng results from ths proposed smulaton approach have led to the development of a desktop hotembossng mprnter for evaluatng the proposed smulaton approach va conductng actual process studes. In ths mprnter, the desred mprntng actuator must have a small footprnt due to the proposed desktop package. In addton, ths actuator must provde a contnuous output force of Ths work fully funded and supported by Sngapore Insttute of Manufacturng Technology (SIMTech) T. J. Teo, C. M. Kew, G. L. Yang and W. Ln are wth Mechatroncs Group, SIMTech, 71 Nanyang Drve, Sngapore , tjteo@simtech.a-star.edu.sg I. -M. Chen s wth School of Mechancal and Aerospace Engneerng, Nanyang Technologcal Unversty, 50 Nanyang Avenue, Sngapore mchen@ntu.edu.sg at least 100 N for rapd small scale mprntng, and a few mllmeters of dsplacement stroke for demoldng or assessng the substrates. Most mportantly, t must offer hghprecson postonng and drect-force control capabltes for accurate and repeatable process studes on mcro-scale feature fabrcatons through the hot-embossng process. Unfortunately, most exstng actuators have lmtatons n meetng all those requrements. Conventonal hydraulc actuators offer hgh output force but are bulky n sze and have poor force control resoluton due to the compressve nature of flud. Smlarly, the lnear-stepper motors are unable to provde postonng and drect-force control although large output force are expected. In addton, the voce-col actuators produce small output forces [3] whle the force generaton of the solenod actuators are nconsstent and nonlnear [4]. On the other hand, pezoelectrc actuators may be capable of achevng hgh-precson resolutons but have lmted dsplacement of up to several hundred mcrons [5]. Although such lmtatons can be overcome through technques such as the magnetostrctve clampng [6], the nchworm clampng [7], and the mpact-force method [8] etc, low payload capacty, slow response speed and poor repeatable moton are the common trade-offs. II. OBJECTIVES Due to the lmtatons of exstng actuators, a novel nanopostonng actuator, termed Flexure-Based Electromagnetc Lnear Actuator (FELA), s employed as the mprntng actuator for the proposed system. It manly comprses of a Lorentz-force Electromagnetc (EM) module and flexurebased support bearngs as shown n Fg. 1 [9]. Currently, FELA s able to acheve a postonng accuracy of ±10 nm over a dsplacement stroke of 4 mm, and a contnuous output force of 60 N/Amp wth an accuracy of ±0.15 N [10]. In ths work, the FELA must be able to transt between the poston and the drect-force control modes. Consequently, an accurate modelng of the system and a proper control strategy are requred to realze the mprntng process. Hence, ths paper focuses on the desgn and modelng of the modelbased controllers for the FELA, and nvestgates the control strateges that wll be used to realze the transton between both control modes. Wth the selected control strategy, FELA s mplemented n the proposed system to realze the mprntng of mcro-szed channels through a hot-embossng process. Expermental results obtaned from the mprnted features wll also be dscussed.

