MATLAB WORKSHOP FOR EE 327FOR EE 327 MWF 8:00-850 AMMWF 8:00-850 AM August 26-30, 2002August 26-30, 2002 Dr. Ali A. Jalali.

MATLAB WORKSHOPMATLAB WORKSHOPMATLAB WORKSHOPMATLAB WORKSHOP

• FOR EE 327FOR EE 327• MWF 8:00-850 AMMWF 8:00-850 AM• August 26-30, 2002 August 26-30, 2002

Dr. Ali A. JalaliDr. Ali A. Jalali


WORKSHOPWORKSHOP

WebPagesWebPages

www.csee.wvu.edu/~jalali

http://www.csee.wvu.edu/~jalali


Lecture # 1Lecture # 1Monday August 26Monday August 26• IntroductionIntroduction• MATLAB DemosMATLAB Demos

• MATLAB BasicsMATLAB Basics

Lecture # 2Lecture # 2Wednesday August 28Wednesday August 28• MATLAB BasicsMATLAB Basics• MATLAB PlotsMATLAB Plots

• MATLAB ExamplesMATLAB Examples

Lecture # 3Lecture # 3Friday August 30Friday August 30• MATLAB FundationMATLAB Fundation• Textbook ExamplesTextbook Examples

• Short QuizShort Quiz


• Lecture # 3Lecture # 3• Friday August 30Friday August 30• MATLAB PlotsMATLAB Plots• MATLAB FundationMATLAB Fundation• Textbook ExamplesTextbook Examples

• Short QuizShort Quiz

MATLAB BasicsMATLAB BasicsMATLAB BasicsMATLAB Basics

• Vectors and Matrices:(Cont.)

EXAMPLE: >> a=2:3, b=[a 2*a;a/2 a]

a = 2 3

b = 2.0000 3.0000 4.0000 6.0000 1.0000 1.5000 2.0000 3.0000

>> c=[b ; b]

c = 2.0000 3.0000 4.0000 6.0000 1.0000 1.5000 2.0000 3.0000 2.0000 3.0000 4.0000 6.0000 1.0000 1.5000 2.0000 3.0000

• Vectors and Matrices:(Cont.)

EXAMPLE: >> a=2:3, b=[a 2*a;a/2 a]

a = 2 3

b = 2.0000 3.0000 4.0000 6.0000 1.0000 1.5000 2.0000 3.0000

>> c=[b ; b]

c = 2.0000 3.0000 4.0000 6.0000 1.0000 1.5000 2.0000 3.0000 2.0000 3.0000 4.0000 6.0000 1.0000 1.5000 2.0000 3.0000

C:\MATLAB6p1\bin\win32\matlab.exe


• Vectors and Matrices:

>> D=c(2:3, 2:3)

D = 1.5000 2.0000 3.0000 4.0000

• >> who Your variables are: D a b c

• >> whosName Size Bytes Class

D 2x2 32 double array a 1x2 16 double array b 2x4 64 double array c 4x4 128 double array

Grand total is 30 elements using 240 bytes


>> D=c(2:3, 2:3)

D = 1.5000 2.0000 3.0000 4.0000

• >> who Your variables are: D a b c

• >> whosName Size Bytes Class

D 2x2 32 double array a 1x2 16 double array b 2x4 64 double array c 4x4 128 double array

Grand total is 30 elements using 240 bytes




Example: >> a=magic(4)

a= 16.0000 2.0000 3.0000 13.0000 5.0000 11.5000 10.0000 8.0000 9.0000 7.0000 6.0000 12.0000 4.0000 14.5000 15.0000 1.0000

>> sum(a) = sum(a') = [34 34 34 34]

• >> trace(a) = 34

• A(i, j) indexes row i, column j

• Indexing starts with 1, not zero.

• >>a(a, 3) = 3>>a(3, 1) = 39>>a(:, 3) = 3 10 6 15


Example: >> a=magic(4)

a= 16.0000 2.0000 3.0000 13.0000 5.0000 11.5000 10.0000 8.0000 9.0000 7.0000 6.0000 12.0000 4.0000 14.5000 15.0000 1.0000

>> sum(a) = sum(a') = [34 34 34 34]

• >> trace(a) = 34

• A(i, j) indexes row i, column j

• Indexing starts with 1, not zero.

