# Fundamentals Of MATLAB

# Fundamentals Of MATLAB

**- Publisher:**Sanguine Publications

**- ISBN:**9789383506248

**- Author:**Dr. A S Aravinda Murthy

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Preface MATLAB is a software tool considered as the abbreviation of MATrix LABoratory whereas Electrical Engineering EE is a speci c branch of engineering. When the context is the study of electrical engineering, a noteworthy feature is that the paradigm of study has qualitative aspects conveying the concepts through fundamental principles and postulates which are well supported by analytical and graphical investigation. The nature of MATLAB with its immense graphics, computational and presentation capabilities along with simulation and animation options makes it a perfect match as a useful tool for carrying out such analytical and graphical investigation. Chronologically, long hand calculation was followed by slide rule which in due course was replaced by pocket calculators. The advent of digital computers and development of programming languages changed the computational capabilities tremendously. Among such software tools, MATLAB suits nicely for use in the eld of Electrical Engineering. The study of an EE system broadly has a de nite pattern - the physical features of the system and the basic principle of operation followed by a detailed analysis. In this context an EE system may be associated with a set of parameters, input variables and output variables. Parameters are generally those which are xed depending upon the physical properties and attributes of the system. Response produced in the system when an input is given and the input itself are together called the system variables. A system can be a multiple input multiple output MIMO system too. A speci c variable in the generated response is designated as the output variable. For example, in as simple an example as an electric iron box, the resistance of the coil, weight of the box are parameters while the input voltage and frequency are the input variables and the heat generated is the output variable. In an electric motor, electromagnetic torque is produced on the rotating member as well as heat in the iron and copper parts of the motor. But, the torque is designated as the output and the heat,as loss . System analysis can be summarised as studying the behaviour of the system by observing the manner of variation of the output variables for changes in the in-

iv put variables and or the system parameters. During this process, the mathematical modelling of the system is formed which may be a differential equation, algebraic equation, linear equation, non linear equation, multiple equations expressed in a matrix form in all of which there is a relationship between the input variables and or their derivatives , output variables and or their derivatives and the parameters. The mathematical analysis of an electrical system is generally preceded by its circuit model. In fact formulating an appropriate circuit model be tting a required analysis is a key feature of studying an electrical system. The circuit model is usually made up of a combination of linear, lumped, nite, passive, bilateral elements, dependant and or independant voltage and or current sources. It is possible that the circuit represents an analogous circuit of a non electrical system or an electromechanical system in which case evaluation of the electrical variable directly evaluates the analogous non electrical variable. For example, an induction motor, an electromechanical device, has an electrical equivalent circuit. The mechanical power developed is associated with the power consumed by a resistor in the circuit model. In general, performance equations are obtained for the circuit using basic circuit principles. These equations may be algebraic or integrodifferential in nature, linear or non linear. The solution for a particular set of independant variables enable the determination of the dependant variables. The solution may some times require an iterative computation as in a major topic of study Load Flow Analysis . The result may be required for a range of input - for example in another major topic of study - Stabilty Analysis , the variation of a variable called the power angle is studied over a range of input time interval. Depending upon the size and number of variables, the mathematical modelling may require matrix representation requiring matrix algebra for computation. Some times a graphical presentation of the result may be preferable to a tabular form. In general, the study of a given system requires a unique mathematical method of analysis as applicable to a speci c context. In this background, MATLAB is an appropriate software tool for evaluation and presentation of the results.