2 Fg. 3. Block dagram of the proposed mpedance control scheme. Fg. 1. FELA prototype. III. HYBRID POSITION/FORCE CONTROL STRATEGY Two control schemes are nvestgated to realze the transton of the FELA between the postonng control and the drect-force control. A. Mode-Swtchng The frst scheme s the mode-swtchng control. It allows the FELA, whch s operatng n a poston control mode, to swtch to a drect-force control mode when a contact force at the tp of the actuator s detected. Ths scheme performs two control-loops,.e., the poston control and the drect-force control, smultaneously and swtches between both control-loops wth respect to varyng condtons. Fg. 2 llustrates the block dagram of the proposed mode-swtchng control scheme whereby two separate Proportonal-Integral- Dervatve (PID) controllers are mplemented to control the postonng and output force of the FELA respectvely. to be desgned. In prevous effort [10], the entre system was treated as a black-box system and MATLAB System Identfcaton Toolkt was used to predct the transfer functon of the plant. However, the predcted transfer functon s just a mathematcal expresson that has no relatonshp wth the physcal parameters of the plant. In ths work, the transfer functon of the plant s modeled through these physcal parameters and the PID controllers are desgned based on the modeled transfer functon. A. Poston PID Controller Desgn For the poston controller, the feedback loop s formed by a lnear optcal encoder from McroE-System (model: M3500). Fg. 4a shows the block dagram of a basc poston closed-loop control system where G Cp (s) represents the poston PID controller and G F p (s) represents the FELA. For poston control, a FELA s treated as a lnear masssprng-damper system as shown n Fg. 4b whereby the mass, m, represents the weght of the movng ar-core col, the stffness, k, represents the stffness of the flexure-based support bearngs, and the damper, b, represents the passve eddy current dampng nherted from the moton between the movng col and the magnets wthn the EM module. Fg. 2. Block dagram of the proposed mode-swtchng control scheme. B. Impedance Control The second scheme adopts an mpedance control that performs a poston control loop ntally before nhertng the command sgnals from a drect-force control loop when a contact force s detected at the actuator tp. Once a contact force s detected, the nherted command sgnals of the drectforce control loop domnate the command sgnals of the poston control loop. Eventually, the command sgnals sent to the FELA wll be provded by the drect-force control loop. Fg. 3 llustrates the block dagram of the proposed mpedance control scheme. IV. MODEL-BASED PID CONTROLLER In both proposed control schemes, two separate sets of PID parameters are used to realze the postonng control mode and the drect-force control mode. Pror to the mplementaton of both control schemes, the PID controllers need Fg. 4. (a) Block dagram of the proposed postonng control system wth FELA represented as (b) a mass-sprng-damper system. Based on Fg. 4a, the transfer functon of the entre closedloop control system s X a (s) X d (s) = K c K p (T d s 2 + s + T 1 ) ms 3 + (b + K c K p T d )s 2 + (k + K c K p )s + K c K p T 1 (1) where X a (s) represents the actual poston, X d (s) represents the desred poston, K c represents the compensaton gan, K p represents the proportonal gan, T represents the ntegral tme, and T d represents the dervatve tme. To determne the control parameters, (1) s compared aganst the transfer functon of a standard thrd-order system so as to formulate the relevant equatons that represent K p, T and T d. The transfer functon of a standard thrdorder system s derved by addng an addtonal pole to the

3 transfer functon of a standard second-order system. The value of the addtonal pole must be at least 5 tmes the value of an undamped natural frequency to ensure that t has mnmal effect on the system characterstc. Hence, the transfer functon of a standard thrd-order system s Based on (8), the output of ths transfer functon s plotted aganst the recorded open-loop step response. Subsequently, the value of the passve eddy current dampng was constantly altered to ft the output of the transfer functon to match the recorded open-loop step response as shown n Fg. 5. G(s) = ω 2 n (s + γ)(s 2 + 2ζ ω n s + ω 2 n ) where ω n represents the undamped natural frequency of the control system, ζ represents the dampng rato of the control system, and γ represents the addtonal real pole. Based on past lterature [12], the undamped natural frequency, whch s expressed by the desred rse tme, T r, and ζ, s gven as ω n = tan 1 [ζ 1 ( 1 ζ 2 )] T r 1 ζ 2 A comparson between the coeffcents of (1) and (2) yelds (2) (3) K p = m(ω2 n + 2ζ ω n γ) k K c (4) T = K ck p mγω 2 n (5) T d = m(γ + 2ζ ω n) b K c K