matlab basics

MATLAB Applications to electrical Engineering

V R SIDDHARTHA ENGINEERING COLLEGEEEE DEPARTMENT

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Introduction to MATLAB MATLAB Basics Vectors and Matrices Loops Plots Examples Simulink Modelling examples

MATLAB

SIMULINK

CONTENTS

Introduction to MATLAB MATLAB Basics Vectors and Matrices Loops Plots Examples

04/21/2023 07:39:39 PM MATLAB PRESENTATION 4

MATLAB has been developed by Math Works ,It is a powerful software package used for high performance scientific numeric computation ,data analysis and visualization

MATLAB stands for MATrix Laboratory

MATLAB provides matrix as one of the basic elements. It provides basic operations like addition , subtraction , multiplication by use of simple mathematical operators

Programs can be run step by step, with full access to all variables, functions etc

MATLAB INTRODUCTION

We need not declare the type and size of any variable in advance and MATLAB is case sensitive and so we have to be careful about the case of variables while using them in our program

MATLAB gives an interactive environment with hundreds of reliable and accurate built in functions. These functions help in providing the solutions to a variety of mathematical problems including matrix algebra ,linear systems ,differential equations ,optimization, nonlinear systems and other scientific and technical computations

It facilitates access to FORTRAN and C codes by means of external interfaces

Rows and columns are always numbered starting at 1

MATLAB matrices are of various types to hold different kinds of data (usually floats or integers)

A single number is really a 1 x 1 matrix in MATLAB

Any matrix can be assigned to any variable

Advantages and Disadvantages of MATLAB

• Advantages: Ease of Use

Platform Independent (All versions of Windows, Linux, Unix, Mac.)

Predefined Functions and Toolboxes

Device-Independent Plotting

Graphical User Interface

Matlab compiler

• Disadvantages:

Interpreted programming language, slower than C++ and

Fortran.

MATLAB BASICS

Introduction to Matlab MATLAB Basics Vectors and Matrices Loops Plots MATLAB examples

Command Window

Workspace

CommandHistory

Change the current directory to the location of your

Matlab file at startup

MATLAB WindowsMATLAB desktop

Workspace: All the information and details of every variable entered into the

command window is displayed here.

Command History : stores history of every command.

Command window: Every operation which we want to perform is to be entered in command window.

Editor Window :This window is used to write any program, which includes many command statements. By using this window one can edit any previously written command.

Figure Window :All the figures are shown in a separate figure window.

3 ways to open a new m-file using MATLAB editor

1. Type >> edit myprogram.m at the command prompt

2. Click on the blank page on MATLAB main window toolbar

3. Click File → New → M-file

Variables1. In MATLAB environment, every variable is an array or matrix

2. Once a variable is entered into the system, you can refer to it later

3. When an expression returns a result that is not assigned to any variable, the system assigns it to a variable named ans, which can be used later

4. You can have multiple assignments on the same line

Ex : a = 2; b = 7; c = a * b5. The who command displays all the variable names you have used6. The whos command displays little more about the variables7. A valid variable name starts with a letter, followed by letters, digits, or underscores8. Avoid creating variables with the same name as a function (such

as i, j, mode, char, size, and inf etc.)9. Check whether a proposed variable name is already in use with

the exist or which function. exist returns 0 if there are no existing variables, functions, or other artifacts with the proposed name

Predefined variables

Break,Case,Catch,continue,else,elseif end,for,function,global,if,otherwise,return,

switch,try ,while,pi,j,I,ans,NaN,inf etc

Creating VectorsCreate vector with equally spaced intervals>> x=0:0.5:pix = 0 0.5000 1.0000 1.5000 2.0000 2.5000 3.0000

Create vector with n equally spaced intervals>> x=linspace(0, pi, 7)x = 0 0.5236 1.0472 1.5708 2.0944 2.6180 3.1416

Equal spaced intervals in logarithm space>> x=logspace(1,2,7)x = 10.0000 14.6780 21.5443 31.6228 46.4159 68.1292 100.0000

Some Built-in functions• mean(A):mean value of a vector• max(A), min (A): maximum and

minimum. • sum(A): summation.• sort(A): sorted vector• median(A): median value• std(A): standard deviation. • det(A) : determinant of a square

matrix • dot(a,b): dot product of two vectors• Cross(a,b): cross product of two vectors• Inv(A): Inverse of a matrix A