• >>a(a, 3) = 3>>a(3, 1) = 39>>a(:, 3) = 3 10 6 15




• >>a(2:3,3:4) = 10 8 2 12

• >>a([1 4],[1 4]) = 16 13 4 1

• >>a(8) = 14

• >>[1:3] + [4:6] = 5 7 9

• A=zeros(2,2); B=(ones(3,2);

C = [ [A-1;B+1], [B+3;A-4] ], C =

-1 -1 4 4 -1 -1 4 4 2 2 4 4 2 2 -4 -4 2 2 -4 -4


• >>a(2:3,3:4) = 10 8 2 12

• >>a([1 4],[1 4]) = 16 13 4 1

• >>a(8) = 14

• >>[1:3] + [4:6] = 5 7 9

• A=zeros(2,2); B=(ones(3,2);

C = [ [A-1;B+1], [B+3;A-4] ], C =

-1 -1 4 4 -1 -1 4 4 2 2 4 4 2 2 -4 -4 2 2 -4 -4



Plotting Elementary Functions: MATLAB supports many types of graph and

surface plots: 2 dimensions line plots (x vs. y), filled

plots, bar charts, pie charts, parametric plots, polar plots, contour plots, density plots, log axis plots, surface plots, parametric plots in 3 dimensions and spherical plots.

To preview some of these capabilities and others as well, enter the command demos.

Plotting Elementary Functions: MATLAB supports many types of graph and

surface plots: 2 dimensions line plots (x vs. y), filled

plots, bar charts, pie charts, parametric plots, polar plots, contour plots, density plots, log axis plots, surface plots, parametric plots in 3 dimensions and spherical plots.

To preview some of these capabilities and others as well, enter the command demos.



Plotting Elementary Functions:

2-D plots: The plot command creates linear x-y plots; if x and y are vectors of the same length, the command plot(x,y) opens a graphics window and draws an x-y plot of the elements of x versus the

elements of y.



Plotting Elementary Functions: >>%Example E1_2a of your textbook on page 23. (file name is E1_2.m) >>t=-1:0.01:1; >>f=4.5*cos(2*pi*t - pi/6); >>%The following statements plot the sequence and label the plot >>plot(t,f),title('Fig.E1.2a'); >>axis([-1,1,-6,6]); >>xlabel('t'); >>ylabel('f(t)'); >>text(-0.6,5,'f(t) = A cos(wt + phi)'); >>grid;

Plotting Elementary Functions: >>%Example E1_2a of your textbook on page 23. (file name is E1_2.m) >>t=-1:0.01:1; >>f=4.5*cos(2*pi*t - pi/6); >>%The following statements plot the sequence and label the plot >>plot(t,f),title('Fig.E1.2a'); >>axis([-1,1,-6,6]); >>xlabel('t'); >>ylabel('f(t)'); >>text(-0.6,5,'f(t) = A cos(wt + phi)'); >>grid;

Plot on next page




>>%Example E1_2a



Plotting Elementary Functions: PLOT(X,Y) plots vector Y versus vector X.TITLE('text') adds text at the top of the current plot. XLABEL('text') adds text beside the X-axis on the current axis. YLABEL('text') adds text beside the Y-axis on the current axis.GRID, by itself, toggles the major grid lines of the

current axes.GTEXT('string') displays the graph window, puts up a cross-hair, and

waits for a mouse button or keyboard key to be pressed.SUBPLOT(m,n,p), or SUBPLOT(mnp), breaks the Figure window into an

m-by-n matrix of small axes.stemDiscrete sequence or "stem" plot. STEM(Y) plots the data sequence

Y as stems from the x axis terminated with circles for the data value.

SEMILOGX(...) is the same as PLOT(...), except a logarithmic (base 10) scale is used for the X-axis.

SEMILOGY(...) is the same as PLOT(...), except a logarithmic (base 10) scale is used for the Y-axis..

Plotting Elementary Functions: PLOT(X,Y) plots vector Y versus vector X.TITLE('text') adds text at the top of the current plot. XLABEL('text') adds text beside the X-axis on the current axis. YLABEL('text') adds text beside the Y-axis on the current axis.GRID, by itself, toggles the major grid lines of the

current axes.GTEXT('string') displays the graph window, puts up a cross-hair, and

waits for a mouse button or keyboard key to be pressed.SUBPLOT(m,n,p), or SUBPLOT(mnp), breaks the Figure window into an

m-by-n matrix of small axes.stemDiscrete sequence or "stem" plot. STEM(Y) plots the data sequence

Y as stems from the x axis terminated with circles for the data value.