p (6) To determne the PID control parameters through (4) to (6), the values of m, k, b, T r, and ζ are requred. In ths work, the mass of the movng col s measured before assemblng the FELA, the stffness of the flexure-based support bearngs s determned expermentally and analytcally [11], the rse tme s based on the desred value, and the dampng rato of the control system s based on the deal value. Through these measurements, the values of several control parameters are obtaned,.e., m = 0.5 Kg, k = 2000 N/m, T r = sec, and ζ = In ths work, the passve eddy current dampng and the compensaton gan are determned through an emprcal approach. Intally, an open-loop step response s obtaned from the FELA. Subsequently, the output and nput are recorded at a samplng tme of 10 msec. The nput s the PC command and the output s n encoder count. The rato of the recorded output and the nput s equvalent to the dc gan of the control system. Based on (1), ths dc gan can also be expressed as DC gan = K c (7) k Hence, the compensaton gan of the entre control system s obtaned through the expermental results and (7). Ths compensaton gan accounts for the quantzaton from the PC command to the FELA poston output n encoder count of the open-loop control system. Based on Fg. 4, the transfer functon of the open-loop system for FELA s gven as G F p (s) = K c ms 2 + bs + k (8) Fg. 5. Open-loop step response and the output of (8) due to the dfferent values of the passve eddy current dampng. From ths emprcal approach, t shows that a small passve eddy current dampng s present n the open-loop system as the output of the transfer functon begns to match the actual open-loop step response when the passve dampng s reduced. From Fg. 5, both data matches when the passve eddy current dampng of the FELA s predcted at 60 N- sec/m. In addton, the compensaton gan of the control system s found to be usng (7). Fnally, these parameters are substtuted nto (4) to (6) to determne the PID parameters for the postonng control of the FELA. B. Drect-Force PID Controller Desgn A sx-axes Force/Torque (F/T) sensor from ATI (model: MINI40) s used as the force feedback encoder to form the closed-loop control system for the FELA to perform a drect-force control (Fg. 6a). In ths work, only one axs (Z-axs) s used as the feedback whle the remanng axes are used to montor the surface algnment between the mold and the substrate durng the mprntng process. Nevertheless, the entre F/T sensor s treated as a lnear sprng-damper system where the sprng stffness, k s, represents the stffness of the stran gauge wthn the F/T sensor whle the damper, b s, represents the frcton between the F/T sensor and the workpece. Fg. 6. (a) Block dagram of a proposed drect-force control system. (b) Schematc dagram of a mass-sprng-damper system wth an addtonal par of sprng-damper representng the force sensor.

4 Based on Fg. 6b, the dynamcs of the system becomes an ntegraton between a mass-sprng-damper system and a sprng-damper system. Hence, the transfer functon of the open-loop system s gven as G F f = K f ms 2 + (b + b s )s + k + k s (9) where K f denotes the compensaton gan for force controller,.e., from the PC nput command to the output analog sgnal of the F/T sensor. For drect-force control, the transfer functon of ths closed-loop control system s expressed as shown n Fg. 7. In ths case, the stffness of the F/T sensor was assumed to be very hgh whle the dampng of the sensor s fxed at 1. From Fg. 7, the stffness was slowly reduced untl both data match. Through ths emprcal approach, the stffness of the F/T sensor s predcted to be at N/m. In addton, the compensaton gan, K c, of the current control system s predcted to be based on (14). F a (s) F d (s) = K f K p (T d s 2 + s + T 1 ) ms 3 + (b t + KK p T d )s 2 + (k t + KK p )s + KK p T 1 (10) where F a (s) represents the actual force generated, X d (s) represents the desred force generated, b t s the combnaton of the frcton between the F/T sensor and workpece, and the passve eddy current dampng,.e., b + b s, whle k t s the combnaton of the stffness of the flexure-based support bearngs and the stffness of the stran gauge wthn the F/T sensor,.e., k + k s. Usng the smlar approach n Part A, a comparson between the coeffcents of (2) and (10) yelds Fg. 7. Open-loop step response and the output of (9) due to the dfferent values of the stffness of the F/T sensor, whle b s = 1. K p = m(ω2 n + 2ζ ω n γ) k t K f (11) T = K f K p mγω 2 n (12) T d = m(γ + 2ζ ω n) b t K f K p (13) For the force controller, (11) to (13) are the expressons that descrbe the three requred PID parameters,.e., K p, T, and T d. From these expressons, the mass of the movng ar-core col, the stffness of the flexure-based support bearngs, and the passve eddy current dampng are known except for the stffness and