Genetic Algorithm-Based Model Order Reduction of Aeroservoelastic Systems with Consistent States

Abstract

This paper presents a model order reduction framework to construct linear parameter-varying reduced-order models of flexible aircraft for aeroservoelasticity analysis and control synthesis in broad two-dimensional flight parameter space. Genetic algorithms are used to automatically determine physical states for reduction and to generate reduced-order models at grid points within parameter space while minimizing the trial-and-error process. In addition, balanced truncation for unstable systems is used in conjunction with the congruence transformation technique to achieve locally optimal realization and "weak" fulfillment of state consistency across the entire parameter space. Therefore, aeroservoelasticity reduced-order models at any flight condition can be obtained simply through model interpolation. The methodology is applied to the pitch-plant model of the X-56A Multi-Use Technology Testbed currently being tested at NASA Armstrong Flight Research Center for flutter suppression and gust load alleviation. The present studies indicate that the reduced-order model with more than 12× reduction in the number of states relative to the original model is able to accurately predict system response among all input-output channels. The genetic-algorithm-guided approach exceeds manual and empirical state selection in terms of efficiency and accuracy. The interpolated aeroservoelasticity reduced-order models exhibit smooth pole transition and continuously varying gains along a set of prescribed flight conditions, which verifies consistent state representation obtained by congruence transformation. The present model order reduction framework can be used by control engineers for robust aeroservoelasticity controller synthesis and novel vehicle design.

Greedy Sampling and Incremental Surrogate Model-based Tailoring of Aeroservoelastic Model Database for Flexible Aircraft

“…The target normalized frequency range  is determined to be 0.01 <  < 5.37 to ensure full coverage of the instability of interest and system response. The detailed model information and the physical meaning of the states is given in [9].…”

“…The future work will focuses on integrating the database tailoring approach with the ASE model construction process, i.e., generating a proper number of the model at the first place, model order reduction framework [8,9], and control synthesis to mitigate the modeling and design workload and develop more robust flight control. The use of the -shifted H2 norm [14] to speed up the tailoring process will also be investigated.…”

“…One of the most widely used approaches to analyze aeroservoelastic (ASE) of flexible aircraft is to construct a large number of linear time invariant (LTI) models with refined grid points to accommodate the entire flight envelope with the model matrices on the grid points dependent on flight parameters. While practically feasible given the present computing and software technologies and platforms, construction and use of a large LTI model database can gives rise to critical issues that may potentially overwhelm the improvement in modeling accuracy, such as significant burdens of model order reduction (MOR) [3][4][5][6][7][8][9][10][11] and flight control design [3,12,13] as the controller must be synthesized for LTI model at each grid point. In particular, for switched linear parameter varying (LPV) controls, a small number of LTI models are preferred in order to reduce the number of controller switching, and hence, mitigate high order dependency on scheduling parameters [14].…”

State consistence of data-driven reduced order models for parametric aeroelastic analysis

“…However, the requirement for system matrix interpolation is that the states at varying flight conditions need to have consistent representation, i.e., coordinates of the states as discussed in Sect 1. In other words, the physical meaning of the states in the ROMs remains the same across the flight envelop [41]. In this section, the state consistence of the ROM obtained by ARX and N4SID is examined by two means: the change of the system matrix elements and the poles with varying flight parameters.…”

“…In contrast, another method to parameterize ROM is the gridded domain [41,42], in which the targeted flight regime is partitioned by grid points. At these grid points, a parametric database of local state-space ROMs is constructed, and each local ROM only captures the aerodynamic or aeroelastic behavior at that flight condition.…”