New Modeling and Control Design Techniques for Smart Deformable Aircraft Structures

Abstract

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,...

Morphing flight control surface for advanced flight performance

“…Ua sin 4 (9) With this information, the complex velocities in the ζ plane may be found and from these the complex velocities in the z plane can be found. These velocities and Bernoulli's equation can then be used to calculate the pressure distribution about the airfoil.…”

“…Recent technologies enable flight vehicles to achieve a high level of flight performance by utilizing the interaction between elastic structures, smart material based distributed sensors and actuators, recent advances in steady and unsteady aerodynamics, and the control system as depicted in Figure 1. A number of approaches have been attempted to achieve this goal using various active materials such as piezoelectric actuators, compact hybrid actuators, electroactive polymers, thin film magnetic shape memory alloys and microjets [4][5][6][7][8][9][10][11][12][13][14] . However, most of these endeavors have not been sufficiently successful in real applications due to the limitations of the actuators and the system integrations.…”

Time-Varying Dynamics of a Micro Air Vehicle with Variable-Sweep Morphing

“…An oscillatory response with decay is demonstrated in Eq. (17). The nature of the oscillations and the decay are both determined by the integrals of real and imaginary parts of these poles.…”

“…The decaying nature of the response, which is similar to the damping of a linear time-invariant system, is determined by the varying magnitude of the exponential in Eq. (17). The resulting envelope is given in Eq.…”

“…Other investigations have considered control of morphing systems [16]. A study using piezoelectric materials designed control only to achieve roll [17]. A variety of other studies that have investigated control have done so mostly in the context of actuation energy [18] and control authority [19] for simple changes in flight condition.…”