Arithmetic Operations and PrecedenceOperation Algebraic Matlab

Form Scalar

addition a + b a + bsubtraction a – b a – bmultiplication a x b a * bdivision a ÷ b a / bExponentiation ab a ^ b

Precedence Operation

1 Parenthesis, innermost first.

2 Exponentiation, left to right

3 Multiplication & division, left to right

4 Addition & subtraction, left to right2^3^4 equals (2^3)^4 2/3*4 equals (2/3)*4 2-3+4 equals (2-3)+4

Function Descriptionexp(x) Exponential (ex)log(x) Natural logarithm

log10(x) Base 10 logarithmsqrt(x) Square root

Trigonometric OperationsFunction Description

sin(x) Computes the sine of x, where x is in radians.

csc(x) Computes the cosec of x, where x is in radians.

sind(x) Computes the sin of x, where x is in degrees.

asin(x) Computes the arcsine or inverse sine of x, where x is in radians.

sinh(x) Computes the hyperbolic sine of x, where x is in radians.

atanh(x) Computes the inverse hyperbolic tangent of x.

Complex Number FunctionsFunction Description

conj(x)Computes the complex conjugate of the complex number x. Thus, if x is equal to a+ib, then conj(x) will be equal to a-ib.

real(x) Computes the real potion of the complex number x.

imag(x) Computes the imaginary potion of the complex number x.

abs(x) Computes the absolute value of magnitude of the complex number x.

angle(x) Computes the angle of the complex number x.

Commands for Managing VariablesCommand Description

clear Removes all variables from the memory.

clear a, b Clears only variables a and b from memory.

who Lists the variables currently in workspace.

whos Displays a lists of the variables currently in the memory and their size together with information about their bytes & class.

Examples>> x=1:3

x = 1 2 3

>> exp(x)

ans = 2.7183 7.3891 20.0855

>> log(x)

ans = 0 0.6931 1.0986

>> sqrt(x)

ans = 1.0000 1.4142 1.7321

Addition,substraction and division of complex numbers

clear;

z1=1+2i;

z2=3+4i;

z3=z1+z2

z4=z1-z2

z5=z1*z2

z6=z1/z2

abs(z2)

angle(z3)

Output

z3 = 4.0000 + 6.0000i

z4 = -2.0000 - 2.0000i

z5 = -5.0000 +10.0000i

z6 = 0.4400 + 0.0800i

ans =5

ans = 0.9828

Solve the following examples using MATLAB

04/21/2023 07:39:41 PM 26

Program to calculate trignometric values

• Program:x=0:30:180;y=[sind(x);cosd(x);tand(x);cscd(x);secd(x);cotd(x)]z=[x;y]

MATLAB PRESENTATION

Solving linear equations

A System of simultaneous linear equations is written , AX =B

A is a given square matrix of order n , B is a given column vector of n components and X is an unknown column vector of n components

we have learn that the solution to AX =b ,can be written as X=A-1b ,where A-1 is the inverse of A

• Example :

Solutions to Systems of Linear Equations (con’t…)

• Solution by Matrix Inverse:Ax = bA-1Ax = A-1bx = A-1b

• MATLAB:>> A = [ 3 2 -1; -1 3 2; 1 -1 -1];>> b = [ 10; 5; -1];>> x = inv(A)*bx = -2.0000 5.0000 -6.0000

Answer:x1 = -2, x2 = 5, x3 = -6

• Solution by Matrix Division:The solution to the equation

Ax = bcan be computed using left division.

