A Polynomial-Based Linear Mapping Strategy for Feedforward Compensation of Hysteresis in Piezoelectric Actuators

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Saeid Bashash ◽  
Nader Jalili
Keyword(s):  
Turning Points ◽  
Three Dimensional ◽  
Piezoelectric Actuators ◽  
Linear Mapping ◽  
Memory Allocation ◽  
Hysteresis Phenomenon ◽  
Mathematical Framework ◽  
Modeling Framework ◽  
Mapping Strategy ◽  
Hysteresis Nonlinearity

A set of memory-based properties is employed in this paper for modeling multiple-path hysteresis response of piezoelectric actuators. These properties, namely, targeting turning points, curve alignment, and wiping-out effect, are applied in a linear mapping strategy to develop a mathematical framework for modeling the hysteresis phenomenon. More specifically, the locations of turning points are detected and recorded for the prediction of future hysteresis trajectory. An internal trajectory is assumed to follow a multiple-segmented path via a continuous connection of several curves passing through every two consequent turning points. These curves adopt their shapes via a linear mapping strategy from the reference hysteresis curves with polynomial configurations. Experimental implementation of the proposed method demonstrates slight improvement over the widely used Prandtl–Ishlinskii hysteresis operator. However, to maintain the level of precision during the operation, a sufficient number of memory units must be included to record the turning points. Otherwise, in the event of memory saturation, two memory-allocation modes, namely, “open” and “closed” strategies, can be implemented. It is shown that the closed memory-allocation strategy demonstrates better performance by keeping the most important target points. The proposed modeling framework is adopted in an inverse model-based control scheme for feedforward compensation of hysteresis nonlinearity. The controller is experimentally implemented on a three-dimensional nanopositioning stage for surface topography tracking, a problem typically encountered in scanning probe microscopy applications.

scholarly journals Modeling and Compensation of Dynamic Hysteresis with Force-Voltage Coupling for Piezoelectric Actuators

Micromachines ◽  
2021 ◽  
Vol 12 (11) ◽  
pp. 1366
Author(s):  
Wen Wang ◽  
Jiahui Wang ◽  
Ruijin Wang ◽  
Zhanfeng Chen ◽  
Fuming Han ◽  
...  
Keyword(s):  
Piezoelectric Actuators ◽  
Hysteresis Phenomenon ◽  
Dynamic Force ◽  
Driving Voltage ◽  
Driving Frequency ◽  
Positioning Accuracy ◽  
Output Displacement ◽  
Dynamic Hysteresis ◽  
Hysteresis Nonlinearity ◽  
The Impact

Piezoelectric actuators are widely used in the field of micro- and nanopositioning due to their high frequency response, high stiffness, and high resolution. However, piezoelectric actuators have hysteresis nonlinearity, which severely affects their positioning accuracy. As the driving frequency increases, the performance of piezoelectric actuators further degrades. In addition, the impact of force on piezoelectric actuators cannot be ignored in practical applications. Dynamic hysteresis with force-voltage coupling makes the hysteresis phenomenon more complicated when force and driving voltage are both applied to the piezoelectric actuator. Existing hysteresis models are complicated, or inaccurate in describing dynamic hysteresis with force-voltage coupling. To solve this problem, a force-voltage-coupled Prandtl–Ishlinskii (FVPI) model is proposed in this paper. First, the influence of driving frequency and dynamic force on the output displacement of the piezoelectric actuators are analyzed. Then, the accuracy of the FVPI model is verified through experiments. Finally, a force integrated direct inverse (F-DI) compensator based on the FVPI model is designed. The experimental results from this study show that the F-DI compensator can effectively suppress dynamic hysteresis with force-voltage coupling of piezoelectric actuators. This model can improve the positioning accuracy of piezoelectric actuators, thereby improving the working accuracy of the micro- or nano-operating system.

scholarly journals The ICON Single-Column Mode

Atmosphere ◽  
2021 ◽  
Vol 12 (7) ◽  
pp. 906
Author(s):  
Ivan Bašták Ďurán ◽  
Martin Köhler ◽  
Astrid Eichhorn-Müller ◽  
Vera Maurer ◽  
Juerg Schmidli ◽  
...  
Keyword(s):  
Data Storage ◽  
Model Development ◽  
Computational Cost ◽  
Three Dimensional ◽  
Shallow Convection ◽  
Modeling Framework ◽  
Additional Tool ◽  
Eddy Simulation ◽  
Single Column ◽  
Stratocumulus Clouds

The single-column mode (SCM) of the ICON (ICOsahedral Nonhydrostatic) modeling framework is presented. The primary purpose of the ICON SCM is to use it as a tool for research, model evaluation and development. Thanks to the simplified geometry of the ICON SCM, various aspects of the ICON model, in particular the model physics, can be studied in a well-controlled environment. Additionally, the ICON SCM has a reduced computational cost and a low data storage demand. The ICON SCM can be utilized for idealized cases—several well-established cases are already included—or for semi-realistic cases based on analyses or model forecasts. As the case setup is defined by a single NetCDF file, new cases can be prepared easily by the modification of this file. We demonstrate the usage of the ICON SCM for different idealized cases such as shallow convection, stratocumulus clouds, and radiative transfer. Additionally, the ICON SCM is tested for a semi-realistic case together with an equivalent three-dimensional setup and the large eddy simulation mode of ICON. Such consistent comparisons across the hierarchy of ICON configurations are very helpful for model development. The ICON SCM will be implemented into the operational ICON model and will serve as an additional tool for advancing the development of the ICON model.

