- Lhachemi, Hugo

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# Lhachemi, Hugo

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- PublicationInput-to-State Stability of a Clamped-Free Damped String in the Presence of Distributed and Boundary DisturbancesThis note establishes the exponential input-to-state stability (EISS) property for a clamped-free damped string with respect to distributed and boundary disturbances. While efficient methods for establishing ISS properties for distributed parameter systems with respect to distributed disturbances have been developed during the last decades, establishing ISS properties with respect to boundary disturbances remains challenging. One of the well-known methods for well-posedness analysis of systems with boundary inputs is the use of a lifting operator for transferring the boundary disturbance to a distributed one. However, the resulting distributed disturbance involves time derivatives of the boundary perturbation. Thus, the subsequent ISS estimate depends on its amplitude, and may not be expressed in the strict form of ISS properties. To solve this problem, we show for a clamped-free damped string equation that the projection of the original system trajectories in an adequate Riesz basis can be used to establish the desired EISS property.
296 - PublicationI-nteract: A Cyber-Physical System for Real-Time Interaction With Physical and Virtual Objects Using Mixed Reality Technologies for Additive ManufacturingThis paper presents I-nteract, a cyber-physical system that enables real-time interaction with real and virtual objects in a mixed reality environment to design 3D models for additive manufacturing. The system has been developed using mixed reality technologies such as HoloLens, for augmenting visual feedback, and haptic gloves, for augmenting haptic force feedback. The efficacy of the system has been demonstrated by generating a 3D model using a novel scanning method to 3D print a customized orthopedic cast for human arm, by estimating spring rates of compression springs, and by simulating interaction with a virtual spring in a mixed reality environment.
273Scopus© Citations 11 - PublicationBoundary feedback stabilization of a reaction–diffusion equation with Robin boundary conditions and state-delayThis paper discusses the boundary feedback stabilization of a reaction–diffusion equation with Robin boundary conditions and in the presence of a time-varying state-delay. The proposed control design strategy is based on a finite-dimensional truncated model obtained via a spectral decomposition. By an adequate selection of the number of modes of the original infinite-dimensional system, we show that the design performed on the finite-dimensional truncated model achieves the exponential stabilization of the original infinite-dimensional system. In the presence of distributed disturbances, we show that the closed-loop system is exponentially input-to-state stable with fading memory.
202Scopus© Citations 22 - PublicationRobustness of constant-delay predictor feedback for in-domain stabilization of reaction–diffusion PDEs with time- and spatially-varying input delaysThis paper discusses the in-domain feedback stabilization of reaction–diffusion PDEs with Robin boundary conditions in the presence of an uncertain time- and spatially-varying delay in the distributed actuation. The proposed control design strategy consists of a constant-delay predictor feedback designed based on the known nominal value of the control input delay and is synthesized on a finite-dimensional truncated model capturing the unstable modes of the original infinite-dimensional system. By using a small-gain argument, we show that the resulting closed-loop system is exponentially stable provided that the variations of the delay around its nominal value are small enough. The proposed proof actually applies to any distributed-parameter system associated with an unbounded operator that 1) generates a -semigroup on a weighted space of square integrable functions over a compact interval; and 2) is self-adjoint with compact resolvent.
148Scopus© Citations 15 - PublicationAn Application of 3D Model Reconstruction and Augmented Reality for Real-Time Monitoring of Additive Manufacturing(Elsevier, 2019-06-14)
; ; ; ; This paper presents a novel scan-based method for the real-time monitoring of additive manufacturing processes. Most traditional scanning techniques used for generating 3D models capture the only outer shape of the object after completion of the printing process. The method proposed in this paper differs as it relies on a layer-by-layer scanning of the 3D object directly during the printing process. This strategy has been successfully implemented with a fused filament 3D printer (PRUSA i3 MK3). Furthermore, in order to offer an increased interaction between the obtained 3D model and the user, a virtual environment has been developed for the augmented reality glasses HoloLens. The novelty of this method lies in the layer-by-layer 3D model reconstruction of both the outer shape and the inner layers of the printed part. It enables the user, directly during the printing process, to view and detect potential defects, not only at the surface but also in the inner layers of the printed object. Therefore, it can provide detailed information about the build quality and can be used as the basis of a decision-making tool.115Scopus© Citations 33 - PublicationPI Regulation of a Reaction-Diffusion Equation with Delayed Boundary ControlThe general context of this work is the feedback control of an infinite-dimensional system so that the closed loop system satisfies a fading-memory property and achieves the setpoint tracking of a given reference signal. More specifically, this paper is concerned with the Proportional Integral (PI) regulation control of the left Neumann trace of a one dimensional reaction-diffusion equation with a delayed right Dirichlet boundary control. In this setting, the studied reaction diffusion equation might be either open-loop stable or unstable. The proposed control strategy goes as follows. First, a finite dimensional truncated model that captures the unstable dynamics of the original infinite-dimensional system is obtained via spectral decomposition. The truncated model is then augmented by an integral component on the tracking error of the left Neumann trace. After resorting to the Artstein transformation to handle the control input delay, the PI controller is designed by pole shifting. Stability of the resulting closed-loop infinite-dimensional system, consisting of the original reaction-diffusion equation with the PI controller, is then established thanks to an adequate Lyapunov function. In the case of a time-varying reference input and a time-varying distributed disturbance, our stability result takes the form of an exponential Input-to-State Stability (ISS) estimate with fading memory. Finally, another exponential ISS estimate with fading memory is established for the tracking performance of the reference signal by the system output. In particular, these results assess the setpoint regulation of the left Neumann trace in the presence of distributed perturbations that converge to a steady-state value and with a time-derivative that converges to zero. Numerical simulations are carried out to illustrate the efficiency of our control strategy.