SEMILOGX(...) is the same as PLOT(...), except a logarithmic (base 10) scale is used for the X-axis.

SEMILOGY(...) is the same as PLOT(...), except a logarithmic (base 10) scale is used for the Y-axis..



Plotting Elementary Functions: By default, the axes are auto-scaled.

This can be overridden by the command axis. If c = [xmin,xmax,ymin,ymax] is a

4-element vector, then axis(c) sets the axis scaling to the prescribed limits.

By itself, axis freezes the current scaling for subsequent graphs; entering axis again returns to auto-scaling.

The command axis('square') ensures that the same scale is used on both axes.

For more information's on axis see help axis. .

Plotting Elementary Functions: By default, the axes are auto-scaled.

This can be overridden by the command axis. If c = [xmin,xmax,ymin,ymax] is a

4-element vector, then axis(c) sets the axis scaling to the prescribed limits.

By itself, axis freezes the current scaling for subsequent graphs; entering axis again returns to auto-scaling.

The command axis('square') ensures that the same scale is used on both axes.

For more information's on axis see help axis. .


MATLAB BasicsMATLAB BasicsMATLAB BasicsMATLAB BasicsPlotting Elementary Functions: • >>%Example 1.2 of your textbook on page 24. (file name is E1_2d.m) • >>t=-0.5:0.01:3; • >>t0=0 • >>u=stepfun(t,t0) • >>gprime=3.17*exp(-1.3*t).*cos(10.8*t + 1.15).*u; % NOTE the use of the .* operator. The terms 3.17*exp(-1.3*t), % cos(10.8*t + 1.15), and u are all vectors. We want the % components of these vectors to be multiplied by the corresponding % components of the other vectors, hence the need to use .* rather than *. % The following statements plot the sequence and label the plot • >>plot(t,gprime); • >>axis([-.5,3,-3,2]); • >>title('Fig.E1.2d'); • >>xlabel('t in seconds'); • >>ylabel('gprime(t)'); • >>text(-0.6,5,'f(t) = A cos(wt + phi)'); • >>grid;

Plotting Elementary Functions: • >>%Example 1.2 of your textbook on page 24. (file name is E1_2d.m) • >>t=-0.5:0.01:3; • >>t0=0 • >>u=stepfun(t,t0) • >>gprime=3.17*exp(-1.3*t).*cos(10.8*t + 1.15).*u; % NOTE the use of the .* operator. The terms 3.17*exp(-1.3*t), % cos(10.8*t + 1.15), and u are all vectors. We want the % components of these vectors to be multiplied by the corresponding % components of the other vectors, hence the need to use .* rather than *. % The following statements plot the sequence and label the plot • >>plot(t,gprime); • >>axis([-.5,3,-3,2]); • >>title('Fig.E1.2d'); • >>xlabel('t in seconds'); • >>ylabel('gprime(t)'); • >>text(-0.6,5,'f(t) = A cos(wt + phi)'); • >>grid;




>>%Example E1.2




Two ways to make multiple plots on a single graph are illustrated by

• >>t = 0:.01:2*pi; • >>y1 = sin(t); y2=sin(2*t); y3=sin(4*t) • >>plot(t,y1,y2,y3) • and by forming a matrix Y containing the functional values as columns • >>t = 0:.01:2*pi; • >>y = [sin(t)', sin(2*t)', sin(4*t)'] • >>plot(t,y) • Another way is with the hold command. The command hold freezes the

current graphics screen so that subsequent plots are superimposed on it. Entering hold again releases the "hold". The commands hold on and hold off are also available.

• One can override the default linotypes and point types. For example, • >>t = 0:.01:2*pi; • >>y1 = sin(t); y2=sin(2*t); y3=sin(4*t) • >>plot(t,y1,'--',y2,':',y3,'+')


Two ways to make multiple plots on a single graph are illustrated by

• >>t = 0:.01:2*pi; • >>y1 = sin(t); y2=sin(2*t); y3=sin(4*t) • >>plot(t,y1,y2,y3) • and by forming a matrix Y containing the functional values as columns • >>t = 0:.01:2*pi; • >>y = [sin(t)', sin(2*t)', sin(4*t)'] • >>plot(t,y) • Another way is with the hold command. The command hold freezes the

current graphics screen so that subsequent plots are superimposed on it. Entering hold again releases the "hold". The commands hold on and hold off are also available.

