EEE 304 Lab Exercise 1: Introduction to MATLAB and SIMULINK
1. Introduction to MATLAB
MATLAB is a high-level technical computing language and interactive environment for algorithm
development, data visualization, data analysis, and numeric computation. Using MATLAB, one can solve
technical computing problems easier than with traditional programming languages, such as C, C++, and
Fortran due to its interpreted nature. The resulting code is vastly more efficient in terms of code
development and debugging time, code reusability and maintainability. Although net speed of execution
is inferior to that of an optimized low-level code, recent versions allow the auto-coding of MATLAB
programs into executables whose speed is often comparable to the more traditional codes.
MATLAB is useful in a wide range of applications, including signal and image processing, communications,
control design, test and measurement, financial modeling and analysis, and computational biology. Add-
on toolboxes (collections of special-purpose MATLAB functions, available separately) extend the MATLAB
environment to solve particular classes of problems in these application areas. MATLAB provides a
number of features for integrating code with other languages and applications and documenting and
sharing work. (See Mathworks website http://www.mathworks.com.)
The objective of this sequence of laboratory exercises is to explore a few fundamental problems arising in
System Theory and, at the same time, develop expertise in problem solving with MATLAB.
1.1 MATLAB Basics: Setting the Path
The MATLAB Integrated Development Environment (IDE) requires that any function or script. to be used
must be within its search path. Additionally, MATLAB, by default, starts at what is called the “Working
Directory” which is always at the top of the search path. In the example below you should set the path to
where your program is so that MATLAB can find your program and execute it (For example:
“C:\Users\cwang135\Documents\MATLAB\EEE304\Lab1”).
+This modifies the MATLAB
path for all subsequent sessions.
Should be avoided except for
cases of tool development Use this to set the path
for the current session
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Fig 1. Setting the path of your program
TIP: You could also add paths by typing the following command
>> addpath(‘C:\Users\cwang135\Documents\MATLAB\EEE304\Lab1’)
So, if you would like more than one directory to be in your path you could programmatically add them in
this manner.
1.2 MATLAB Commands
There are two ways to use MATLAB. One is to type the MATLAB Command in the “Command Window”.
For example, the MATLAB Command “bench” is to compare your computer execution speed with other
computers by computing some task. By typing “bench” and press the “Enter” key, you will see some
figures and a table about your computer execution speed.
>> bench
If you want to know more information about “bench”, type “help bench” as below and press the “Enter”
key.
>> help bench
You will find more information about what “bench” does and how to use it.
TIP: The MATLAB documentation is another way of accessing help about commands. It is graphically
pleasing and provides links to tutorials and examples at times.
>> doc bench
If there are more than a few commands to be entered and you would wish to repeat these commands by
varying parameters, the second, more elegant, way to use MATLAB is to write a script. with extension
name “.m”. MATLAB scripts are very useful in that they can be saved for later use, you could divide them
into “sections”, and you could also run each line in the script. one at a time. Let us look at an example of
how to do so.
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Fig 2. Opening a new script.
As shown in Fig 2, open a new script. and type in the following commands and save the script. with name
‘eee304.m’.
x=1;
y=2;
z=x+y;
Click to open a new
script. window
Typing the name of
the .m file is like
running a command
The variables involved
in all commands run
are displayed in the
“workspace”
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Fig 3. Executing a script.
When you type the filename in the command window and press ‘Enter’, the file will be executed as shown
in Fig. 3.
>> eee304
These three commands will add the variables x and y and assign the result to the variable z. All variables
involved in executing commands are stored in what is called the MATLAB “workspace”, see Fig. 3.
In MATLAB, applying a “;” semicolon after the end of a command will suppress any outputs in the
command window. To see what MATLAB creates at the end of each command output, simply do not add
the semicolon at the end. Try running the script. “eee304.m” again but this time take out all three
semicolons.
TIP: in order to clear the command window of any previous output, type
>> clc
TIP: to clear workspace and start anew, type
>> clear all
2. MATLAB System Commands
In this section, we will work with commands that are useful in the analysis of systems. For detailed help,
consult the MATLAB Manual, or use the built-in “help” or “doc” commands.
