Now showing 1 - 10 of 15
  • Publication
    An LMI condition for the robustness of constant-delay linear predictor feedback with respect to uncertain time-varying input delays
    This paper discusses the robustness of the constant-delay predictor feedback in the case of an uncertain time-varying input delay. Specifically, we study the stability of the closed-loop system when the predictor feedback is designed based on the knowledge of the nominal value of the time-varying delay. By resorting to an adequate Lyapunov–Krasovskii functional, we derive an LMI-based sufficient condition ensuring the exponential stability of the closed-loop system for small enough variations of the time-varying delay around its nominal value. These results are extended to the feedback stabilization of a class of diagonal infinite-dimensional boundary control systems in the presence of a time-varying delay in the boundary control input.
    Scopus© Citations 33  159
  • Publication
    Boundary feedback stabilization of a reaction–diffusion equation with Robin boundary conditions and state-delay
    (Elsevier, 2020-06) ;
    This 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.
    Scopus© Citations 22  200
  • Publication
    Feedback Stabilization of a Class of Diagonal Infinite-Dimensional Systems With Delay Boundary Control
    (IEEE Transactions on Automatic Control, 2021-01) ;
    This article studies the boundary feedback stabilization of a class of diagonal infinite-dimensional boundary control systems. In the studied setting, the boundary control input is subject to a constant delay while the open-loop system might exhibit a finite number of unstable modes. The proposed control design strategy consists of two main steps. First, a finite-dimensional subsystem is obtained by truncation of the original infinitedimensional system (IDS) via modal decomposition. It includes the unstable components of the IDS and allows the design of a finite-dimensional delay controller by means of the Artstein transformation and the pole-shifting theorem. Second, it is shown via the selection of an adequate Lyapunov function that: 1) the finite-dimensional delay controller successfully stabilizes the original IDS and 2) the closed-loop system is exponentially input-to-state stable (ISS) with respect to distributed disturbances. Finally, the obtained ISS property is used to derive a small gain condition ensuring the stability of an IDS-ODE interconnection.
    Scopus© Citations 28  301
  • Publication
    An Application of 3D Model Reconstruction and Augmented Reality for Real-Time Monitoring of Additive Manufacturing
    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.
    Scopus© Citations 32  112
  • Publication
    Input-to-State Stability of a Clamped-Free Damped String in the Presence of Distributed and Boundary Disturbances
    This 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.
      289
  • Publication
    Control Law Realification for the Feedback Stabilization of a Class of Diagonal Infinite-Dimensional Systems With Delay Boundary Control
    Recently, a predictor feedback control strategy has been reported for the feedback stabilization of a class of infinite-dimensional Riesz-spectral boundary control systems exhibiting a finite number of unstable modes by means of a delay boundary control. Nevertheless, for real abstract boundary control systems exhibiting eigenstructures defined over the complex field, the direct application of such a control strategy requires the embedding of the control problem into a complexified state-space which yields a complex-valued control law. This letter discusses the realification of the control law, i.e., the modification of the design procedure for obtaining a real-valued control law for the original real abstract boundary control system. The obtained results are applied to the feedback stabilization of an unstable Euler-Bernoulli beam by means of a delay boundary control.
      156Scopus© Citations 9
  • Publication
    Exponential input-to-state stabilization of a class of diagonal boundary control systems with delay boundary control
    This 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.
    Scopus© Citations 11  304
  • Publication
    I-nteract: A Cyber-Physical System for Real-Time Interaction With Physical and Virtual Objects Using Mixed Reality Technologies for Additive Manufacturing
    This 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.
      269Scopus© Citations 11
  • Publication
    PI Regulation of a Reaction-Diffusion Equation with Delayed Boundary Control
    The 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.
    Scopus© Citations 24  346
  • Publication
    On the design of cyber-physical control system for a smart pedelec (Ebike)
    We present a cyber-physical control system for deployment on a smart pedelec (Ebike). The goal of the control is to manage the interaction between a human and a motor intervention, for applications in which we wish to control physical aspects of the cycling behaviour (e.g. heart rate and breathing rate). The basis of the control is a pitchfork bifurcation system, augmented using ideas from gain-scheduling. Experiments have been conducted, showing the validity of the proposed control strategy. A use case dealing with the regulation of human ventilation characteristics in response to exogenous pollution measurements is presented.
      231Scopus© Citations 8