dampng of the F/T sensor. As a result, a smlar emprcal approach used n Part A, s adopted to determne these parameters. In ths case, an open-loop step response of the FELA s obtaned expermentally through a step command nput except that the output refers to the sngleaxs force measurement. The rato of the output and the nput s equvalent to the dc gan of the current closed-loop system. From (9), ths dc gan n the steady-state condton s also expressed as DC gan = K f k + k s (14) Based on (9), the output of ths transfer functon s plotted aganst the recorded open-loop step response wth the assumpton that the mass of the ar-core col, the stffness of the flexure-based support bearngs, the passve eddy current dampng reman unchanged. The value of the F/T stffness was ntally adjusted to ft the output of (9) to match the actual open-loop step response of the open-loop system as Fg. 8. Open-loop step response and the output of (9) due to the dfferent values of dampng of the F/T sensor, whle k s = N/m. Next, the stffness of the F/T sensor s fxed at the predcted value whle the dampng value of the sensor was constantly adjusted to match the output of the transfer functon wth the actual open-loop step response of the open-loop system as shown n Fg. 8. Usng a smlar approach, the dampng of the F/T sensor was assumed to be very hgh. From Fg. 8, t shows that the dampng value was slowly reduced untl the output of transfer functon matches the open-loop step response of the system. Eventually, the dampng of the F/T sensor s predcted to be 400 N-sec/m. Wth the values of the stffness and the dampng of the F/T sensor predcted, (11) to (13) are subsequently used to determne the PID parameters. For drect-force control, the settlng tme s more crucal than the rse tme because t wll be appled n the mprntng

5 process. Hence, a settlng tme of 3 msec and a dampng rato of 0.76 are used n ths predcton. In ths secton, both PID-based controllers and all PID parameters obtaned wll be used to form the proposed control schemes. Each control scheme s separately mplemented on the FELA to perform a transton between the poston control and the drect-force control modes. V. COMPARISON BETWEEN BOTH CONTROL STRATEGIES For the mode-swtchng control, the poston control mode frst moved the FELA to ts maxmum stroke at a velocty of 2 mm/sec before the drect-force control mode takes over wth a targeted output force of 30 N once after a contact force was detected. From Fg. 9a, the FELA started movng to ts targeted poston and stopped ts advancement at about 50 µm after a contact force was detected. After swtchng to the drect-force control mode, the FELA reached the targeted force at 300 msec. However, the sudden surge n command sgnal caused a sudden pressng effect that s reflected n the force and poston profles at about 140 msec. Ths sudden surge s caused by the ntegrator of the force PID controller. In ths control scheme, both PID controllers operate smultaneously. When the FELA was operatng n the poston control mode, the errors bult up n the force PID controller as the targeted force was not reached. Subsequently, these accumulated errors caused a surge n the output command sgnals. Thus, ths control scheme loses ts effectveness durng the transton between the poston control and drect-force control modes. the command sgnals and operated the FELA to reach ts targeted force at about 200 msec. The force output n Fg. 9b suggests that the output force slowly approaches the desred force wthout any sudden surge. The command sgnals plot also suggests that ths control scheme provdes a constant gradent n the command sgnal whch n turn resulted n a smooth transton between the poston and force operatons. Although mode-swtchng control offers a more rapd response, such a smooth transton from the mpedance control s essental as t prevents the templates or substrates from beng damaged durng the mprntng processes. Consequently, the mpedance method s chosen to realze the hybrd poston/force control of a FELA. VI. FABRICATION OF MICRO-CHANNELS The desktop hot-embossng mprnter wth FELA beng set up to realze the hot-embossng process s shown n Fg. 10a. Here, the FELA s fxed vertcally downwards wth an embossng head mounted on ts end-effector. Ths embossng head, whch carres the template (Fg. 10b), has two cartrdge heaters for heatng up the template. Through the embossng head, the FELA presses the template onto the substrate (Fg. 10c) that s placed on an embossng base. Ths embossng base has three cartrdge heaters for heatng up the substrate. All cartrdge heaters are desgned to heat up the template, and the substrate to 200 C wthn a mnute. Temperatures of these cartrdge heaters are controlled by the temperature controllers wth the thermocouple formng the feedback loop. Durng the hot-embossng process, the slcon