Matab Basic Tutorial

MATLAB Basics Tutorial
Vectors Functions Plotting Polynomials Matrices Printing Using M-files in MATLAB Getting help in MATLAB
Key MATLAB Commands used in this tutorial are: plot polyval roots conv deconv inv eig poly

MATLAB is an interactive program for numerical computation and data visualization; it is used extensively by control engineers for analysis and design. There are many differenttoolboxes available which extend the basic functions of MATLAB into different application areas; in these tutorials, we will make extensive use of the Control Systems Toolbox. MATLAB is supported on Unix, Macintosh, and Windows environments; a student version of MATLAB is available for personal computers. For more information on MATLAB, contact the MathWorks. The idea behind these tutorials isthat you can view them in one window while running MATLAB in another window. You should be able to re-do all of the plots and calculations in the tutorials by cutting and pasting text from the tutorials into MATLAB or an m-file.

Vectors
Let's start off by creating something simple, like a vector. Enter each element of the vector (separated by a space) between brackets, and set it equal to avariable. For example, to create the vector a, enter into the MATLAB command window (you can "copy" and "paste" from your browser into MATLAB to make it easy):
a = [1 2 3 4 5 6 9 8 7]

MATLAB should return:
a = 1 2 3 4 5 6 9 8 7

Let's say you want to create a vector with elements between 0 and 20 evenly spaced in increments of 2 (this method is frequently used to create a time vector):
t =0:2:20

t = 0 2 4 6 8 10 12 14 16 18 20

Manipulating vectors is almost as easy as creating them. First, suppose you would like to add 2 to each of the elements in vector 'a'. The equation for that looks like:
b = a + 2 b = 3 4 5 6 7 8 11 10 9

Now suppose, you would like to add two vectors together. If the two vectors are the same length, it is easy. Simply add the two as shown below:
c = a+ b c = 4 6 8 10 12 14 20 18 16

Subtraction of vectors of the same length works exactly the same way.

Functions
To make life easier, MATLAB includes many standard functions. Each function is a block of code that accomplishes a specific task. MATLAB contains all of the standard functions such as sin, cos, log, exp, sqrt, as well as many others. Commonly used constants such as pi, and i or jfor the square root of -1, are also incorporated into MATLAB.
sin(pi/4) ans = 0.7071

To determine the usage of any function, type help [function name] at the MATLAB command window. MATLAB even allows you to write your own functions with the function command; follow the link to learn how to write your own functions and see a listing of the functions we created for this tutorial.

PlottingIt is also easy to create plots in MATLAB. Suppose you wanted to plot a sine wave as a function of time. First make a time vector (the semicolon after each statement tells MATLAB we don't want to see all the values) and then compute the sin value at each time.
t=0:0.25:7; y = sin(t); plot(t,y)

The plot contains approximately one period of a sine wave. Basic plotting is very easy in MATLAB, andthe plot command has extensive add-on capabilities. I would recommend you visit the plotting page to learn more about it.

Polynomials
In MATLAB, a polynomial is represented by a vector. To create a polynomial in MATLAB, simply enter each coefficient of the polynomial into the vector in descending order. For instance, let's say you have the following polynomial:

To enter this into MATLAB,just enter it as a vector in the following manner
x = [1 3 -15 -2 9] x = 1 3 -15 -2 9

MATLAB can interpret a vector of length n+1 as an nth order polynomial. Thus, if your polynomial is missing any coefficients, you must enter zeros in the appropriate place in the vector. For example,

would be represented in MATLAB as:
y = [1 0 0 0 1]

You can find the value of a polynomial using the...