Loewner-based Data-driven Iterative Structured Control Design

Stability enforcement remains a challenge in data-driven control paradigms, where no parametrised model of the system is available. For instance, the system's instabilities can be estimated in order to enforce a closed-loop stability constraint on the controller reduction step. In order to avoid this preliminary estimation of instabilities, this paper proposes to embed a closed-loop stability constraint in the design. To that extent, an optimization problem is formulated in order to improve matching between the reference model and the closed-loop while maintaining internal stability. The proposed iterative procedure to solve this problem is illustrated on two numerical examples

A Frequency-Limited H2 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 based on the SVD-Tangential model order reduction framework is proposed. Grounded 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

Optimal Modal Truncation

This paper revisits the modal truncation from an optimisation point of view. In particular, the concept of dominant poles is formulated with respect to different systems norms as the solution of the associated optimal modal truncation problem. The latter is reformulated as an equivalent convex integer or mixed-integer program. Numerical examples highlight the concept and optimisation approach

Data-driven approximation of a high fidelity gust-oriented flexible aircraft dynamical model

International audienceComputing responses to discrete gusts are sizing steps when designing and optimizing a new aircraft structure and geometry. Indeed, this is part of the imposed clearance certifications requested by the flight authorities. During the aircraft preliminary design phase, this clearance is done by intensive simulations, however, due to the involved models complexity, these latter are time consuming and imply an important computational burden. Especially as these simulations are involved at different steps of the aircraft optimisation process e.g. by aeroelastic, flight and control engineers. In this paper we propose a systematic way to fasten the gust simulation step and simplify the analysis by mean of data-driven model approximation in the Loewner framework. The proposed approach gathers recent advances in aeroelastic modelling and model approximation techniques. As illustrated on a high fidelity long range aircraft model, the drastic reduction of the simulation time does not induce any significant loss of accuracy

Interpolatory Methods for Generic BizJet Gust Load Alleviation Function

The paper's main contribution concerns the use of interpolatory methods to solve end to end industrial control problems involving complex linear dynamical systems. More in details, contributions show how the rational data and function interpolation framework is a pivotal tool (i) to construct (frequency-limited) reduced order dynamical models appropriate for model-based control design and (ii) to accurately discretise controllers in view of on-board computer-limited implementation. These contributions are illustrated along the paper through the design of an active feedback gust load alleviation function, applied on an industrial generic business jet aircraft use-case. The closed-loop validation and performances evaluation are assessed through the use of an industrial dedicated simulator and considering certification objectives. Although application is centred on aircraft applications, the method is not restrictive and can be extended to any linear dynamical systems.Comment: 23 pages, 9 figures, submitted to journa

A state-space model for loads analysis based on tangential interpolation

International audienceIn this work an approach for the generation of a generalized state-space aeroservoelastic model based tangential interpolation, also known as Loewner rational interpolation, is presented. The resulting differential algebraic system (DAE) system is reduced to a set of ordinary differential equations (ODE) by residualization of the non-proper part of the transfer function matrix. The generalized state-space is of minimal order and allows for the application of the force summation method (FSM) for the aircraft loads recovery, which shows a superior convergence when compared to the mode displacement method (MDM) for an increasing number of generalized coordinates for the cut loads recovery. Compared to the classical rational function approximation (RFA) approach, the presented method provides a minimal order realization with exact interpolation of the unsteady aerodynamic forces in tangential directions, avoiding any selection of poles (lag states). After a demonstration of the tangential interpolation techniques on the transcendental Theodorsen and Sears functions, the new approach is applied to the generation of an aeroservoelastic model for loads evaluation of the NASA Common Research model under atmospheric disturbances, showing an excellent agreement with the reference model in the frequency domain. Applications include the aerodynamic transfer function matrices generated by either potential flow or linearized computational fluid dynamics (CFD) solvers. The resulting aeroservoelastic model of minimal order is used for the design of an Hinf-optimal controller for gust loads alleviation (GLA)

Improved mode tracking for the p-L flutter solution method based on aeroelastic derivatives

In this work an improved mode tracking algorithm is developed for the p-L flutter solution method. Compared to the original criterion used for sorting the aeroelastic modes, the approach presented herein uses aeroelastic derivatives in order to predict the flutter solution at the next parameter value. The present method allows for a more robust and efficient sorting of the aeroelastic modes for configurations where the number of real and complex poles resulting from the representation of the aerodynamic term is high, ensuring a proper tracking of the modes corresponding to the structural degrees of freedom. The flutter p-L method together with the proposed mode tracking algorithm is applied to a 2 degrees-of-freedom airfoil configuration with high-fidelity unsteady aerodynamics and to the common research aeroelastic model representing a transport aircraft configuration. For the latter, a modified doublet-lattice method valid throughout the complex plane is used for the reference solution, allowing for the first time to validate the p-L flutter solution method for general configurations. The results show that the p-L method is able to truly represent the aeroelastic damping when compared to the classical p-k and g methods