Identification of the harmonic transfer functions of a helicopter rotor

Abstract

Identification of the time periodic dynamics of a helicopter rotor system is necessary for effective controller design and analysis. The transfer properties of a linear time periodic (LTP) system can be described by harmonic transfer functions (HTF) that give the input-output relationship between the Fourier coefficients of the input signal and those of the output signal. A method for identifying harmonic transfer functions of linear time periodic systems is developed in this thesis. The system identification scheme employs a least square estimation technique to obtain HTF estimates. This least square estimation problem is under-determined; therefore, an additional assumption, that the transfer function is smooth, is made in the ID scheme to achieve a well-posed problem. The estimates are calculated by applying a quadratic penalty to the curvature of the transfer functions. The identification scheme has been implemented in MATLAB, and partly coded in C programming language for maximum computational efficiency. This system ID method has been validated with analytical results for a few well-known LTP systems. The validation results show excellent agreement between the identified and analytical transfer functions.