Applied Active Control for a Nonlinear Aeroelastic Structure

Abstract

Linear and nonlinear aeroelastic response is examined using a unique test apparatus that allows for experiments of plunge and pitch motion of a wing with prescribed stiffness characteristics. The addition of a control surface, combined with an active control system, extends the stable ight region. Unsteady aerodynamics are modeled with an approximation to Theodorsen's theory appropriate for the low reduced frequencies associated with the experiment. Incorporated with a full-state feedback control law, an optimal observer is utilized to stabilize the system above the open-loop utter velocity. Coulomb damping and hardening of the pitch stiffness are included to examine nonlinear control behavior. The nonlinear model is tested using the control laws developed from an extension of linear theory. Each model is simulated using MATLAB ® and compared with experimental results of the active control system. Excellent correlation between theory and experiment is achieved. Using an optimal observer and full-state feedback, the linear and nonlinear systems are stabilized at velocities that exceed the open-loop utter velocity. Limited control is achieved when the system is undergoing limit cycle oscillations. Nomenclature a = nondimensional distance from the midchord to the elastic axis b = semichord of wing (reference length) C.k/ = Theodorsen's function c = nondimensional distance from midchord to control surface hinge c h = plunge degree of freedom structural damping coef cient c ® = pitch degree of freedom structural damping coef cient e = nondimensional distance from midchord to control surface leading edge g = acceleration due to gravity h = plunge displacement coordinate I ® = mass moment of inertia about the elastic axis K = full-state feedback gains k = reduced frequency .b!=u 1 / k h = plunge degree of freedom structural spring constant k ® = pitch degree of freedom structural spring constant L = estimator gains L.t / = lift of the wing M f = friction moment caused by Coulomb damping M.t / = moment of the wing about the elastic axis m = mass of the wing Q = state weighting matrix N Q = process noise covariance R = control weighting matrix N R = measurement noise covariance u = freestream velocity x ®= nondimensional distance between elastic axis and the center of mass ® = pitch displacement coordinatē = control surface de ection coordinate 1 A = difference in peak amplitudes of the free vibration ¹ h = static coef cient of friction in the plunge direction ¹ ® = static coef cient of friction in the pitch direction ½ = density of air ! = frequency of motion

Control of a Nonlinear Wing Section Using Leading- and Trailing-Edge Surfaces

“…This model has proven to be adequate for low reduced frequency, subsonic flow, as validated by the experiments. 7,8,15 The wing section modeled by these equations of motion has been built for experiments on the nonlinear aeroelastic test apparatus (NATA) 16 in the 2 × 3 ft low-speed wind tunnel. A unique feature of NATA is the presence of two cams that are fabricated to permit prescribed nonlinear responses in pitch and plunge.…”

“…The control laws developed were applied to a wing section with a single, full-span, trailing-edge control surface and validated in windtunnel experiments. Block and Strganac 7 made use of Theodorsen's unsteady aerodynamic model and implemented a linear controller derived via the linear quadratic regulator (LQG) approach combined with a Kalman estimator to provide the additional, nonmeasurable states resulting from Theodorsen's function and servomotor dynamics. The controller stabilized the system if activated during the transient phase of the motion, but its capability was limited once the system was entrained in LCO motion.…”

Friction Compensation in TP Model Form - AeroelasticWing as an Example System

“…The aeroelastic wing model with nonlinear friction was validated by experiments in [44]. Similar models with linear friction were used in [45] [46], [47] and [48].…”

Experimental Nonlinear Control for Flutter Suppression in a Nonlinear Aeroelastic System

“…Of more relevance to the present work is a series of publications by Strganac and colleagues [9][10][11][12][13][14], in which the application of active control on aeroelastic systems with hardening-type structural nonlinearities has been investigated both theoretically also experimentally, through the use of quasi-steady aeroelastic models. These studies utilised the feedback linearisation nonlinear control method, in conjunction with LQR control as the linear control objective.…”