Frequency Response Sensitivity Functions for Helicopter Frequency Domain System Identification

This paper addresses some aspects of frequency domain based, state space system identification. A frequency response sensitivity function is developed, and applied to the problem of identifying a coupled rotor-fuselage helicopter model from simulated frequency sweep data. This function indicates how sensitive the frequency response of the model is, at every frequency of interest, to perturbations of the model parameters. This information can be used to tailor the identification process by indicating what frequency bands and what inputs are best suited for the identification of a given parameter. The paper also presents expressions for an efficient calculation of the derivatives of this sensitivity function. This enables faster implementations of the frequency response matching problem and of the calculation of accuracy metrics. The sensitivity functions are used to partition an identification problem that covers a very wide frequency band into two identifications over smaller frequency bands. Such frequency-banded identification appears possible, faster, and slightly more accurate for the case studied in the paper. A possible application of this technique is the identification of a coupled rotor-fuselage system from separate low frequency flight tests and higher frequency, rotor wind tunnel tests. The results indicate that the use of the frequency response sensitivity function can help automate some decisions typically left to the analyst's judgment.