Discrete Modeling and Sliding Mode Control of Piezoelectric Actuators

With the ability to generate fine displacements with a resolution down to sub-nanometers, piezoelectric actuators (PEAs) have found wide applications in various nano-positioning systems. However, existence of various effects in PEAs, such as hysteresis and creep, as well as dynamics can seriously degrade the PEA performance or even lead to instability. This raises a great need to model and control PEAs for improved performance, which have drawn remarkable attention in the literature. Sliding mode control (SMC) shows its potential to the control of PEA, by which the hysteresis and other nonlinear effects can be regard as disturbance to the dynamic model and thus rejected or compensated by its switching control. To implement SMC in digital computers, this research is aimed at developing novel discrete models and discrete SMC (DSMC)-based control schemes for PEAs, along with their experimental validation. The first part of this thesis concerns with the modeling and control of one-degree of freedom (DOF) PEA, which can be treated as a single-input-single-output (SISO) system. Specifically, a novel discrete model based on the concept of auto-regressive moving average (ARMA) was developed for the PEA hysteresis; and to compensate for the PEA hysteresis and improve its dynamics, an output tracking integrated discrete proportional-integral-derivative-based SMC (PID-SMC) was developed. On this basis, by making use of the availability of PEA hysteresis models, two control schemes, named “the discrete inversion feedforward based PID-SMC” and “the discrete disturbance observer (DOB)-based PID-SMC”, were further developed. To illustrate the effectiveness of the developed models and control schemes, experiments were designed and conducted on a commercially available one-DOF PEA, as compared with the existing ones. The second part of the thesis presents the extension of the developed modeling and control methods to multi-DOF PEAs. Given the fact that details with regard to the PEA internal configurations is not typically provided by the manufacturer, a state space model based on the black box system identification was developed for the three-DOF PEA. The developed model was then integrated in the output tracking based discrete PID-SMC, with its effectiveness verified through the experiments on a commercially available three-DOF PEA. The superiority of the proposed control method over the conventional PID controller was also experimentally investigated and demonstrated. Finally, by integrating with a DOB in the discrete PID-based SMC, a novel control scheme is resulted to compensate for the nonlinearities of the three-DOF PEA. To verify its effectiveness, the discrete DOB based PID-SMC was applied in the control experiments and compared with the existing SMC. The significance of this research lies in the development of the discrete models and PID-based SMC for PEAs, which is of great help to improve their performance. The successful application of the proposed method in the control of multi-DOF PEA allows the application of SMC to the control of complicated multi-inputs-multi-outputs (MIMO) systems without details regarding the internal configuration. Also, integration of the inversion based feedforward control and the DOB in the SMC design has been proven effective for the tracking control of PEAs

