R ESEARCH D IRECTIONS

1. RESEARCH DIRECTIONS Srinivasa M. Salapaka Laboratory for Information and Decision Systems Massachusetts Institute of Technology Department of Mechanical Engineering Iowa State University March 25, 2003

2. Outline • Research Directions • Nanopositioning • Micro-Cantilever Dynamics • Nanofriction • Clustering Algorithms • Image deblurring

3. ROBUST BROADBAND NANOPOSITIONING

4. MOTIVATION • Nanopositioning • High Bandwidth • High throughputs • High throughput requirements in probing material surfaces • Binding affinity between materials, other properties • High speed requirements for studying biosystems • Cell dynamics, probing living systems • Faster scanning requirements in various engineering applications • Ultra high density data reading and writing • Enabling feature in many studies and applications • Studies of cell dynamics require micro/nano-second imaging capabilities • Ultrahigh precision • Specifications are often in the angstrom regime • In scanning probe technologies molecular and atomic forces are routinely probed • Robustness • Necessary for reliability in view of • Uncertainty in model and environment • Diverse users –do not have the engineering expertise

5. MOTIVATION • Nanopositioning system • High precision (probing at nanoscale) • High bandwidth (high throughputs) • Robustness (reliability and repeatability) Needs of Combinatorial Chemistry

6. OBJECTIVE • Robust Broadband Nanopositioning System with • 500 Hz for large scans (100 m £ 100 m) • nanometer resolution • 1 MHz for small scans (2 m £ 2 m) • subnanometer resolution • Compatible for scanning probe applications

7. APPROACH • Novel Device Architecture • Novel paradigm for robustness, bandwidth and resolution

8. Proposed design • Two stage scanning • Large Scans • Motion possible by flexure based design • Sample-holders on steel platforms • Heavy (smaller bandwidths) • Actuation by stack-piezos • Large forces, large travels (100 m) • Small Scans • Cylindrical Piezoactuators • Sample kept on actuator itself • Smaller travels (2 m) • Lighter (higher bandwidths) • Integrate the two • Put the small scanner on top of large scanner

9. Head top EOD, Laser Laser to photodiode Head Laser from EOD Mirror Microcantilever Microcantilever Holder Support Plate X-Y-Z small range nanopositioner Large range nanopositioner A Schematic of PROPOSED Nanoscope

10. Large Range Scanner

11. PRESENT STATUS AND FUTURE DIRECTIONS • Developed a precise paradigm to address: • High Bandwidth • High Resolution • Robustness • Modern control tools • Model the plant • Quantify and characterize the challenges • Design feedback laws • Practically eliminated hysteresis and creep • Obtained 60-70 times improvement in the bandwidth over current popular systems • Substantial improvement in the reliability and repeatability

12. Results (cont’d.) creep hysteresis bandwidth Repeatability Reliability tracking

13. Results • Large Scanners • Identified and addressed design challenges • on bandwidth, precision and robustness • Piezo actuation is predominant; hysteresis and creep nonlinearities, design constraints • Sensors can deteriorate open loop performance • Employed modern control tools to address these challenges and achieved • Performance • controllers to achieve the desired tradeoff between resolution and bandwidth • Robustness • By addressing model uncertainties

14. Preview based control design • Improve tracking performance • For a priori known reference trajectories Feed forward Controller Plant + - • feedforward controller in addition to feedback controller • To give desired input ud such that Gud(t)=xr(t) Anticipatory Control design for better tracking performance

15. Preliminary Simulation Results • significant improvement in performance • Substantial reduction in error

16. Multi-Input Multi-Output Control Design Gxx Gxy ¼ 0 Gyx Gyy

17. Multi-Input Multi-Output Control Design • MIMO design • Significant coupling effects • Gyx greater than Gyy in some frequencies • Carry out control design for the MIMO model • Glover McFarlane, Nominal and Robust H1 • Multi-objective design • Actuation constraints • Specified by H1 norm • Resolution specifications • addressed by H2 norm Control Design for plant model that includes X-Y coupling

18. Integration into the nanoscope • Integrate the probing head with the positioning system • Sample holder capable of moving in Z direction • Control of tip-sample separation • MIMO control design • for positioner and cantilever system (3 £ 3 model) • Account for tip-sample interactions • Nonlinear models • Observer based control design • z-displacements are measured but velocities are not measured • Observers useful for compensation designs for nanofriction Control Design for plant model that include positioning (X-Y) and probing (Z) aspects

