arXiv subjects

Jesus-Pablo Toledo-Zucco

Publications and source records attributed to Jesus-Pablo Toledo-Zucco.

5 recordsLinked to original sources

arXiv2025

Reduced-order Smith predictor for state feedback control with guaranteed stability

This article deals with the implementation of the Smith Predictor for state feedback control in state space representation. The desired control law, obtained using partial differential equations and backstepping control, contains an integral term that has to be approximated for implementation. In this article, we propose a new way to implement this control law using a dynamic controller. The control law is composed of a state feedback term and a dynamic term that approaches the integral term that has to be estimated for implementation. Using a Lyapunov functional, we provide sufficient conditions, in terms of a linear matrix inequality, to guarantee that the closed-loop system is stable when the proposed control law is applied. We use three examples, taken from the literature, to show the benefits of the proposed approach.

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arXiv2024

Turbidity Control in Sedimentation Columns by Direction Dependent Models

Sedimentation is a crucial phenomenon in recovering water from slurries by separating solid-liquid. Thickeners and sedimentation columns are equipments widely used in the process industry to reclaim water from process slurries. This contribution addresses the problem of controlling the turbidity of the recovered water in a sedimentation column by manipulating the underflow. The phenomenological model describing the turbidity is too complex to be used in a control strategy, and it is difficult to identify its parameters using plant measurements. This work proposes an empirical piece-wise time-delay model for modeling the turbidity at the top of the column to circumvent these problems. A systematic design procedure is developed to tune a Proportional Integral controller guaranteeing closed-loop stability for systems modeled as a piece-wise time delay model. Experiments in a pilot plant validate the theoretical results and illustrate the control performance under various operational scenarios.

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arXiv2024

Structure-Preserving Discretization and Model Order Reduction of Boundary-Controlled 1D Port-Hamiltonian Systems

This paper presents a systematic methodology for the discretization and reduction of a class of one-dimensional Partial Differential Equations (PDEs) with inputs and outputs collocated at the spatial boundaries. The class of system that we consider is known as Boundary-Controlled Port-Hamiltonian Systems (BC-PHSs) and covers a wide class of Hyperbolic PDEs with a large type of boundary inputs and outputs. This is, for instance, the case of waves and beams with Neumann, Dirichlet, or mixed boundary conditions. Based on a Partitioned Finite Element Method (PFEM), we develop a numerical scheme for the structure-preserving spatial discretization for the class of one-dimensional BC-PHSs. We show that if the initial PDE is passive (or impedance energy preserving), the discretized model also is. In addition and since the discretized model or Full Order Model (FOM) can be of large dimension, we recall the standard Loewner framework for the Model Order Reduction (MOR) using frequency domain interpolation. We recall the main steps to produce a Reduced Order Model (ROM) that approaches the FOM in a given range of frequencies. We summarize the steps to follow in order to obtain a ROM that preserves the passive structure as well. Finally, we provide a constructive way to build a projector that allows to recover the physical meaning of the state variables from the ROM to the FOM. We use the one-dimensional wave equation and the Timoshenko beam as examples to show the versatility of the proposed approach.

math.NA↗

arXiv2024

Scattering-Passive Structure-Preserving Finite Element Method for the Boundary Controlled Transport Equation with a Moving Mesh

A structure-preserving Finite Element Method (FEM) for the transport equation in one- and two-dimensional domains is presented. This Distributed Parameter System (DPS) has non-collocated boundary control and observation, and reveals a scattering-energy preserving structure. We show that the discretized model preserves the aforementioned structure from the original infinite-dimensional system. Moreover, we analyse the case of moving meshes for the one-dimensional case. The moving mesh requires less states than the fixed one to produce solutions with a comparable accuracy, and it can also reduce the overshoot and oscillations of Gibbs phenomenon produced when using the FEM. Numerical simulations are provided for the case of a one-dimensional transport equation with fixed and moving meshes.

math.NA↗

arXiv2023

Infinite-dimensional observers for high order boundary-controlled port-Hamiltonian systems

This letter investigates the design of a class of infinite-dimensional observers for one dimensional (1D) boundary controlled port-Hamiltonian systems (BC-PHS) defined by differential operators of order $N \geq 1$. The convergence of the proposed observer depends on the number and location of available boundary measurements. \textcolor{hector}{Asymptotic convergence is assured for $N\geq 1$, and provided that enough boundary measurements are available, exponential convergence can be assured for the cases $N=1$ and $N=2$.} Furthermore, in the case of partitioned BC-PHS with $N=2$, such as the Euler-Bernoulli beam, \textcolor{hector}{it is shown} that exponential convergence can be assured considering less available measurements. The Euler-Bernoulli beam model is used to illustrate the design of the proposed observers and to perform numerical simulations.

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