Modeling and Control of Piezoelectric Actuators

Piezoelectric actuators (PEAs) utilize the inverse piezoelectric effect to generate fine displacement with a resolution down to sub-nanometers and as such, they have been widely used in various micro- and nanopositioning applications. However, the modeling and control of PEAs have proven to be challenging tasks. The main difficulties lie in the existence of various nonlinear or difficult-to-model effects in PEAs, such as hysteresis, creep, and distributive vibration dynamics. Such effects can seriously degrade the PEA tracking control performances or even lead to instability. This raises a great need to model and control PEAs for improved performance. This research is aimed at developing novel models for PEAs and on this basis, developing model-based control schemes for the PEA tracking control taking into account the aforementioned nonlinear effects. In the first part of this research, a model of a PEA for the effects of hysteresis, creep, and vibration dynamics was developed. Notably, the widely-used Preisach hysteresis model cannot represent the one-sided hysteresis of PEAs. To overcome this shortcoming, a rate-independent hysteresis model based on a novel hysteresis operator modified from the Preisach hysteresis operator was developed, which was then integrated with the models of creep and vibration dynamics to form a comprehensive model for PEAs. For its validation, experiments were carried out on a commercially-available PEA and the results obtained agreed with those from model simulations. By taking into account the linear dynamics and hysteretic behavior of the PEA as well as the presliding friction between the moveable platform and the end-effector, a model of the piezoelectric-driven stick-slip (PDSS) actuator was also developed in the first part of the research. The effectiveness of the developed model was illustrated by the experiments on the PDSS actuator prototyped in the author's lab. In the second part of the research, control schemes were developed based on the aforementioned PEA models for tracking control of PEAs. Firstly, a novel PID-based sliding mode (PIDSM) controller was developed. The rational behind the use of a sliding mode (SM) control is that the SM control can effectively suppress the effects of matched uncertainties, while the PEA hysteresis, creep, and external load can be represented by a lumped matched uncertainty based on the developed model. To solve the chattering and steady-state problems, associated with the ideal SM control and the SM control with boundary layer (SMCBL), the novel PIDSM control developed in the present study replaces the switching control term in the ideal SM control schemes with a PID regulator. Experiments were carried out on a commercially-available PEA and the results obtained illustrate the effectiveness of the PIDSM controller, and its superiorities over other schemes of PID control, ideal SM control, and the SMCBL in terms of steady state error elimination, chattering suppression, and tracking error suppression. Secondly, a PIDSM observer was also developed based on the model of PEAs to provide the PIDSM controller with state estimates of the PEA. And the PIDSM controller and the PIDSM observer were combined to form an integrated control scheme (PIDSM observer-controller or PIDSMOC) for PEAs. The effectiveness of the PIDSM observer and the PIDSMOC were also validated experimentally. The superiority of the PIDSMOC over the PIDSM controller with σ-β filter control scheme was also analyzed and demonstrated experimentally. The significance of this research lies in the development of novel models for PEAs and PDSS actuators, which can be of great help in the design and control of such actuators. Also, the development of the PIDSM controller, the PIDSM observer, and their integrated form, i.e., PIDSMOC, enables the improved performance of tracking control of PEAs with the presence of various nonlinear or difficult-to-model effects

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

Dynamics and Control of Flexure-based Large Range Nanopositioning Systems.

The objective of this thesis is to demonstrate desktop-size and cost-effective flexure-based multi-axis nanopositioning capability over a motion range of several millimeters per axis. Increasing the motion range will overcome one of the main drawbacks of existing nanopositioning systems, thereby significantly improving the coverage area in nanometrology and nanomanufacturing applications. A single-axis nanopositioning system, comprising a symmetric double parallelogram flexure bearing and a traditional-architecture moving magnet actuator, is designed, fabricated, and tested. A figure of merit for the actuator is derived and shown to directly impact the system-level trade-offs in terms of range, resolution, bandwidth, and temperature rise. While linear feedback controllers provide good positioning performance for point-to-point commands, the tracking error for dynamic commands prove to be inadequate due to the nonlinearities in the actuator and its driver. To overcome this, an iterative learning controller is implemented in conjunction with linear feedback to reduce the periodic component of the tracking error by more than two orders of magnitude. Experimental results demonstrate 10 nm RMS tracking error over 8 mm motion range in response to a 2 Hz bandlimited triangular command. For the XY nanopositioning system, a lumped-parameter model of an existing XY flexure bearing is developed in order to understand the unexplained variation observed in the transfer function zeros over the operating range of motion. It is shown that the kinematic coupling, due to geometric nonlinearities in the beam mechanics, and small dimensional asymmetry, due to manufacturing tolerances, may conspire to produce complex-conjugate nonminimum phase zeros at certain operating points in the system's workspace. This phenomenon significantly restricts the overall performance of the feedback control system. After intentional use of large asymmetry is employed to overcome this problem, independent feedback and iterative learning controllers are implemented along each axis. Experimental results demonstrate 20 nm RMS radial tracking error while traversing a 2 mm diameter circle at 2 Hz.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/107086/1/parmar_1.pd