• One can override the default linotypes and point types. For example, • >>t = 0:.01:2*pi; • >>y1 = sin(t); y2=sin(2*t); y3=sin(4*t) • >>plot(t,y1,'--',y2,':',y3,'+')



Plotting Elementary Functions: • Colors Line Styles • y yellow . point• M magenta o circle• C cyan x x-mark• R red + plus • G green - solid• B blue * star• W white : dotted• K black -. Dashdot• -- dashed

More mark types are; square(s), diamond(d), up-triangle(v), down-triangle(^), left-triangle(<), right-triangle(>), pentagram(p), hexagram(h)

See also help plot for more line and mark color.

Plotting Elementary Functions: • Colors Line Styles • y yellow . point• M magenta o circle• C cyan x x-mark• R red + plus • G green - solid• B blue * star• W white : dotted• K black -. Dashdot• -- dashed

More mark types are; square(s), diamond(d), up-triangle(v), down-triangle(^), left-triangle(<), right-triangle(>), pentagram(p), hexagram(h)

See also help plot for more line and mark color.



Plotting Elementary Functions: The command subplot can be used to partition the screen so that up to

four plots can be viewed simultaneously. See help subplot. • Example for use of subplot: • >>% Line plot of a chirp • >> x=0:0.05:5; • >> y=sin(x.^2); • >> subplot(2,2,1), plot(x,y); • >> % Bar plot of a bell shaped curve • >> x = -2.9:0.2:2.9; • >> subplot(2,2,2), bar(x,exp(-x.*x)); • >> % Stem plot • >> x = 0:0.1:4; • >> subplot(2,2,3), stem(x,y) • >> % Polar plot • >> t=0:.01:2*pi; • >> subplot(2,2,4), polar(t,abs(sin(2*t).*cos(2*t)));

Plotting Elementary Functions: The command subplot can be used to partition the screen so that up to

four plots can be viewed simultaneously. See help subplot. • Example for use of subplot: • >>% Line plot of a chirp • >> x=0:0.05:5; • >> y=sin(x.^2); • >> subplot(2,2,1), plot(x,y); • >> % Bar plot of a bell shaped curve • >> x = -2.9:0.2:2.9; • >> subplot(2,2,2), bar(x,exp(-x.*x)); • >> % Stem plot • >> x = 0:0.1:4; • >> subplot(2,2,3), stem(x,y) • >> % Polar plot • >> t=0:.01:2*pi; • >> subplot(2,2,4), polar(t,abs(sin(2*t).*cos(2*t)));




>>%Example Subplot



Loading and Saving:

• When using MATLAB, you may wish to leave the program but save the vectors and matrices you have defined.

• SAVE, Save workspace variables to disk.SAVE FILENAME saves all workspace variables to the binary "MAT-file" named FILENAME.mat.

• The data may be retrieved with LOAD. • If FILENAME has no extension, .mat is assumed.

SAVE, by itself, creates the binary "MAT-file" named 'matlab.mat'. • It is an error if 'matlab.mat' is not writable. • To save the file to the working directory, type• >>save filename • SAVE FILENAME X saves only X. • SAVE FILENAME X Y Z saves X, Y, and Z.

where "filename" is a name of your choice. To retrieve the data later, type.

Loading and Saving:

• When using MATLAB, you may wish to leave the program but save the vectors and matrices you have defined.

• SAVE, Save workspace variables to disk.SAVE FILENAME saves all workspace variables to the binary "MAT-file" named FILENAME.mat.

• The data may be retrieved with LOAD. • If FILENAME has no extension, .mat is assumed.

SAVE, by itself, creates the binary "MAT-file" named 'matlab.mat'. • It is an error if 'matlab.mat' is not writable. • To save the file to the working directory, type• >>save filename • SAVE FILENAME X saves only X. • SAVE FILENAME X Y Z saves X, Y, and Z.

where "filename" is a name of your choice. To retrieve the data later, type.



Loading and Saving:

• LOAD Load workspace variables from disk. • LOAD FILENAME retrieves all variables from a file given a

full pathname or a MATLABPATH relative partial pathname (see PARTIALPATH).

