cdgi 406 simulation lab 4manual 406 sem 406

EXPERIMENT:2 EVALUATION OF TRANSMISSION LINE PARAMETERS

ELECTRICAL AND ELECTRONICSENGINEERING LABORATORY

EX -406

Electrical Engineering Simulation Lab-1 -

CHAMELIDEVI SCHOOL OF ENGINEERING,CHAMELIDEVI GROUP OF INSTITUTIONS,INDOREFourth SEMESTEREX-406Electrical Engineering Simulation Lab-1 List of Experiments

1. INTRODUCTION TO MODELLING AND SIMULATION2. INTRODUCTION TO MATLAB.3. GENERATION OF BASIC SIGNALS ON MATLAB.4. PLOT A SINUSOIDAL WAVEFORM(1 PEAK & 1 RAD/SEC), DIFFERENTIATE IT & OBSERVE BOTH THE WAVEFORM ON SCOPE5. USE SIMULINK TO SOLVE THE FOLLOWING DIFFERENTIAL EQUATION.6. DEVELOP A SIMULINK MODEL TO GENERATE SINE & COSINE WAVEFORM OF MAGNITUDE 5 AND FREQUENCY 50 HZ USING SINE & COSINE TRIGONOMETRIC FUNCTION7. INTRODUCTION TO SIMULINK & STUDY OF VARIOUS BLOCKSETS

INDEX

Sl. No.Expt. No.Name of the ExperimentDate ofConductionDate ofSubmissionSignatureof Staff

Experiment 1

AIM: Introduction to Modelling and Simulation

WHAT IS MODELING?

Modeling is the process of producing a model; a model is a representation of the construction and working of some system of interest. One purpose of a model is to enable the analyst to predict the effect of changes to the system. On the one hand, a model should be a close approximation to the real system and incorporate most of its salient features. On the other hand, it should not be so complex that it is impossible to understand and experiment with it. A good model is a judicious tradeoff between realism and simplicity. Simulation practitioners recommend increasing the complexity of a model iteratively. An important issue in modeling is model validity. Model validation techniques include simulating the model under known input conditions and comparing model output with system output. Generally, a model intended for a simulation study is a mathematical model developed with the help of simulation software. Mathematical model classifications include deterministic (input and output variables are fixed values) or stochastic (at least one of the input or output variables is probabilistic); static (time is not taken into account) or dynamic (time-varying interactions among variables are taken into account). Typically, simulation models are stochastic and dynamic.

WHAT IS SIMULATION? A simulation of a system is the operation of a model of the system. The model can be reconfigured and experimented with; usually, this is impossible, too expensive or impractical to do in the system it represents. The operation of the model can be studied, and hence, properties concerning the behavior of the actual system or its subsystem can be inferred. In its broadest sense, simulation is a tool to evaluate the performance of a system, existing or proposed, under different configurations of interest and over long periods of real time. Simulation is used before an existing system is altered or a new system built, to reduce the chances of failure to meet specifications, to eliminate unforeseen bottlenecks, to prevent under or over-utilization of resources, and to optimize system performance. Figure 1 is a schematic of a simulation study. The iterative nature of the process is indicated by the system under study becoming the altered system which then becomes the system under study and the cycle repeats. In a simulation study, human decision making is required at all stages, namely, model development, experiment design, output analysis, conclusion formulation, and making decisions to alter the system under study. The only stage where human intervention is not required is the running of the simulations, which most simulation software packages perform efficiently. The important point is that powerful simulation software is merely a hygiene factor - its absence can hurt a simulation study but its presence will not ensure success. Experienced problem formulators and simulation modelers and analysts are indispensable for a successful simulation study.

STEPS INVOLVED IN SIMULATION AND MODELING

Modeling The steps involved in developing a simulation model, designing a simulation experiment, and performing simulation analysis are: Step 1. Identify the problem. Step 2. Formulate the problem. Step 3. Collect and process real system data. Step 4. Formulate and develop a model. Step 5. Validate the model. Step 6. Document model for future use. Step 7. Select appropriate experimental design. Step 8. Establish experimental conditions for runs. Step 9. Perform simulation runs. Step 10. Interpret and present results. Step 11. Recommend further course of action

HOW TO DEVELOP A SIMULATION MODEL? Simulation models consist of the following components: system entities, input variables, performance measures, and functional relationships. Almost all simulation software packages provide constructs to model each of the above components. Modeling is arguably the most important part of a simulation study. Indeed, a simulation study is as good as the simulation model.

