2. Outline
• Motivation
• Model Description
• Past Work
• Parameter Estimation for the AMS
• Conclusions
• Future Work
3. Motivation-Active Machining System
• ETREMA Products, Inc.
• Active Mat.: Terfenol-D
• High-Speed Milling
(4,000 RPM)
Courtesy of http://www.etrema-usa.com/
5. Introduction to Model
• Know Terfenol-D exhibits a physical
lengthening in response to magnetic field.
• Goal is to implement accurate controller in
the use of machining.
• Requires an accurate model representation.
• Need to model how rod tip displacement
(assume uniform strain) varies nonlinearly in
response to magnetic field.
9. Dissipativity of HEM
• If a system is dissipative, it loses energy.
• “The energy at final time is less than or equal to
initial energy plus input energy.”
• Showed dissipativity of
– Preisach model
– HEM with negligible thermal relaxation for supply rates
and
– HEM with thermal relaxation for same supply rates
• Statement of stability and helps design controllers
HM MH
11. Previous Work and Future Directions
• Prior work
– Homogenized Energy and Lumped Rod Model
– Parameter Estimation with HEM using normal/lognormal
and general densities.
– Modeling of temperature dependence.
• Direction
– Drastically reduce parameter estimation time for the
HEM/LRM.
– Enforce density shapes and incorporate modeling of
physical behaviors.
– Deliver a nearly black box parameter estimation routine.
15. Densities-Galerkin Expansions
Use Galerkin Expansion to Approximate General Densities
Advantages: 1. Smaller parameter space (8+3(N+1)/2 vs. 8+6N)
2. Decrease in Runtime.
3. Smoother den. approx. Better for controls.
16. Cubic Galerkin Expansion-
No Density Constraints
Left: Displacement vs. field. Center: Interaction field density. Right: Coercive Field Density. N=7, 4 Pt. Gaussian Quadrature.
Example of how close fit to displacement can be obtained while violating physical density behavior.
25. Alternate Optimization Routines
• Differential Evolution
– Evolution Alg./No initial population
– Only simple constraint bounds (upper,lower)
– Creates new population by differencing
alternate members and adding other member.
• Patternsearch
– Direct Search/initial population
– Allows for constraints
– Choose optimal search via a specified
pattern.
26. Temperature Dependence
Terfenol-D behavior as temperature rises:
• Reduction of saturation magnetization
• Decrease in hysteresis in H-M relation
• Change to anhysteretic H-M relation
through the freezing temperature
How may we incorporate this behavior into
the HEM for ferromagnetics?
27. Temperature Dependence
Using a Helmholtz Energy which incorporates Temperature
from which are yielded
through the relation
29. Conclusions
• Showed the HEM to be dissipative.
• Greatly reduced the time required to
perform accurate parameter estimation.
• Begin optimization with more accurate
initial estimates (in some cases).
• Constrained densities to have quasi-
physical characteristics.
• Incorporated temperature dependence
into model.
30. Future Work
• Investigate external optimization routines
(donlp2 and NLPQLP)
– Current Model Evaluations is a C implementation.
– MATLAB interface for optimization routine comes
at a cost of function handles, calls, and passes.
– Data sorting occurs at every model call.
– Preliminary results support the robustness of
several of these “industrial-grade” solvers.
31. Future Work
• Obtain better initial parameter estimates
– We can obtain good initial estimates for HEM
given magnetization vs. field data.
– Can we obtain LRM parameters given strain
and magnetization data?
– Can we obtain model parameters if only given
strain vs. field data?
32. Future Work
• Data exhibits behavior which may be attributed to 90-
degree switching
• Obtain estimates using a model which incorporates 90-
degree switching.
• Parameters will be more difficult to estimate and bound
with this model.
33. Future Work
• In too many cases, we’ve had to use
constraints to enforce desired density
behavior.
– Identify other densities which do not require
these bulk constraints.
– Hope to reduce number of parameters to
estimate for densities.
34. Future Work
• Combine work into black-box parameter
estimation scheme for the AMS.
– This work must be executable on the AMS
when delivered.
– "Hands- off" implementation required for
general users.
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