Convolution/Volterra Reduced-Order Modeling for Nonlinear Aeroelastic Limit Cycle Oscillation Analysis and Control

Abstract

A methodology for leveraging a combination of linear (through convolution integrals) and nonlinear (through Volterra series) reduced-order modeling (ROM) development was demonstrated on both a two- and three-degree-of-freedom (2-DOF and 3-DOF, respectively) aeroelastic system. The linear/nonlinear ROM approach was demonstrated against previous work in the field for a 2-DOF system and subsequently extended to a 3-DOF (flapped airfoil) system. Excellent agreement was demonstrated at limit cycle oscillation (LCO) onset (flutter) prediction between computational fluid dynamics, linear ROMs, and nonlinear ROMs. Although linear ROMs were sufficient to predict LCO onset, the nonlinear Volterra correction was required to estimate the amplitude of post-LCOs. Corrections that accounted for more coupling between degrees of freedom predicted the amplitudes more accurately. A study was undertaken to determine the minimal training set required to produce reasonable LCO amplitude estimates of the 3-DOF airfoil. A controller was also implemented in an effort to mitigate LCO onset and flutter divergence and to demonstrate the usefulness and power of leveraging the ROM for control design. A full-state feedback controller, tuned via a linear quadratic regulator (LQR), was shown to be effective in controlling the system below LCO onset. However, beyond LCO onset, this specific linear controller structure was observed to be ineffective in controlling the system. Future work will evaluate nonlinear control methods in which the ROM can be deployed as a part of the control system to update the LQR gains in a fully coupled approach.