2.1 Create a LTI system by Transfer Function Models
Related Function: tf.
Arguments: numerator polynomial, denominator polynomial, sampling time (optional).
You can create the transfer function 44)(
2 ssH
by
>> h = tf([4] , [1 0 4])
Note that in the “tf” command the two inputs are the coefficients of the numerator and denominator
polynomials up to the highest order of the polynomial in the expression. In this example, the output “h” is
called a “system” object in MATLAB. In many MATLAB examples and documentation, such objects are
referred to as “SYS”.
2.2 Step and Bode Frequency Response of LTI Models
Related Function: bode, step
The command,
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>> bode(SYS)
draws the Bode plot of the LTI model SYS (created with tf or other system creation commands). The
frequency range and number of points are chosen automatically (a manual selection is possible, see “help
bode”).
Likewise the
>> step(SYS)
command generates the step response of the LTI model SYS. For multi-input models, independent step
commands are applied to each input channel. The time range and number of points are chosen
automatically. The final time of simulation can be modified with the optional second input argument of
time, see “doc step”.
2.3 Continuous to Discrete Time System Conversion
Related Function: c2d
In order to convert a continuous time LTI system to a discrete one, i.e. discretization, use the MATLAB c2d
command as follows:
>> c2d(SYS,TS)
where, SYS is the continuous time system object and TS is the sample time. Compare the step responses
of a system and its discretization, for different sample times: e.g.,
>> step(SYS,c2d(SYS,TS));
where TS is varied.
2.4 Frequency Analysis of a Signal
Related Function: fft
FFT stands for Fast Fourier Transform. This command implements the Discrete Fourier transform.
evaluated at discrete frequencies. It is particularly useful when one wants to know the frequency contents
of a sampled signal. The use of the FFT command can be seen with the example below.
Create a script. file named EEE304_fftTest.m and copy the following piece of code in it.
clear all; close all;
fs = 1000; % specify sampling rate, samples per second =
Hz
t = 0:1/fs:0.3; % create time vector: 0 to 0.3 second
w = 0.1; % specify width of pulse
y = rectpuls((t-0.1),w); % generate the rectangular pulse with delay
plot(t,y) % plot to view the pulse signal
xlabel('t (sec)'); ylabel('y(t)')
%% compute FFT and plot it. Double ‘%%’ breaks the code into sections
no_pts = 2^nextpow2(length(y)); % create the no. of points of FFT
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Y = fft(y,no_pts)/(no_pts); % generate FFT and divide by no_pts to
normalize fft;
f = fs/2*linspace(0,1,length(y)/2); % generate freq vector
figure % open a new figure window
plot(f,2*abs(Y(1:floor(length(y)/2)))); %plot single-sided amplitude spectrum
with linear scale
ylabel('|Y(f)|'); xlabel('f (Hz)')
figure
semilogx(f,20*log10((2*abs(Y(1:floor(length(y)/2)))))); %plot single-sided
amplitude spectrum with log dB scales
ylabel('|Y(f)| (dB)'); xlabel('f (Hz)')
Run the script. by calling its name from the MATLAB command window. This script. may come in handy
later if you need discrete Fourier Transforms of a generated signal.
TIP: In MATLAB, valid variable names must always start with letters, no spaces, dashes or special
characters are allowed other than the underscore ‘_’ character. For more see
“http://www.mathworks.com/help/matlab/matlab_prog/variable-names.html”
2.5 Filtering
The response of a linear system to arbitrary inputs can be computed with the MATLAB command lsim.
>> lsim(SYS,U,T)
plots the time response of the LTI model SYS to the input signal described by U having time T. The time
vector T consists of regularly spaced time samples and U is a matrix with as many columns as inputs and
whose i-th row specifies the input value at time T(i). For example, try the following (either in command
line or via script)
>> h = tf([3],[1 2 3])
>> [u,t] = gensig('square',15,30,0.1);
>> lsim(h,u,t)
This simulates the response of a single-input model h to the input u(t) which is a periodic pulse wave with
a period of 15 seconds for 30 seconds, with time increment of 0.1 seconds. For discrete-time models, U
should be sampled at the same rate as SYS (T is then redundant and can be omitted or set to the empty
matrix).
