Frequency domain system identification of helicopter blades with trailing edge flaps

Abstract

In forward flight, the dynamics of a rigid flapping rotor blade, with and without a trailing edge flap, are represented by an ordinary differential equation with periodically time varying coefficients. Existing frequency domain system identification techniques were developed only for linear time invariant (LTI) systems. A linear time periodic (LTP) system, such as the rigid helicopter blade with a piezo-actuated flap, cannot be identified using these existing LTI techniques, because the sinusoidal test input signal is not appropriate for LTP systems. Thus, a new frequency domain system identification methodology for LTP systems is introduced. The LTP system identification theory is based on a new test input signal, which is the Fourier series of a periodic signal modulated by a sinusoid. Applying what is essentially harmonic balance, an LTP state space model in the time domain can be transformed to an infinite dimensional LTI harmonic balance state space model. In addition, the harmonic state space model leads to the concept of a harmonic transfer function in the frequency domain. A spectral theory for LTP systems, which is analogous to that for LTI systems, is then developed using a sinusoidally modulated complex Fourier series expansion, and is advantageous because it leads to a Fourier transformation that reproduces the harmonic balance state space model. The flapping helicopter blade model contains several parameters that may not be certain a priori, for example, the Lock number, and advance ratio. A procedure is developed to identify these uncertain parameters when the structure of the underlying helicopter dynamics is well understood. The system identification and parameter optimization procedures are validated using computer models of a helicopter rigid blade flapping in forward flight. *Copyright © 1996 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. Presented at the AIAA/ASME Adaptive Structures Forum, 18-19 April, Salt LaJce City, UT. t Student Member, AIAA, AHS. ^Member, AIAA, AHS. Tel: (301) 405-1927, Fax: (301) 3149001. Email: wereley@eng.umd.edu.