19. Short Range Scanner • For high bandwidth • Low mass essential • Cylindrical piezos – scanner cum actuator • Can be run open-loop • Inverse dynamic schemes • Inverse hysteresis models • Alternatively use closed loop control loop design • Design/implement sensors for detection of lateral motion • Employ the control design procedure as done for large range scanner Smaller lighter scanner implies faster scanning

20. Lateral motion sensors for AFM • Previous experience • Designed sensors for shell piezos (J scanner in an AFM) • Designed sensors based on optical levers • Used them for feedback • Loop shaping control laws • Obtained substantial improvement in the performance • Resolution in order of few nm (1kHz) • Bandwidth improvement of over 20 times

21. Another untried approach • Build a new nanoscope with control design in mind • Make small scanners • Lighter and therefore high resonant frequencies • Faster scanners • Bigger coupling effects • More burden on control design • Upshot • Simpler device design • More emphasis on control design • Achieve higher bandwidths Shift the emphasis from device design to control design and achieve faster scanning rates

22. CLUSTERING

23. X What Is Clustering? • Clustering • Separation of set of objects into groups such that objects in one group are more ‘similar’ than those in other • find the optimal partition {Rj} of the domain  and the allocation of representative locations • Combinatorially complex problem • Interpret and design d(x,rj) • Adapt and modify Deterministic Annealing Algorithm • Simulations

24. MOTIVATION • Chemoinformatics, Combinatorial Discovery • Search by elimination through a ‘chemical space’ for a ‘backbone’ compound (drug discovery) • Enormous number of possible molecular combinations • Requires clustering algorithms to narrow the search • Essential in data mining, data compression, facility location, machine learning

25. OBJECTIVE Develop and adapt clustering algorithms for Combinatorial Discovery

26. Present status and future directions • Partition a ‘large’ space ‘optimally’ into a given number of ‘cells’ and specify ‘representative locations under constraints • Similar to dividing ‘chemical space’ into clusters with representative elements • Developed fast algorithms under which • a new class of problems were for the first time identified • precise mathematical formulations were provided • Algorithms developed that are fast • The developed algorithms utilized on real life systems

27. EXAMPLE SYSTEM

28. IMAGE RECONSTRUCTION

29. MOTIVATION • Blurred images in scanning probe microscopy • The tip-geometry convolves with the sample to provide a blurred image

30. Objective • Deblurred using deconvolution methods • Modeled as convolution equation: y=h*x • y is observed data, h is blurring function, x is original data • Deconvolution is obtaining x given y • Equivalent to solving a system of structured system of equations of the form Ax=b • A is usually very large Develop and implement deconvolution algorithms for image deblurring

31. Present Status and future directions • Developed algorithms for solving deconvolution equations • Significant reductions in the computational expense • domain is not necessarily rectangular or continuous • Common in microscopy • Scans of different areas in a sample • Implement these algorithms for deblurring applications • Study other convolutions in microscopy • Geometric convolution

32. Practical Example Systems • Deblurring function: hn1n2=exp(-(n12+n22)/104) • Substantial reduction in computational expense

33. MICROCANTILEVER BASED DEVICES

34. Micro-Cantilever Arrays • Multi-Cantilever arrays • Parallel probing • Higher throughputs • Coupling effects • Modeling and Analysis • Associated control design • Distributed control structure • Individual actuation and sensing • Fabrication and implementation issues Parallel and faster probing to obtain higher throughputs

35. Micro-cantilever Sample Dynamics • Understanding micro-cantilever-sample dynamics • Essential to probing surfaces at nanoscales • Important for designing X-Y positioning systems • Studying complex dynamics • Dependence on model parameters • Complex dynamics shown analytically and observed in experiments • Important to identify avoidable conditions for imaging • Use them as test beds to study rich dynamics • Previous experience • Obtained a model to describe an AFM experiment • Proved and observed complex dynamics

36. NANOFRICTION

37. Nano-friction • Widely studied area • Fundamental understanding of interfacial phenomena • nanotribology • Study these phenomena in micro/nanostructures • Magnetic storage systems, nanolithography • System theoretic approach • Not explored • Obtain models to model friction at nanoscales • Explain observed phenomena • Use control tools to compensate for friction • Use observer based design • Friction compensation important in applications • nanolithography System theoretic modeling, analysis and compensation for nano-friction

38. Nano-friction (cont’d.) • Preliminary work • Dynamic model for AFM • With friction model using JKR theory • Simulation of model show stick-slip motion • feedback laws to compensate stick-slip demonstrated in simulation • Substantial reduction of error in tracking • z-velocities were obtained from the model in the control design • Proposed work • Implement observer based design • Develop models to explain more observed phenomena