Pierre Vuillemin

Introduction to MORE: A MOdel REduction toolbox

In many highly technological engineering fields, the use of dedicated computer-based dynamical system modeling software often leads to large dimensional Linear Time Invariant (LTI) models. These kind of models, composed of a large amount of variables might render drastically inefficient many analysis, control design and optimization techniques. As a matter of fact, considerable attention has been devoted to the development of model reduction - or approximation - techniques to eliminate irrelevant state variables. This paper presents a new freely-available MATLAB©-based toolbox for approximation of medium and large-scale LTI dynamical models, called MORE (MOdel REduction), which implements a collection of very recent advanced algorithms for LTI dynamical model reduction purpose.

H2 optimal and frequency limited approximation methods for large-scale LTI dynamical systems

Model order reduction over a bounded frequency range is more adapted than the standard H2 approximation whenever the entire frequential behaviour of the large-scale model is not needed or not accurately known. However most of the methods that enable to reduce a model on a limited frequency range are based on the use of weights. Yet their determination is often an issue for engineers. That is why, in this paper, two weight-free model approximation algorithms are proposed. They are based on recent algorithms that achieve local H2 optimal model reduction (see Gugercin (2007), Van Dooren et al. (2008) and Gugercin et al. (2008)). The proposed algorithms efficiency are validated both on a standard benchmark and on an industrial use case.

Business Jet Large-Scale Model Approximation and Vibration Control

Abstract In this paper, a procedure allowing to design an H∞-based low order anti-vibration controller is proposed. The contributions of the paper lie in the first specification and application of recent (i) model approximation and (ii) H∞ structured controller tuning techniques on a complex aeroelastical aircraft model, used by engineers to design control strategies. The entire procedure – i.e. approximation and control – is assessed on a Business Jet large-scale generic model, highlighting the effectiveness of the approach in a concrete use-case.

Longitudinal Manoeuvre Load Control of a Flexible Large-Scale Aircraft

Abstract This paper discusses the design and validation of an integrated long range flexible aircraft load controller, at a single flight/mass configuration. The contributions of the paper are in twofold: (i) first, a very recent frequency-limited model approximation technique is used to reduce the dimension of the large-scale aeroservoelastic aircraft model over a finite frequency support while guaranteeing optimal mismatch error, secondly, (ii) a structured controller is designed using an ℋ ∞ -objective and coupled with an output saturation strategy to achieve flight performance and load clearance, i.e. wing root bending moment saturation. The entire procedure - approximation and control - is finally assessed on the high fidelity large-scale aircraft model, illustrating the effectiveness of the procedure on a high fidelity model, used in the industrial context in the load control validation process.

Approximation of stability regions for large-scale time-delay systems using model reduction techniques

In this paper, the problem of determining the approximate stability regions of large-scale time-delay systems (LS TDS) is solved using model approximation techniques. To achieve this, an ℋ2-oriented approximation algorithm, referred to as TF-IRKA [1], is considered. This algorithm has been shown to be well suited for the approximation of infinite-dimensional systems into finite-dimensional ones. We show here how model reduction can be used to approximate time-delay systems with multiple delays and estimate their stability regions. Discussions regarding the adaptation of existing algorithms to the considered problem are also provided. Several numerical examples illustrate the efficiency and accuracy of the approach.

Global stability validation of an uncertain large-scale aircraft model

A methodology to generate a parameter dependent uncertain large-scale aeroservoelastic aircraft model, with guaranteed bounds on the approximation error is firstly obtained using adavanced approximation and interpolation techniques. Secondly, the global stability of the aforementionned uncertain parameter dependent aircraft model, represented as a Linear Fractional Representation (LFR), subject to actuator saturation and dynamical uncertainties, is addressed through the use of an irrational multiplier-based Integral Quadratic Constraint (IQC) approach. The effectiveness of the approach is assessed on a complex set of aeroservoelastic aircraft models.

A Frequency-Limited \(\mathcal{H}_2\) Model Approximation Method with Application to a Medium-Scale Flexible Aircraft

In this paper, the problem of approximating a medium-scale MIMO LTI dynamical system over a bounded frequency range is addressed. A new method grounded on the SVD-Tangential model order reduction framework is proposed. Based on the frequency-limited gramians defined in [5], the contribution of this paper is to propose a frequency-limited iterative SVD-Tangential interpolation algorithm (FL-ISTIA) to achieve frequency-limited model approximation without involving weighting filters. The efficiency of the approach is addressed both on standard benchmark and on an industrial flexible aircraft model.

Model Reduction for Norm Approximation: An Application to Large-Scale Time-Delay Systems

The computation of \(\mathscr {H}_2\) and \(\mathscr {H}_{2,\varOmega }\) norms for LTI Time-Delay Systems (TDS) are important challenging problems for which several solutions have been provided in the literature. Several of these approaches, however, cannot be applied to systems of large dimension because of the inherent poor scalability of the methods, e.g., LMIs or Lyapunov-based approaches. When it comes to the computation of frequency-limited norms, the problem tends to be even more difficult. In this chapter, a computationally feasible solution using \(\mathscr {H}_2\) model reduction for TDS, based on the ideas provided in [3], is proposed. It is notably demonstrates on several examples that the proposed method is suitable for performing both accurate model reduction and norm estimation for large-scale TDS.

Stability Analysis of a Set of Uncertain Large-Scale Dynamical Models With Saturations: Application to an Aircraft System

From a sparse set of large-scale linear time-invariant dynamical models, a methodology to generate a low-order parameter-dependent and uncertain model, with guaranteed bounds on the approximation error, is first obtained using advanced approximation and interpolation techniques. Second, the stability of the aforementioned model, represented as a linear fractional representation and subject to actuator saturation and dynamical uncertainties, is addressed through the use of an irrational multiplier-based integral quadratic constraint approach. The effectiveness of the approach is assessed on a complex set of aeroservoelastic aircraft models used in an industrial framework for control design and validation purposes.

Poles residues descent algorithm for optimal frequency-limited ℋ 2 model approximation

Model approximation of multiple-inputs/multiple-outputs (MIMO) linear dynamical systems over a bounded frequency range can be expressed as an optimization problem in terms of the frequency-limited ℋ2-norm. In this paper, a new formulation of the frequency-limited ℋ2 model approximation error is presented and its gradient derived. It is then used in a descent algorithm which does not require to solve any Lyapunov equations but one eigenvalue problem for the full-order model. The efficiency of the method is illustrated through numerical benchmarks.