• If FILENAME has no extension LOAD looks for FILENAME and FILENAME.mat and treats it as a binary "MAT-file".

• If FILENAME has an extension other than .mat, it is treated as ASCII.LOAD, by itself, uses the binary "MAT-file" named 'matlab.mat'. It is an error if 'matlab.mat' is not found.LOAD FILENAME X loads only X.LOAD FILENAME X Y Z ... loads just the specified variables.

• >>load x, y, z • See help save and help load for more information..

Loading and Saving:

• LOAD Load workspace variables from disk. • LOAD FILENAME retrieves all variables from a file given a

full pathname or a MATLABPATH relative partial pathname (see PARTIALPATH).

• If FILENAME has no extension LOAD looks for FILENAME and FILENAME.mat and treats it as a binary "MAT-file".

• If FILENAME has an extension other than .mat, it is treated as ASCII.LOAD, by itself, uses the binary "MAT-file" named 'matlab.mat'. It is an error if 'matlab.mat' is not found.LOAD FILENAME X loads only X.LOAD FILENAME X Y Z ... loads just the specified variables.

• >>load x, y, z • See help save and help load for more information..



M-Files: • M-files are macros of MATLAB commands

that are stored as ordinary text files with the extension "m", that is filename.m.

• An M-file can be either a function with input and output variables or a list of commands.

• All of the MATLAB file in EE 327 textbook are contained in M-files that are available at the site http://www.csee.wvu.edu/~jalali.

M-Files: • M-files are macros of MATLAB commands

that are stored as ordinary text files with the extension "m", that is filename.m.

• An M-file can be either a function with input and output variables or a list of commands.

• All of the MATLAB file in EE 327 textbook are contained in M-files that are available at the site http://www.csee.wvu.edu/~jalali.



M-Files: The following describes the use of M-files on a PC version ofMATLAB. • MATLAB requires that the M-file must be stored either in the

working directory or in a directory that is specified in the MATLAB path list.

• For example, consider using MATLAB on a PC with a user-defined M-file stored in a directory called "\MATLAB\MFILES";.

• Then to access that M-file, either change the working directory by typing cd\matlab\mfiles from within the MATLAB command window or by adding the directory to the path.

• Permanent addition to the path is accomplished by editing the \MATLAB\matlabrc.m file.

• Temporary modification to the path is accomplished by typing path(path,'\matlab\mfiles') from within MATLAB.

M-Files: The following describes the use of M-files on a PC version ofMATLAB. • MATLAB requires that the M-file must be stored either in the

working directory or in a directory that is specified in the MATLAB path list.

• For example, consider using MATLAB on a PC with a user-defined M-file stored in a directory called "\MATLAB\MFILES";.

• Then to access that M-file, either change the working directory by typing cd\matlab\mfiles from within the MATLAB command window or by adding the directory to the path.

• Permanent addition to the path is accomplished by editing the \MATLAB\matlabrc.m file.

• Temporary modification to the path is accomplished by typing path(path,'\matlab\mfiles') from within MATLAB.



M-Files: • The M-files associated with this textbook

should be downloaded from the EE 327 site and copied to a subdirectory named "\MATLAB\users"; and then this directory should be added to the path.

• The M-files that come with MATLAB are already in appropriate directories and can be used from any working directory.

M-Files: • The M-files associated with this textbook

should be downloaded from the EE 327 site and copied to a subdirectory named "\MATLAB\users"; and then this directory should be added to the path.

• The M-files that come with MATLAB are already in appropriate directories and can be used from any working directory.



M-Files Functions: • As an example of M-file that defines a function,

create a file in your working directory named yplusx.m that contains the following commands:

• function z = yplusx(y,x) • z = y + x; • The following commands typed from within

MATLAB demonstrate how this M-file is used: • x = 2; • y = 3; • z = yplusx(y,x) • MATLAB M-files are most efficient when written in a way that utilizes matrix or vector operations.

M-Files Functions: • As an example of M-file that defines a function,

create a file in your working directory named yplusx.m that contains the following commands:

• function z = yplusx(y,x) • z = y + x; • The following commands typed from within

MATLAB demonstrate how this M-file is used: • x = 2; • y = 3; • z = yplusx(y,x) • MATLAB M-files are most efficient when written in a way that utilizes matrix or vector operations.