scholarly journals Marine boundary layer cloud regimes and POC formation in a CRM coupled to a bulk aerosol scheme

2013 ◽  
Vol 13 (24) ◽  
pp. 12549-12572 ◽  
Author(s):  
A. H. Berner ◽  
C. S. Bretherton ◽  
R. Wood ◽  
A. Muhlbauer
Keyword(s):  
Boundary Layer ◽  
Marine Boundary Layer ◽  
Three Dimensional ◽  
Two Dimensional ◽  
State Variables ◽  
Liquid Water Path ◽  
Modeling Framework ◽  
Boundary Layer Cloud ◽  
Cloud Regimes ◽  
Layer Cloud

Abstract. A cloud-resolving model (CRM) coupled to a new intermediate-complexity bulk aerosol scheme is used to study aerosol–boundary-layer–cloud–precipitation interactions and the development of pockets of open cells (POCs) in subtropical stratocumulus cloud layers. The aerosol scheme prognoses mass and number concentration of a single lognormal accumulation mode with surface and entrainment sources, evolving subject to processing of activated aerosol and scavenging of dry aerosol by clouds and rain. The CRM with the aerosol scheme is applied to a range of steadily forced cases idealized from a well-observed POC. The long-term system evolution is explored with extended two-dimensional (2-D) simulations of up to 20 days, mostly with diurnally averaged insolation and 24 km wide domains, and one 10 day three-dimensional (3-D) simulation. Both 2-D and 3-D simulations support the Baker–Charlson hypothesis of two distinct aerosol–cloud "regimes" (deep/high-aerosol/non-drizzling and shallow/low-aerosol/drizzling) that persist for days; transitions between these regimes, driven by either precipitation scavenging or aerosol entrainment from the free-troposphere (FT), occur on a timescale of ten hours. The system is analyzed using a two-dimensional phase plane with inversion height and boundary layer average aerosol concentrations as state variables; depending on the specified subsidence rate and availability of FT aerosol, these regimes are either stable equilibria or distinct legs of a slow limit cycle. The same steadily forced modeling framework is applied to the coupled development and evolution of a POC and the surrounding overcast boundary layer in a larger 192 km wide domain. An initial 50% aerosol reduction is applied to half of the model domain. This has little effect until the stratocumulus thickens enough to drizzle, at which time the low-aerosol portion transitions into open-cell convection, forming a POC. Reduced entrainment in the POC induces a negative feedback between the areal fraction covered by the POC and boundary layer depth changes. This stabilizes the system by controlling liquid water path and precipitation sinks of aerosol number in the overcast region, while also preventing boundary layer collapse within the POC, allowing the POC and overcast to coexist indefinitely in a quasi-steady equilibrium.

Topology of ray surfaces in low-velocity zones

1979 ◽  
Vol 69 (2) ◽  
pp. 369-378
Author(s):  
George A. McMechan
Keyword(s):  
Guided Waves ◽  
Turning Points ◽  
Three Dimensional ◽  
Focal Depth ◽  
Low Velocity ◽  
Low Velocity Zone ◽  
Ray Trajectories ◽  
Definition Of ◽  
Single Set ◽  
Velocity Zone

abstract Plotting of three-dimensional ray surfaces in p-Δ-z space provides a means of determining p-Δ curves for any focal depth. A region of increasing velocity with depth is represented in p-Δ-z space by a trough, and a region of decreasing velocity, by a crest. Two sets of ray trajectories, the arrivals refracted outside a low-velocity zone, and the guided waves inside the zone, can be merged into a single set along the ray that splits into two at the top of the low-velocity zone. This ray is common to both sets. This construction provides continuity of the locus of ray turning points through the low-velocity zone and thus allows definition of p-Δ curves inside as well as outside the low-velocity zone.

scholarly journals Mechanics unlocks the morphogenetic puzzle of interlocking bivalved shells

2019 ◽  
Vol 117 (1) ◽  
pp. 43-51 ◽  
Author(s):  
Derek E. Moulton ◽  
Alain Goriely ◽  
Régis Chirat
Keyword(s):  
Pattern Formation ◽  
Growth Process ◽  
Shell Growth ◽  
Point Of View ◽  
Mathematical Framework ◽  
Bivalve Mollusks ◽  
Modeling Framework ◽  
Mechanistic Basis ◽  
Developmental Point ◽  
Rigid Shell