Simulation modeling comprises the following steps: Simulation Step 1. Identify the problem. Enumerate problems with an existing system. Produce requirements for a proposed system. Step 2. Formulate the problem. Select the bounds of the system, the problem or a part thereof, to be studied. Define overall objective of the study and a few specific issues to be addressed. Define performance measures - quantitative criteria on the basis of which different system configurations will be compared and ranked. Identify, briefly at this stage, the configurations of interest and formulate hypotheses about system performance. Decide the time frame of the study. Identify the end user of the simulation model. Problems must be formulated as precisely as possible. Step 3. Collect and process real system data. Collect data on system specifications, input variables, as well as performance of the existing system. Identify sources of randomness in the system, i.e., the stochastic input variables. Select an appropriate input probability distribution for each stochastic input variable and estimate corresponding parameter(s). Step 4. Formulate and develop a model. Develop schematics and network diagrams of the system (How do entities flow through the system?). Translate these conceptual models to simulation software acceptable form. Verify that the simulation model executes as intended. Verification techniques include traces, varying input parameters over their acceptable range and checking the output, substituting constants for random variables and manually checking results, and animation. Step 5. Validate the model. Compare the model's performance under known conditions with the performance of the real system. Perform statistical inference tests and get the model examined by system experts. For major simulation studies, experienced consultants advocate a structured presentation of the model by the simulation analyst(s) before an audience of management and system experts. Step 6. Document model for future use. Document objectives, assumptions and input variables in detail. Step 7. Select appropriate experimental design. Select a performance measure, a few input variables that are likely to influence it, and the levels of each input variable. When the number of possible configurations is large and the simulation model is complex, common second-order design classes should be considered. Step 8. Establish experimental conditions for runs. Address the question of obtaining accurate information and the most information from each run. Determine if the system is stationary (performance measure does not change over time) or non-stationary (performance measure changes over time). Generally, in stationary systems, steady-state behavior of the response variable is of interest. Alternately, use common random numbers to compare alternative configurations by using a separate random number stream for each sampling process in a configuration. Identify output data most likely to be correlated. Step 9. Perform simulation runs. Perform runs according to steps 7-8 above. Step 10. Interpret and present results. Compute numerical estimates (e.g., mean, confidence intervals) of the desired performance measure for each configuration of interest. To obtain confidence intervals for the mean of auto-correlated data, the technique of batch means can be used. In batch means, original contiguous data set from a run is replaced with a smaller data set containing the means of contiguous batches of original observations. The assumption that batch means are independent may not always be true; increasing total sample size and increasing the batch length may help. Test hypotheses about system performance. Construct graphical displays (e.g., pie charts, histograms) of the output data. Document results and conclusions. Step 11. Recommend further course of action. This may include further experiments to increase the precision and reduce the bias of estimators, to perform sensitivity analyses, etc.

HOW TO DESIGN A SIMULATION EXPERIMENT? A simulation experiment is a test or a series of tests in which meaningful changes are made to the input variables of a simulation model so that we may observe and identify the reasons for changes in the performance measures. The number of experiments in a simulation study is greater than or equal to the number of questions being asked about the model (e.g., Is there a significant difference between the mean delay in communication networks A and B?, Which network has the least delay: A, B, or C? How will a new routing algorithm affect the performance of network B?). Design of a simulation experiment involves answering the question: what data need to be obtained, in what form, and how much? The following steps illustrate the process of designing a simulation experiment. Most simulation packages provide run statistics (mean, standard deviation, minimum value, maximum value) on the performance measures, e.g., wait time (non-time persistent statistic), inventory on hand (time persistent statistic). Notwithstanding the facts that there are no data collection errors in simulation, the underlying model is fully known, and replications and configurations are user controlled, simulation results are difficult to interpret. An observation may be due to system characteristics or just a random occurrence. Normally, statistical inference can assess the significance of an observed phenomenon, but most statistical inference techniques assume independent, Most types of simulation data are autocorrelated, and hence, do not satisfy this assumption. Analysis of simulation output data consists of the following steps.

HOW TO PERFORM SIMULATION ANALYSIS?

