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

This paper describes a method to construct reduced-order models for high-dimensional nonlinear systems. It is assumed that the nonlinear system has a collection of equilibrium operating points parameterized by a scheduling variable. First, a reduced-order linear system is constructed at each equilibrium point using state, input, and output data. This step combines techniques from proper orthogonal decomposition, dynamic mode decomposition, and direct subspace identification. This yields discrete-time models that are linear from input to output but whose state matrices are functions of the scheduling parameter. Second, a parameter varying linearization is used to connect these linear models across the various operating points. The key technical issue in this second step is to ensure the reduced-order linear parameter varying system approximates the nonlinear system even when the operating point changes in time. Copyright c © 2016 John Wiley & Sons, Ltd.

A method to construct reduced‐order parameter‐varying models

This paper presents a new state-space model interpolation of local estimates technique to compute linear parameter-varying (LPV) models for parameter-dependent systems using a set of linear time-invariant models obtained for fixed operating conditions. The technique is based on observability and controllability properties and has three strong appeals, compared with the state of the art in the literature. First, it works for continuous-time as well as discrete-time multiple-input multiple-output systems depending on multiple scheduling parameters. Second, the technique is automatic to some extent, in the sense that, after the model selection, no user interaction is required at the different steps of the method. Third, the resulting interpolating LPV model is numerically well-conditioned such that it can be used for modern LPV control design. Moreover, the proposed technique guarantees that the local models have a coherent state-space representation encompassing existing results as a particular case. The benefits of the approach are demonstrated on a simulation example and on an experimental data set obtained from a vibroacoustic setup.

Interpolated Modeling of LPV Systems

https://ntrs.nasa.gov/api/citations/20170009839/downloads/20170009839.pdf

LPV Modeling of a Flexible Wing Aircraft Using Modal Alignment and Adaptive Gridding Methods.

A model order reduction method is proposed for models of aeroservoelastic vehicles in the linear parameter-varying (LPV) systems framework, based on state space interpolation of modal forms. The dynamic order of such models is usually too large for control synthesis and implementation since they combine rigid body dynamics, structural dynamics and unsteady aerodynamics. Thus, model order reduction is necessary. For linear timeinvariant (LTI) models, order reduction is often based on balanced realizations. For LPV models, this requires the solution of a large set of linear matrix inequalities (LMIs), leading to numerical issues and high computational cost. The proposed approach is to use well developed and numerically stable LTI techniques for reducing the LPV model locally and then to transform the resulting collection of systems into a consistent modal representation suitable for interpolation. The method is demonstrated on an LPV model of the body freedom flutter vehicle, reducing the number of states from 148 to 15. The accuracy of the reduced order model (ROM) is confirmed by evaluating the ν-gap metric with respect to the full order model and by comparison to another ROM obtained by state-of-the-art LPV balanced truncation techniques.

/pdf/modal-matching-for-lpv-model-reduction-of-aeroservoelastic-2cqqpsywr7.pdf

Modal Matching for LPV Model Reduction of Aeroservoelastic Vehicles

In the civilian aeronautical industry, flexible air-craft models are often built and validated at frozen flight and mass configurations. Unfortunately, these medium(large)-scale models derived from high fidelity numerical tools are generally not well adapted for simulation, control and analysis. In this paper, a methodology to derive a reduced-order Linear Parameter Varying (LPV) model from a set of medium(large)-scale Linear Time Invariant (LTI) models describing a given system at frozen configurations is described. The proposed methodology is in three steps: (i) first, local model approximation is applied using recent advances in SVD-Krylov methods, (ii) then, an appropriate base change is applied to allow interpolation, (iii) and finally, an LPV model is derived and converted into a Linear Fractional Representation (LFR) of suitable size for analysis and control purposes. Results are thoroughly assessed on a set of industrial aeroelastic aircraft models.

http://www.researchgate.net/profile/Charles_Poussot-Vassal/publication/224254014_Flexible_aircraft_reduced-order_LPV_model_generation_from_a_set_of_large-scale_LTI_models/links/0fcfd50c076d992273000000.pdf

C. Roos

Papers

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

Flexible aircraft reduced-order LPV model generation from a set of large-scale LTI models