Nanotechnology is the science of understanding matter and the control of matter at dimensions of 100 nm or less. Encompassing nanoscale science, engineering, and technology, nanotechnology involves imaging, measuring, modeling, and manipulation of matter at this level of precision. An important aspect of research in nanotechnology involves precision control and manipulation of devices and materials at a nanoscale, i.e., nanopositioning. Nanopositioners are precision mechatronic systems designed to move objects over a small range with a resolution down to a fraction of an atomic diameter. The desired attributes of a nanopositioner are extremely high resolution, accuracy, stability, and fast response. The key to successful nanopositioning is accurate position sensing and feedback control of the motion. This paper presents an overview of nanopositioning technologies and devices emphasizing the key role of advanced control techniques in improving precision, accuracy, and speed of operation of these systems.

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A Survey of Control Issues in Nanopositioning

Structural vibrations and hysteresis nonlinearities in piezoactuators have been fundamental limitations when using these actuators for high-speed precision-positioning applications. Positioning speed (bandwidth) is limited by structural vibrations, typically, to about one-tenth the fundamental vibrational frequency of the piezoprobe. Further, precision in positioning is limited by hysteresis nonlinearities, which can result in signie cant errors for large-range positioning applications. This paper shows that signie cant improvements in precision and bandwidth can be achieved by using an inversion-based approach to compensate for hysteresis and vibrations in the piezodynamics. Theapproach decouplestheinversion into 1 )inversion of thehysteresisnonlinearity and 2 )inversion ofthe structuraldynamics,toe ndaninputvoltageproe lethatachievesprecisiontracking ofa desiredpositiontrajectory. Theapproachisappliedtoapiezoactuator,andexperimentalresultsshowthatanorderofmagnitudeimprovement in positioning speed is achieved, while maintaining precision tracking of the desired position trajectory. I. Introduction P IEZOACTUATORS can achieve nanometer resolution positioning and are hence increasingly being used for ultraprecision positioning in aerospace applications, 1;2 vibration control, scanning probe microscopy for surface characterization, and nanofabrication. 3i5 Two major limitations of present positioning techniquesusing piezoactuatorsare 1 )lowoperating bandwidthdue to positioning errors caused by structural vibrations at high speeds and 2) low precision for relatively large-range displacements (due to errors caused by hysteresis nonlinearities ), resulting in restricted positioning range. This paper presents a method to improve both the accuracy and the speed of piezoactuators by using an inversionbased approach to e nd the voltage input to the piezoactuators that compensates for the hysteresis nonlinearities and the structural vibrations. This approach e rst decouples the system dynamics into two separate subsystems that model 1 ) the hysteresis nonlinearity

Creep, Hysteresis, and Vibration Compensation for Piezoactuators: Atomic Force Microscopy Application

The tracking control accuracy of piezoceramic actuators is limited due to their inherent hysteresis nonlinearity. This paper presents a computer-based tracking control approach for a piezoceramic actuator based on incorporating a feedforward loop with a PID (proportional-integral-derivative) feedback controller. The hysteresis nonlinearity of the piezoceramic actuator is modeled in the feedforward loop by using the classical Preisach model. Experiments were performed on a stacked piezoceramic actuator for tracking sinusoidal waveforms with signal frequencies ranging from 0.1-20 Hz. A comparison was made between a feedforward control scheme, a regular PID feedback control scheme, and a PID feedback control scheme with hysteresis modeling in the feedforward loop. The results show that the tracking control performance is greatly improved by augmenting the feedback loop with a model of hysteresis in the feedforward loop. The maximum error in tracking a sinusoidal waveform is about half that obtained using a regular PID controller.

Tracking control of a piezoceramic actuator

A nonlinear lumped-parameter model of a piezoelectric stack actuator has been developed to describe actuator behavior for purposes of control system analysis and design, and, in particular, for microrobotic applications requiring accurate position and/or force control. In formulating this model, the authors propose a generalized Maxwell resistive capacitor as a lumped-parameter causal representation of rate-independent hysteresis. Model formulation is validated by comparing results of numerical simulations to experimental data. Validation is followed by a discussion of model implications for purposes of actuator control.

