Thomas W. Strganac

Applied Active Control for a Nonlinear Aeroelastic Structure

Linear and nonlinear aeroelasticresponseisexamined using a uniquetest apparatusthat allowsforexperiments 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 e 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 e 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 extensionoflineartheory.EachmodelissimulatedusingMATLAB ® andcomparedwithexperimentalresultsofthe active control system. Excellent correlation between theory and experiment isachieved. Using an optimal observer and full-state feedback, the linear and nonlinear systems are stabilized at velocities that exceed the open-loop e utter velocity. Limited control is achieved when the system is undergoing limit cycle oscillations.

Nonlinear Control of a Prototypical Wing Section with Torsional Nonlinearity

With the increase in popularity of active materials for control actuation, renewed interest is evident in the derivation of control methodologies for aeroelastic systems. It has been known for some time that prototypical aeroelastic wing sections can exhibit a broad class of pathological response regimes when the system includes certaintypesofnonlinearities.Weinvestigatenonlinearcontrollawsforaeroelasticsystemsthatincludepolynomial structural nonlinearities and study the closed-loop stability of the system. It is shown that locally asymptotically stable(nonlinear)feedbackcontrollerscanbederivedfortheaeroelasticsystemusingpartialfeedbacklinearization techniques. In this case, the stability results are necessarily local in nature and are derived by considering stability of theassociated zero dynamics subsystem. Itis also demonstrated that globally stable (nonlinear)adaptivecontrol methods can be derived for a class of aeroelastic systems under consideration. Numerical simulations are used to provide empirical validation of some of the results.

IDENTIFICATION AND CONTROL OF LIMIT CYCLE OSCILLATIONS IN AEROELASTIC SYSTEMS

Nonlinearities in the aeroelastic system induce pathologies such as the observed store-induced limit cycle oscillations found with certain high-performance aircraft configurations. Many prior studies, including efforts by these authors, focus on the nonlinear behavior of the uncontrolled, nonlinear aeroelastic system. These studies are briefly reviewed. More importantly, there is limited study for the active control of these nonlinear aeroelastic systems. Although a linear controller may stabilize the nonlinear system under some circumstances, empirical evidence suggests that these control methods -will prove unreliable in strongly nonlinear regimes and that stability is not guaranteed. Herein, the authors describe the development of control strategies appropriate for these nonlinear systems. A nonlinear controller, and the resulting closed-loop stability, based on a partial feedback linearization are discussed. The approach depends upon the exact cancellation of the nonlinearity and, as a co_nsequence, the authors introduce an adaptive method in which guarantees of stability are evident. The authors present experimental results obtained using the adaptive controller.

Stability and Control of a Structurally Nonlinear Aeroelastic System

The authors examine the stability properties of a class of nonlinear controls derived via feedback linearization techniques for a structurally nonlinear prototypical two-dimensional wing section. In the case in which the wing section has a single trailing-edge control surface, the stability of partial feedback linearization to achieve plunge primary control is studied. It is shown for this case that the zero dynamics associated with the closed-loop system response are locally asymptotically stable for a range of e ow speeds and elastic axis locations. However, there exist locations of the elastic axis and speeds of the subsonic/incompressible e ow for which this simple feedback strategy exhibits a wide range of bifurcation phenomena. Both Hopf and pitchfork bifurcations evolve parametrically in terms of the e ow speed and elastic axis location. In the case in which the wing section has two control surfaces, the global stability of adaptive control techniques derived from full feedback linearization is studied. In comparison with partial or full feedback linearization techniques, the adaptive control strategies presented do not require explicit knowledge of the form of the structural nonlinearity.

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

The control of nonlinear aeroelastic response of a wing section with a continuous stiffening-type structural nonlinearity is examined through analytical and experimental studies. Motivated by the limited effectiveness of using a single, trailing-edge control surface for the suppression of limit-cycle oscillations of a typical wing section, improvements in the control of limit-cycle oscillations are investigated through the use of multiple control surfaces, namely, an additional leading-edge control surface. The control methodology consists of a feedback linearization approach that transforms the system equations of motion via Lie algebraic methods and a model reference adaptive control strategy that augments the closed-loop system to account for inexact cancellation of nonlinear terms due to modeling uncertainty. Specifically, uncertainty in the nonlinear pitch stiffness is examined. It is shown through simulations and experiments that globally stabilizing control may be achieved by using two control surfaces.

