Analytical Model of a Magnetic Fluid Deformable Mirror

  • Zhizheng WuEmail author
  • Azhar Iqbal
  • Foued Ben Amara


In this chapter, an analytical model of a magnetic fluid deformable mirror (MFDM) is presented. The model describes the dynamic response of the MFDM surface shape to the applied control magnetic field. The model is derived from the fundamental principles governing the deformation of the mirror surface under the influence of a magnetic field generated by an array of electromagnetic coils. The MFDM is modeled as a horizontal layer of a magnetic fluid. The free surface of the fluid layer serves as the deformable mirror. The dynamically varying shape of the mirror is described in terms of the deflection of the deformable surface as measured with respect to its flat state. The deflection at any surface location is obtained by analytically solving the equations governing the coupled fluid-magnetic system that constitutes the mirror. The model is presented for both the Cartesian and the cylindrical coordinate systems.


Magnetic Field Mode Shape Magnetic Fluid Surface Shape Fluid Layer 
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  1. Bashtovoi VG, Rosensweig RE (1993) Excitation and study of sub-critical waves on a magnetic fluid surface. J Magn Magn Mater 122:234–240CrossRefGoogle Scholar
  2. Blums E, Cebers A, Maiorov MM (1997) Magnetic fluids. de Gruyter, BerlinGoogle Scholar
  3. Chen T, Francis B (1996) Optimal sampled data control systems. Springer, BerlinzbMATHGoogle Scholar
  4. Cowley MD, Rosensweig RE (1967) The interfacial stability of a ferromagnetic fluid. J Fluid Mech 30(4):671–688zbMATHCrossRefGoogle Scholar
  5. Haberman R (2003) Applied partial differential equations with Fourier series and boundary value problems. Prentice-Hall, Englewood CliffGoogle Scholar
  6. Rosensweig RE (1997) Ferrohydrodynamics. Dover Publications, New YorkGoogle Scholar
  7. Skogestad S, Postlethwaite I (2005) Multivariable feedback control: analysis and design. Wiley, ChichesterGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Shanghai UniversityShanghaiChina, People’s Republic
  2. 2.University of TorontoTorontoCanada

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