Control of a Three-Degree-of-Freedom Airfoil with Limit-Cycle Behavior

Abstract

¢(1 ¡ k p k i ) sin a which on rearranging and solving for the sectional leading-edge suction (equal to the local vortex lift) becomesThis expression suggests that the reduction in C (s) with increasing sweep is counterbalanced by the rearward shift in the wing's a.c. location with increasing sweep. This implies that the relative invariance of vortex lift with increasing K is a result of reduced trailing-edge effects such that the net vortex lift coef cient remains relatively constant. ConclusionsPolhamus's leading-edge suction analogy estimates that the vortex lift coef cient of delta wings is relatively insensitive to wing sweep. This is despite the reduction in vortex strength and increased vortex displacementfrom the wing surface that results from increasing sweep. An analytical investigation suggests that the invariance of the vortex lift coef cient is a result of increasing slenderness reducing trailing-edge effects. The analysis yields a simple explicit relationship between the a.c. and leading-edge sweep of a delta wing. This in turn allows the prediction of the a.c. and its variance with angle of attack for thin planar delta wings. AcknowledgmentThe author would like to thank Harry Hoeijmakers of the Department of Mechanical Engineering, Twente University, The Netherlands for his helpful comments. IntroductionL IMIT-CYCLE oscillations (LCOs) resulting from control surface freeplay are of concern in many aircraft because they typically occur at a dynamic pressure well below that of the linear utter boundary.The stabilityand performanceof the aeroservoelasticsystem is of particularimportancein the presence of such nonlinearities that can develop during the life cycle of the aircraft. Results presented by Vipperman et al. 1 served to demonstrate that the control surface actuators can be used to provide successfully gust alleviation and extend the utter boundary for a three-degree-of-freedom, linear, aeroelastic model. Additionally, Vipperman et al., 2 as well as Frampton and Clark, 3 demonstrated that robust control strategies can be applied in the design of compensatorsfor a family of dynamic pressures.The purpose of this work is to investigate the effect of control surface freeplay nonlinearities on the closed-loop performance of a three-degree-of-freedom aeroelastic system. In particular, control systems designed for an open-loop linear three-degree-of-freedom system were applied to a nonlinear three-degree-of-freedom system and evaluated for their performance. It is vital that these linear compensators display stable, closed-loop response in the presence of freeplay nonlinearities that may evolve over the life cycle of the aircraft. Results from this study indicate that the limit-cycle amplitudes in both pitch and plunge can be attenuated signi cantly through the application of controllers designed for a linear threedegree-of-freedom aeroelastic system. The primary mechanism of control serves to convert high-amplitude, low-frequency LCOs to low-amplitude, high-frequency LCOs for the case considered.In p...

Adaptive control of a nonlinear aeroelastic system

“…They have also designed and installed an experimental rotating slotted cylinder (RSC) gust generator in the Duke University low-speed wind tunnel, which was used to create a periodic or a linear frequency sweep gust excitation field [9]. Using these experimental facilities, a series of theoretical and experimental studies, such as flutter and LCOs [10], gust responses and alleviation [11], and flutter/LCO control [12,13] have been completed. An experimental high-aspect ratio wing aeroelastic model with a device to provide a controllable slender body tip mass distribution for flutter suppression has been constructed by Tang and Dowell [14].…”

Nonlinear Aeroelasticity

“…And once nonlinear aeroelastic models have reached a state of maturity sufficient for their consideration in the design process, then active and adaptive control can potentially provide for even greater flight vehicle performance. The discussion of active and adaptive control is beyond the scope of this paper, but the reader may wish to consult the work of Heeg [113], Lazarus, et al [114,115], Ko, et al [68][69][70], Block and Strganac [67], Vipperman, et al [116], Bunton and Denegri [8], Clark et al [117], Frampton et al [118], Rule et al [119], Richards et al [120] and Platanitis and Strganac [121].…”

Untitled

“…And once nonlinear aeroelastic models have reached a state of maturity sufficient for their consideration in the design process, then active and adaptive control can potentially provide for even greater flight vehicle performance. The discussion of active and adaptive control is beyond the scope of this paper, but the reader may wish to consult the work of Heeg [113], Lazarus, et al [114,115], Ko, et al [68][69][70], Block and Strganac [67], Vipperman, et al [116], Bunton and Denegri [8], Clark et al [117], Frampton et al [118], Rule et al [119], Richards et al [120] and Platanitis and Strganac [121].…”