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Modeling piezoelectric stack actuators for control of micromanipulation

The piezoelectric actuator (PEA) is a well-known device for managing extremely small displacements in the range from 10 pm to 100 /spl mu/m. When developing a control system for a piezo-actuated positioning mechanism, the actuator dynamics have to be taken into account. An electromechanical piezo model, based on physical principles, is presented in this paper. In this model, a first-order differential equation is adopted to describe the hysteresis effect, and a partial differential equation is used to describe the mechanical behavior. Since, in practice, a PEA is most often used as an actuator for positioning mechanisms, we considered the influence of such a mechanism on the overall mechanical behavior of PEA and positioning mechanism together. For a well-designed mechanism, the overall mechanical behavior practically equals that of a single mass-spring-damper system, of which the undamped eigenfrequency and the relative damping can be designed favorably. With respect to traditional voltage steering, charge steering has the advantage that no hysteresis is encountered between electrical input and elongation. Electrical steering configurations for both cases of steering are presented. Finally, for the case of charge steering, we derived the total model of a piezo-actuated positioning mechanism. This model is dominated by the mechanical model, which could be designed favorably. Therefore, this model gives a broad range of possibilities for model-based controller design.

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Modeling piezoelectric actuators

A major deficiency of piezoceramic actuators is that their open-loop control accuracy is seriously limited by hysteresis. This paper discusses the adaptation of the Preisach model to describe the nonlinear hysteresis behavior of these actuators. The adapted model is used to predict the response of a piezoceramic actuator to a sinusoidal input and a triangular input. The predictions are compared with experimental measurements on a stacked piezoceramic actuator. The model reproduces the hysteresis loop of the actuator to within 3% over the entire working range of 0–15 μm. This opens the possibility of incorporating the model into a control loop in order to overcome the accuracy problem.

Modeling hysteresis in piezoceramic actuators

This paper presents a new approach for modeling the hysteresis nonlinearity of a piezoceramic actuator using a modified generalized Preisach model, and the use of this model in a linearizing control scheme. The developed generalized Preisach model relaxes the congruency requirement on the hysteresis loops of a piezoceramic actuator, which must be satisfied when using the classical Preisach model. The congruency property is experimentally proved to not hold when running the actuator on a minor hysteresis loop. A numerical expression of the model is derived in terms of first- and second-order reversal curve experimental datasets. Output prediction using this model is performed on both an exponentially decayed sinusoidal input signal and an arbitrary input signal, and the results show that the model can accurately reproduce the hysteresis response with an error of less than 2.7%. A tracking control system for a piezoceramic actuator is also developed by combining a PID feedback controller with a hysteresis linearizing scheme in a feed-forward loop. The results show that this new control system can achieve 0.25 μm tracking control accuracy, which is 80 and 50% less than that obtained when using an open-loop controller and a regular feedback control system, respectively.

Generalized preisach model for hysteresis nonlinearity of piezoceramic actuators

This paper discusses the design and characterization of a new, single-axis, low-profile, piezo-driven vertical motion micropositioning stage for use in laser welding applications. A low-profile configuration is attained by mounting the piezo actuator horizontally and using a novel lever arrangement to transfer the horizontal motion of the actuator into the desired vertical motion. An analytical model for the static and dynamic behavior of the stage is presented, along with finite element (FE) modeling verification. A 200 μm motion-range stage was built, and tests show that the stage has a vertical stiffness of 6.0 N/μm and a resonance frequency of 364 Hz. The results are in very close agreement to those predicted by the model.

Design and characterization of a low-profile micropositioning stage

A general approach for the design of flexure-hinge type lever mechanisms that are commonly used in the design of translational micro-positioning stages is presented in this paper. The paper focuses on the development of design equations that can accurately predict the behavior of such stages especially the “lost motion” due to hinge stretching. The development of these equations is based on a static analysis of a general configuration of a single-axis, translational, flexure-hinge type, piezo-driven micro-positioning stage using a multi-lever structure. The displacement ratio between the input and output motions of one of the levers, plus the stiffness at either end of this lever are obtained based on the analysis. The overall displacement and stiffness of the micro-positioning stage are then obtained by cascading the individual results from every lever. The developed equations include the effects of the flexure hinge bending and stretching. The developed equations were applied to design of a vertical motion micro-positioning stage. The stiffness and displacement of this stage are predicated by these equations, which are compared to the stiffness and displacement directly obtained from the finite element modeling and actual testing of the same micro-positioning stage. The comparison shows that the analytical approach gave nearly similar results (within 10%), which implies that the developed equations can accurately predict the characteristics of flexure-hinge type lever mechanisms.

Musa Jouaneh

Papers

Tracking control of a piezoceramic actuator

Modeling hysteresis in piezoceramic actuators

Generalized preisach model for hysteresis nonlinearity of piezoceramic actuators

Design and characterization of a low-profile micropositioning stage

Modeling of flexure-hinge type lever mechanisms