Méthodes basées sur le contrôle pour l'indentification de structures non-linéaires

One of the key roles of structural engineering is to describe how a structure vibrates, or "responds", when a dynamic load, or "excitation", is applied to it. Often, the assumption of linear behavior is adopted, meaning that the response to a combination of excitation signals is the combination of the responses to the signals taken individually. When this assumption does not hold, complex dynamical phenomena can arise, including the coexistence of multiple responses for the same excitation, the sudden transition from one such response to another, or responses that are not stable. They render the experimental interrogation of engineering structures particularly challenging. An emerging family of testing methods, termed control-based methods, uses feedback loops and controllers to make the interrogation exhaustive and predictable. In this context, this thesis investigates carefully two recently-introduced methods, namely control-based continuation during which the excitation is corrected or generated by a controller, and phase-locked loop testing which imposes the phase lag between the response and the excitation using feedback control. In the first part of the thesis, we aim to deepen the understanding of control-based methods with the objective to design and tune experiments more systematically, reducing the need for trial and error. In the second part of the thesis, new developments exploiting adaptive filtering are carried out to expand the capabilities of both control-based continuation and phase-locked loop testing, but also to tackle dynamical features that were never identified experimentally before. Finally, this thesis opens the way towards more robust control-based methods and, eventually, to their industrial application.Un des buts premiers de l'ingénierie des structures est de décrire comment une structure vibre, ou "répond", lorsqu'une charge dynamique, ou "excitation", lui est appliquée. Souvent, l'hypothèse de comportement dynamique linéaire est adoptée: la réponse à une combinaison d'excitations est la combinaison des réponses aux excitations prises individuellement. Quand cette hypothèse n'est pas vérifiée, des phénomènes dynamiques complexes peuvent se produire comme, par exemple, la coexistence de plusieurs réponses à la même excitation, la transition subite d'une de ces réponses à une autre ou des réponses qui ne sont pas stables. Ces phénomènes rendent l'interrogation expérimentale des structures particulièrement difficile. De nouvelles méthodes basées sur le contrôle et utilisant des boucles de rétroaction sont apparues pour rendre l'interrogation exhaustive et prévisible. Dans ce contexte, cette thèse étudie en détail deux méthodes récemment introduites: la continuation basée sur le contrôle durant laquelle l'excitation est corrigée ou générée par un contrôleur et les tests en boucle à verrouillage de phase avec une boucle de rétroaction imposant le retard de phase entre la réponse et l'excitation. La première partie de cette thèse vise à approfondir la compréhension de ces méthodes afin de concevoir les expériences plus efficacement, notamment en diminuant le recours à des essais-erreurs. La seconde partie exploite le filtrage adaptatif pour étendre le champ d'action des méthodes ainsi que pour étuider des phénomènes dynamiques qui n'ont jamais été identifiés expérimentalement de cette manière. Finalement, cette thèse ouvre la voie à des méthodes basées sur le contrôle plus robustes et, un jour, à leur application industrielle

Experimental Characterization of Superharmonic Resonances Using Phase-Lock Loop and Control-Based Continuation

Experimental characterization of nonlinear structures usually focuses on fundamental resonances. However, there is useful information about the structure to be gained at frequencies far away from those resonances. For instance, non-fundamental harmonics in the system's response can trigger secondary resonances, including superharmonic resonances. Using the recently-introduced definition of phase resonance nonlinear modes, a phase-locked loop feedback control is used to identify the backbones of even and odd superharmonic resonances, as well as the nonlinear frequency response curve in the vicinity of such resonances. When the backbones of two resonances (either fundamental or superharmonic) cross, modal interactions make the phase-locked loop unable to stabilize some orbits. Control-based continuation can thus be used in conjunction with phase-locked loop testing to stabilize the orbits of interest. The proposed experimental method is demonstrated on a beam with artificial cubic stiffness exhibiting complex resonant behavior. For instance, the frequency response around the third superharmonic resonance of the third mode exhibits a loop, the fifth superharmonic resonance of the fourth mode interacts with the fundamental resonance of the second mode, and the second superharmonic resonance of the third mode exhibits a branch-point bifurcation and interacts with the fourth superharmonic resonance of the fourth mode

A Consistency Analysis of Phase-Locked-Loop Testing and Control-Based Continuation for a Geometrically Nonlinear Frictional System

Two of the most popular vibration testing methods for nonlinear structures are control-based continuation and phase-locked-loop testing. In this paper, they are directly compared on the same benchmark system, for the first time, to demonstrate their general capabilities and to discuss practical implementation aspects. The considered system, which is specifically designed for this study, is a slightly arched beam clamped at both ends via bolted joints. It exhibits a pronounced softening-hardening behavior as well as an increasing damping characteristic due to the frictional clamping. Both methods are implemented to identify periodic responses at steady-state constituting the phase-resonant backbone curve and nonlinear frequency response curves. To ensure coherent results, the repetition variability is thoroughly assessed via an uncertainty analysis. It is concluded that the methods are in excellent agreement, taking into account the inherent repetition variability of the system

Stabilisation par retour d'état non-invasif de systèmes lisses et non-lisses

Unstable periodic orbits of nonlinear structures can be stabilized through differential control of the displacement. However, nonlinearities in the system generate non-fundamental harmonics that are fed back into the excitation signal, affecting the structure’s response and making the controller invasive. Adaptive filters are used to perform an online estimation of the Fourier coefficients of the displacement signal in order to cancel the invasiveness. The performance of the method is discussed for simulated experiments possessing smooth and non-smooth nonlinearities

Online Control-Based Continuation of Nonlinear Structures Using Adaptive Filtering

peer reviewedControl-Based Continuation uses feedback control to follow stable and unstable branches of periodic orbits of a nonlinear system without the need for advanced post-processing of experimental data. CBC relies on an iterative scheme to modify the harmonic content of the control target and obtain a non-invasive control signal. This scheme currently requires to wait for the experiment to settle down to steady-state and hence runs offline (i.e. at a much lower frequency than the feedback controller). This paper proposes to replace this conventional iterative scheme by adaptive filters. Adaptive filters can directly synthesize the control target adequately and can operate online (i.e. at the same frequency as the feedback controller). This novel approach is found to significantly accelerate convergence to non-invasive steady-state responses to the extent that the structure response can be characterized in a continuous amplitude sweep. Importantly, the stabilizing effect of the controller is not affected

Comparison Between Control-Based Continuation and Phase-Locked Loop Methods for the Identification of Backbone Curves and Nonlinear Frequency Responses

Tribomechadynamics Research Cam

Comparison between Control-Based Continuation and Phase-Locked Loop Methods for the Identification of Backbone Curves & Nonlinear Frequency Responses

Control-based continuation (CBC) and phase-locked loops (PLL) are two experimental testing methods that have demonstrated great potential for the non-parametric identification of key nonlinear dynamic features such as nonlinear frequency responses and backbone curves. Both CBC and PLL exploit stabilizing feedback control to steer the dynamics of the tested system towards the responses of interest and overcome important difficulties experienced when applying conventional testing methods such as sine sweeps to nonlinear systems. For instance, if properly designed, the feedback controller can prevent the system from exhibiting untimely transitions between coexisting responses or even losing stability due to bifurcations. This contribution aims to highlight the similarities that exist between CBC and PLL and present the first thorough comparison of their capabilities. Comparisons are supported by numerical simulations as well as experimental data collected on a conceptually simple nonlinear structure primarily composed of a thin curved beam. The beam is doubly clamped and exhibits nonlinear geometric effects for moderate excitation amplitudes