Root Locus Approach to Determining Stability of an Uncertain Aeroelastic System

A computationally efficient methodology is presented to identify the stability region(s) of a family of linearized models developed from a nonlinear three-degree-of-freedom aeroelastic airfoil model. The proposed method rewrites the Jacobian of the nonlinear aeroelastic model into a form lending itself to a root locus stability analysis concerning a structural stiffness parameter. The results from the root locus analysis are then mapped to regions in the airspeed and pitch angle plane. A quadratic Lyapunov stability analysis is also provided to benchmark these stability regions where stiffness is a function of pitch angle, varying the system parameter. The Lyapunov stability analysis is done multiple times with decreasing finite bounds on the parameter rate of change. The results are compared to the root locus results. It is determined that the root locus stability boundary also accurately captures the Lyapunov stability boundary for a small, bounded rate of change.