Step 1. Identify the problem Step 2. Formulate the problem Step 3. Collect and process real system data Step 4. Formulate and develop a model Step 5. Validate the model Step 6. Document model for future use Step 7. Select appropriate experimental design Step 8. Establish experimental conditions for runs Step 9. Perform simulation runs Step 10. Interpret and present results Step 11. Recommend further course of action

WHAT MAKES A PROBLEM SUITABLE FORSIMULATION MODELING AND ANALYSIS?

In general, whenever there is a need to model and analyze randomness in a system, simulation is the tool of choice. More specifically, situations in which simulation modeling and analysis is used include the following: It is impossible or extremely expensive to observe certain processes in the real world, Problems in which mathematical model can be formulated but analytic solutions are either impossible or too complicated, It is impossible or extremely expensive to validate the mathematical model describing the system, e.g., due to insufficient data.Applications of simulation abound in the areas of government, defense, computer and communication systems, manufacturing, transportation (air traffic control), health care, ecology and environment, sociological and behavioral studies, biosciences, epidemiology, services (bank teller scheduling), economics and business analysis.

HOW TO SELECT SIMULATION SOFTWARE?

Although a simulation model can be built using general purpose programming languages which are familiar to the analyst, available over a wide variety of platforms, and less expensive, most simulation studies today are implemented using a simulation package. The advantages are reduced programming requirements; natural framework for simulation modeling; conceptual guidance; automated gathering of statistics; graphic symbolism for communication; animation; and increasingly, flexibility to change the model. There are hundreds of simulation products on the market, many with price tags. Naturally, the question of how to select the best simulation software for an application arises. Metrics for evaluation include modeling flexibility, ease of use, modeling structure (hierarchical v/s flat; object-oriented v/s nested), code reusability, graphic user interface, animation, dynamic business graphics, hardware and software requirements, statistical capabilities, output reports and graphical plots, customer support, and documentation. The two types of simulation packages are simulation languages and application-oriented simulators (Table 2). Simulation languages offer more flexibility than the application-oriented simulators. On the other hand, languages require varying amounts of programming expertise. Application-oriented simulators are easier to learn and have modeling constructs closely related to the application. Most simulation packages incorporate animation which is excellent for communication and can be used to debug the simulation program; a "correct looking" animation, however, is not a guarantee of a valid model. More importantly, animation is not a substitute for output analysis.

BENEFITS OF SIMULATION MODELING AND ANALYSIS According to practitioners, simulation modeling and analysis is one of the most frequently used operations research techniques. When used judiciously, simulation modeling and analysis makes it possible to: Obtain a better understanding of the system by developing a mathematical model of a system of interest, and observing the system's operation in detail over long periods of time. Test hypotheses about the system for feasibility. Compress time to observe certain phenomena over long periods or expand time to observe a complex phenomenon in detail. Study the effects of certain informational, organizational, environmental and policy changes on the operation of a system by altering the system's model; this can be done without disrupting the real system and significantly reduces the risk of experimenting with the real system. Experiment with new/unknown situations about which only weak information is available. Identify the "driving" variables - ones that performance measures are most sensitive to - and the inter-relationships among them. Identify bottlenecks in the flow of entities (material, people, etc.) or information. Use multiple performance metrics for analyzing system configurations. Employ a systems approach to problem solving. Develop well designed and robust systems and reduce system development time.

WHAT ARE SOME PITFALLS TO GUARD AGAINST IN SIMULATION? Simulation can be a time consuming and complex exercise, from modeling through output analysis that necessitates the involvement of resident experts and decision makers in the entire process. Following is a checklist of pitfalls to guard against. Unclear objective. Using simulation when an analytic solution is appropriate. Invalid model. Simulation model too complex or too simple. Erroneous assumptions. Undocumented assumptions. This is extremely important and it is strongly suggested that assumptions made at each stage of the simulation modeling and analysis exercise be documented thoroughly. Using the wrong input probability distribution. Replacing a distribution (stochastic) by its mean (deterministic). Using the wrong performance measure. Bugs in the simulation program. Using standard statistical formulas that assume independence in simulation output analysis. Initial bias in output data. Making one simulation run for a configuration. Poor schedule and budget planning. Poor communication among the personnel involved in the simulation study.

