Model Order Reduction of Aeroservoelastic Model of Flexible Aircraft

Abstract

This paper presents a holistic model order reduction (MOR) methodology and framework that integrates key technological elements of sequential model reduction, consistent model representation, and model interpolation for constructing high-quality linear parameter-varying (LPV) aeroservoelastic (ASE) reduced order models (ROMs) of flexible aircraft. The sequential MOR encapsulates a suite of reduction techniques, such as truncation and residualization, modal reduction, and balanced realization and truncation to achieve optimal ROMs at grid points across the flight envelope. The consistence in state representation among local ROMs is obtained by the novel method of common subspace reprojection. Model interpolation is then exploited to stitch ROMs at grid points to build a global LPV ASE ROM feasible to arbitrary flight condition. The MOR method is applied to the X-56A MUTT vehicle with flexible wing being tested at NASA/AFRC for flutter suppression and gust load alleviation. Our studies demonstrated that relative to the fullorder model, our X-56A ROM can accurately and reliably capture vehicles dynamics at various flight conditions in the target frequency regime while the number of states in ROM can be reduced by 10X (from 180 to 19), and hence, holds great promise for robust ASE controller synthesis and novel vehicle design.

Genetic Algorithm-Guided, Adaptive Model Order Reduction of Flexible Aircrafts

“…It is then followed by the balanced truncation to further refine the model from the input/output channel energy perspective. There are two points of particular note: (1) rather than relying on the user's experience and trial-and-error iteration, a genetic algorithm-based procedure was developed to "intelligently" determine which states to retain (or remove) in the aforementioned truncation and residualization (see Section B below); (2) in contrast to the previous research [6,7] including ours, the modal reduction approach based on the real and ordered eigenstructure decomposition was not used in the present effort. This is because the modal frequency varies significantly across the broad 2D flight parameter space and the full models at various grid points have the different number of complex and real poles, and the use of modal reduction causes substantial state inconsistence among locally reduced ROMs.…”

“…The challenge is to determine which states to keep (or remove). In previous efforts this is performed based on the understanding of the vehicles dynamics [2,11], iterative process [1], retention of the states corresponding to leading modes [7], etc., which are mostly empirical. In the present effort, we developed a global optimization approach using genetic algorithm to automatically determine which states to reduce with minimal reliance on user's experience and trial-and-error process while maintaining dynamics of the original system.…”

“…To mitigate this issue, one of the most widely used methods is to project the individual ROMs onto a common subspace, followed by matrix interpolation as discussed in [3,7,16]. The common subspace R shared by all local ROMs is obtained by the singular value decomposition (SVD) of the concatenated right projection matrices V i at grid points; i.e., RSΦ T ≈[V 1 , …V ns ], where V i is the column subspace in ܸ ෨ corresponding to the retained states in balanced truncation, i.e., Eq.…”

“…In the sequential MOR the truncation and residualization methods were first applied to the states of sensors, actuators, aerodynamic lags, rigid bodies, elastic structures of the full-order X-56A MUTT ASE model on the grid points. In contrast to previous efforts [1,2,7], for the first time a genetic algorithm (GA) was used for automated selection of unimportant states in the aerodynamic lag and the elastic modes to truncate/residualize, which not only eliminates the manual and trialand-error process for state screening, but also improves MOR accuracy and performance given state budgets. The balanced truncation for unstable systems was also utilized to further remove states with minor contribution to the input/output energy of the system in the local reduced model.…”

“…Next, the method of congruence transformation was employed to remedy the issue of inconsistent state representation among the local ROMs caused by the flight parameters-dependent transformation as discussed above. Different from the previous approach of reprojection onto a common subspace [3,4,7], the congruence transformation allows "weak" fulfillment of the "Modal Assurance Criterion" (MAC) and ROM interpolation to construct a unified LPV ROM applicable across broader flight envelope. Finally, an adaptive grid refinement strategy was developed to selectively add grid points at the regions where system response is susceptible to the flight parameters and ensure smooth interpolation and transition of ROMs within the domain.…”