Loops and If statements (Control Flow): • Loops and if statements are available, but should be used

sparingly since they are computationally inefficient. • An example of the use of the command for is

for k=1:10, x(k) = cos(k); end

This creates a 1x10 vector x containing the cosine of the positiveintegers from 1 to 10. • This operation is performed more efficiently with the

commands k = 1:10; x = cos(k);

• which utilizes a function of a vector instead of a for loop.

Loops and If statements (Control Flow): • Loops and if statements are available, but should be used

sparingly since they are computationally inefficient. • An example of the use of the command for is

for k=1:10, x(k) = cos(k); end

This creates a 1x10 vector x containing the cosine of the positiveintegers from 1 to 10. • This operation is performed more efficiently with the

commands k = 1:10; x = cos(k);

• which utilizes a function of a vector instead of a for loop.



If statements: • An if statement can be used to define conditional

statements. • An example is

if(a <= 2), b = 1; elseif(a >=4) b = 2; else b = 3; end

• The allowable comparisons between expressions are >=, <=, <, >, ==, and ~=.

If statements: • An if statement can be used to define conditional

statements. • An example is

if(a <= 2), b = 1; elseif(a >=4) b = 2; else b = 3; end

• The allowable comparisons between expressions are >=, <=, <, >, ==, and ~=.



While Loops statements (Control Flow): • While for loop evaluates a group of commands a fixed number of times,• A while loop evaluates a group of statements an infinite number of times.• The general form of a while loop is

while expression commands…end

The command… between the while and end statements are executed aslong as ALL expression are true.• Example (computing the special MATLAB value eps. ESP is a variable it is different from esp.)

>>num=0; EPS=1; >>while (1+EPS)>1

EPS=EPS/2; num=num+1; end >>num num = 53. >>EPS=2*EPS EPS= 2.2204e-16

MATLAB USED 16 digit so eps is near 10^-16.

While Loops statements (Control Flow): • While for loop evaluates a group of commands a fixed number of times,• A while loop evaluates a group of statements an infinite number of times.• The general form of a while loop is

while expression commands…end

The command… between the while and end statements are executed aslong as ALL expression are true.• Example (computing the special MATLAB value eps. ESP is a variable it is different from esp.)

>>num=0; EPS=1; >>while (1+EPS)>1

EPS=EPS/2; num=num+1; end >>num num = 53. >>EPS=2*EPS EPS= 2.2204e-16

MATLAB USED 16 digit so eps is near 10^-16.



User Defined Variable: • Several of the M-files written for this textbook employ a user-

defined variable which is defined with the command input. For example, suppose that you want to run an M-file with different values of a variable T.

• The following command line within the M-file defines the value:

T = input('Input the value of T: ')

• Whatever comment is between the quotation marks is displayed to the screen when the M-file is running, and the user must enter an appropriate value.

• Use help command for: diary, save, load, who and whos find out more about them.

User Defined Variable: • Several of the M-files written for this textbook employ a user-

defined variable which is defined with the command input. For example, suppose that you want to run an M-file with different values of a variable T.

• The following command line within the M-file defines the value:

T = input('Input the value of T: ')

• Whatever comment is between the quotation marks is displayed to the screen when the M-file is running, and the user must enter an appropriate value.

• Use help command for: diary, save, load, who and whos find out more about them.


MATLAB ExamplesMATLAB ExamplesMATLAB ExamplesMATLAB Examples

• Some on line Demos and Examples.

• Some on line Demos and Examples.


SimulinkSimulinkSimulinkSimulink• Graphical block diagram capability

– Can drag and drop components (called blocks)

• Extensive library of blocks available– DSP Blockset is one

• Real-time Workshop

• Graphical block diagram capability– Can drag and drop components (called

blocks)

• Extensive library of blocks available– DSP Blockset is one

• Real-time Workshop


SimulinkSimulinkSimulinkSimulink• An environment for building and

simulating models.– Continuous, discrete or hybrid systems– Linear and nonlinear components– Can simulate asynchronous events

• Closely integrated with MATLAB and toolboxes

• An environment for building and simulating models.– Continuous, discrete or hybrid systems– Linear and nonlinear components– Can simulate asynchronous events

• Closely integrated with MATLAB and toolboxes


• A typical Simulink model includes Sources, Systems and Sinks.• A typical Simulink model includes Sources, Systems and Sinks.

