Introduction to Matlab and Simulink Dr Martin Brown

Introduction to Matlab and Simulink Dr Martin Brown E 1 k, Control Systems Centre School of Electrical and Electronic Engineering University of Manchester Tel: 0161 306 4672 martin. brown@manchester. ac. uk EEE Intranet EE-M 110 EFIS, W 1 06 -07 1

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, we’re 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 we’re not covering everything to do with Matlab and Simulink in these 4*2 hour lectures Also, after every lecture block in this module, there is a 1 hour lab scheduled – programming is a practical activity EE-M 110 EFIS, W 1 06 -07 2

Resources Mathworks Information • Mathworks: http: //www. mathworks. com • Mathworks Central: http: //www. mathworks. com/matlabcentral • http: //www. mathworks. com/applications/controldesign/ • http: //www. mathworks. com/academia/student_center/tutorials/launchpad. html Matlab Demonstrations • Matlab Overview: A demonstration of the Capabilities of Matlab http: //www. mathworks. com/cmspro/online/4843/req. html? 13616 • Numerical Computing with Matlab http: //www. mathworks. com/cmspro/online/7589/req. html? 16880 • Select Help-Demos in Matlab Help • Select “Help” in Matlab. Extensive help about Matlab, Simulink and toolboxes • Matlab Homework Helper http: //www. mathworks. com/academia/student_center/homework/ • Newsgroup: comp. soft-sys. matlab Matlab/Simulink student version (program and book ~£ 50) http: //www. mathworks. com/academia/student_center 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. EE-M 110 EFIS, W 1 06 -07 3

Introduction to Matlab Click on the Matlab icon/start menu initialises the Matlab environment: Variable browser Command window 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 EE-M 110 EFIS, W 1 06 -07 4

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 EE-M 110 EFIS, W 1 06 -07 5

Basic Matlab Operations >> >> >> >> % This is a comment, y = 5*3 + 2^2; x = [1 2 4 5 6]; x 1 = x. ^2; E = sum(abs(x). ^2); P = E/length(x); x 2 = x(1: 3); z = 1+i; a = real(z); b = imag(z); plot(x); t = 0: 0. 1: 100; x 3=exp(-t). *cos(t); plot(t, x 3, ‘x’); EE-M 110 EFIS, W 1 06 -07 it starts with a “%” % simple arithmetic % create the vector “x” % square each element in x % Calculate signal energy % Calculate av signal power % Select first 3 elements in x % Create a complex number % Pick off real part % Pick off imaginary part % Plot the vector as a signal % Generate sampled time % Generate a discrete signal % Plot points 6

Introduction to 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) vs, vc Signals and systems are simulated over a particular time. t EE-M 110 EFIS, W 1 06 -07 7

Starting and Running Simulink Type the following at the Matlab command prompt >> 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 EE-M 110 EFIS, W 1 06 -07 8

Signals and Systems in Simulink Two main sets of libraries for building simple simulations in Simulink: • Signals: Sources and Sinks • Systems: Continuous and Discrete EE-M 110 EFIS, W 1 06 -07 9

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 … EE-M 110 EFIS, W 1 06 -07 10

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 EE-M 110 EFIS, W 1 06 -07 11

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 (2 D/3 D), figures GUIDE Simulink EE-M 110 EFIS, W 1 06 -07 12

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 1. Use the help and lookfor commands and look at the normal Matlab help section in the pull down menu (F 1). How does the sin() function work? 2. Evaluate expressions such as 7*8/9, 8^2, 6+5 -3 3. Using the in-built Matlab functions, evaluate sin(0), sin(pi/2), abs(-3) 4. Using the editor, write a Matlab script to solve the quadratic equation 2 x 2 -10 x + 12 = 0 5. Evaluate, using a for loop, the first twenty numbers of the Fibonacci series 1. xn = xn-1 + xn-2, x 0 = 1, x 1 = 1 6. Create the two vectors [1 2 3], [4 5 6] and calculate their inner product 7. Create the 3*3 matrix A = [1 2 3; 4 5 6; 7 8 9] and the column vector b = [1 2 3], and multiply the two together A*b. 8. Solve the equation A*x = b, where A and b are given in (6) 9. Modify (8), so that you neglect the 3 rd row & column of information. 10. … http: //www. facstaff. bucknell. edu/maneval/help 211/exercises. html EE-M 110 EFIS, W 1 06 -07 13

Day 2: Laboratory 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 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: exp 1 = ‘ 5*6 + 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 0: pi/20: 2*pi 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 2 p, then use the data to sample the function sin(x 1)*cos(x 2). 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/(1+3 s) 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/(1+2 s+s^2). EE-M 110 EFIS, W 1 06 -07 14