348Scopus© Citations 25 - PublicationOn Design for Additive Manufacturing: Review of Challenges and Opportunities utilising Visualisation Technologies(IEEE, 2019-06-19)
; ; ; ; ; Design for additive manufacturing poses new challenges and opportunities for manufacturers to produce highly customised parts while reducing cost, production time and improving quality. Manufacturing constraints of conventional manufacturing methods, such as geometric complexity limitations and workpiece handling, have shaped the landscape of computer-aided design tools, which are therefore not suitably adapted to design for additive manufacturing. Furthermore, computer-aided design tools require a high level of training to produce appropriate models. Augmented reality and feedback technologies pose an interesting opportunity for design for additive manufacturing, whereby the interaction with 3D models in an augmented or virtual design space can provide intuitive feedback to engineers and designers, providing fast validation of designs, parametric modelling and opportunities for training and use in both professional and amateur designer communities. This paper will explore and review the opportunities this exciting new technology provides.323Scopus© Citations 7 - PublicationExponential input-to-state stabilization of a class of diagonal boundary control systems with delay boundary controlThis paper deals with the exponential input-to-state stabilization with respect to boundary disturbances of a class of diagonal infinite-dimensional systems via delay boundary control. The considered input delays are uncertain and time-varying. The proposed control strategy consists of a constant-delay predictor feedback controller designed on a truncated finite-dimensional model capturing the unstable modes of the original infinite-dimensional system. We show that the resulting closed-loop system is exponentially input-to-state stable with fading memory of both additive boundary input perturbations and disturbances in the computation of the predictor feedback.
306Scopus© Citations 11 - PublicationISS of a Clamped-Free Damped String for the Configurations Associated with the Loss of the Riesz-Spectral PropertiesThis paper deals with the Input-to-State Stability (ISS) of a clamped-free damped string with respect to boundary disturbances for the configurations associated with the loss of the Riesz-spectral properties. Specifically, for most of the values of the physical parameters (namely the stiffness parameter and the damping coefficient), the ISS property of the clamped free damped string can be established based on the fact that the underlying disturbance-free operator is a Riesz-spectral operator. However, such a Riesz-spectral property does not hold true for certain configurations of the physical parameters of the damped string. This paper specifically investigates the establishment of an ISS estimate for these configurations. The proposed strategy relies on the projection of the original system trajectories in a Riesz basis obtained by adequately completing the set of eigenvectors of the disturbance-free operator.
186 - PublicationOn the derivation of stability properties for time-delay systems without constraint on the time-derivative of the initial conditionStability of retarded differential equations is closely related to the existence of Lyapunov-Krasovskii functionals. Even if a number of converse results have been reported regarding the existence of such functionals, there is a lack of constructive methods for their selection. For certain classes of time-delay systems for which such constructive methods are lacking, it was shown that Lyapunov-Krasovskii functionals that are also allowed to depend on the time-derivative of the state-trajectory are efﬁcient tools for the study of the stability properties. However, in such an approach the initial condition needs to be assumed absolutely continuous with a square integrable weak derivative. In addition, the stability results hold for initial conditions that are evaluated based on the magnitude of both the initial condition and its time-derivative. The main objective of this paper is to show that, for certain classes of time-delay systems, the aforementioned stability results can actually be extended to initial conditions that are only assumed continuous and that are evaluated in uniform norm.
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