A Regulator and Filter for Tracking Aerodynamic Force

A closed-loop control system has been developed and tested for tracking prescribed values of aerodynamic force on a NACA 4412 airfoil. The system includes a measurement-based estimator - utilizing a low-dimensional model of the perturbation flow based on the method of proper orthogonal decomposition - and a stochastic correlation between the measurement and the state estimate. The system employs a nonlinear approximation of the performance output, defined as unsteady oscillations in the lift coefficient, and an extended Kalman filter, based on the nonlinear estimators. The control objective is to reduce or eliminate lift oscillations by tracking a prescribed, constant value. Using a proportional-integral regulator, control-in-the-loop computational fluid dynamics (CFD) simulations demonstrate that lift oscillations are reduced by a factor of approximately six - with and without the extended Kalman filter in the loop. The filter reduces noise in the output approximation and state estimates that result from measurement noise with some improvement in tracking