Parametric Reduced-Order Modeling of the Unsteady Vortex-Lattice Method

A method for frequency-limited balancing of the unsteady vortex-lattice equations is introduced that results in compact models suitable for computational-intensive applications in load analysis, aeroelastic optimization, and control synthesis. The balancing algorithm relies on a frequency-domain solution of the vortex-lattice equations that effectively eliminates the cost associated to the wake states. It is obtained from a Z transform of the underlying discrete-time equations, and it requires no additional geometrical or kinematic assumptions for the lifting surfaces. Parametric reduced-order modeling is demonstrated through interpolation over 1) projection matrices, 2) state-space realizations, and 3) transfer functions, which trade accuracy, robustness, and cost. Methods are finally exemplified in the dynamic stability of a T-tail configuration with varying incidence. Numerical studies show that a very small number of balanced realizations is sufficient to accurately capture the unconventional aeroelastic response of this system, which includes in-plane kinematics and steady loads, over a wide range of operation conditions.