References Banks, J., J. S. Carson, II, and B. L. Nelson. 1996. Discrete-Event System Simulation, Second Edition, Prentice Hall. Bratley, P., B. L. Fox, and L. E. Schrage. 1987. A Guide to Simulation, Second Edition, Springer-Verlag. Fishwick, P. A. 1995. Simulation Model Design and Execution: Building Digital Worlds, Prentice-Hall. Freund, J. E. 1992. Mathematical Statistics, Fifth Edition, Prentice-Hall. Hogg, R. V., and A. T. Craig. 1995. Introduction to Mathematical Statistics, Fifth Edition, Prentice-Hall. Kleijnen, J. P. C. 1987. Statistical Tools for Simulation Practitioners, Marcel Dekker, New York. Law, A. M., and W. D. Kelton. 1991. Simulation Modeling and Analysis, Second Edition, McGraw-Hill. Law, A. M., and M. G. McComas. 1991. Secrets of Successful Simulation Studies, Proceedings of the 1991 Winter Simulation Conference, ed. J. M. Charnes, D. M. Morrice, D. T. Brunner, and J. J. Swain, 21-27. Institute of Electrical and Electronics Engineers, Piscataway, New Jersey. Maria, A., and L. Zhang. 1997. Probability Distributions, Version 1.0, July 1997, Monograph, Department of Systems Science and Industrial Engineering, SUNY at Binghamton, Binghamton, NY 13902. Montgomery, D. C. 1997. Design and Analysis of Experiments, Third Edition, John Wiley. Naylor, T. H., J. L. Balintfy, D. S. Burdick, and K. Chu. 1966. Computer Simulation Techniques, John Wiley. Nelson, B. L. 1995. Stochastic Modeling: Analysis and Simulation, McGraw-Hill.

Experiment 2AIM: Generation of Basic signals on Matlab(i) To procure sufficient knowledge in MATLAB to solve the power system Problems.

(ii) To write a MATLAB program.

SOFTWARE REQUIRED

(i) MATLAB

1.INTRODUCTION TO MATLAB

MATLAB is a high performance language for technical computing. It integrates computation, visualization and programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.

MATLAB is numeric computation software for engineering and scientific calculations. MATLAB is primary tool for matrix computations. MATLAB is being used to simulate random process, power system, control system and communication theory.

MATLAB comprising lot of optional tool boxes and block set like control system, optimization, and power system and so on.

1.1.TYPICAL USES INCLUDE

Math and computation.

Algorithm development.

Modeling, simulation and prototype.

Data analysis, exploration and Visualization.

Scientific and engineering graphics.

Application development, including graphical user interface building. MATLAB is a widely used tool in electrical engineering community. It can be used for simple mathematical manipulation with matrices for understanding and teaching basic mathematical and engineering concepts and even for studying and simulating actual power system and electrical system in general. The original concept of a small and handy tool has evolved to become an engineering work house. It is now accepted that MATLAB and its numerous tool boxes replace and/or enhance the usage of traditional simulation tool for advanced engineering applications.

Engineering personnel responsible for studies of electrical power system, control system and power electronics circuits will benefit from the MATLAB. To expertise in Electrical System Simulation one should have a basic understanding of electric circuits, power system and power electronics.

1.2. GETTING STARTED WITH MATLAB

To open the MATLAB applications double click the Matlab icon on the desktop. This will open the MATLAB window space with Matlab prompt as shown in the fig.1.

Fig-1: MATLAB window space

To quit from MATLAB type

>> quit (Or) >>exit To select the (default) current directory click ON the icon [] and browse for the folder named D:\SIMULAB\xxx, where xxx represents roll number of the individual candidate in which a folder should be created already.

When you start MATLAB you are presented with a window from which you can enter commands interactively. Alternatively, you can put your commands in an M- file and execute it at the MATLAB prompt. In practice you will probably do a little of both. One good approach is to incrementally create your file of commands by first executing them.M-files can be classified into following 2 categories,

Script M-files Main file contains commands and from which functions can also be called.Function M-files Function file that contains function command at the first line of the M-file. M-files to be created by you should be placed in your default directory. The M-files developed can be loaded into the work space by just typing the M-file name.

To load and run a M-file named ybus.m in the workspace. >>ybus

These M-files of commands must be given the file extension of .m. However M-files are not limited to being a series of commands that you dont want to type at the MATLAB window, they can also be used to create user defined function. It turns out that a MATLAB tool box is usually nothing more than a grouping of M-files that someone created to perform a special type of analysis like control system design and power system analysis. Any of the matlab commands (eg: sqrt) is really an M-file.

