Introduction to Matlab and Simulink

1
Introduction to Matlab and Simulink

• Dr Martin Brown
• E1k, Control Systems Centre
• School of Electrical and Electronic Engineering
• University of Manchester
• Tel [phone]
• martin.brown_at_manchester.ac.uk
• EEE Intranet

2
Background and Aims

• Matlab and Simulink have become a defacto
  standard for system modelling, simulation and
  control
• It is assumed that you know how to use these
  tools and develop Matlab and Simulink programs on
  this MSc.
• Over the next two weeks, were going to have a
  rapid introduction to Matlab and Simulink
  covering
• Introduction to Matlab and help!
• Matrix programming using Matlab
• Structured programming using Matlab
• System (and signal) simulation using Simulink
• Modelling and control toolboxes in Matlab
• Note that were not covering everything to do
  with Matlab and Simulink in these 42 hour
  lectures
• Also, after every lecture block in this module,
  there is a 1 hour lab scheduled programming is
  a practical activity

3
Resources

• Mathworks Information
• Mathworks http//www.mathworks.com
• Mathworks Central http//www.mathworks.com/matlab
  central
• http//www.mathworks.com/applications/controldesig
  n/
• http//www.mathworks.com/academia/student_center/t
  utorials/launchpad.html
• Matlab Demonstrations
• Matlab Overview A demonstration of the
  Capabilities of Matlab http//www.mathworks.com/cm
  spro/online/4843/req.html?13616
• Numerical Computing with Matlab
  http//www.mathworks.com/cmspro/online/7589/req.ht
  ml?16880
• Select Help-Demos in Matlab
• Matlab Help
• Select Help in Matlab. Extensive help about
  Matlab, Simulink and toolboxes
• Matlab Homework Helper http//www.mathworks.com/ac
  ademia/student_center/homework/
• Newsgroup comp.soft-sys.matlab
• Matlab/Simulink student version (program and book
  50) http//www.mathworks.com/academia/student_ce
  nter
• Other Matlab and Simulink Books
• Mastering Matlab 6, Hanselman Littlefield,
  Prentice Hall
• Mastering Simulink 4, Dabney Harman, Prentice
  Hall
• Matlab and Simulink Student Version Release 14
• lots more on mathworks, amazon, . It is
  important to have one reference book.

4
Introduction to Matlab
Command window
Variable browser

• Click on the Matlab icon/start menu initialises
  the Matlab environment
• The main window is the dynamic command
  interpreter which allows the user to issue Matlab
  commands
• The variable browser shows which variables
  currently exist in the workspace

Command history
5
Matlab Programming Environment

• Matlab (Matrix Laboratory) is a dynamic,
  interpreted, environment for matrix/vector
  analysis
• Variables are created at run-time, matrices are
  dynamically re-sized,
• User can build programs (in .m files or at
  command line) using a C/Java-like syntax
• Ideal environment for model building, system
  identification and control (both discrete and
  continuous time
• Wide variety of libraries (toolboxes) available

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Basic Matlab Operations

• gtgt This is a comment, it starts with a
• gtgt y 53 22 simple arithmetic
• gtgt x 1 2 4 5 6 create the vector x
• gtgt x1 x.2 square each element in x
• gtgt E sum(abs(x).2) Calculate signal energy
• gtgt P E/length(x) Calculate av signal power
• gtgt x2 x(13) Select first 3 elements in x
• gtgt z 1i Create a complex number
• gtgt a real(z) Pick off real part
• gtgt b imag(z) Pick off imaginary part
• gtgt plot(x) Plot the vector as a signal
• gtgt t 00.1100 Generate sampled time
• gtgt x3exp(-t).cos(t) Generate a discrete
  signal
• gtgt plot(t, x3, x) Plot points

7
Introduction to Simulink

• Simulink is a graphical, drag and drop
  environment for building simple and complex
  signal and system dynamic simulations.
• It allows users to concentrate on the structure
  of the problem, rather than having to worry (too
  much) about a programming language.
• The parameters of each signal and system block is
  configured by the user (right click on block)
• Signals and systems are simulated over a
  particular time.

