A new method for multi-input flight maneuver design for system identification is presented. The method consists of injecting "full-harmonic" orthogonal multisine signals into the flight control system. Orthogonality is achieved by repeating maneuvers with changing multisine polarities. The multisines can contain the same frequency content, which can simplify frequency response estimation and allow for long flight maneuvers to be split into several shorter maneuvers while maintaining the same frequency resolution and minimum frequency. An input allocation scheme is presented that augments the multisines to size the vehicle response amplitude about a specific degree of freedom. The developed approach was demonstrated through flight testing of a small octocopter in near-hover conditions. The input allocation scheme was utilized successfully to increase excitation about the yaw axis. Electrical power, motor speed, and rigid-body dynamic models were identified and are shown to predict the vehicle and motor responses accurately. The models are parameterized primarily by rotor thrust and torque coefficients, making them suitable for analysis of aircraft flight dynamics and individual rotor aerodynamics. The results demonstrate that the near-hover flight dynamics can be modeled accurately by neglecting rotor hub moments, variations in rotor coefficients, gyroscopic moments in roll and pitch, and aerodynamic interaction effects.
Figures & tables
A =
rotor area, ft 2
ax,ay,az =
body-axis accelerometer measurements, g
Cx,Cy =
rotor x- and y-axis force coefficients expressed in body frame
CT,CQ =
rotor thrust and torque coefficients
d =
rotor hub distance, ft
Fx,Fy,Fz =
body x-, y-, and z-axis forces, lb
Ix,Iy,Iz =
vehicle roll, pitch, and yaw moments of inertia, slug-ft 2
Table 1
Figure 2
Parameter
Symbol
Value
Units
Weight
W
18.6
lb
Roll moment of inertia
Ix
0.370
slug-ft 2
Pitch moment of inertia
Iy
0.393
slug-ft 2
Yaw moment of inertia
Iz
0.662
slug-ft 2
Rotor radius
R
0.625
ft
Rotor hub distance
d
1.725
ft
Table 2: GAMMA aircraft characteristics.
Figure 3: PTIs as implemented on GAMMA.
Figure 4: Example time domain comparison of single-maneuver, alternating-harmonic orthogonal multisines and multi-maneuver, full-harmonic orthogonal multisines.
Figure 5: Example frequency domain comparison of single-maneuver, alternating-harmonic orthogonal multisines and multi-maneuver, full-harmonic orthogonal multisines under open-loop and closed-loop conditions.
Figure 6: GAMMA flying at NASA’s Langley Research Center ALIFT facility.
Figure 7: Model parameter estimation procedure.
Figure 8: GAMMA response to multisine PTIs.
Figure 9: Comparison of measured rigid-body forces and moments and model fit in the frequency domain for a single multisine maneuver.
Figure 10: Normalized residuals of vehicle force and moment models for entire model development data set.
Figure 11: Comparison of measured motor acceleration and model fit in the frequency domain for a single multisine maneuver.
Figure 12: Normalized residuals of motor acceleration models for entire model development data set.
Figure 13: Model parameter estimates for each rotor system.
Parameter
θ^
s(θ^) (%)
Parameter
θ^
s(θ^) (%)
Parameter
θ^
s(θ^) (%)
Table 3: Model parameter estimates and standard errors.