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, α. 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, KI, Kp, and Kd, 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.