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A new modeling and control design speci cally tailored to smart aeroelastic systems is presented. The control problem is to achieve a roll maneuver with a desired roll rate using a piezoelectric material laminated exible wing subject to aerodynamic eld. This multidisciplinary system of an elastic structure with piezoelectric actuating and sensing under external aerodynamic load is modeled with an integrated nite element method. The deformed structure for obtaining the speci c roll rate is made up of new mass and stiffness matrices, which are functions of the steady-state input electric potential to piezoelectric actuators. The resulting model in the generalized coordinates, which has a mass matrix, a nonsymmetric aerodynamic damping matrix, and a nonsymmetric stiffness matrix (due to aerodynamic stiffness), is then transformed to real but nonorthogonal modal coordinates and a reduced-order model is developed. A new control design algorithm based on reciprocal state-space framework is introduced to achieve the desired roll rate and to dissipate vibrations by applying acceleration feedback. Nomenclatureelectric eld [e] = piezoelectric constant matrix [ N e] = transformed piezoelectric constant matrix F = forcing function f = external forcing function G = system matrix in reciprocal state-space framework G c = closed-loop system matrix in reciprocal state-space framework g =¸.M 2 ¡ 2/=U a .M 2 ¡ 1/ H = input distribution matrix in reciprocal state-space framework I = angular moment of inertia J = Jacobian (structure) J a = Jacobian (aerodynamic) J d = Jacobian (deformed) J = performance index K = stiffness matrix K = control gain K A = aerodynamic stiffness matrix K q = structural stiffness matrix K q Á = piezoelectric coupling matrix K ÁÁ = dielectric stiffness matrix L = lift [L] = differential operator l = length of wing M = mass matrix M = Mach number M R = rolling moment m = mass of wing N = structural shape function P = roll rate Q = surface charge Q = weighting matrix in linear quadratic regulator (LQR) framework q = generalized coordinates q = ½ a U 2 a =2 R = weighting matrix in LQR framework S = strain vector S = optimal parameter T = stress vector [T ] = transformation matrix t = time coordinate t = surface traction U 1 = air velocity u; v; w = displacements u = displacement vector u = input vector in state-space framework V = voltage X = structural coordinates x; y; z = structural coordinates x 0 ; y 0 ; z 0 = principal axes x = state vector y = output vector in state-space framework ® = angle of attack = transformed coordinates 0 = desired roll angle change°= shear strain 1p = aerodynamic pressure difference ± = variational operator ±T = rst variation of kinetic energy ±U = rst variation of potential energy ±W = rst variation of work done by external force ["] = dielectric matrix 2 = modi ed shape function µ = skew angle 3 = frequency matrix 3 i = frequency = 2q= p .M 2 ¡ 1/ »;´; = element local coordinates ½ a = air density Á = roll angle 805 Downloaded by UNIVERSITY OF CALIFORNIA -DAVIS on February 7,...

There is an increasing need for aperture antenna devices that incorporate multifunctional capability. One popular solution to this problem is the use of an “active aperture antenna” that is able to vary the direction and shape of its radiation pattern by using actuators to alter the shape of the reflector. This study focuses on the use of a pre-curved piezoceramic actuator, referred to as a THUNDER actuator, to change the shape of a prototype reflector. These actuators offer greater force, deflection and higher strength than traditional PZT actuators, while maintaining cost effectiveness. In this study the design of a prototype antenna structure that can accommodate deflection experiments and far-field radiation pattern tests is presented. The theoretical relationship between the dish deflection and the input voltage is established in two stages. In the first stage, the deflection at the end of the actuator is determined using a combination of Hamilton’s principle and laminated composite curved beam theory. The piezoelectric properties of the actuator are also considered during this stage. In the second stage, the deflection at the tip of the dish is calculated using geometric relationships, with the assumption that the remaining portion of the dish moves as a rigid body. The resulting deflection equations yield results that closely match the experimental quasi-static deflection results for a given input voltage, despite the presence of hysteresis. A dynamic model for a THUNDER actuator is developed based on experimental frequency response measurements. Positive Positioned Feedback (PPF) control is implemented on the system, in order to reduce position overshoot and oscillations in the transient response of the structure. The controller yields an improvement in the transient response in both simulation and experiments. Finally, the controlled system is utilized to transmit radiation in the far field.