Limit cycle oscillation amplitude tailoring based on describing functions and μ analysis

Freeplay is a nonlinearity commonly encountered in aeroservoelastic applications which is known to cause Limit Cycle Oscillations (LCOs), limited amplitude flutter phenomena not captured by a linear analysis. Uncertainties in the models are also known to play an important role in triggering instabilities which might not be present in the nominal case, or altering their features in an unpredictable way. This paper shows the process to build a framework to study the nonlinear behavior of a typical section affected by a freeplay in the control surface and uncertainties in its parameters' values. Starting from the definition of the nominal aeroelastic model, the nonlinear framework is implemented by means of the Describing Function (DF) method and robust analysis is introduced by means of μ technique. In addition, it is shown an idea to perform a tailoring of the LCO graph of the system with the practical goal to limit the oscillation amplitude. Implications and advantages of using DF and μ as primary tools are highlighted, and prowess of the methodology is showcased with an example.