Nanopositionnement 3D à base de mesure à courant tunnel et piezo-actionnement

The objective of this thesis was to elaborate high performance control strategies and their real-time validation on a tunneling current-based 3D nanopositioning system developed in GIPSA-lab. The thesis lies in the domain of micro-/nano mechatronic systems (MEMS) focused on applications of fast and precise positioning and scanning tunneling microscopy (STM). More precisely, the aim is to position the metallic tunneling tip (like in STM) over the metallic surface using piezoelectric actuators in X, Y and Z directions and actuated micro-cantilever (like in Atomic Force Microscope AFM), electrostatically driven in Z direction, with high precision, over possibly high bandwidth. However, the presence of different adverse effects appearing at such small scale (e.g. measurement noise, nonlinearities of different nature, cross-couplings, vibrations) strongly affect the overall performance of the 3D system. Therefore a high performance control is needed. To that end, a novel 3D model of the system has been developed and appropriate control methods for such a system have been elaborated. First the focus is on horizontal X and Y directions. The nonlinear hysteresis and creep effects exhibited by piezoelectric actuators have been compensated and a comparison between different compensation methods is provided. Modern SISO and MIMO robust control methods are next used to reduce high frequency effects of piezo vibration and cross-couplings between X and Y axes. Next, the horizontal motion is combined with the vertical one (Z axis) with tunneling current and micro-cantilever control. Illustrative experimental results for 3D nanopositioning of tunneling tip, as well as simulation results for surface topography reconstruction and multi-mode cantilever positioning, are finally given.L'objectif de la thèse est l'élaboration de lois de commande de haute performance et leur validation en temps réel sur une plateforme expérimentale 3D de nano-positionnement à base de courant à effet tunnel, développée au laboratoire GIPSA-lab. Elle s'inscrit donc dans le cadre des systèmes micro-/nano-mécatronique (MEMS), et de la commande. Plus précisément, le principal enjeu considéré est de positionner la pointe métallique à effet tunnel (comme en microscopie à effet tunnel STM) contre la surface métallique en utilisant des actionneurs piézoélectriques en X, Y et Z et un micro-levier (comme en microscopie à force atomique AFM) actionné électrostatiquement en Z avec une grande précision et une bande passante élevée. Cependant, la présence de différents effets indésirables apparaissant à cette petite échelle (comme le bruit de mesure, des non-linéarités de natures différentes, les couplages, les vibrations) affectent fortement la performance globale du système 3D. En conséquence, une commande de haute performance est nécessaire. Pour cela, un nouveau modèle 3D du système a été développé et des méthodes de contrôle appropriées pour un tel système ont été élaborées. Tout d'abord l'accent est mis sur de positionnement selon les axes X et Y. Les effets d'hystérésis et de fluage non linéaires présents dans les actionneurs piézoélectriques ont été compensés et une comparaison entre les différentes méthodes de compensation est effectuée. Des techniques modernes de commande robuste SISO et MIMO sont ensuite utilisées pour réduire les effets des vibrations piézoélectriques et des couplages entre les axes X et Y. Le mouvement horizontal est alors combiné avec le mouvement vertical (Axe Z) et une commande du courant tunnel et du micro-levier. Des résultats expérimentaux illustrent le nano positionnement 3D de la pointe, et des résultats de simulation pour la reconstruction de la topographie de la surface ainsi que le positionnement du micro-levier à base d'un modèle multi-modes

Development of novel high-performance six-axis magnetically levitated instruments for nanoscale applications

This dissertation presents two novel 6-axis magnetic-levitation (maglev) stages that are capable of nanoscale positioning. These stages have very simple and compact structure that is advantageous to meet requirements in the next-generation nanomanufacturing. The 6-axis motion generation is accomplished by the minimum number of actuators and sensors. The first-generation maglev stage is capable of generating translation of 300 ??m in x, y and z, and rotation of 3 mrad about the three orthogonal axes. The stage demonstrates position resolution better than 5 nm rms and position noise less than 2 nm rms. It has a light moving-part mass of 0.2126 kg. The total power consumption by all the actuators is only around a watt. Experimental results show that the stage can carry, orient, and precisely position an additional payload as heavy as 0.3 kg. The second-generation maglev stage is capable of positioning at the resolution of a few nanometers over a planar travel range of several millimeters. A novel actuation scheme was developed for the compact design of this stage that enables 6-axis force generation with just 3permanent-magnet pieces. Electromagnetic forces were calculated and experimentally verified. The complete design and construction of the second-generation maglev stage was performed. All the mechanical part and assembly fixtures were designed and fabricated at the mechanical engineering machine shop. The single moving part is modeled as a pure mass due to the negligible effect of the magnetic spring and damping. Classical as well as advanced controllers were designed and implemented for closed-loop feedback control. A nonlinear model of the force was developed and applied to cancel the nonlinearity of the actuators over the large travel range. Various experiments were conducted to test positioning, loading, and vibration-isolation capabilities. This maglev stage has a moving-part mass of 0.267 kg. Its position resolution is 4 nm over a travel range of 5 ?? 5 mm in the x-y plane. Its actuators are designed to carry and precisely position an additional payload of 2 kg. Its potential applications include semiconductor manufacturing, micro-fabrication and assembly, nanoscale profiling, and nano-indentation