TIP: See also the signal processing Function “filter” which performs the same operation albeit with slightly
different commands.
A different approach is to use the SIMULINK GUI environment to perform. the simulation (more details will
follow).
2.6 Filter Design
Design a Butterworth filter (lowpass, highpass or bandstop)
Related Function: butter
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The MATLAB “butter” command allows us to create butterworth filters of lowpass, highpass, bandpass or
bandstop type.
>> [B,A] = butter(N,Wn,’type’); % the analog Butterworth filter
The command returns two vectors B and A, which are the coefficients of the Nth order digital butterworth
filter with normalized cutoff frequency at Wn with respect to sampling frequency fs. The “type”
parameter can be “high”, “low”, “bandpass” or “stop”.
Let us look at how the butterworth filter can be used to filter some noise. Create a new .m file and save it
with the following list of commands.
clear all; close all;
fs=1000;% sampling frequency 1000Hz
% generate noise
% the length of noise is 1024 points. It is normally distributed.
noise=randn(1,1024);
% compute FFT and plot it.
no_pts = 2^nextpow2(length(noise)); % create the no. of points of FFT
AF_noise = fft(noise,no_pts)/(no_pts); % normalized FFT of noise
f = fs/2*linspace(0,1,length(noise)/2); %the frequency range
figure % create new figure window
plot(f,2*abs(AF_noise(1:floor(length(noise)/2)))); %plot with linear scales
ylabel('|noise(f)|'); xlabel('f (Hz)')
title('Single-sided amplitude spectrum of noise data')
%% Now let us filter the noise and look at its spectrum
% bandpass filter
Wn=[50 200]; % pass band is 50~200Hz
%fir fliter
n = 2; %order n
Wn = Wn/(fs/2); %normalized cutoff frequency [50 200]/sampling frequency/2
[b,a] = butter(n,Wn,'bandpass');
noise_filt = filter(b,a,noise);
% compute FFT and plot it.
no_pts = 2^nextpow2(length(noise_filt)); % create the no. of points of FFT
AF_noise_filt = fft(noise_filt,no_pts)/(no_pts); % normalized FFT of filtered
noise
f = fs/2*linspace(0,1,length(noise_filt)/2); %the frequency range
figure
plot(f,2*abs(AF_noise_filt(1:floor(length(noise_filt)/2)))); %plot with linear
scales
ylabel('|filtered noise(f)|'); xlabel('f (Hz)')
title(''Single-sided amplitude spectrum of filtered noise data')
%% Let us view both filtered and unfiltered spectrum at the same time
figure
subplot(2,1,1),plot(f,2*abs(AF_noise(1:floor(length(noise)/2)))); %plot with
linear scales
ylabel('|noise(f)|'); xlabel('f (Hz)')
title(''Single-sided amplitude spectrum of noise data')
subplot(2,1,2),plot(f,2*abs(AF_noise_filt(1:floor(length(noise_filt)/2))));
%plot with linear scales
ylabel('|filtered noise(f)|'); xlabel('f (Hz)')
title(''Single-sided amplitude spectrum of filtered noise data')
You could choose to run the entire script. at once or you could select each section by clicking and bringing
the cursor anywhere in that section then hitting the “Run Section” button as shown in Fig. 4.
3. Introduction to SIMULINK
SIMULINK is a platform. for multi-domain simulation and Model-Based Design of dynamic systems. It
provides an interactive graphical environment and a customizable set of block libraries that allows for an
accurate design, simulation, implementation, and testing of control, signal processing, communications,
and other time-varying system applications.
Add-on products extend the SIMULINK environment with tools for specific modeling and design tasks and
for code generation, algorithm implementation, test, and verification.
SIMULINK is integrated with MATLAB, providing immediate access to an extensive range of tools for
algorithm development, data visualization, data analysis and access, and numerical computation.
3.1 Using SIMULINK to Build a Model
Hit “run section”
when the section is
selected, it will have a
yellow background.
