Modeling of Control Systems (original) (raw)
CONSTRUCTION OF AN RL CIRCUIT, MODELING THE GOVERNING DIFFERENTIAL EQUATION AND COMPARISON BETWEEN THE ANALYTICAL SOLUTION AND EXPERIMENTAL DATA (Atena Editora), 2024
This article proposes the modeling of the ordinary differential equation referring to a resistor-inductor (RL) electrical circuit, obtaining the analytical solution and comparison with experimental data (charge and electrical current) obtained from an electrical circuit that It was built with recyclable materials. This practical approach aims to sharpen the student's interest in the discipline and the undergraduate course, offering them another incentive for your stay at the university. As in other disciplines, teaching the theory of ordinary differential equations (ODE) can be associated with practical experiments, allowing the connection between theory and practice, providing opportunities for efficient learning of the content covered and the perception of how mathematics is embedded in various events around us. Furthermore, mathematical modeling is an interesting, powerful and enlightening artifice, as it allows a better visualization of the laws and properties that govern the studied event. Following this path, this work contemplates the modeling of the ordinary differential equation that governs the movement of charge and current in an RL electrical circuit, its analytical resolution and the comparison between the analytical results and experimental data obtained from the electrical circuit. This way, Kirchoff's second law and concepts from the theory of electricity were used to model the ordinary differential equation that governs the RL circuit. The analytical solution of this problem was obtained by the integrating factor method, as the ordinary differential equation governing the electrical circuit has the characteristics of being linear and first order. The construction of a circuit was carried out using recyclable materials that can be found in homes, schools, universities or in places that receive electronic waste. The construction of the circuit made it possible to obtain experimental data (charge and electric current), which were measured using a multimeter. Subsequently, these data were compared with those obtained by the analytical solution. The relative error obtained shows the compatibility between the data obtained by the experiment and the analytical solution. The objective of this work is to bridge the gap between theory and practice. This way, the text has a practical educational teaching and learning nature, bringing to the public the importance of associating concepts and properties with problem solving.
Electrical Circuit Theory and Technology
'Electrical Circuit Theory and Technology, Revised second Edition' provides coverage for a wide range of courses that contain electrical principles, circuit theory and technology in their syllabuses, from introductory to degree level. The chapter 'Transients and Laplace transforms', which had been removed from the second edition due to page restraints, has been included in this edition in response to popular demand. The text is set out in four parts as follows: PART 1, involving chapters 1 to 12, contains 'Basic Electrical Engineering Principles' which any student wishing to progress in electrical engineering would need to know. An introduction to electrical circuits, resistance variation, chemical effects of electricity, series and parallel circuits, capacitors and capacitance, magnetic circuits, electromagnetism, electromagnetic induction, electrical measuring instruments and measurements, semiconductor diodes and transistors are all included in this section. PART 2, involving chapters 13 to 22, contains 'Electrical Principles and Technology' suitable for Advanced GNVQ, National Certificate, National Diploma and City and Guilds courses in electrical and electronic engineering. D.c. circuit theory, alternating voltages and currents, single-phase series and parallel circuits, d.c. transients, operational amplifiers, three-phase systems, transformers, d.c. machines and threephase induction motors are all included in this section. PART 3, involving chapters 23 to 45, contains 'Advanced Circuit Theory and Technology' suitable for Degree, Higher National Certificate/Diploma and City and Guilds courses in electrical and electronic/telecommunications engineering. The two earlier sections of the book will provide a valuable reference/revision for students at this level. Complex numbers and their application to series and parallel networks, power in a.c. circuits, a.c. bridges, series and parallel resonance and Q-factor, network analysis involving Kirchhoff's laws, mesh and nodal analysis, the superposition theorem, Thévenin's and Norton's theorems, delta-star and star-delta transforms, maximum power transfer theorems and impedance matching, complex waveforms, harmonic analysis, magnetic materials, dielectrics and dielectric loss, field theory, attenuators, filter networks, magnetically coupled circuits, transmission line theory and transients and Laplace transforms are all included in this section. PART 4 provides a short, 'General Reference' for standard electrical quantities -their symbols and units, the Greek alphabet, common prefixes and resistor colour coding and ohmic values. At the beginning of each of the 45 chapters learning objectives are listed. At the end of each of the first three parts of the text is a handy reference of the main formulae used. xviii Electrical Circuit Theory and Technology It is not possible to acquire a thorough understanding of electrical principles, circuit theory and technology without working through a large number of numerical problems. It is for this reason that 'Electrical Circuit Theory and Technology, Revised second Edition' contains some 740 detailed worked problems, together with over 1100 further problems, all with answers in brackets immediately following each question. Over 1100 line diagrams further enhance the understanding of the theory. Fourteen Assignments have been included, interspersed within the text every few chapters. For example, Assignment 1 tests understanding of chapters 1 to 4, Assignment 2 tests understanding of chapters 5 to 7, Assignment 3 tests understanding of chapters 8 to 12, and so on. These Assignments do not have answers given since it is envisaged that lecturers could set the Assignments for students to attempt as part of their course structure. Lecturers' may obtain a complimentary set of solutions of the Assignments in an Instructor's Manual available from the publishers via the internet -see below. 'Learning by Example' is at the heart of 'Electrical Circuit Theory and Technology, Revised second Edition'.
Circuits, Systems and Signal Processing
2018
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Introduction to Electric Circuits
This book covers the material normally found in first and second year syllabuses on the topic of electric circuits. It is intended for use by degree and diploma students in electrical and electronic engineering and in the associated areas of integrated, manufacturing and mechanical engineering. The two most important areas of study for all electrical and electronic engineering students are those of circuit theory and electromagnetic field theory. These lay the foundation for the understanding of the rest of the subjects which make up a coherent course and they are intimately related. Texts on one of them invariably and inevitably have references to the other. In Chapter 2 of this book the ingredients of electric circuits are introduced and the circuit elements having properties called capacitance and inductance are associated with electric and magnetic fields respectively. Faraday's law is important in the concept of mutual inductance and its effects. Reference is made, therefore, to electromagnetic field theory on a need to know basis, some formulae being presented without proof. The level of mathematics required here has been kept to a realistic minimum. Some facility with algebra (transposition of formulae) and knowledge of basic trigonometry and elementary differentiation and integration is assumed. I have included well over a hundred worked examples within the text and a similar number of problems with answers. At the end of each chapter there is a series of self-assessment test questions. Ray Powell Nottingham, November 1994 This Page Intentionally Left Blank This Page Intentionally Left Blank 6 Check the validity of the statement that the volt per metre is equivalent to the newton per coulomb.
Circuit Analysis I with MATLAB® Applications
This text includes the following chapters and appendices: • Basic Concepts and Definitions • Analysis of Simple Circuits • Nodal and Mesh Equations - Circuit Theorems • Introduction to Operational Amplifiers • Inductance and Capacitance • Sinusoidal Circuit Analysis • Phasor Circuit Analysis • Average and RMS Values, Complex Power, and Instruments • Natural Response • Forced and Total Response in RL and RC Circuits • Introduction to MATLAB • Review of Complex Numbers • Matrices and Determinants Each chapter contains numerous practical applications supplemented with detailed instructions for using MATLAB to obtain quick and accurate answers.