Answer:x1 = -2, x2 = 5, x3 = -6

NOTE: left division: A\b b A right division: x/y x y

MATLAB:>> A = [ 3 2 -1; -1 3 2; 1 -1 -1];>> b = [ 10; 5; -1];>> x = A\bx = -2.0000 5.0000 -6.0000

“linsolve” command

• Solve the system:

• A*S=B• MATLAB Code:

04/21/2023 07:39:42 PM

>> A=[5,-2,-3;0,4,3;1,-1,9];>> B=[-3,-2,60]'; % Note vector transpose (‘)>> S=linsolve(A,B)S = 1.0000 -5.0000 6.0000

‘’ Solve ‘’ command

MATLAB CODE OUTPUT

1)Quadratic equation x2 -7x +12 = 0

>> Eq = X^2-7*X+12;>>S= Solve(Eq); (or)solve('x^2-7*x+12=0')

s = 3 4

2) X4-7X3+3X2-5X+9=0

>> Eg= X^4-7*X^3+3X^2-5X+9=0; >>S=solve(Eg);

S= 6.6304 ,1.06 ,-0.34 – 1.077 and -0.34 + 1.077

The solve command used to solve quadratic equations. The function returns the roots of the equation Example :

EX: syms a b c x fun=a*x^2+b*x+c; solve(fun,x)

Output:ans = -(b + (b^2 - 4*a*c)^(1/2))/(2*a) -(b - (b^2 - 4*a*c)^(1/2))/(2*a)

Expand and the Collect commands

• The expand and the collect command expands and collects an equation respectively. The following example demonstrates the concepts

MATLAB Code :

Factor command :

• The factor command factorizes an expression and the simplify command simplifies an expression.

Examples :MATLAB code Answer

factor(x^3 - y^3) (x - y)*(x^2 + x*y + y^2)

factor([x^2-y^2,x^3+y^3]) [ (x - y)*(x + y), (x + y)*(x^2 - x*y + y^2)]

simplify((x^4-16)/(x^2-4)) x^2 + 4

Simplify((x^3-y^3)/(x-y) X^2+x*y+y^2

‘Polyval’ command:

‘POLYVAL’ command Evaluates polynomial in a matrix senseEx 1:>> a=[1 2 3]; % polynomial X2 + 2X +3 >> polyval(a,1) % polynomial is evaluated at ‘1’ans =6

>>a=[1 2 3]>>b= 1:5>>C=polyval(a,b) Output :C=[6 11 18 27 38]

Polyval and poly

EX :(with breakpoints)clcclearp=[1 2 1]x=-2:1:2y=polyval(p,x)plot(x,y)r=roots(p)q=poly(r)

‘Diff’ command

• MATLAB provides the diff command for computing symbolic derivatives

• Examples :MATLAB CODE ANSWER

syms tf = 3*t^2 + 2*t^(-2);diff(f)

6*t - 4/t^3

f = x*exp(-3*x);diff(f, 2)

9*x*exp(-3*x) - 6*exp(-3*x)

Integration:

• MATLAB Code :syms x int(2*x)ans = x^2

For example, to calculate the value of we writeint(x, 4, 9)ans = 65/2

Dsolve command:

MATLAB provides the dsolve command for solving differential equations symbolically. The most basic form of the dsolve command for finding the solution to a single equation is :

second order differential equation as: y" - y = 0, y(0) = -1, y'(0) = 2.

MATLAB Code : dsolve('D2y - y = 0','y(0) = -1','Dy(0) = 2')

ans = exp(t)/2 - (3*exp(-t))/2

Polynomial Algebra (Convolution Operator)

82026218)445)(23( 2345232 xxxxxxxxxx

• Polynomial products and factoring:

MATLAB code :For onvolution For Deconvolution

>> p1=[1,3,2];>> p2=[1,5,4,4];>> pc=conv(p1,p2)pc = 1 8 21 26 20 8

>> deconv(pc,p2)ans = 1 3 2>> deconv(pc,p1)ans = 1 5 4 4

Mathematics Example:Polynomial Roots

• Find the roots of the following system:

• MATLAB code:

812 2 xxy

04/21/2023 07:39:43 PM

>> roots([12 -1 -8])ans = 0.8592 -0.7759

Finding the Maxima and Minima of a Curve

ExampleLet us find the stationary points of the function f(x) = 2x3 + 3x2 − 12x + 17 syms x;y = 2*x^3 + 3*x^2 - 12*x + 17; % defining the function ezplot(y)

Our aim is to find some local maxima and minima on the graph, so let us find the local maxima and minima for the interval [-2, 2] on the

syms x;y = 2*x^3 + 3*x^2 - 12*x + 17; ezplot(y, [-2, 2])

