| Abstract: | A computer-implemented method of determining the pitch stability of an
airfoil system, comprising using a computer to numerically integrate a
differential equation of motion that includes terms describing PID
controller action. In one model, the differential equation characterizes
the time-dependent response of the airfoil's pitch angle, .alpha.. The
computer model calculates limit-cycles of the model, which represent the
stability boundaries of the airfoil system. Once the stability boundary
is known, feedback control can be implemented, by using, for example, a
PID controller to control a feedback actuator. The method allows the PID
controller gain constants, K.sub.I, K.sub.p, and K.sub.d, to be
optimized. This permits operation closer to the stability boundaries,
while preventing the physical apparatus from unintentionally crossing the
stability boundaries. Operating closer to the stability boundaries
permits greater power efficiencies to be extracted from the airfoil
system. |