A robust loop-shaping approach to fast and accurate nanopositioning

Peer reviewedPreprin

MICROCANTILEVER-BASED FORCE SENSING, CONTROL AND IMAGING

This dissertation presents a distributed-parameters base modeling framework for microcantilever (MC)-based force sensing and control with applications to nanomanipulation and imaging. Due to the widespread applications of MCs in nanoscale force sensing or atomic force microscopy with nano-Newton to pico-Newton force measurement requirements, precise modeling of the involved MCs is essential. Along this line, a distributed-parameters modeling framework is proposed which is followed by a modified robust controller with perturbation estimation to target the problem of delay in nanoscale imaging and manipulation. It is shown that the proposed nonlinear model-based controller can stabilize such nanomanipulation process in a very short time compared to available conventional methods. Such modeling and control development could pave the pathway towards MC-based manipulation and positioning. The first application of the MC-based (a piezoresistive MC) force sensors in this dissertation includes MC-based mass sensing with applications to biological species detection. MC-based sensing has recently attracted extensive interest in many chemical and biological applications due to its sensitivity, extreme applicability and low cost. By measuring the stiffness of MCs experimentally, the effect of adsorption of target molecules can be quantified. To measure MC\u27s stiffness, an in-house nanoscale force sensing setup is designed and fabricated which utilizes a piezoresistive MC to measure the force acting on the MC\u27s tip with nano-Newton resolution. In the second application, the proposed MC-based force sensor is utilized to achieve a fast-scan laser-free Atomic Force Microscopy (AFM). Tracking control of piezoelectric actuators in various applications including scanning probe microscopes is limited by sudden step discontinuities within time-varying continuous trajectories. For this, a switching control strategy is proposed for effective tracking of such discontinuous trajectories. A new spiral path planning is also proposed here which improves scanning rate of the AFM. Implementation of the proposed modeling and controller in a laser-free AFM setup yields high quality image of surfaces with stepped topographies at frequencies up to 30 Hz. As the last application of the MC-based force sensors, a nanomanipulator named here MM3A® is utilized for nanomanipulation purposes. The area of control and manipulation at the nanoscale has recently received widespread attention in different technologies such as fabricating electronic chipsets, testing and assembly of MEMS and NEMS, micro-injection and manipulation of chromosomes and genes. To overcome the lack of position sensor on this particular manipulator, a fused vision force feedback robust controller is proposed. The effects of utilization of the image and force feedbacks are individually discussed and analyzed for use in the developed fused vision force feedback control framework in order to achieve ultra precise positioning and optimal performance

Modeling and Control of Piezoactive Micro and Nano Systems

Piezoelectrically-driven (piezoactive) systems such as nanopositioning platforms, scanning probe microscopes, and nanomechanical cantilever probes are advantageous devices enabling molecular-level imaging, manipulation, and characterization in disciplines ranging from materials science to physics and biology. Such emerging applications require precise modeling, control and manipulation of objects, components and subsystems ranging in sizes from few nanometers to micrometers. This dissertation presents a comprehensive modeling and control framework for piezoactive micro and nano systems utilized in various applications. The development of a precise memory-based hysteresis model for feedforward tracking as well as a Lyapunov-based robust-adaptive controller for feedback tracking control of nanopositioning stages are presented first. Although hysteresis is the most degrading factor in feedforward control, it can be effectively compensated through a robust feedback control design. Moreover, an adaptive controller can enhance the performance of closed-loop system that suffers from parametric uncertainties at high-frequency operations. Comparisons with the widely-used PID controller demonstrate the effectiveness of the proposed controller in tracking of high-frequency trajectories. The proposed controller is then implemented in a laser-free Atomic Force Microscopy (AFM) setup for high-speed and low-cost imaging of surfaces with micrometer and nanometer scale variations. It is demonstrated that the developed AFM is able to produce high-quality images at scanning frequencies up to 30 Hz, where a PID controller is unable to present acceptable results. To improve the control performance of piezoactive nanopositioning stages in tracking of time-varying trajectories with frequent stepped discontinuities, which is a common problem in SPM systems, a supervisory switching controller is designed and integrated with the proposed robust adaptive controller. The controller switches between two control modes, one mode tuned for stepped trajectory tracking and the other one tuned for continuous trajectory tracking. Switching conditions and compatibility conditions of the control inputs in switching instances are derived and analyzed. Experimental implementation of the proposed switching controller indicates significant improvements of control performance in tracking of time-varying discontinuous trajectories for which single-mode controllers yield undesirable results. Distributed-parameters modeling and control of rod-type solid-state actuators are then studied to enable accurate tracking control of piezoactive positioning systems in a wide frequency range including several resonant frequencies of system. Using the extended Hamilton\u27s principle, system partial differential equation of motion and its boundary conditions are derived. Standard vibration analysis techniques are utilized to formulate the truncated finite-mode state-space representation of the system. A new state-space controller is then proposed for asymptotic output tracking control of system. Integration of an optimal state-observer and a Lyapunov-based robust controller are presented and discussed to improve the practicability of the proposed framework. Simulation results demonstrate that distributed-parameters modeling and control is inevitable if ultra-high bandwidth tracking is desired. The last part of the dissertation, discusses new developments in modeling and system identification of piezoelectrically-driven Active Probes as advantageous nanomechanical cantilevers in various applications including tapping mode AFM and biomass sensors. Due to the discontinuous cross-section of Active Probes, a general framework is developed and presented for multiple-mode vibration analysis of system. Application in the precise pico-gram scale mass detection is then presented using frequency-shift method. This approach can benefit the characterization of DNA solutions or other biological species for medical applications

Robust Repetitive Controller for Fast AFM Imaging

Currently, Atomic Force Microscopy (AFM) is the most preferred Scanning Probe Microscopy (SPM) method due to its numerous advantages. However, increasing the scanning speed and reducing the interaction forces between the probe's tip and the sample surface are still the two main challenges in AFM. To meet these challenges, we take advantage of the fact that the lateral movements performed during an AFM scan is a repetitive motion and propose a Repetitive Controller (RC) for the z-axis movements of the piezo-scanner. The RC utilizes the profile of the previous scan line while scanning the current line to achieve a better scan performance. The results of the scanning experiments performed with our AFM set-up show that the proposed RC significantly outperforms a conventional PI controller that is typically used for the same task. The scan error and the average tapping forces are reduced by 66% and 58%, respectively when the scan speed is increased by 7-fold

A Multi-mode Transverse Dynamic Force Microscope - Design, Identification and Control

This is the author accepted manuscript. The final version is available from IEEE via the DOI in this record.The transverse dynamic force microscope (TDFM) and its shear force sensing principle permit true non-contact force detection in contrast to typical atomic force microscopes. The two TDFM measurement signals for the cantilever allow, in principle, two different scanning modes of which, in particular, the second presented here permits a full-scale non-contact scan. Previous research mainly focused on developing the sensing mechanism, whereas this work investigates the vertical axis dynamics for advanced robust closed-loop control. This paper presents a new TDFM digital control solution, built on field-programmable gate array (FPGA) equipment running at high implementation frequencies. The integrated control system allows the implementation of online customizable controllers, and raster-scans in two modes at very high detection bandwidth and nano-precision. Robust control algorithms are designed, implemented, and practically assessed. The two realized scanning modes are experimentally evaluated by imaging nano-spheres with known dimensions in wet conditions.Engineering and Physical Sciences Research Council (EPSRC