template and the PMMA substrate s heated up to 120 C pror to the mprntng. The FELA then carres the template towards the substrate and provdes a constant mprntng force of 60 N for fve mnutes upon contact. Subsequently, the template wll be de-molded from the substrate leavng the mprnted mcro-channels on the substrate. Fg. 9. Force, poston and command sgnal obtaned from (a) modeswtchng and (b) mpedance control modes. For the mpedance control, the poston control mode frst moved the FELA to ts maxmum stroke at a velocty of 1 mm/sec before the drect-force control mode took over wth a targeted output force of 25 N once after a contact force was detected. From Fg. 9b, the FELA started movng to ts targeted poston and detected a contact force at about 10 µm. The drect-force control mode then domnated Fg. 10. (a) FELA setup for a hot-embossng process to mprnt mcro-szed features n (b) the template onto (c) the PMMA substrate. VII. EXPERIMENTAL RESULTS AND INVESTIGATIONS The mprnted mcro-channels on the substrate and the mcro-features from the template are taken from a hgh-

6 resoluton optcal mcroscope, and are shown n Fg. 11. The actual features from the template (Fg. 11b) has a wdth of 33.3 µm. The mprnted features on the substrate has a measured wdth of 33.7 µm (Fg. 11a). In addton, the wdth of a par of mcro-channels from the template s 83.7 µm, whle the wdth of a par of mcro-channels on the substrate s 83.3 µm. Both measurements have shown that the mprnted mcro-szed features on the substrate are close to the actual feature from the template wth an accuracy of ±0.4 µm. Fg. 11. (a) The mprnted mcro-channels on the substrate from (b) the mcro-szed features of the template. After the ntal attempt, templates wth mcro-szed features n a parallel lne arrangement have been used for more n-depth evaluatons. A total of fve templates are used n ths evaluaton. The parallel lnes n each of these templates have specfc heghts and wdths as shown n Table I. Accordng to the measured data, the wdths of the mcro-channels between the substrates and templates for all fve samples are very close. The mprnt qualty s extremely good n sample 1 and 2 wth the wdths and heghts of the substrates beng close to the templates. TABLE I MEASUREMENTS OF THE IMPRINTED FEATURES FROM THE SUBSTRATES AND THE TEMPLATES. Feature Slcon template PMMA Wdth (µm) Heght (µm) Wdth (µm) Heght (µm) Wdth (µm) Heght (µm) Wdth (µm) Heght (µm) Wdth (µm) Heght (µm) However, t s nterestng to note that the mprnted feature heght from samples 3 to 5 become shorter than the template feature heghts. For example, the varaton between the heght of the features on sample 3 and from the template was about 6.8% (refer to Table I). These results ndcate that the reducton of the wdth of the template feature ncreases the dffcultly n replcatng the heght of the template-feature on the substrate. Ths can be due to the ar trapped between the template and the substrate, whch hnders the transfer of these features. Hence, ths effort has also dentfed some ssues of the hot-embossng process n fabrcatng features wth wdth sze smaller than 100 µm. VIII. CONCLUSIONS A hgh-precson actuator,.e., FELA, that performs the mprntng task n a desktop-szed hot-embossng mprnter s presented. Modelng of two effectve model-based PID controllers to allow the FELA to perform hgh-precson postonng tasks and drect-force mprntng tasks respectvely s dscussed n detal. Here, a systematc approach n dentfyng the unknown physcal parameters of FELA s presented and has shown to be an effectve tool for system dentfcaton. In addton, the performances of two control schemes,.e., the mode-swtchng and the mpedance control, are nvestgated and the latter s dentfed as the most effectve control scheme to acheve a smooth mprntng process. Wth the ad of the mpedance control scheme and the model-based PID controllers, the FELA s tasked to automate the mprntng tasks durng the fabrcaton of the mcro-channels on PMMA va the hot-embossng process. Results have shown that the features wth wdth sze of more than 100 µm can be drectly replcated on the substrate. Most mportantly, the success of usng FELA to automate the requred mprntng tasks have shown the effcency and effectveness of the mplemented mpedance control and the two model-based PID controllers. REFERENCES [1] C. M. Kew, W. -J. Ln, T. J. Teo, J. L. Tan, W. Ln and G. L. Yang, Fnte Element Analyss of PMMA Pattern Formaton durng Hot Embossng Process, Proc. of IEEE/ASME Internatonal Conference on Advance Intellgent Mechatroncs, Sngapore, 2009, pp [2] C. R. Ln, R. H. Chen and C. Hung, The Charactersaton and Fnte- Element Analyss of a Polymer under Hot Pressng, Internatonal Journal of Advanced Manufacturng Technology, vol. 20, 2002, pp [3] B. Sprenger, O. Bnzel, and R. 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