The cursor must
be in the section
to be executed
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This example shows how to build a model using some of the model-building commands and actions. A
“model” is the SIMULINK equivalent of a code in MATLAB or other languages. The model integrates a sine
wave and displays the result along with the sine wave. The block diagram of the model is shown in Fig. 5.
To create the model, first create a new model as shown in Fig. 6.
Alternatively you may enter
>> Simulink
in the MATLAB Command Window. Then a window appears and asks you to select an operation; choose
“Blank Model”. The SIMULINK model window will open and it will be empty, see Fig. 7.
Click here to start
a new model.
In order to complete the model, you then need to copy blocks into a new model file (.slx) by opening the
“library browser” window. Go to View -> Library Browser. Then the blocks can be found from the
following SIMULINK block libraries as shown in Fig. 8:
Sources library (the Sine Wave block)
Sinks library (the Scope block)
Continuous library (the Integrator block)
Signal Routing library (the Mux block)
Copying is performed either by drag-and-drop, or with the standard Windows commands (ctrl-C, ctrl-V).
You can copy a Sine Wave block from the Sources library, using the Library Browser (Windows only) or the
Sources library window (UNIX and Windows). 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 the Sources
node to display the Sources library blocks. Finally, click the Sine Wave node to select the Sine Wave block.
See Fig. 8 for how the Library Browser should look after you have done this.
Now drag a copy of the Sine Wave block from the browser and drop it in the model window. Alternatively,
you may right-click on the “sine wave” block and select “Add block to model …”
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.
TIP: Another method of adding blocks introduced in R2016a is to simply click in the model and start typing
the name of the block. A search bar will open and sort search the blocks based on the typed character.
With all the blocks copied into the model window, the model should look like Fig. 10.
If you examine the blocks, you see an angle bracket on the right of the Sine Wave block and two on the
left of the Mux block. The > symbol pointing out of a block is an output port; if the symbol points to a
block, it is an input port. A signal travels out of an output port and into an input port of another block
through a connecting line. When the blocks 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 crosshairs. 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 crosshairs as it approaches the Mux block as shown in Fig. 12.
Now release the mouse button. The blocks are connected as shown in Fig. 12. You can also connect the
line to the block by releasing the mouse button while the pointer is over the block. If you do, the line is
connected to the input port closest to the cursor's position.
In Fig. 5, a branch line connects the Sine Wave output to the Integrator block carrying 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 in Fig. 12. To weld a connection to an existing line, follow these steps as shown in Fig. 13:
1. First, position the pointer on the line between the Sine Wave and the Mux block.
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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.
Note that an alternative procedure, not using the ctrl key, is to begin from the input port of the integrator
and connect to a point on the sine wave signal line. However, if the final point is not exactly on the signal
line the connection is not made and the input line remains dashed.
Finish making block connections. When you're done, your model should look like the one in Fig. 5.
Now set up SIMULINK to run the simulation for 10 seconds. First, open the Configuration Parameters
dialog box by choosing “Model Configuration Parameters” from the “Simulation” menu. On the dialog box
that appears, notice that the “Stop time” is set to 10.0 (its default value). Leave all other parameters as
their default value.
Close the Configuration Parameters dialog box by clicking the OK button. SIMULINK applies the
parameters and closes the dialog box.
Now double-click the Scope block to open its display window. Finally, choose “Start” from the
“Simulation” menu and watch the simulation output on the Scope.
The simulation stops when it reaches the stop time specified in the Configuration Parameters dialog box
or when you choose Stop from the “Simulation” menu or click the “Stop” button on the model window's
toolbar (Windows only).
To save this model, choose “Save” from the “File” menu and enter a filename and location. That file
contains the description of the model.
To terminate SIMULINK and MATLAB, just close the MATLAB window. You can also enter “quit” in the
MATLAB Command Window. If you want to leave SIMULINK but not terminate MATLAB, just close all
SIMULINK windows.
3.2 Adjusting Sine Wave Parameters
For the Sine Wave block, there are some adjustable parameters. By double-clicking on the component, a
dialog is shown as in Fig. 16. You can adjust the parameters in this dialog.