Laplace and Inverse Laplace Transforms

MATLAB Code Answer

laplace(a) 1/s^2

laplace(t^2) 2/s^3

ilaplace(1/s^3) t^2/2

Fourier Transforms and Inverse Fourier Transforms

MATLAB Code Answer

f = exp(-2*x^2); FT = fourier(f)

FT = (2^(1/2)*pi^(1/2)*exp(-w^2/8))/2

f = ifourier(-2*exp(-abs(w))) f =-2/(pi*(x^2 + 1))

Transfer function representation Using Matlab

• MatLab• >>num = [1 -2 1 -6.3];• >>den = [1 0.05 -3.14];• >>f = tf(num,den)

14.305.0

Example

Examples

Matlab Programming for Engineers

Introduction to Matlab Matlab Basics Vectors and Matrices Loops Plots MATLAB examples

Matrix Index• The matrix indices begin from 1 (not 0 (as in C)) • The matrix indices must be positive integer

Given:

A(-2), A(0)

Error: ??? Subscript indices must either be real positive integers or logicals.

A(4,2)Error: ??? Index exceeds matrix dimensions.

Vectors and Matrices• Vectors (arrays) are defined as• >> v = [1, 2, 4, 5]• >> w = [1; 2; 4; 5]

>> A = [1,2,3;4,-5,6;5,-6,7]

Vectors and Matrices

• How do we assign values to matrices ?

Columns separated by space or a comma

Rows separated by semi-colon

>>> A=[1 2 3;4 5 6;7 8 9]A = 1 2 3 4 5 6 7 8 9>>>

• How do we access elements in a matrix or a vector?

>>> A(2,3)ans = 6

>>> A(:,3)ans = 3 6 9

>>> A(1,:)ans = 1 2 3

>>> A(2,:)ans = 4 5 6

• Arithmetic operations – Matrices

Performing operations to every entry in a matrix

Add and subtract>>> A=[1 2 3;4 5 6;7 8 9]A = 1 2 3 4 5 6 7 8 9>>>

>>> A+3ans = 4 5 6 7 8 9 10 11 12

>>> A-2ans = -1 0 1 2 3 4 5 6 7

Multiply and divide>>> A=[1 2 3;4 5 6;7 8 9]A = 1 2 3 4 5 6 7 8 9>>>

>>> A*2ans = 2 4 6 8 10 12 14 16 18

>>> A/3ans = 0.3333 0.6667 1.0000 1.3333 1.6667 2.0000 2.3333 2.6667 3.0000

Power>>> A=[1 2 3;4 5 6;7 8 9]A = 1 2 3 4 5 6 7 8 9>>>

A^2 = A * A

To square every element in A, use the element–wise operator .^

>>> A.^2ans = 1 4 9 16 25 36 49 64 81

>>> A^2ans = 30 36 42 66 81 96 102 126 150

Performing operations between matrices>>> A=[1 2 3;4 5 6;7 8 9]A = 1 2 3 4 5 6 7 8 9

>>> B=[1 1 1;2 2 2;3 3 3]B = 1 1 1 2 2 2 3 3 3

393837

262524

131211

272421

505050

323232

141414

0000.36667.23333.20000.35000.20000.20000.30000.20000.1

3/93/83/72/62/52/41/31/21/1

729512343

362516

Tril/triu commands>> a=[1 2 3;4 5 6;7 8 9]a = 1 2 3 4 5 6 7 8 9

>> tril(a)ans =

1 0 0 4 5 0 7 8 9>> triu(a)ans =

1 2 3 0 5 6 0 0 9

• To extracts a sub matrix such that it contains all the elements corresponding to row number and column number

)2:1,2:1(

Long Array, Matrix • t =1:10

t = 1 2 3 4 5 6 7 8 9 10• k =2:-0.5:-1

k = 2 1.5 1 0.5 0 -0.5 -1

• X = [1:4; 5:8]

x = 1 2 3 4 5 6 7 8

Generating Vectors from functions• zeros(M,N) MxN matrix of zeros

• ones(M,N) MxN matrix of ones

• rand(M,N) MxN matrix of uniformly distributed

random numbers on (0,1)

x = zeros(1,3)x =

x = ones(1,3)x =

x = rand(1,3)x =0.9501 0.2311 0.6068

Concatenation of Matrices• x = [1 2], y = [4 5], z=[ 0 0]

A = [ x y]

1 2 4 5

B = [x ; y]

1 2 4 5

C = [x y ;z] Error:??? Error using ==> vertcat CAT arguments dimensions are not consistent.

