An iterative SVD-tangential interpolation method for medium-scale MIMO systems approximation with application on flexible aircraft

Abstract

Abstract-In this paper, the problem of medium-scale MIMO LTI systems approximation is addressed. The proposed methodology, inspired from recent developments in the model reduction community (i.e. [1], [2], [3]), consists of combining the features of the SVD reduction approach with the tangential interpolation ones. The contributions of the paper are in two folds: (i) it provides a simple but numerically robust and effective procedure, namely, Iterative SVD-Tangential Interpolation Algorithm (ISTIA), to approximate any medium-scale MIMO LTI system and, (ii) it assesses the efficiency of the proposed methodology on a medium-scale industrial aeroelastical aircraft model, on which different H∞ control design methodologies are evaluated, illustrating on a complex industrial framework, the efficiency of the proposed approximation algorithm.

Generation of a reduced-order LPV/LFT model from a set of large-scale MIMO LTI flexible aircraft models

“…With reference to Fig. 4, it is clear that the ISTIA provides the best results in terms of approximation error, which is not that surprising (see Poussot-Vassal, 2011). It also appears that the approximation quality is not as good with the mISTIA as with the ISTIA or the BT.…”

“…The underlying idea is either to construct X and Y (when using the Sylvester-like approaches-Corollary 1) or to find the optimal interpolation points and directions (when using the tangential approachesTheorem 2). For more details, the reader is invited to refer to Gugercin et al (2008), Van-Dooren et al (2008) (2008) ideas, a simple but very efficient hybrid algorithm has been proposed by Poussot-Vassal (2011). This algorithm, called ISTIA, for Iterative SVD-Tangential Interpolation Algorithm, allows (i) to preserve stability at each iteration (provided that A is stable) thanks to the computation of a single Gramian, and (ii) to ensure good frequency response fitting through the use of the one-sided tangential interpolation.…”

“…In contrast, a purely numerical approach using Krylov-based methods (Gallivan, Vanderope, & Van-Dooren, 2004;Gugercin, 2008;Van-Dooren, Gallivan, & Absil, 2008) is proposed in this paper. Based on a reduction algorithm recently developed in Poussot-Vassal (2011), an extended procedure is proposed here to obtain reduced-order models with consistent modal content and accurate frequency responses. Note that this reduction step is often omitted in existing works, where small-scale models are directly considered (see e.g.…”

Model reduction using a frequency-limited -cost

“…These methods often use computationally effective Krylov-based algorithms which makes these techniques suitable for large-scale problems. Examples of these algorithms are Xu and Zeng (2011), Beattie and Gugercin (2007) and Poussot-Vassal (2011). Recently two variants of these methods have been published.…”

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

“…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].…”