Real-Time Simulation of an Atomic Force Microscope Cantilever
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1 Real-Time Simulation of an Atomic Force Microcope Cantilever Róbert Barabá, Zoltán Gyurkó, Department of Automation, Budapet Univerity of Technology and Economy 1111 Budapet, Budafoki út 8, F.II., Hungary Phone: , Fax: Zoltán Puklu Széchenyi Itván Univerity, Egyetem tér 1, H-926 Győr, Hungary Abtract One of the main reearch topic of our department i the advanced control trategie. The real-time imulation of the Atomic Force Microcope (furthermore AFM) offered u a remote environment for telemanipulation. A pecial mater device for AFM i till under development at our department. In thi paper, telemanipulation, and working of the real AFM device introduced, and the reult are preented. Thoe advanced control trategie ha ued for thi mater device. The aim of thi paper i to introduce the current tate of the development. 1. Introduction to Telemainpulation Telemanipulation i a proce where the operator ha ome tak done at the far environment where he/he cannot be phyically. The firt modern mater-lave ytem teleoperator wa developed by Goertz at Argonne National Laboratory [3] in Telemanipulation i divided into two trongly coupled procee. One proce i the interaction between the operator and the mater device, the other i the interaction between the lave device and the far environment contact. The mater device repreent the far environment at the operator ite, and the lave device repreent the operator at the remote ite. The information flow between the operator and remote ite can be een on Fig.1, where only three type of information are feedback: viual, audio and ene of touch. The human being get ix type of ening from the environment urrounding them but only ome of thee ening are ued during telemanipulation. When human ue thi device only
2 to move object and the reaction force from the far environment ha no ignificant effect on the performance, then meaurement of the operator poition and viual feedback may be enough. But if uch tak are to be performed when the reaction of the environment i important and the lave device can make damage in the far environment like when crewing a bolt or aembling omething, then we need force feedback to improve efficiency. Force feedback increae the feeling of telepreence. Telepreence i the pychological feeling of being there in an environment baed on a technologically founded immerion environment. Figure 1: Information tream of the Telemanipulation Figure 2: Telemanipulation in the virtual reality It hould provide the ideal enation, i.e. we get the neceary information fed back from the lave to the mater ide in a natural way to have the feeling of being phyically at the ditant location. Force feedback not only increae efficiency, but it help to filter the maller impreciion of the operator. 1.1 Telemanipulation in the virtual reality A pecial intance of telemanipulation i telemanipulation in the virtual reality. It i beneficial when the operator i learning performing dangerou tak uch a working with radioactive material or exploive; or when the operator i learning
3 working in a pecial imulated virtual environment. For example real time airplane, helicopter or ubmarine imulator belong to thi cae. Telemanipulation in the virtual reality application i hown on Fig. 2. The operator wear a headmounted device giving viual feedback and an arm and glove type mater device giving tactical enation. The operator can ee the viual object and can touch and move them. A hort ummary of the mater device can be found in the [1]. 1.2 Micro/nano telemanipulation A micro tele-operation ytem ha been contructed, which enable human operator to operate micro tak, uch a aembly or manufacturing. A haptic interface provide the operator with the feeling that he/he touche the expanded micro object with hi/her finger. A micro tele-operation ytem hown in Fig. 3. The local ite ytem i the haptic device and the controller, and the remote ite i the Nano-Robot Sytem and it controller. The Teleoperation Control reponible for a proper coupling between the macro and micro world. In the following ection a poible olution i given for the proper coupling: virtual coupling impedance. 1.3 Virtual coupling impedance Force and poition caling i an important iue in the micro/nano remote environment. There are baically two approache: linear and nonlinear caling. In the cae of linear caling a ingle correponding contant i ued between the micro/nano force/poition and macro force/poition: x ( t) = α x ( t) F ( t) = α F ( t) p f (1) where x * and F * are the caled value, α p and α p are the contant poition cale repectively. In cae of nonlinear caling which i alo called impedance caling [2], force are caled independently with repect to their length caling power relation a follow x = α px( t) (2) 3 2 F = α M && x + α B x& + α K x p V p Where M V i the virtual ma, B V i the virtual vicoity contant and K V i the virtual tiffne. Note that thi caling method i imilar to the concept of virtual impedance, which i well-known in the control theory of manipulator. In thi paper the name virtual coupling impedance i ued intead of virtual impedance concept to avoid confuion of virtual impedance between information V p V
4 tranfer and virtual impedance of an object in virtual reality. Impedance caling give better performance in micro/nano telemanipulation application becaue of the bandwidth effect. In thi approach, the inertial force can be magnified o that the operator can feel cloe to hi/her daily experience. But thi approach require precie environment parameter while the linear caling doe not. Figure 3: The tructure of a teleoperated nano manipulation ytem. Figure 4: Telemanipulation in the micro/nano pace uing virtual coupling impedance The bandwidth effect i the difference between the bandwidth mater force feedback device and the lave micro/nano actuator. A a rule the micro/nano actuator ha a maller time contant than the macro force feedback device. So an impedance caling i neceary to avoid intabilitie and unreliable force feeling. Dynamically caled telemanipulation of micro/nano environment i hown on Figure 4. The applied force by the operator i compared with the caled micro/nano force. The difference force i the input of the virtual impedance (V()). The output of V() i the reference poition both of the mater (M()) and the lave (S()) ytem. Let u uppoe that the mater and lave device are fater than the virtual coupling impedance. In thi chae the operator can feel the virtual coupling
