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This paper presents a systematic approach to modeling electrical circuits using state-space techniques. It outlines the method for deriving transfer functions from input to output and demonstrates the process with an example circuit involving resistors, capacitors, and inductors. By reformulating circuit equations into matrix form, the paper illustrates how to represent circuit dynamics succinctly, providing insights into the energy states within the system.
The performances of a transfer function characteristic of RLC-circuit is investigated and modeled in this paper. The ever increasing demand for electronics has led to the continuous search for the most readily available means of providing better performance of the system. The method of analyzing RLC circuit is never constant and since the resistor (R), inductor (L), and the capacitor (C) are use in every electronic system, a proper understanding of system is necessary to know what happen to system when any of parameter is alter. The design methodology employed in this work involves: the modeling of the equation of the RLC circuit, developing appropriate algorithms to imitate the real life behavior of an RLC circuit, Appling matlab codes in the m-file and carrying out analysis of the designed RLC circuit in the Matlab GUI. Result obtained showed good proper behavior of the system when the input parameters were varied.
IEEE Control Systems Magazine, 1995
he problem of computing the closed T loop transfer function of a linear system represented by its block diagram or by its flow graph is of importance in CAD programs designed for the analysis of linear systems. Mason's rule [ 11 is one of the available techniques to perform such calculations, but it requires searching into the graph for different paths and loops and becomes slow as system complexity increases. In this paper, a method is developed to efficiently compute the closed loop transfer function and intermediate transfer functions of a linear system.
Mathematical and Computational Applications
The RLC circuit is a basic building block of the more complicated electrical circuits and networks. The present study introduces a novel and simple numerical method for the solution this problem in terms of Taylor polynomials in the matrix form. Particular and general solutions of the related differential equation can be determined by this method. The method is illustrated by a numerical application and a quite good agreement is observed between the results of the present method and those of the exact method.
Asian journal of applied science and technology, 2022
Example: Suppose a linear system is represented by the differential equation d 2 y dt 2 + a 1 dy dt + a 0 y = u s 2 Y (s) + a 1 sY (s) + a 0 Y (s) = U (s). Taking Laplace Transforms with zero initial conditions, (s 2 + a 1 s + a 0)Y (s) = U (s) we see that the transfer function is G(s) = Y (s) U (s) = 1 s 2 + a 1 s + a 0. Remarks: – The transfer function is always computed with all initial conditions equal to zero. – The transfer function is the Laplace Transform of the impulse response function. [To see this, set U (s) = 1.] The transfer function of any linear system is a rational function G(s) = n(s) d(s) = b m s m + · · · + b 1 s + b 0 a n s n + · · · + a 1 s + a 0 where n(s), d(s) are the numerator and denominator polynomials of G(s), respectively – G(s) is proper if m = deg n(s) ≤ n = deg d(s) – G(s) is strictly proper if m < n. – For a proper or strictly proper rational function, the difference α = n − m is called the relative degree of the transfer function.
BIBECHANA, 2021
The time varying currents and voltages resulting from the sudden application of sources usually due to switching are transients. An RLC circuit is an electrical circuit consisting of a resistor, an inductor, and a capacitor, connected in series or in parallel. The transient response is dependent on the value of the different characteristics of damping factor (i.e., over damped, critically damped and under damped). We have computed the numerical solutions of second order differential equation with initial value problem (IVP) by using Explicit (Forward) Euler method, Third order Runge-Kutta (RK3) methods and Butchers fifth order Runge-Kutta (BRK5). The observation compares this numerical solution of ODEs obtained by above-mentioned methods among them with necessary visualization and analysis of the error. These iterative methods will be extended and implement to analyze the transient analysis of an RLC circuit. We have examined the superiority of those methods over one another. The B...