Indexing Matrices• Indexing using parentheses

>> A(2,3)

• Index submatrices using vectorsof row and column indices >> A([2 3],[1 2])

• Ordering of indices is important!>> B=A([3 2],[2 1])>> B=[A(3,2),A(3,1); A(2,2);A(2,1)]

Indexing Matrices(Cond) • Index complete row or column using

the colon operator >> A(1,:)

• Can also add limit index range>> A(1:2,:)>> A([1 2],:)

• General notation for colon operator>> v=1:5>> w=1:2:5

Matrix Concatenation Functions

The following functions combine existing matrices to form a new matrix.

Function Description

cat Concatenate matrices along the specified dimension.

horzcat Horizontally concatenate matrices.

vertcat Vertically concatenate matrices.

repmat Create a new matrix by replicating and tiling existing matrices.

blkdiag Create a block diagonal matrix from existing matrices

This example constructs a new matrix C by concatenating matrices A and B in a vertical direction

Example : >>A = ones(2, 5) * 6; % 2-by-5 matrix of 6's

>>B = rand(3, 5); % 3-by-5 matrix of random values

>>C = [A; B] % Vertically concatenate A and B

Output :C = 6.0000 6.0000 6.0000 6.0000 6.0000 6.0000 6.0000 6.0000 6.0000 6.0000 0.9501 0.4860 0.4565 0.4447 0.9218 0.2311 0.8913 0.0185 0.6154 0.7382 0.6068 0.7621 0.8214 0.7919 0.1763

Example :

1 2 3 4 5 6 7 8 9

>> b=repmat(a,2,3)

1 2 3 1 2 3 1 2 3 4 5 6 4 5 6 4 5 6 7 8 9 7 8 9 7 8 9 1 2 3 1 2 3 1 2 3 4 5 6 4 5 6 4 5 6 7 8 9 7 8 9 7 8 9

Creating a Block Diagonal Matrix

• The blkdiag function combines matrices in a diagonal direction and all other elements of the matrix are set to zero

>>A = magic(3); >>B = [-5 -6 -9; -4 -4 -2]; >>C = eye(2) * 8;

>>D = blkdiag(A, B, C)

• Output:D = 8 1 6 0 0 0 0 0 3 5 7 0 0 0 0 0 4 9 2 0 0 0 0 0 0 0 0 -5 -6 -9 0 0 0 0 0 -4 -4 -2 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 8

Example

Diagonal elements

fprintf ,Disp commands

Disp(x)Disp(‘string’)

disp(x) displays the arrayIf X is a string, the text is displayed

Ex :z=2+3i;fprintf('z= ');disp(z)

Output :Z= 2+3i

Format Code Purpose

%s Format as a string.

%d Format as an integer.

%f Format as a floating point value.

%e Format as a floating point value in scientific notation.

%g Format in the most compact form: %f or %e.

\n Insert a new line in the output string.

\t Insert a tab in the output string.

The fscanf and fprintf commands behave like C scanf and printf functions. They support the following format codes:

Fprintf examples :

>> n=2;>> fprintf('value is %d\n',n)

Output:value is 2

fprintf('I have %d brother and %d sister\n',1,1)Output :I have 1 brother and 1 sister

>> fprintf(‘This is %s department , we got %d years of NBA accrediation/n','EEE',5)

Output : This is EEE department ,we got 5 years of NBA accrediation/n>>

‘input ‘ command

Example :x=input('enter the value of x');y=input('enter the value of y');z=x+y;fprintf('the value of z is %d\n',z)

Output:enter the value of x30enter the value of y0the value of z is 30

Write the program to display 6th table

6*1=66*2=126*3=186*4=246*5=306*6=366*7=426*8=486*9=546*10=60

n=input('enter n value');for i=1:10 fprintf('%d*%d=%d\n',n,i,n*i)end

Importing data files into MATLAB

1.First create text file with name ‘data’2.In matlab file , load data.txt

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