One of the more generally useful matlab tool boxes is simulink a drag and-drop dynamic system simulation environment. This will be used extensively in laboratory, forming the heart of the computer aided control system design (CACSD) methodology that is used. >>simulink At the matlab prompt type simulink and brings up the Simulink Library Browser. Each of the items in the Simulink Library Browser are the top level of a hierarchy of palette of elements that you can add to a simulink model of your own creation. At this time expand the simulink pallete as it contains the majority of the elements you will use in this course. Simulink has built into it a variety of integration algorithm for integrating the dynamic equations. You can place the dynamic equations of your system into simulink in four ways. 1 Using integrators1. Using transfer functions.2. Using state space equations.3. Using S- functions (the most versatile approach) Once you have the dynamics in place you can apply inputs from the sources palettes and look at the results in the sinks palette.

Finally the most important MATLAB features are its help. At the MATLAB Prompt simply typing helpdesk gives you access to searchable help as well as all the MATLAB manuals. >>helpdesk

To get the details about the command name sqrt, just type >>help sqrt

Where sqrt is the command name and you will get pretty good description in the MATLAB window as follows./SQRT Square root. SQRT(X) is the square root of the elements of X. Complex results are produced if X is not positive. See also SQRTM.

Overloaded methods help sym/sqrt.m

1.3MATLAB WORKSPACE The workspace is the window where you execute MATLAB commands (Ref. figure-1). The best way to probe the workspace is to type whos. This command shows you all the variables that are currently in workspace. You should always change working directory to an appropriate location under your user name.

Another useful workspace-like command is >>clear all

It eliminates all the variables in your workspace. For example start MATLAB and execute the following sequence of commands >>a=2;>>b=5; >>whos>>clear all The first two commands loaded the two variables a and b to the workspace and assigned value of 2 and 5 respectively. The clear all command clear the variables available in the work space. The arrow keys are real handy in MATLAB. When typing in long expression at the command line, the up arrow scrolls through previous commands and down arrow advances the other direction. Instead of retyping a previously entered command just hit the up arrow until you find it. If you need to change it slightly the other arrows let you position the cursor anywhere.

Finally any DOS command can be entered in MATLAB as long as it is preceded by any exclamination mark. >>!dir1.4MATLAB Data Types

The most distinguishing aspect of MATLAB is that it allows the user to manipulate vectors (like 5+j8) and matrices with the same ease as manipulating scalars (like5,8). Before diving into the actual commands everybody must spend a few moments reviewing the main MATLAB data types. The three most common data types you may see are,

1) arrays 2) strings 3) structures. As for as MATLAB is concerned a scalar is also a 1 x 1 array. For example clear your workspace and execute the commands.

>>a=4.2: >>A=[1 4;6 3]; >>whos Two things should be evident. First MATLAB distinguishes the case of a variable name and that both a and A are considered arrays. Now lets look at the content of A and a.

>>a >>A

Again two things are important from this example. First anybody can examine the contents of any variables simply by typing its name at the MATLAB prompt. Second, when typing in a matrix space between elements separate columns, whereas semicolon separate rows. For practice create the matrix in your workspace by typing it in all the MATLAB prompt.

>>B= [3 0 -1; 4 4 2;7 2 11];(use semicolon(;) to represent the end of a row) >>B Arrays can be constructed automatically. For instance to create a time vector where the time points start at 0 seconds and go up to 5 seconds by increments of 0.001

>>mytime =0:0.001:5;Automatic construction of arrays of all ones can also be created as follows, >>myone=ones (3,2)Note: Any MATLAB command can be terminated by a semicolon, which suppressed any echo information to the screen.

1.5Scalar versus Array Mathematical Operation

Since MATLAB treats everything as an array, you can add matrices as easily as scalars.Example: >>clear all >> a=4; >> A=7; >>alpha=a+A; >>b= [1 2; 3 4]; >>B= [6 5; 3 1]; >>beta=b+BOf course cannot violate the rules of matrix algebra which can be understood from the following example. >>clear all >>b=[1 2;3 4]; >>B=[6 7]; >>beta=b*BIn contrast to matrix algebra rules, the need may arise to divide, multiply, raise to a power one vector by another, element by element. The typical scalar commands are used for this +,-,/, *, ^ except you put a . in front of the scalar command. That is, if you need to multiply the elements of [1 2 3 4] by [6 7 8 9], just type...

