On-Demand Aerodynamics in Integrally Actuated Membranes with Feedback Control

This paper is a numerical investigation on model reduction and control system design of integrally actuated membrane wings. A high-fidelity electroaeromechanical model is used for the simulation of the dynamic fluid–structure interaction between a low-Reynolds-number flow and a dielectric elastomeric wing. Two reduced-order models with different levels of complexity are then derived. They are based on the projection of the full-order discretization of fluid and structure on modal shapes obtained from eigenvalue analysis and proper orthogonal decomposition. The low-order systems are then used for the design of proportional–integral–derivative and linear–quadratic–Gaussian feedback schemes to control wing lift. When implemented in the full-order model, closed-loop dynamics are in very good agreement with the reduced-order model for both tracking and gust rejection, demonstrating the suitability of the approach. The control laws selected in this work were found to be effective only for low-frequency disturba...

[1]  Ismet Gursul,et al.  Unsteady fluid–structure interactions of membrane airfoils at low Reynolds numbers , 2009 .

[2]  David R. Williams,et al.  Low-Reynolds Number Wing Response to an Oscillating Freestream with and without Feed Forward Control , 2009 .

[3]  A. Gent A New Constitutive Relation for Rubber , 1996 .

[4]  Zhijin Wang,et al.  Unsteady fluid–structure interactions of a pitching membrane wing , 2013 .

[5]  Xuanhe Zhao,et al.  Electromechanical instability on dielectric polymer surface: Modeling and experiment , 2013 .

[6]  Daniella E. Raveh,et al.  Reduced-Order Models for Nonlinear Unsteady Aerodynamics , 2001 .

[7]  Hiroshi Naito,et al.  Active control of vortex shedding: an explanation of the gain window. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  P. Beran,et al.  Reduced-order modeling: new approaches for computational physics , 2004 .

[9]  Peter J. Schmid,et al.  Reduced order models for closed loop control: comparison between POD, BPOD, and global modes , 2012 .

[10]  Mark N. Glauser,et al.  Feedback Control of Separated Flows , 2004 .

[11]  W. Oates,et al.  Aerodynamic control of micro air vehicle wings using electroactive membranes , 2013 .

[12]  Jeffrey P. Thomas,et al.  Proper Orthogonal Decomposition Technique for Transonic Unsteady Aerodynamic Flows , 2000 .

[13]  Earl H. Dowell,et al.  Three-Dimensional Transonic Aeroelasticity Using Proper Orthogonal Decomposition-Based Reduced-Order Models , 2001 .

[14]  Z. Suo Theory of dielectric elastomers , 2010 .

[15]  Yongsheng Lian,et al.  Proper Orthogonal Decomposition for Three-Dimensional Membrane Wing Aerodynamics , 2003 .

[16]  C. Rowley,et al.  Feedback control of unstable steady states of flow past a flat plate using reduced-order estimators , 2009, Journal of Fluid Mechanics.

[17]  C. Farhat,et al.  Efficient non‐linear model reduction via a least‐squares Petrov–Galerkin projection and compressive tensor approximations , 2011 .

[18]  Li Cheng,et al.  Closed-loop-controlled vortex shedding and vibration of a flexibly supported square cylinder under different schemes , 2004 .

[19]  Rafael Palacios,et al.  Electro-aeromechanical modelling of actuated membrane wings , 2015 .

[20]  Ismet Gursul,et al.  Effect of pre-strain and excess length on unsteady fluid–structure interactions of membrane airfoils , 2009 .

[21]  Bret Stanford,et al.  Aerodynamic Coefficients and Deformation Measurements on Flexible Micro Air Vehicle Wings , 2007 .

[22]  Wei Shyy,et al.  Numerical Simulations of Membrane Wing Aerodynamics for Micro Air Vehicle Applications , 2005 .

[23]  Raymond E. Gordnier,et al.  High fidelity computational simulation of a membrane wing airfoil , 2008 .

[24]  Wei Shyy,et al.  Computational model of flexible membrane wings in steady laminar flow , 1995 .

[25]  O. von Helversen,et al.  The energy cost of flight: do small bats fly more cheaply than birds? , 1998, Journal of Comparative Physiology B.

[26]  Mark N. Glauser,et al.  Models for controlling airfoil lift and drag , 2004 .

[27]  Siva S. Banda,et al.  Optimal Feedback Control of Vortex Shedding Using Proper Orthogonal Decomposition Models , 2001 .

[28]  Jian Sun,et al.  Adaptive Reduced-Order-Model-Based Control-Law Design for Active Flutter Suppression , 2012 .

[29]  Rye M. Waldman,et al.  Aerodynamic Characterization of a Wing Membrane with Variable Compliance , 2014 .

[30]  David Galbally,et al.  Non‐linear model reduction for uncertainty quantification in large‐scale inverse problems , 2009 .

[31]  S. Pope Turbulent Flows: FUNDAMENTALS , 2000 .

[32]  Azzeddine Soulaïmani,et al.  Investigations of nonlinear aeroelasticity using a reduced order fluid model based on POD method , 2007 .

[33]  Rafael Palacios,et al.  Leading- and trailing-edge effects on the aeromechanics of membrane aerofoils , 2013 .