Electrostatic control of a membrane using adaptive feedback linearization

Scharf, Daniel P.; Hyland, David C.; Washabaugh, Peter D.

doi:10.2514/6.1998-4139

Cited by 2 publications

(1 citation statement)

References 7 publications

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“…For the last decade, shape controls of membrane surfaces have been discussed with a rim actuation [13][14][15] or a membrane interior actuation [16][17][18][19][20][21][22][23]. However, only a few studies have been devoted to membrane-vibration mitigation.…”

Section: B Preceding Studies 1 Studies On Shape and Vibration Contrmentioning

confidence: 99%

Distributed and Localized Active Vibration Isolation in Membrane Structures

Sakamoto

Park

Miyazaki

2006

Journal of Spacecraft and Rockets

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Once a membrane starts vibrating, suppressing the vibration is very difficult. Thus, the present study primarily aims at isolating a membrane from major disturbance sources, that is, from support structures. The present study introduces weblike suspension cables around a membrane and develops in theory a vibration-isolation strategy applied only along the cables. First, collocated small actuators/sensors are attached at the interfaces of the cables and the membrane to realize a distributed cable-tension control. Second, linear theory-based localized controllers are designed for suspension-cable substructural models. The feedback laws for these two kinds of controllers are derived employing a partitioned equation of motion. The resultant control system is lightweight, simple, low order, robust, and redundant. A series of transient analyses using a geometrically nonlinear finite-element method corroborates the effectiveness of the proposed vibration-isolation strategy. Nomenclatureactuator influence matrix for substructure controller B = actuator influence matrix for interface force canceling controller C = constraint Boolean matrix D = partitioned damping matrix D g = assembled damping matrix E = Young's modulus f = function f = partitioned nodal external force vector f D = nodal d'Alembert's force vector f g = global nodal external force vector f u = control force vector G h = feedback gain matrix G h1 = gain matrix for displacement G h2 = gain matrix for velocity h = thickness I = identity matrix J = scalar performance/cost index K = partitioned stiffness matrix K g = assembled stiffness matrix K i = stiffness matrix of ith substructure L = assembly Boolean matrix M = partitioned mass matrix M g = assembled mass matrix P = Riccati matrix for optimal control Q = state weighting matrix q = partitioned nodal displacement vector q g = global nodal displacement vector R = control input weighting matrix t = time u = control input u h = control input of substructure controller u = control input of interface force canceling controller v 0 = amplitude of prescribed velocity x = state vector x, y, z = Cartesian coordinates b = scalar weighting of strain energy b = scalar weighting of kinetic energy T i = tension change in ith interface force canceling controller T i = generated tension in ith interface force canceling controller " i = strain change in collocated sensors/actuators at ith boundary node f = residual transmission force between substructures t = time step size " = design strain b = localized Lagrange multiplier vector bi = ith component of b = Poisson's ratio = total energy functional = density Subscripts h = homogenous localized-substructure controller ic = inner-catenary cable m = membrane opc = outer-perimeter cable tie = tie cable = interface force canceling controller (cable-tension controller)

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