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Nonlinear control of a membrane mirror strip actuated axially and in bending

Renno, Jamil M. and Inman, Daniel J. and Chevva, Konda Reddy (2009) Nonlinear control of a membrane mirror strip actuated axially and in bending. AIAA Journal, 47 (3). pp. 484-493. ISSN 0001-1452. doi:10.2514/1.31166.

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The sliding mode technique is used to control the deformation of a membrane mirror strip augmented with two macrofiber composite bimorphs located near the ends of the strip. The first bimorph is actuated in bending and the second is actuated axially. The structure is modeled as an Euler-Bernoulli beam under tensile load and the macrofiber composite patches are modeled as monolithic piezoceramic wafers. To cast the system into a finite-dimensional state-space form, the finite element method is used, and the model presented accounts for the dynamics of the augmented bimorphs. The membrane strip is placed under uniform tension. Because one of the bimorphs acts axially, the resulting tension in the membrane strip is discontinuous at the location of this bimorph and, consequently, the obtained model is nonlinear. First, we validate the model experimentally by considering the system in its quasi-linear state, then we consider the control problem. We formulate the regulation problem by using the sliding mode technique. Additionally, to allow coupling this system with an adaptive optics scheme, the shape-control problem is considered as well. The control law uses both actuators: the bending and axial bimorphs. However, a system singularity dictates using a switching command to avoid this singularity. Various examples are presented for the regulation and shape-control problems. The simulation results demonstrate the efficacy of the proposed control law.

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Additional Information:©2008 by the American Institute of Aeronautics and Astronautics, Inc. Received 20 March 2007; revision received 15 September 2008; accepted for publication 11 October 2008. . Funding for this work is administered by the Center of Intelligent Material Systems and Structures on behalf of the U.S. Air Force Office of Scientific Research under grant FA9550-06-1-0143. The authors wish to thank Dan K. Marker of the Advanced Optics and Imaging Division at the U.S. Air Force Research Lab for motivating this work. The authors appreciate the fruitful discussions and valuable suggestions of Eric J. Ruggiero of the Performance Technologies Laboratory at GE Global Research Center.
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U.S. Air Force Office of Scientific ResearchFA9550-06-1-0143
Issue or Number:3
Record Number:CaltechAUTHORS:20090415-153103348
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:13991
Deposited By: Tony Diaz
Deposited On:16 Apr 2009 18:41
Last Modified:08 Nov 2021 22:42

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