Feedback control of limit cycle oscillations and transonic buzz, using the nonlinear transonic small disturbance aerodynamics

Abstract

In this paper, a systematic method to suppress transonic buzz with feedback is presented. A trailing edge control surface in the form of part-span flap was used only to modify and control the unsteady aerodynamic loading on the wing. The flap rotation was used to provide feedback, which consisted of a weighted linear combination of the amplitudes of the principal modes of the structure, referred to as the control law. A linear, optimal feedback control law, that is synthesized systematically based on pseudo-spectral time domain analysis, may be used in principle, to assess its capacity to actively suppress the buzz in the transonic flow domain by using a servo-controlled control surface to modify the unsteady, nonlinear aerodynamic loads on the wing. Thus, it is essential that a set of feasible control laws are first constructed. In this paper, this is done by applying the doublet-lattice method. Restrictions, such as near-zero structural damping in the flap mode, were imposed on the aeroelastic model to facilitate the occurrence of transonic buzz. The feasible set of control laws were then assessed using the nonlinear transonic small disturbance theory and an optimum control is selected to suppress the buzz. The essential differences of the behaviour of the closed-loop system in nonlinear transonic flow, when compared to the applications of linear optimal control in linear potential flow, are presented and discussed.