IEEE Transactions on Power Systems, 2011
This paper compares the computational performances of four model order reduction methods applied to large-scale electric power RLC networks transfer functions with many resonant peaks. Two of these methods require the state-space or descriptor model of the system, while the third requires only its frequency response data. The fourth method is proposed in this paper, being a combination of two of the previous methods. The methods were assessed for their ability to reduce eight test systems, either of the single-input single-output (SISO) or multiple-input multiple-output (MIMO) type. The results indicate that the reduced models obtained, of much smaller dimension, reproduce the dynamic behaviors of the original test systems over an ample range of frequencies with high accuracy.
Applied Mathematical Sciences, 2013
This paper presents a new algorithm for computing the transfer function from state equations for linear system. This algorithm employs an approximation method, which uses Krylov subspace techniques for linear system. We have focused on the Lanczos-based using the properties of Schur complemnts. This approach reduces the computation of transfer function from state equation for linear system.
SPIE Proceedings, 2015
This paper presents a new method, called the transfer matrix method for obtaining transfer functions among the state variables of a linear time-invariant (LTI) system defined in either a block diagram or the corresponding signal flow graph. The procedures introduced in this paper for obtaining the transfer function require only knowledge on matrix operations, which are easy to explain and remember. Advanced control engineers can automate the symbolic matrix operation by using existing software such as Mathematica.
WSEAS Transactions on Circuits and Systems
− Nowadays, there are lots of classic and alternative method that has been used to obtain and compute transfer function for a linear network. Although, problems still occur especially in the number of nodes, loops and simultaneous equations that need to be solved by this approaches. A proposed approach called NIRE (Network-Impedance Relationship Equation) will solve these problems by developing fixed equations for obtaining transfer function, rather than to extract its nodes, loops or simultaneous equations of its network. In this approach, the only required parameters are the network's impedance connections which will be taken from two sources which are from the input terminal and output impedance. The approach has been developed in an algorithm using software called MATLAB. It can be adapted in a computerbased application and also can be introduced as an alternative method in obtaining transfer function for educational purpose.
2013 36th International Convention on Information and Communication Technology, Electronics and Microelectronics (MIPRO), 2013
This paper describes a procedure for identifying the transfer function parameters by using Matlab's System Identification Toolbox (SIT). The procedure is explained for obtaining numerical data using a digital oscilloscope in a format suitable for loading the data into Matlab and processing within the SIT. The measured data series connected RLC circuits were analyzed. Also, using the speed response of separately excited DC motor with and without smoothing coil was measured, and transfer functions were obtained.
ATBU Journal of Science, Technology and Education, 2016
Abstract: The aim of this paper is to develop a systemic methodology for second order circuits by switched DC sources. The paper presents a unified approach through Matlab/Simulink to determining the transient response of linear RC, RL and RLC circuits; and although the methods presented in the chapter focus only on first and second order circuits, the approach to the transient solution is quite general. Practical applications of the second order circuits are presented and analogies are introduced to emphasize the general nature of the solution methods and their applicability to a wide range of physical systems. Key Words: RC, RL and RLC circuits , Second Order System, Overdamped System, Critically damped System, Underdamped System
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.
Scientific computing in electrical …, 2007
Applied Mathematics and Computation, 2007
Today, the transfer function between any two nodes of any linear flowgram are obtained either by applying the step-bystep classical elimination of nodes and branches or by applying the Mason's rules, both of them being manual, tedious in many cases procedures and therefore prone to human errors. In this paper we facilitate the derivation of the transfer function in two different ways. The first one consists on reducing, when it were possible, the flowgram obtaining, manually, a simpler but equivalent subflowgram to which we apply the above mentioned procedures. Thus the time elapsed in the process as well as the probability of mistakes commission diminishes. The second way consists in deriving the transfer function using a user friendly software developed by us in this paper and that apply in an automatic form the Mason's rules to the flowgram under study to derive any of the possible transfer function without errors and in a very short process time. In each case, the software works on the equivalent subflowgram obtained during the computer process in the same form as it is manually obtained. Finally, we apply the tool here presented to some examples of biological systems.
MATLAB Applications for the Practical Engineer, 2014
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