Harvard - Boston University - University of Maryland

Highlights of CDCSS-UMD Accomplishments

Presentation to Dr. Randy Zachery

Army Research Office

May 25, 2004 at Harvard University

Harvard - Boston University - University of Maryland

Accomplishments• Adaptive Optics

- Proof-of-concept experimental demonstration of the liquid crystal light valve (LCLV)-based high resolution wave-front control system (nonlinear Zernike filter realization)

- Simulation results show effectiveness against atmospheric turbulence

- Global nonlinear stability analysis for the continuous system model of the wave-front control system

- Patent disclosure (PS-2001-078) jointly to University of Maryland and Army Research Laboratory: Wave-front phase sensors based on optically or electrically controlled phase spatial light modulators for wave-front sensing and control (M.A. Vorontsov, E. W. Justh, L. Beresnev, P. S. Krishnaprasad, J. Ricklin)

Harvard - Boston University - University of Maryland

From nonlinear Zernike filters to high-resolution adaptive optics

Harvard - Boston University - University of Maryland

Accomplishments• Modeling, Computation and Control of Magnetostrictive Hysteresis

- Effective numerical computation of magnetostrictive hysteresis in materials such as Terfenol-D using the Landau-Lifshitz-Gilbert (LLG) equation to model ferromagneto-dynamics, and elastic rod theory to model actuator movement

- Hierarchical tree-structured Fast Multipole Algorithm to compute magnetostatic term in effective field, coupled to a new Cayley transform- based geometric integrator for solving the LLG equation, to compute theoretical hysteresis curves

- Modeling of rate-dependent phenomena in hysteretic actuators due to eddy current effects by a novel extension of the Preisach model

- Fast inversion algorithm for Preisach-type model to compute control signals for tracking specified output trajectories.

- New Hamilton-Jacobi theory for robust control of hysteretic systems

Harvard - Boston University - University of Maryland

Sectional view of the Etrema magnetostrictive actuator

Harvard - Boston University - University of Maryland

Higher Order Geometric Integrator— Performance Comparision

Comparison of integration schemes on a 2 by 2 by 4 grid, using the result of RK4 with much smaller stepsize as the benchmark. RK4: Runge-Kutta 4-th order, MP: Mid-point rule. Cay_RK4: Cayley transform with RK4.

Harvard - Boston University - University of Maryland

Higher Order Geometric Integrator— Performance Comparision

Comparison of performance on norm preserving

Harvard - Boston University - University of Maryland

Higher Order Geometric Integrator— Summary of Features

• Fast

– Explicit

– On the right track

• Accurate due to high order

• Norm preserving

Method Stepsize (sec.) Time (sec.)RK4 2 10 -13 1656RK4 6 10 –13 953

Mid-Point 6 10 –13 789 Cayley-RK4 6 10 –13 367