Sources Systems Sinks

1. Sinewaves2. Function

Generators3. From MATLAB

workspace4. From Disk Files

1. Interconnectionof Linear and Nonlinear blocks

1. Displays scopes2. FFT scopes3. To MATLAB

workspace4. To disk files

Simulink ModelSimulink ModelSimulink ModelSimulink Model

z

1Unit Delay

SumSine Wave

Scope1

Scope

0.9Gain1

2

Gain

Simple Simulink ModelSimple Simulink ModelSimple Simulink ModelSimple Simulink Model

Simulink Block LibrariesSimulink Block Libraries

• Simulink contains block libraries, which contain components that can be used to build models.

• A block library can itself have other libraries as blocks. Example: When you first start Simulink:

Simulink Block Library 2.2Copyright (c) 1990-1998 by The MathWorks, Inc.

Sources Sinks NonlinearLinearDiscrete

Demos

In1 Out1

Connections

Blocksets & Toolboxes

XY Graph

simout

To Workspace

untitled.mat

To File

STOP

Stop Simulation

Scope

0

Display

Sinks is itself ablock library of

components

Building a Simulink Model

SumSine Wave

Model Window

Linear BlocksLibrary

Sources Library

Use left mouse button todrag blocks to themodel window

Uniform RandomNumber

Step

Sine Wave

SignalGenerator

RepeatingSequence

RandomNumber

Ramp

PulseGenerator

untitled.mat

From File

[T,U]

From Workspace

Discrete PulseGenerator

12:34

Digital Clock

1

Constant

Clock

Chirp Signal

Band-LimitedWhite Noise

(s-1)

s(s+1)

Zero-Pole

1

s+1

Transfer Fcn

Sum

x' = Ax+Bu y = Cx+Du

State-Space

1

SliderGain

K

MatrixGain

s

1

Integrator

1

Gain

Dot Product

du/dt

Derivative


SumSine Wave

1

GainSumSine Wave

1

Gain

SumSine Wave

1

Gain

Use the left mousebutton to click on a portand drag a connection

SumSine Wave Scope

1

Gain

SumSine Wave Scope

1

Gain

Use the right mousebutton to click on a line

to drag a branch line

Connecting BlocksConnecting Blocks


More Simulink BasicsMore Simulink Basics• Double-click on a block to open its Dialog Box.

Parameters for the block can be set in this box.– Example: setting the amplitude, frequency, phase and

sampling frequency of the sinewave source.

• Click on the HELP button on the Dialog Box for a block to launch the Web Browser opened at the HELP file for that component.

• After selecting a block, you can rotate, flip or resize it. These operations are useful in creating a more “readable” block diagram.

Setting Simulation ParametersSetting Simulation Parameters

• The Simulation menu item on the model’s window can be used to set simulation parameters.

• You can specify the appropriate solver that is to be used. For discrete-time systems use– the Fixed-step Discrete solver if there is only a single

sample time.– The Variable-step Discrete solver for multirate systems.

• You can also specify variables that are to be obtained from or returned to the MATLAB workspace.

• The Simulation menu item on the model’s window can be used to set simulation parameters.

• You can specify the appropriate solver that is to be used. For discrete-time systems use– the Fixed-step Discrete solver if there is only a single

sample time.– The Variable-step Discrete solver for multirate systems.

• You can also specify variables that are to be obtained from or returned to the MATLAB workspace.

SubsystemsSubsystems• You can select portions of your model using the mouse and make them

into a subsystem.

• You can created a masked subsystem, that hides the complexity of the subsystem from the user.

This figure demonstratesa simple first order IIR filter

Zero-OrderHold

OriginalSignal

In1Out1

My 1st orderfilter

FunctionGenerator

FilteredSignal

This figure demonstratesa simple first order IIR filter

Zero-OrderHold

OriginalSignal

In1Out1

My 1st orderfilter

FunctionGenerator

FilteredSignal

1

Out1

z

1

Unit Delay

Sum

B0

B0

A1

A1

1

In1



End of Lecture # 3End of Lecture # 3

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MATLAB WORKSHOP FOR EE 327FOR EE 327 MWF 8:00-850 AMMWF 8:00-850 AM August 26-30, 2002August 26-30, 2002 Dr. Ali A. Jalali.

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d plots

parametric plots

surface plots

y plots vector y

polar plots

contour plots

density plots

spherical plots