State Space Identification Applied to Rotorcraft Flight Testing

The mathematics underlying state space identification using subspace analysis is presented with a derivation for the analysis of stochastic data. Subspace analysis was applied to data from four flight tests: ramp gun firing; steady, low airspeed, level flight; high rate of descent; and a hard landing. In the ramp gun firing application, the subspace analysis derived for stochastic data was used for vibration analysis of the free response between shots. The vibration analysis calculated the ramp structural frequencies, damping, and mode shapes. In the remaining three flight tests, the subspace algorithm N4SID was used for calculating the state space matrices for purposes of simulating the flight data. In the low airspeed application, a model created from 25% of the flight data was able to simulate the airspeed within six knots in the range from 0 to 60 knots, for all flight headings. The high rate of descent simulation showed that subspace analysis replicates the high rates of descent, including flights with large excursions in the collective and elevator controls. The hard landing is accurately simulated including the peak values of landing gear loads. In general, the state space matrices obtained using subspace analysis will accurately simulate flight data or calculate the vibration characteristics.