Basic Properties and Stability of Fractional-Order Reset Control Systems

Reset control is introduced to overcome limitations of linear control. A reset controller includes a linear controller which resets some of states to zero when their input is zero or certain non-zero values. This paper studies the application of the fractional-order Clegg integrator (FCI) and compares its performance with both the commonly used first order reset element (FORE) and traditional Clegg integrator (CI). Moreover, stability of reset control systems is generalized for the fractional-order case. Two examples are given to illustrate the application of the stability theorem.Comment: The 12th European Control Conference (ECC13), Switzerland, 201

Fractional Order Hybrid Systems and Their Stability

This paper deals with hybrid systems (HS) with fractional order dynamics and their stability. The stability of two particular types of fractional order hybrid systems (FOHS), i.e., switching and reset control systems, is studied. Common Lyapunov method, as well as its frequency domain equivalence, are generalized for the former systems and, for the latter, H$_{\beta}$-condition is used --frequency domain equivalence of Lyapunov-like method for reset control systems. The applicability and efficiency of the proposed methods are shown by some illustrative examples.Comment: 14th International Carpathian Control Conference, Krak\'ow-Rytro, Poland, May 26-29, 2013. arXiv admin note: text overlap with arXiv:1303.530

Fractional calculus in economic growth modelling : the spanish and portuguese cases

This work presents a fractional order approach to model the growth of national economies, namely, their gross domestic products (GDPs). Land area, arable land, population, school attendance, gross capital formation, exports of goods and services, general government final consumption expenditure and money and quasi money are taken as variables to describe GDP. The particular cases of the national economies of Spain and Portugal are studied along the last five decades. Results show that fractional models have a better performance than the other alternatives considered in the literature.info:eu-repo/semantics/publishedVersio

Economic growth in the European Union modelled with fractional derivatives: first results

Este documento presenta modelos de crecimiento económico para todos los Estados de la Unión Europea (UE), ya sea desde 1970 o desde el año de su adhesión a la UE. Se obtienen modelos de orden entero y fraccionario, donde el producto interno bruto (PIB) está en función de la superficie del país, la formación bruta de capital (GCF), las exportaciones de bienes y servicios, y el promedio de años de asistencia a la escuela.This paper presents models of economic growth for all states of the European Union (EU), since either 1970 or the year of accession to the EU. Both integer and fractional order models are obtained, where the gross domestic product (GDP) is a function of the country’s land area, gross capital formation (GCF), exports of goods and services, and average years of school attendance.peerReviewe

Fractional order modelling of contact with the environment in flexible robot applications

[Abstract] The control of flexible robots that interact with the environment presents some difficulties because the mechanical environment is unknown. In this kind of applications, force robust control rather than position control is required. The purpose of this paper is to model the mechanical impedance of the environment contacted by a flexible link based on the well-known spring-damper system typically used in the literature, considering models of both integer and fractional order. In particular, four models are identified: 1) linear regression model, 2) spring-damper model, 3) spring-damper model that also includes a spring for the robotic arm, and 4) fractional order extension of spring-damper model. Experimental results (impacts with ten different objects) are given to identify the parameters of the considered models. The goodness of the adjustment is analyzed by a set of performance indices. The results show that fractional models may have better performance in comparison with classical alternatives proposed in the literature for the objects used in this study.[Resumen] El control de robots flexibles que interactúan con el entorno presenta algunas dificultades porque se desconoce el entorno mecánico. En este tipo de aplicaciones, se requiere un control robusto en lugar de un control de posición. El propósito de este trabajo es modelar la impedancia mecánica del entorno contactado por un enlace flexible basado en el conocido sistema de amortiguador de resortes que se usa típicamente en la literatura, considerando modelos de orden entero y fraccional. En particular, se identifican cuatro modelos: 1) modelo de regresión lineal, 2) modelo de amortiguador de resorte, 3) modelo de amortiguador de resorte que también incluye un resorte para el brazo robótico, y 4) extensión de orden fraccional del modelo de amortiguador de resorte. Se dan resultados experimentales (impactos con diez objetos diferentes) para identificar los parámetros de los modelos considerados. La bondad del ajuste se analiza mediante un conjunto de índices de rendimiento. Los resultados muestran que los modelos fraccionarios pueden tener un mejor rendimiento en comparación con las alternativas clásicas propuestas en la literatura para los objetos utilizados en este estudio.Ministerio de Economía y Competitividad; DPI2016-80547-

Creating auto-grading exercises with MATLAB Grader for automatic control courses

[Resumen] Recientemente, el desarrollo de recursos interactivos está recibiendo gran atención en titulaciones de ingeniería para apoyar la enseñanza, especialmente tras la pandemia derivada por el coronavirus. Entre estos recursos, los que tienen la capacidad de corrección y/o calificación automática son los preferidos tanto por los estudiantes como el profesorado. Asimismo, la implementación de una evaluación formativa eficaz es uno de los principales retos de los docentes para mejorar realmente el proceso de enseñanza aprendizaje. Este trabajo presenta un ejemplo de aplicación de MATLAB® Grader , una herramienta de autor basada en web que permite a los instructores proporcionar una evaluación automática de diferentes tipos de problemas de ingeniería, no solo los clásicos ejercicios de programación, y, en consecuencia, informar a los estudiantes sobre su rendimiento de una manera rápida y eficaz. En concreto, se presentan una serie de problemas de diseño clásicos de control automático con fines ilustrativos.[Abstract] Recently, the development of interactive resources is receiving great attention in engineering degrees to support teaching, especially after coronavirus pandemic. Among such resources, those that have the ability of automatic correction and/or grading are preferred for both students and faculty. Likewise, the implementation of an e ective formative assessment is one of the main challenges for academy in order to actually improve the teaching-learning process. This paper presents an example of application of MATLAB® Grader , a web-based authoring tool that allows instructors to provide automatic evaluation of di erent kinds of engineering problems, not only classic coding exercises, and, consequently, inform students about their performance in a quick and e ective manner. Specifically, a series of classical design problems of automatic control are given for illustrative purposes