Controlling Limit Cycle Oscillation Amplitudes in Nonlinear Aeroelastic Systems

Abstract

The paper focuses on the design of nonlinear state feedback controllers to minimize the amplitude of limit cycle oscillations exhibited by nonlinear aeroelastic systems. Nonlinear normal modes are computed for the closed-loop system to represent the flutter mode dynamics using a single mode. The effectiveness of nonlinear normal modes as a tool to capture the limit cycle oscillation growth is demonstrated. The harmonic balance method is used to estimate the amplitude and frequency of the limit cycle oscillations exhibited by the flutter mode. Analytical estimates of sensitivities of limit cycle amplitude with respect to the introduced control parameters are derived and shown to match closely to the sensitivities computed numerically using the finite difference method on a time marching simulation of the complete aeroelastic system. A multi-objective optimization problem that minimizes the estimate of limit cycle oscillation amplitude and an approximate measure of control cost is solved using the analytical sensitivities. Numerical simulation results are used to verify that minimizing the estimate of the limit cycle amplitude of the flutter nonlinear normal mode corresponds closely to minimizing the simulated limit cycle amplitude of the complete aeroelastic system.