>>[1 2 3 4].*[6 7 8 9]

1.6Conditional Statements

Like most Programming languages, MATLAB supports a variety of conditional statements and looping statements. To explore these simply type >>help if>>help for >>help whileExample : >>if z=0 >>y=0 >>else>>y=1/z>>end

Looping :>>for n=1:2:10>>s=s+n^2>>end- Yields the sum of 1^2+3^2+5^2+7^2+9^21.7PLOTTING

MATLABs potential in visualizing data is pretty amazing. One of the nice features is that with the simplest of commands you can have quite a bit of capability.

Graphs can be plotted and can be saved in different formulas.

>>clear all >>t=0:10:360; >>y=sin (pi/180 * t);

To see a plot of y versus t simply type, >>plot(t,y)To add label, legend, grid and title use >>xlabel (Time in sec); >>ylabel (Voltage in volts) >>title (Sinusoidal O/P); >>legend (Signal);

The commands above provide the most plotting capability and represent several shortcuts to the low-level approach to generating MATLAB plots, specifically the use of handle graphics. The helpdesk provides access to a pdf manual on handle graphics for those really interested in it.

1.8Functions

As mentioned earlier, a M-file can be used to store a sequence of commands or a user-defined function. The commands and functions that comprise the new function must be put in a file whose name defines the name of the new function, with a filename extension of '.m'.A function is a generalized input/output device. That is you can give some input.(arguments) and provides some output. MATLAB functions allow you much capability to expand MATLABs usefulness. We will just touch on function here as you may find them beneficial later.We will start by looking at the help on functions :>>help functionWe will create our own function that given an input matrix returns a vector containing the admittance matrix(y) of given impedance matrix(z)

z=[5 2 4; 1 4 5]as input, the output would be,

y=[0.2 0.5 0.25;1 0.25 0.2] which is the reciprocal of each elements.To perform the same name the function admin and noted that admin must be stored in a function M-file named admin.m. Using an editor, type the following commands and save as admin.m.admin.m :function y = admin(z) y = 1./zreturnSimply call the function admin from the workspace as follows,>>z=[5 2 4; 1 4 5] >>admin(z)

The output will be, ans = 0.2 0.5 0.25 1 0.25 0.2Otherwise the same function can be called for any times from any script file provided the function M-file is available in the current directory.

With this introduction anybody can start programming in MATLAB and can be updated themselves by using various commands and functions available. Concerned with the Power System Simulation Laboratory, initially solve the Power System Problems manually, list the expressions used in the problem and then build your own MATLAB program or function.

Experiment 3AIM: Generation of Basic signals on Matlab.

REQUIREMENT:Matlab software.

THEORY :Simple Waveforms

Frequency is the number of cycles per second and is measured in Hertz (Hz). Wavelength is inversely proportional to frequency i.e. Wavelength varies as 1/Frequency The general form of the sine wave we shall use (quite a lot of) is as follows: y = A*sin(2n*Fw/Fs)

Where: A is the amplitude of the wave, Fw is the frequency of the wave, Fs is the sample frequency, n is the sample index. MATLAB function: sin() usedworks in radians

PROGRAMS ON MATLABPROGRAM 1:PERIOD 1 SIMPLE SINE WAVE % Basic 1 period Simple Sine wavei=0:0.2:2*pi;y = sin(i);figure(1)plot(y);Title(Simple 1 Period Sine Wave);OUTPUT OF THE PROGRAM

PROGRAM 2:SineWave Amplitude is -1 to +1.To change amplitude multiply by some gain (amp):% Now Change amplitudeamp = 2.0;y = amp*sin(i);figure(2)plot(y);title(Simple 1 Period Sine Wave Modified Amplitude);

OUTPUT OF THE PROGRAM :

PROGRAM 3:% To plot n cycles of a waveformncyc = 2;n=0:floor(ncyc*F_s/F_w);y = amp*sin(2*pi*n*F_w/F_s);figure(4)plot(y);title(N Cycle Duration Sine Wave);

