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Delay-Based Controllers Design for Dynamical Systems

Abstract : This thesis studies the use of delay-based controllers for dynamical systems. Applications, experimentation, and theoretical problematics are addressed. The main focus of the study is the conception of delay-based controllers inspired by the well-known PID controllers. Also, and equally important, we study the design of such controllers. More precisely, we develop methods to find the proper choice of the controller's parameters assuring stability for different types of controllers. To this end, the thesis embraces the use of linear differential models and analysis due to its elegant frequency-based interpretation. In this regard, the stability properties of these systems are governed by their characteristic equation, which for time-delay systems are the so-called quasi-polynomials or polynomials with constant coefficients. Thus, this thesis studies the behavior of the roots of these functions with respect to variations of their parameters (coefficients and time delay values) through well-known roots crossing stability. Numeric methods and analytical observations are developed in this sense. In particular, we study applications, dc/dc converters, the Furuta pendulum, haptic devices, and the MPPT-PV (maximum power point tracking - photovoltaic) problem. Through the use of the proportional-delayed, proportional-delay-based derivative, proportional-delayed integral, and proportional-delayed-integral controllers. Also, we propose a solution to the classical delay-based control problem of stabilizing a chain of any number of oscillators by applying a single delay block.
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Submitted on : Wednesday, June 23, 2021 - 6:03:22 PM
Last modification on : Friday, June 25, 2021 - 3:34:35 AM


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  • HAL Id : tel-03269160, version 1


José-Enrique Hernández-Díez. Delay-Based Controllers Design for Dynamical Systems. Optimization and Control [math.OC]. Université Paris-Saclay; Universidad Autónoma de San Luis Potosí, 2021. English. ⟨NNT : 2021UPASG018⟩. ⟨tel-03269160⟩



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