156 research outputs found
Control and State Estimation of the One-Phase Stefan Problem via Backstepping Design
This paper develops a control and estimation design for the one-phase Stefan
problem. The Stefan problem represents a liquid-solid phase transition as time
evolution of a temperature profile in a liquid-solid material and its moving
interface. This physical process is mathematically formulated as a diffusion
partial differential equation (PDE) evolving on a time-varying spatial domain
described by an ordinary differential equation (ODE). The state-dependency of
the moving interface makes the coupled PDE-ODE system a nonlinear and
challenging problem. We propose a full-state feedback control law, an observer
design, and the associated output-feedback control law via the backstepping
method. The designed observer allows estimation of the temperature profile
based on the available measurement of solid phase length. The associated
output-feedback controller ensures the global exponential stability of the
estimation errors, the H1- norm of the distributed temperature, and the moving
interface to the desired setpoint under some explicitly given restrictions on
the setpoint and observer gain. The exponential stability results are
established considering Neumann and Dirichlet boundary actuations.Comment: 16 pages, 11 figures, submitted to IEEE Transactions on Automatic
Contro
Robust Compensation of Delay and Diffusive Actuator Dynamics Without Distributed Feedback
[EN] This paper deals with robust observer-based output-feedback stabilization of systems whose actuator dynamics can be described in terms of partial differential equations (PDEs). More specifically, delay dynamics (first-order hyperbolic PDE) and diffusive dynamics (parabolic PDE) are considered. The proposed controllers have a PDE observer-based structure. The main novelty is that stabilization for an arbitrarily large delay or diffusion domain length is achieved, while distributed integral terms in the control law are avoided. The exponential stability of the closed loop in both cases is proved using Lyapunov functionals, even in the presence of small uncertainties in the time delay or the diffusion coefficient. The feasibility of this approach is illustrated in simulations using a second-order plant with an exponentially unstable mode.This work was supported in part by Project TIN2017-86520-C3-1-R, Ministerio de Economia y Competitividad, in part by the 16/17 UPV Mobility Award, and in part by the FPI-UPV 2014 Ph.D. Grant, Universitat Politecnica de Valencia, Spain.Sanz Diaz, R.; GarcĂa Gil, PJ.; Krstic, M. (2019). Robust Compensation of Delay and Diffusive Actuator Dynamics Without Distributed Feedback. IEEE Transactions on Automatic Control. 64(9):3663-3675. https://doi.org/10.1109/TAC.2018.2887148S3663367564
Stability analysis of a singularly perturbed coupled ODE-PDE system
International audienceThis paper is concerned with a coupled ODE-PDE system with two time scales modeled by a perturbation parameter. Firstly, the perturbation parameter is introduced into the PDE system. We show that the stability of the full system is guaranteed by the stability of the reduced and the boundary-layer subsystems. A numerical simulation on a gas flow transport model is used to illustrate the first result. Secondly, an example is used to show that the full system can be unstable even though both subsystems are stable when the perturbation parameter is introduced into the ODE system
Adaptive compensation of diffusion-advection actuator dynamics using boundary measurements
International audience— For (potentially unstable) Ordinary Differential Equation (ODE) systems with actuator delay, delay compensation can be obtained with a prediction-based control law. In this paper, we consider another class of PDE-ODE cascade, in which the Partial Differential Equation (PDE) accounts for diffusive effects. We investigate compensation of both convec-tion and diffusion and extend a previously proposed control design to handle both uncertainty in the ODE parameters and boundary measurements. Robustness to small perturbations in the diffusion and convection coefficients is also proved
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