5 impedance loaded with the force from the nano word. Thi configuration i hown on Figure 5. Figure 5: The concept of virtual coupling impedance for micro/nano telemanipulation Figure 6: The Baic tructure of a conventional AFM device 2. The AFM Device 2.1 Layout of the AFM device The Atomic Force Microcope (AFM) i ued a a 3-D topology microcope, contact manipulation tool, or a force enor. The baic tructure of a conventional AFM ytem i hown in Figure 6. The baic component of AFM are the MEMS fabricated flexible cantilever beam, the deflection meaurement ytem with atomic reolution, and XYZ poitioner with atomic reolution. Cantilever ha a
6 meaured pring contant k c, reonant frequency f r, 1-4 µm length and few micrometer thickne and very harp conical, pyramidal or cylindrical tip with 1 of nanometer apex radiu. Cantilever beam deflection can be meaured uing a laer light with four-cell photodiode, conductance meaurement, or piezoreitance or piezoelectricity meaurement depending on the cantilever type and purpoe. Uing piezoelectric actuator with or without integrated enor, the z poition of the tip or ample i changed until there i a contact between the cantilever tip apex and ample atom. Due to long-range or hort-range attractive or repulive interatomic force, the cantilever i deflected a depending on the tipample ditance. 2.2 The imple model of AFM device Thi ection contain the model of the AFM which wa ued a a real-time remote environment for telemanipulation. The cantilever of AFM can be modeled a a imple 1DOF Spring-Ma-Damper ytem. Thi model i valid only during approaching and/or touching the ample. In thi paper focued on thi baic movement of the AFM. Becaue of the bandwith effect, the local ite ee only the virtual coupling impedance. For thi reaon it i not neceary a high computing capacity to model the AFM device with 1 khz natural frequencie. Computing capacity i focued only the Spring-Ma-Damper ytem which hown on Fig. 7. But the computing of the nano force i neceary and thee force are highly nonlinear. The following force wa modeled: Non contact force: Van Der Waal, Elektrotatic and Capillar Contact force: tiffne and damping of the ample The gravity force can be neglected. U=4nm Frame u(t) x(t) kc bc x=1nm mc h(t) Liquid layer Sample Figure 7: The real-time model of the AFM a a imple harmonic ocillator
7 3 Fcapapp ditance "h" [m] x 1-8 Fcapret ditance "h" [m] x 1-9 Fcap ditance "h" [m] x FvdW ditance "h" [m] 2 x Fel -3 Fnoncon ditance "h" [m] ditance "h" [m] m && x c () t + 2m b ( x& () t + u& () t ) + k ( x x ) c c Figure 8: The non contact nano force c F = non. con l ( h( t) ) Bh& ( t) u( h( t) Ll ) F ( h() t ) B h& ( t) Where m c the ma, k c the tiffne and b c damping coefficient of the cantilever. F noncon i the um of the noncontact force and the F con i the contact force. con (3) h h () t < a () t a 3. Experimental Reult 3.1 Simulation of the nano force The nano force can be een on Figure 8. The upper row i the capillar force. The capillar force i acting, when the tip of cantilever reach the liqud layer on the ample. The thickne of the liquid layer i 1 nm, which can be een on the upper left corner. The van der Waal and the electrotatic force ha ame hape, but the electrotatic force i about 1 time tronger. Figure 9: The block diagram of the experimental reult
8 1.1 x X(t) [m] Time "t" [ec] Figure 1: The movement of peak of the cantilever 3.2 Simulation of the AFM device The connection diagram of the real-time imulation of the cantilever can be een on Figure 9. The cantilever box contain the tate pace model of the cantilever. The nonlinear nano force are in the nano force block. The firt tep of the imulation to build the block diagram into Simulink. Simulink i a block-oriented imulation environment under Matlab. Then come the non-real-time imulation. In thi cae the imulation running on the PC own CPU. Parameter can be eaily change in thi tage. The lat tep, when the program of the imulation i downloaded into the DSP. The deflection of the cantilever x(t) can be een of Fig 11. When the frame on (Figure 7.) accelerating toward ample then the tate poition x =1nm decreaed. When the frame ha top, the deflection increaing. The vibration caued by the non contact force. The h(t) denote the ditance between the ample and the tip. An approaching can be een On Figure 11. The initial ditance i 3nm. After the firt econd the frame tart to approach the ample. When the tip reach h(t)=1 nm, then the tip connect to the water layer. Capillar force i acting between the tip and the liquid layer. After the 8 th econd the frame ha topped. The tip i in the liquid layer, where acting the capillar, electrotatic and the van der Waal force. Thoe force excited the vibration. Fig. 11. The ditance between the tip of the cantilever and the urface of the ample h(t)
9 Concluion In thi paper a real-time imulated nano virtual reality i introduced. Thi virtual reality ued a a far environment for telemanipulation. In the experimental reult nano force and real-time imulation wa introduced. Floating point DSP i ued a a real-time hardware. In thi paper focued only the nano virtual reality. A pecial mater device i under development at our department. The floating point DSP hardware ha enough computing power to control the mater device and calculate the nano world. Mater device will connect to the DSP hardware, which contain the control of mater device and nano virtual reality. Acknowledgement The author wih to thank to Prof. Hideki Hahimoto and hi reearch fellow from Univerity of Tokyo and PhD. for their upport. Reference [1] Péter Korondi, Peter T. Szeme, and Hideki Haimoto: "Human Interface for Telelmanipulation" EPE-PEMC2-9 th Power Electronic and Motion Control International Conference, Koice, Slovak Republic 5-7 Septemeber 2 [2] J. E. Colgate: Robut Impedance haping telemanipulation. IEEE Tranaction on Robotic and Automation, 9(4): , Aug [3] T.B. Sheridan, Telerobotic Automatica, Vol. 25, No. 4, pp , 1989.
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