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Starting and Running Simulink

• Type the following at the Matlab command prompt
• gtgt simulink
• The Simulink library should appear
• Click File-New to create a new workspace, and
  drag and drop objects from the library onto the
  workspace.
• Selecting Simulation-Start from the pull down
  menu will run the dynamic simulation. Click on
  the blocks to view the data or alter the run-time
  parameters

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Signals and Systems in Simulink

• Two main sets of libraries for building simple
  simulations in Simulink
• Signals Sources and Sinks
• Systems Continuous and Discrete

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Basic Simulink Example

• Copy sine wave source and scope sink onto a
  new Simulink work space and connect.
• Set sine wave parameters modify to 2 rad/sec
• Run the simulation
• Simulation - Start
• Open the scope and leave open while you change
  parameters (sin or simulation parameters) and
  re-run
• Many other Simulink demos

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Day 1 Matrix Programming in Matlab

• Full notes/syntax will be recorded in the diary
• Setting directory and diary
• Simple maths
• Matlab workspace, and help
• Variables, comments, complex numbers and
  functions
• Matlab desktop and management
• Script m-files
• Arrays
• Creating and assigning arrays, standard arrays
• Array indexing and orientation
• Array operators
• Array manipulation
• Array sorting, sub-array searching and
  manipulation functions
• Array size and memory utilization
• Control structures
• for and while loops
• if else and switch decisions

12
Day 2 Structured Matlab Programming

• Full notes/syntax will be recorded in the diary
• Functions
• Input and output arguments
• File structure, search path
• Exception handling
• Debugging and profiling
• Strings
• Dynamic function and expression evaluation
• Cell arrays
• Data structures
• Data plotting (2D/3D), figures
• GUIDE
• Simulink

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Day 1 Laboratory

• Remember
• Change directory to your local filespace so that
  your work is saved
• Turn on the diary on to save the commands and
  results from the lab session to a file for future
  reference
• Questions
• Use the help and lookfor commands and look at the
  normal Matlab help section in the pull down menu
  (F1). How does the sin() function work?
• Evaluate expressions such as 78/9, 82, 65-3
• Using the in-built Matlab functions, evaluate
  sin(0), sin(pi/2), abs(-3)
• Using the editor, write a Matlab script to solve
  the quadratic equation
• 2x2 -10x 12 0
• Evaluate, using a for loop, the first twenty
  numbers of the Fibonacci series
• xn xn-1 xn-2, x0 1, x1 1
• Create the two vectors 1 2 3, 4 5 6 and
  calculate their inner product
• Create the 33 matrix A 1 2 3 4 5 6 7 8 9
  and the column vector b 1 2 3, and multiply
  the two together Ab.
• Solve the equation Ax b, where A and b are
  given in (6)
• Modify (8), so that you neglect the 3rd row
  column of information.
• http//www.facstaff.bucknell.edu/maneval/help211
  /exercises.html

14
Day 2 Laboratory

• Write a function that returns the two roots of a
  quadratic equation, given the three arguments a,
  b and c. Test the function from the command line
• Write a function that returns the mean and
  standard deviation of a vector of numbers (input
  vector). While Matlab supplies the mean() and
  std() functions, try just using the sum() and
  length() functions.
• Write a function that reverses the order of
  letters in a string, and returns the new string.
• Use the eval() Matlab function to evaluate
  strings such as
• exp1 56 7
• Note this, and feval(), is very useful for
  dynamic programming
• Use a cell array to store a list of expressions,
  stored as strings. Then use eval() and a for
  loop to iterate over the expressions and evaluate
  them.
• Create two simple data structures to modify your
  solution to (1). Use one data structure to pack
  the parameters of the quadratic equation into a
  single variable, and use another to return the
  roots inside a single data structure
• Create the vector 0pi/202pi and use it to
  sample the sin() function. Plot the results and
  edit the figure window to put labels on the
  figure. Save the figure (.fig) and export a .jpg
  file.
• Use the meshgrid() function to sample a 2
  dimensional input space between 0 and 2p, then
  use the data to sample the function
  sin(x1)cos(x2). Plot the results using the
  mesh() function.
• Create a GUI that prompts the user for a number
  and then displays double that number next to the
  entered value.
• Start Simulink and using a sin() source and a
  scope sink, view the signal over 10 seconds.
• Change the frequency of the sin() source and
  again compare the results. Next change the
  simulation length.
• Build the first order system H(s) 1/(13s) in
  the model and pass a sin() signal through the
  system. Make sure you run the simulation for a
  long enough time for the transients to die down
  and the system to settle.
• Replace the first order system in (6) with the
  second order system, what is the difference when
  the system settles down H(s) 1/(12ss2).