OUTPUT OF THE PROGRAM

PROGRAM 4 :% Cosine is same as Sine (except 90 degrees out of phase)clear allamp=2;ncyc=1F_s = 11025;F_w = 440;n=0:floor(ncyc*F_s/F_w);yc = amp*cos(2*pi*n*F_w/F_s);y = amp*sin(2*pi*n*F_w/F_s);figure(5);hold onplot(yc,'b');plot(y,'r');title('Cos (Blue)/Sin (Red) Plot (Note Phase Difference)');hold off;

OUTPUT OF THE PROGRAM:

RESULT-Basic signals are generated in MATLAB

Experiment 4AIM: Plot a sinusoidal Waveform(1 Peak & 1 rad/sec), Differentiate it & observe both the waveform on scopeREQUIREMENT:Matlab software.THEORY:Step1: Open a new model. Open the simulink library browser. On clicking the same library a set of box will appear. Click on the sine wave block and drag it to the model window to add a source in your model.Step2: Save the model by .mdl extension. Step 3: Add more blocks as shown in table below. Block Location

Sine wave Source

DerivativeContinous

MultiplexerCommonly used blocks

ScopeSink

Step 4:Make a connection between blocks according to the required condition.BLOCK DIAGRAM:

Step 5: Edit the block parameter. To edit a particular block parameter double click on it a new box will open. We can edit amplitude, frequency and phase.Step 6:Running simulation and viewing output. After making a model and adding parameters we can run simulation in following way.

By play button. Selecting start from simulation menu.RESULT : WAVEFORM

Hence the response is studied.

Experiment 5

AIM: Use Simulink to solve the following differential equation.=0

REQUIREMENT:Matlab software.THEORY:Step1: Open a new model. Open the simulink library browser. On clicking the same library a set of box will appear. Click on the sine wave block and drag it to the model window to add a source in your model.Step2: Save the model by .mdl extension. Step 3: Add more blocks as shown in table below. Block Location

Sine wave Source

IntegratorContinous

GainCommonly used blocks

ScopeSink

Step 4:Make a connection between blocks according to the required condition.BLOCK DIAGRAM:


By play button. Selecting start from simulation menu.

RESULT:


EXAMPLES : , where f(t)=2sin 4t & initial condition y(0)=1Step1: Open a new model. Open the simulink library browser. On clicking the same library a set of box will appear. Click on the sine wave block and drag it to the model window to add a source in your model.Step2: Save the model by .mdl extension. Step 3: Add more blocks as shown in table below. Block Location

Sine wave Source

IntegratorContinous


ScopeSink

Sum Commonly used blocks

Step 4:Make a connection between blocks according to the required condition.

BLOCK DIAGRAM:



RESULT:

Hence the response is studied.Experiment 6AIM: Develop a simulink model to generate sine & cosine waveform of magnitude 5 and frequency 50 Hz using sine & cosine trigonometric functionREQUIREMENT:Matlab software.THEORY:Step1: Open a new model. Open the simulink library browser. On clicking the same library a set of box will appear. Click on the sine wave block and drag it to the model window to add a source in your model.Step2: Save the model by .mdl extension. Step 3: Add more blocks as shown in table below. Block Location

Sine wave Source

Cosine waveSource

Multiplexer Commonly used blocks

ConstantCommonly used blocks



Clock Source

Product Commonly used blocks


Product Commonly used blocks

ScopeSink

ProductCommonly used blocks

Step 4:Make a connection between blocks according to the required condition.

BLOCK DIAGRAM:



RESULT:


Experiment 7

AIM:

Introduction to simulink & study of various blocksets

THEORY:Simulink is a software package for modeling, simulating, and analyzing dynamical systems. It supports linear and nonlinear systems, modeled in continuous time, sampled time, or a hybrid of the two. Systems can also be multirate, i.e., have different parts that are sampled or updated at different rates. For modeling, Simulink provides a graphical user interface (GUI) for building models as block diagrams, using click-and-drag mouse operations. With this interface, we can draw the models just as we would with pencil and paper. Simulink includes a comprehensive block library of sinks, sources, linear and nonlinear components, and connectors. We can also customize and create our own blocks Models are hierarchical. This approach provides insight into how a model is organized and how its parts interact. After define a model, & we can simulate it, using a choice of integration methods, either from the Simulink menus or by entering commands in MATLAB's command window. The menus are particularly convenient for interactive work, while the command-line approach is very useful for running a batch of simulations. Using scopes and other display blocks, we can see the simulation results while the simulation is running. In addition, we can change parameters and immediately see what happens, for "what if" exploration. The simulation results can be put in the MATLAB workspace for post processing and visualization. And because MATLAB and Simulink are integrated, we can simulate, analyze, and revise our models in either environment at any point. Now step by step will see the process.