Positioning Control System for a Large Range 2D Platform with Submicrometre Accuracy for Metrological and Manufacturing Applications

The importance of nanotechnology in the world of Science and Technology has rapidly increased over recent decades, demanding positioning systems capable of providing accurate positioning in large working ranges. In this line of research, a nanopositioning platform, the NanoPla, has been developed at the University of Zaragoza. The NanoPla has a large working range of 50 mm × 50 mm and submicrometre accuracy. The NanoPla actuators are four Halbach linear motors and it implements planar motion. In addition, a 2D plane mirror laser interferometer system works as positioning sensor. One of the targets of the NanoPla is to implement commercial devices when possible. Therefore, a commercial control hardware designed for generic three phase motors has been selected to control and drive the Halbach linear motors.This thesis develops 2D positioning control strategy for large range accurate positioning systems and implements it in the NanoPla. The developed control system coordinates the performance of the four Halbach linear motors and integrates the 2D laser system positioning feedback. In order to improve the positioning accuracy, a self calibration procedure for the characterisation of the geometrical errors of the 2D laser system is proposed. The contributors to the final NanoPla positioning errors are analysed and the final positioning uncertainty (k=2) of the 2D control system is calculated to be ±0.5 µm. The resultant uncertainty is much lower than the NanoPla required positioning accuracy, broadening its applicability scope.<br /

Flexure-based nanopositioning systems : integrated design and control

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 209-219).This thesis deals with the design and control of flexure-based mechanisms for applications requiring multi-degree-of-freedom positioning and alignment. Example applications include positioning a probe or sample in atomic force microscopy, alignment of tool and sample in stamping processes, and fine-positioning of wafer steppers in semiconductor manufacturing. Such applications necessitate nanopositioning systems that satisfy critical functional requirements, such as load-capacity, bandwidth, resolution, and range. Therefore, a systematic approach for design and control is an important tool for research and development for flexure-based nanopositioning systems. In this thesis, a novel methodology is presented for generating flexure-based topologies that can meet performance requirements, such as those dictating structural strength or dynamical behavior. We present performance metrics that allow for the generation of topologies that are tuned for a desired level of structural strength or modal separation. The topology generation is aimed as a valuable addition to the design toolkit, facilitating novel designs that could not have been conceived otherwise. The parameters within any particular topology could be adjusted at a subsequent phase through a detailed shape and size optimization. The thesis also proposes a controller generation approach. Unlike existing controller parameterizations, a novel parameterization formulated in this thesis allows for directly tuning the sensitivity transfer function of the closed-loop system. Tuning sensitivity is critical in mitigating the effects of disturbances affecting the system, as well as those arising from cross-coupling and parasitic error motions. Further, an integrated methodology for design and control is presented. This methodology uses the design topology generation approach and controller generation approach proposed in the thesis. The key distinction of our design for control approach is that the design is iterated over topologies and not just parameters within a selected topology. A simple one-degree-of-freedom positioning system example is worked out to detail the steps of the proposed integrated design and control methodology. A novel design topology that is ideally suited for achieving a desired design and control performance is derived using this methodology. Finally, the hardware design and control of a novel flexure-based nanopositioner implementation for scanning probe microscopy are presented to illustrate the effectiveness of the approaches discussed in this thesis.by Vijay Shilpiekandula.Ph.D