Brachiopods and mollusks are 2 shell-bearing phyla that diverged from a common shell-less ancestor more than 540 million years ago. Brachiopods and bivalve mollusks have also convergently evolved a bivalved shell that displays an apparently mundane, yet striking feature from a developmental point of view: When the shell is closed, the 2 valve edges meet each other in a commissure that forms a continuum with no gaps or overlaps despite the fact that each valve, secreted by 2 mantle lobes, may present antisymmetric ornamental patterns of varying regularity and size. Interlocking is maintained throughout the entirety of development, even when the shell edge exhibits significant irregularity due to injury or other environmental influences, which suggests a dynamic physical process of pattern formation that cannot be genetically specified. Here, we derive a mathematical framework, based on the physics of shell growth, to explain how this interlocking pattern is created and regulated by mechanical instabilities. By close consideration of the geometry and mechanics of 2 lobes of the mantle, constrained both by the rigid shell that they secrete and by each other, we uncover the mechanistic basis for the interlocking pattern. Our modeling framework recovers and explains a large diversity of shell forms and highlights how parametric variations in the growth process result in morphological variation. Beyond the basic interlocking mechanism, we also consider the intricate and striking multiscale-patterned edge in certain brachiopods. We show that this pattern can be explained as a secondary instability that matches morphological trends and data.

scholarly journals Publisher Correction to: Three-dimensional tumor growth in time-varying chemical fields: a modeling framework and theoretical study

2019 ◽  
Vol 20 (1) ◽  
Author(s):  
Markos Antonopoulos ◽  
Dimitra Dionysiou ◽  
Georgios Stamatakos ◽  
Nikolaos Uzunoglu
Keyword(s):  
Tumor Growth ◽  
Theoretical Study ◽  
Three Dimensional ◽  
Time Varying ◽  
Modeling Framework ◽  
Chemical Fields

Following publication of the original article [1], the authors noticed that the following errors were introduced by pdf/html formatting issues.

scholarly journals Simulation of the remanence influence on the transient states in a single-phase multiwinding transformer

2017 ◽  
Vol 66 (1) ◽  
pp. 41-54 ◽  
Author(s):  
Andrzej Wilk ◽  
Michał Michna
Keyword(s):  
Magnetic Flux ◽  
Experimental Validation ◽  
Single Phase ◽  
Magnetic Hysteresis ◽  
Hysteresis Phenomenon ◽  
Capacitor Discharge ◽  
Hysteresis Nonlinearity ◽  
Transformer Model ◽  
The Mathematical Model ◽  
Discharge Test

Abstract This paper presents the mathematical model of a single-phase multi-winding core type transformer taking into account magnetic hysteresis phenomenon based on the feedback Preisach model (FPM). The set of loop differential equations was developed for a K-th winding transformer model where the flux linkages of each winding includes flux Φ common to all windings as a function of magneto motive force Θ of all windings. The first purpose of this paper is to implement a hysteresis nonlinearity involved in the Φ(Θ) function which also accounts residual magnetic flux. The second purpose of this paper is experimental validation of the developed transformer model in a capacitor discharge test and several different values of residual magnetic flux.

Beyond Cloud Microphysics: Representing Subgrid-Scale Processes in Lagrangian Cloud Models

2020 ◽  
Author(s):  
Fabian Hoffmann
Keyword(s):  
Three Dimensional ◽  
Cloud Microphysics ◽  
Mixed Phase ◽  
Droplet Growth ◽  
Subgrid Scale ◽  
Modeling Framework ◽  
Mixing Processes ◽  
New Approach ◽  
Cloud Models ◽  
Mixed Phase Clouds

<p>While the use of Lagrangian cloud microphysical models dates back as far as the 1950s, the integration of this framework into fully-coupled, three-dimensional dynamical models is only possible for about 10 years. In addition to the highly accurate and detailed representation of cloud microphysical processes, these so-called Lagrangian Cloud Models (LCMs) also allow for new ways of representing subgrid-scale dynamical processes and their effects on the microphysical development of clouds, typically neglected or only crudely parameterized due to computational constraints.</p><p>In this talk, I will present a new approach in which supersaturation fluctuations on the subgrid-scale of a large-eddy simulation (LES) model are represented by an economical, one-dimensional model that represents turbulent compression and folding. With a resolution comparable to direct numerical simulation (DNS), inhomogeneous and finite rate mixing processes are explicitly resolved. Applications of this modeling approach for warm-phase shallow cumuli and stratocumuli, and first applications for mixed-phase clouds will be discussed. Generally, clouds susceptible to inhomogeneous mixing show a reduction in the droplet number concentration and stronger droplet growth, in agreement with theory. Stratocumulus entrainment rates tend to be lower using the new approach compared to simulations without it, indicating a more appropriate representation of the entrainment-mixing process. Finally, the Wegner-Bergeron-Findeisen-Process, leading to a rapid ice formation in mixed-phase clouds, is decelerated.</p><p>All in all, this new modeling framework is capable of bridging the gap between LES and DNS, i.e., it enables representing all scales relevant to cloud physics, from entire cloud fields to the smallest turbulent fluctuations, in a single model, allowing to study their interactions explicitly and granting new insights.</p>

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