STEP1-How to Build a Simple Model

This example shows you how to build a model using many of the model building Commands and actions you will use to build your own models. The instructions for Building this model in this section are brief. The model integrates a sine wave and Displays the result, along with the sine wave. The block diagram of the model looks like this.

To create the model, first type simulink in the MATLAB command window. On Microsoft Windows, the Simulink Library Browser appears.

To create a new model, select Model from the new submenu of the Simulink library Windows File menu. To create a new model on Windows, select the New Model button on the Library Browser's toolbar.

Simulink opens a new model window.

To create this model, you will need to copy blocks into the model from the following Simulink block libraries:

Sources library (the Sine Wave block)Sinks library (the Scope block)Continuous library (the Integrator block)Signals & Systems library (the Mux block)

To copy the Sine Wave block from the Library Browser, first expand the Library Browser tree to display the blocks in the Sources library. Do this by clicking on the Sources node to display the Sources library blocks. Finally, click on the Sine Wave node to select the Sine Wave block. Here is how the Library Browser should look after you have done this.

Now drag the Sine Wave block from the browser and drop it in the model window.Simulink creates a copy of the Sine Wave block at the point where you dropped the node icon. To copy the Sine Wave block from the Sources library window, open the Sources window by double-clicking on the Sources icon in the Simulink library window. (On Windows, you can open the Simulink library window by right-clicking the Simulink node in the Library Browser and then clicking the resulting Open Library button.) Simulink displays the Sources library window.

Now drag the Sine Wave block from the Sources window to your model window.

Copy the rest of the blocks in a similar manner from their respective libraries into the model window. You can move a block from one place in the model window to another by dragging the block. You can move a block a short distance by selecting the block, then pressing the arrow keys. With all the blocks copied into the model window, the model should look something likethis.

If you examine the block icons, you see an angle bracket on the right of the Sine Waveblock and two on the left of the Mux block. The > symbol pointing out of a block is anoutput port; if the symbol points to a block, it is an input port. A signal travels out of anoutput port and into an input port of another block through a connecting line. When theblocks are connected, the port symbols disappear.

Now it's time to connect the blocks. Connect the Sine Wave block to the top input port of The Mux block. Position the pointer over the output port on the right side of the Sine Wave block. Notice that the cursor shape changes to cross hairs.

Hold down the mouse button and move the cursor to the top input port of the Mux block.Notice that the line is dashed while the mouse button is down and that the cursor shape changes to double-lined cross hairs as it approaches the Mux block.

Now release the mouse button. The blocks are connected. You can also connect the line to the block by releasing the mouse button while the pointer is inside the icon. If you do, the line is connected to the input port closest to the cursor's position.\

If you look again at the model at the beginning of this section, you'll notice that most of the lines connect output ports of blocks to input ports of other blocks. However, one line connects a line to the input port of another block. This line, called a branch line, connects the Sine Wave output to the Integrator block, and carries the same signal that passes from the Sine Wave block to the Mux block. Drawing a branch line is slightly different from drawing the line you just drew. To weld a connection to an existing line, follow these steps:

1. First, position the pointer on the line between the Sine Wave and the Mux block.

2. Press and hold down the Ctrl key (or click the right mouse button).Press the mouse button, then drag the pointer to the Integrator block's input port or over the Integrator block itself.

3. Release the mouse button. Simulink draws a line between the starting point and the Integrator block's input port.

Finish making block connections. When you're done, your model should look something like this.

Now, open the Scope block to view the simulation output. Keeping the Scope window open, set up Simulink to run the simulation for 10 seconds. First, set the simulation parameters by choosing Simulation Parameters from the Simulation menu. On the dialog box that appears, notice that the Stop time is set to 10.0 (its default value).

Close the Simulation Parameters dialog box by clicking on the OK button. Simulink applies the parameters and closes the dialog box. Choose Start from the Simulation menu and watch the traces of the Scope block's input.

The simulation stops when it reaches the stop time specified in the Simulation Parameters dialog box or when you choose Stop from the Simulation menu. To save this model, choose Save from the File menu and enter a filename and location. That file contains the description of the model.

RESULT-Studied simulation & its blockset

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