Data-driven nonlinear aeroelastic models of morphing wings for control

Accurate and efficient aeroelastic models are critically important for enabling the optimization and control of highly flexible aerospace structures, which are expected to become pervasive in future transportation and energy systems. Advanced materials and morphing wing technologies are resulting in next-generation aeroelastic systems that are characterized by highly-coupled and nonlinear interactions between the aerodynamic and structural dynamics. In this work, we leverage emerging data-driven modeling techniques to develop highly accurate and tractable reduced-order aeroelastic models that are valid over a wide range of operating conditions and are suitable for control. In particular, we develop two extensions to the recent dynamic mode decomposition with control (DMDc) algorithm to make it suitable for flexible aeroelastic systems: 1) we introduce a formulation to handle algebraic equations, and 2) we develop an interpolation scheme to smoothly connect several linear DMDc models developed in different operating regimes. Thus, the innovation lies in accurately modeling the nonlinearities of the coupled aerostructural dynamics over multiple operating regimes, not restricting the validity of the model to a narrow region around a linearization point. We demonstrate this approach on a high-fidelity, three-dimensional numerical model of an airborne wind energy (AWE) system, although the methods are generally applicable to any highly coupled aeroelastic system or dynamical system operating over multiple operating regimes. Our proposed modeling framework results in real-time prediction of nonlinear unsteady aeroelastic responses of flexible aerospace structures, and we demonstrate the enhanced model performance for model predictive control. Thus, the proposed architecture may help enable the widespread adoption of next-generation morphing wing technologies

Identification of interpolating affine LPV models for mechatronic systems with one varying parameter

This paper presents a technique to identify an affine parameter-dependent model based on a set of Linear-Time-Invariant (LTI) models that are identified in local operating points of the varying system. The systems under investigation are mechatronic systems in which the dynamic behaviour is depending on a single varying parameter. By fitting specific pole and zero loci on the poles and zeros of the local LTI models, an affine state-space model can be constructed. Since the resulting affine model is well conditioned and has a low complexity, it is suitable to be used for Linear-Parameter-Varying (LPV) control. The applicability of the presented technique is shown on an industrial pick-and-place machine with position-dependent dynamics. © 2008 EUCA.status: publishe

Reduced order modelling through system identification using stochastic filtering

This thesis presents a novel approach to model order reduction, through system identification and using stochastic filtering. Order reduction is a particularly relevant application in the automotive context, as the generation of simplified simulation models for the whole vehicle and its subsystems is an increasingly important aspect of vehicle design. First, grey-box parameter identification of vehicle handling dynamics is explored, including identification of a combined-slip tyre model. This introductory study serves as an intermediate step to review three alternative stochastic filters: identifying forms of the unscented Kalman filter, extended Kalman filter and particle filter are here compared for effectiveness, complexity and computational efficiency. Despite being initially merely considered as a stepping stone towards black-box identification, this phase of the PhD generated its own and independent outcomes and might be viewed as a spin-off of the main research topic. All three filters appear suited to system identification and could operate in on-line model predictive controllers or estimators, with varying levels of practicability at different sampling rates. Work on black-box system identification then starts through a non-linear Kalman filter, extended to identify all the parameters of a canonical linear state-space structure. In spite of all model parameters being unknown at the start, the filter is able to evolve parameter estimates to achieve 100$\%$ accuracy in noise-free test cases, and is also proven to be robust to noise in the measurements. The canonical form ensures that a minimal number of parameters need to be identified and produces additional information in terms of eigenvalues and dominant modes. After extensive testing in the linear domain, state-space is extended into a non-linear framework, with each parameter becoming a non-linear function of system inputs or states. Parameter variation is first constrained by cubic spline polynomials, to provide continuity and maintain relatively small extended state-parameter vectors. This early approach is later simplified, with each element of state-space generated through unconstrained, generic non-linear functions and defined through a number of equally spaced, fixed nodes. Conditioning and convergence are maintained through the definition of additional system outputs, based on specific functions of the non-linear node ordinates. Unlike other methods published in the literature, this new approach does not focus on a specific non-linear structure, but consists in the prescription of a generic and yet simple non-linear state-space model structure, that allows various non-linearities to be identified and approximated solely based on inputs and outputs. The method is illustrated in practice through simple non-linear examples and test cases, which include the identification of a full vehicle model, a highly non-linear brake model and CFD data. These applications show that it is possible to easily expand the order of the system and the complexity of the non-linearities, to achieve higher accuracy while ensuring good parameter conditioning. The approach is completely black-box and requires no physical understanding of the process for successful identification, making it an ideally suited mechanism for order reduction of high order simulation models. In addition to high order simulation data, the developed approach can be used as a tool for conventional system identification and applied to experimental test data as well.</div