Adaptive Feedback Linearization for the Control of a Typical Wing Section with Structural Nonlinearity

Earlier results by the authors showed constructions of Lie algebraic, partial feedback linearizing control methods for pitch and plunge primary control utilizing a single trailing edge actuator. In addition, a globally stable nonlinear adaptive control method was derived for a structurally nonlinear wing section with both a leading and trailing edge actuator. However, the global stability result described in a previous paper by the authors, while highly desirable, relied on the fact that the leading and trailing edge actuators rendered the system exactly feedback linearizable via Lie algebraic methods. In this paper, the authors derive an adaptive, nonlinear feedback control methodology for a structurally nonlinear typical wing section. The technique is advantageous in that the adaptive control is derived utilizing an explicit parameterization of the structural nonlinearity and a partial feedback linearizing control that is parametrically dependent is defined via Lie algebraic methods. The closed loop stability of the system is guaranteed to be stable via application of La Salles invariance principle.

Aeroelastic Response of a Rigid Wing Supported by Nonlinear Springs

Nonlinear aeroelastic behavior is examined. This research extends the efforts of several recent investigations that address freeplay or piecewise nonlinearities in aeroelastic systems; however, in the studies described herein the authors address continuous nonlinearities such as those found in structural systems that exhibit spring hardening or softening effects. The authors describe a unique e utter test apparatus designed to permit experimental investigations of prescribed nonlinear response. The results of complementary analytical and experimental studies are presented for a nonlinear aeroelastic system limited to two degrees of freedom. Nomenclature

Computational and Experimental Investigation of Limit Cycle Oscillations of Nonlinear Aeroelastic Systems

A wide variety of pathologies, such as store-induced limit-cycle oscillations, have been observed on high-performance aircraft and have been attributed to transient nonlinear aeroelastic effects. Ignoring the nonlinearity of the structure or the aerodynamics will lead to inaccurate prediction of these nonlinear aeroelastic phenomena. The current paper presents the development and representative results of a high-fidelity multidisciplinary analysis tool that accurately predicts limit-cycle oscillations (LCOs) of an aeroelastic system with combined structural and aerodynamic nonlinearities. Wind-tunnel measurements have been carried out to validate the findings of the investigation. The current investigation concentrates on the prediction of the critical physical terms that dominate the mechanism of LCO. The aeroelastic computations predict LCO amplitudes and frequencies in very close agreement with the experimental data. The results emphasize the importance of modeling the nonlinearities of both the fluid and structure for the accurate prediction of LCO for nonlinear aeroelastic systems.

Numerical Model of Unsteady Subsonic Aeroelastic Behavior

A method for predicting unsteady, subsonic aeroelastic responses was developed. The technique accounts for aerodynamic nonlinearities associated with angles of attack, vortex-dominated flow, static deformations, and unsteady behavior. The fluid and the wing together are treated as a single dynamical system, and the equations of motion for the structure and flow field are integrated simultaneously and interactively in the time domain. The method employs an iterative scheme based on a predictor-corrector technique. The aerodynamic loads are computed by the general unsteady vortex-lattice method and are determined simultaneously with the motion of the wing. Because the unsteady vortex-lattice method predicts the wake as part of the solution, the history of the motion is taken into account; hysteresis is predicted. Two models are used to demonstrate the technique: a rigid wing on an elastic support experiencing plunge and pitch about the elastic axis, and an elastic wing rigidly supported at the root chord experiencing spanwise bending and twisting. The method can be readily extended to account for structural nonlinearities and/or substitute aerodynamic load models. The time domain solution coupled with the unsteady vortex-lattice method provides the capability of graphically depicting wing and wake motion.

Investigations of aeroelastic response for a system with continuous structural nonlinearities

Measurements and predictions of aeroelastic response are examined for a wing section mounted to permit continuous nonlinear structural response. Nonlinear behavior is introduced using a unique model support system designed to permit prescribed nonlinear stiffness characteristics. The wing section is limited to pitch and plunge response. Tailored experiments establish nonlinear responses such as limit cycle oscillations, and these results are predicted with an analytical model.