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-

Digital twins of rotary motion and cart-pendulum platforms for education in automatic control

[Abstract] Modern educational systems, similarly to Industry 4.0, are focusing their efforts to the development of new digital resources that allow to understand, simulate, predict, and optimize real systems through virtual replicas. In this sense, digital twins (DTs), which are high-fidelity virtual or digital representations of a physical product or process, are turning into a disruptive trend in the education sector and its influence is expected to be significant on future of many degrees, especially in engineering. This paper presents the DTs of three educational platforms which are widely used in automatic control for educative purposes: rotary motion equipment developed by Quanser, and a cart-pendulum platform developed by Feedback Instruments. The DTs have been built in the MATLAB®/Simulink© environment thanks to the physical modeling toolbox SimscapeTM through blocks contained in its libraries rather than using mathematical models. A set of possible control exercises that can be performed by students of automatic control courses are proposed, which are supported by the use of these educative resources.Junta de Extremadura; GR2116

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

Modeling of the human vestibular system and integration in a simulator for the study of orientation and balance control

[Abstract] Biologically, the vestibular feedback is critical to the ability of human body to balance in different conditions. This paper presents a human-inspired orientation and balance control of a three degree- of-freedom (DOF) simulator that emulates a person sitting in a platform. In accordance with the role in humans, the control is essentially based on the vestibular system (VS), which regulates and stabilizes gaze during head motion, by means of modeling the behavior of the semicircular canals and otoliths in the presence of stimuli, i.e., linear and angular accelerations/velocities derived by the turns experienced by the robot head on the three Cartesian axes. The semicircular canal is used as the angular velocity sensor to perform the postural control of the robot. Simulation results in the MATLAB/Simulink environment are given to show that the orientation of the head in space (roll, pitch and yaw) can be successfully controlled by a proportional-integral-derivative (PID) with noise filter for each DOF.[Resumen] Biológicamente, la retroalimentación vestibular es crítica para la capacidad del cuerpo humano para equilibrarse en diferentes condiciones. Este artículo presenta una orientación inspirada por el hombre y el control de equilibrio de un simulador de tres grados de libertad (DOF) que emula a una persona sentada en una plataforma. De acuerdo con el papel en los humanos, el control se basa esencialmente en el sistema vestibular (VS), que regula y estabiliza la mirada durante el movimiento de la cabeza, mediante el modelado del comportamiento de los canales semicirculares y los otolitos en presencia de estímulos, es decir, aceleraciones / velocidades lineales y angulares derivadas de los giros experimentados por la cabeza del robot en los tres ejes cartesianos. El canal semicircular se utiliza como sensor de velocidad angular para realizar el control postural del robot. Los resultados de la simulación en el entorno de MATLAB / Simulink se proporcionan para mostrar que la orientación de la cabeza en el espacio (balanceo, inclinación y guiñada) se puede controlar con éxito mediante un derivado proporcional-integral (PID) con filtro de ruido para cada DOF

Study in COMSOL of the generation of traveling waves in an AEF robot by piezoelectric actuation

[Abstract] This paper presents a study of motion of an artificial eukaryotic flagellum (AEF) microrobot in COMSOL Multiphysics®. The microrobot is essentially a body, consisting of an aluminum beam structure with two piezoelectric patches bonded on its surface. It requires the same voltage with different frequencies or phases be applied to each piezoelectric or use one of the piezoelectrics as absorber in order to generate a traveling wave on the body. Different types of actuation are simulated to demonstrate that a non-reciprocal motion can be obtained with this kind of configuration.[Abstract] Este artículo presenta un estudio del movimiento de un microrobot de eukaryotic flagellum (AEF) en COMSOL Multiphysics®. El microrobot es esencialmente un cuerpo, que consiste en una estructura de vigas de aluminio con dos parches piezoeléctricos adheridos en su superficie. Requiere que se aplique la misma tensión con diferentes frecuencias o fases a cada piezoeléctrico o use uno de los piezoeléctricos como absorbente para generar una onda viajera en el cuerpo. Se simulan diferentes tipos de actuación para demostrar que se puede obtener un movimiento no recíproco con este tipo de configuración.Ministerio de Economía y Competitividad; DPI2016-80547-