Modeling of Control Systems (original) (raw)
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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.
ECE 231 - Circuits and Systems I
2018
Course Catalog Description (including prerequisites and co-requisites): A first course in circuits and systems, covering the basic concepts of electric circuit theory. Topics include basic circuit elements, loop and node analysis, network theorems, sinusoidal steady-state analysis, power, resonance, mutual inductance, and ideal transformers.
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.
Mathematical models of control systems are mathematical expressions which describe the relationships among system inputs, outputs and other inner variables. Establishing the mathematical model describing the control system is the foundation for analysis and design of control systems. Systems can be described by differential equations including mechanical systems, electrical systems, thermodynamic systems, hydraulic systems or chemical systems etc. The response to the input (the output of the system) can be obtained by solving the differential equations, and then the characteristic of the system can be analyzed. The mathematical model should reflect the dynamics of a control system and be suitable for analysis of the system. Thus, when we construct the model, we should simplify the problem to obtain the approximate model which satisfies the requirements of accuracy. Mathematical models of control systems can be established by theoretical analysis or practical experiments. The theoretical analysis method is to analyze the system according to physics or chemistry rules (such as Kirchhoff's voltage laws for electrical systems, Newton's laws for mechanical systems and Law of Thermodynamics). The experimental method is to approximate the system by the mathematical model according to the outputs of certain test input signals, which is also called system identification. System identification has been developed into an independent subject. In this chapter, the theoretical analysis method is mainly used to establish the mathematical models of control system. There are a number of forms for mathematical models, for example, the differential equations, difference equations and state equations in time domain, the transfer functions and block diagram models in the complex domain, and the frequency characteristics in the frequency domain. In this chapter, we shall study the differential equation, transfer function and block diagram formulations.
ECE 232 - Circuits and Systems II
2018
Course Catalog Description (including prerequisites and co-requisites): A continuation of circuits and systems with special emphasis on transient response. Topics include Laplace transform analysis, transfer functions, convolution, Bode diagrams, and Fourier series. Prerequisites: ECE 231. Co-requisite: Math 222.
Electrical Engineering Formulas
, teaches graduate and under graduate courses in electrical engineering in the fields of circuits and control systems. He earned a Ph.D. in electrical engineering from the U.S. Naval Postgraduate School, an M.S. from the University of Colorado, and a B.S. from Clarkson University. Highly concerned with the discipline of electrical engineering and its wide value to social and economic needs, he has written and lectured internationally on the contributions and advances in electrical engineering.