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Mat Lab Program

BBS COLLEGE OF ENGINEERING & TECH.

NUMERICAL TECNIQUE LAB (MAT LAB)

SUBMITTED TO – Mr. Amit Gupta

SUBMITTED BY – Umesh Kumar Maurya
Roll No: 1113821044
EN Branch:2 nd Year(3 rd sem)

PROGRAM-1
OBJECT : TO FIND THE SOLUTION OF THE LINEAR EQUATIONS?
LINEAR EQUATIONS : x+4y+6z=1
2x+4y+6z=4
6x+8y+9z=7
MATLAB PROGRAM -
A=[1 4 6;2 4 6;6 8 9];
In v(A)
ans = -1.0000 1.0000 0.0000
1.5000 -2.2500 0.5000
-0.6667 1.3333 -0.3333
B=[1;4;7];
X=ans*B ;
X = 3.0000
-4.0000
2.3333

PROGRAM-2
OBJECT : TO FIND THE EIGEN VALUES AND EIGEN VECTORS OF GIVEN MATRIX A ?
Given Matrix : A=
MATLAB PROGRAM -
A=[1 2 3;3 5 7;2 4 7];
[V,D]= eig(A);
V = -0.2918 -0.7440 -0.1276
-0.7156 0.6497 -0.8191
-0.6346 -0.1560 0.5594
D = 12.4 304 0 0
0 -0.1171 0
0 0 0.6868

PROGRAM-3
OBJECT : FIND THE ROOTS OF GIVEN POLYNOMIAL-
P(x)= 20x 3 +5x 2 -2x+1
MATLAB PROGRAM-
P=[20 5 -2 1];
r=roots(P) ;
r = -0.5751
0.1625 + 0.2460i
0.1625 - 0.2460i

PROGRAM-4(A)
OBJECT: CONSIDER THESYSTEM AND CONVERTIT INTO STATE SPACE EQUIVALENT:
G=5/(S 2 +2S+10)
MATLAB PROGRAM :
num=[0 0 5];
den=[1 2 10];
G=tf(num,den)
Transfer function:
5
--------------
s^2 + 2 s + 10
[A,B,C,D]=tf2ss(num,den)
A = -2 -10
1 0
B = 1
0
C = 0 5

PROGRAM-4(B)

OBJECTIVE : CONSIDER THE SYSTEM AND CONVERT IT INTO TRANSFER FUNCTION WHERE A=[-2 -10;1 0],B=[1;0],C=[0 5]& D=0?
MATLAB PROGRAM :
A=[-2 -10;1 0];
B=[1;0];
C=[0 5];
D=0;
[num,den]=ss2tf(A,B,C,D)
num =
0 0.0000 5.00 00
den =
1.0000 2.0000 10.0000
G=tf(num,den1)
Transfer function:
5
------------
S^2+2s+10

PROGRAM-5

OBJECT : OBTAIN THE RESPONSE Y(t) OF THE FOLLOWING A= [-1 -0.5;1 0] ; B=[ 0.5;0]; C=[1 0]
SYSTEM AND INITIAL CONDITIONS ARE X(0)=[0 0] WHERE U(t) IS THE STEP INPUT OCCURING AT y=0 OR U(t)=0
MATLAB PROGRAM :
A=[-1 -0.5;1 0];
B=[0.5;0];
C=[1 0];
D=0;
sys=ss(A,B,C,D)
a = x1 x2
x1 -1 -0.5
x2 1 0
b = u1
x1 0.5
x2 0
c = x1 x2
y1 1 0
d = u1
y1 0
Continuous-time model.
step(sys)
STEP RESPONSE OF THE SYSTEM

PROGRAM-6
OBJECT : TO FIND THE STEP RESPONSSE OF GIVEN TRANSFER FUNCTION-
TRANSFER FUNCTION : s+1/(s+2)*(s+5)
MATLAB PROGRAM -
s=tf('s');
g=(s+1)/((s+2)*(s+5))
Transfer function: s + 1
--------------
s^2 +7 s + 10
step(g)
STEP RESPPONSE OF THE GIVEN FUNCTION

PROGRAM-7
OBJECT: COMPUTE φ(x)OR STATE TRANSFER MATRIX OF THE FOLLOWING MATRIX A-
A=
MATLAB PROGRAM:
A=[0 1;-2 -3];
B=sym(‘t’);
C=expm(A*B)
C=

PROGRAM-8
OBJECT : EVALUATE THE DERIVATIVE OF POLYNOMIAL-
MATLAB PROGRAM:
A=[4 5 8 9];
C=polyder(A)
C=[12 10 8]
Hence polynomial, C=12x 2 +10x+8

PROGRAM-9
OBJECT : EVALUATE THE CONVOLUTION OF POLYNOMIAL A AND B WHERE -
A=x 3 +3x+5 & B=3x 2 +5x+7
MATLAB PROGRAM:
A=[1 3 5];
B=[3 5 7];
C=conv(A,B)
C=[3 14 37 46 35]
Hence polynomial, C=3x 4 +14x 3 +37x 2 +46x+35

PROGRAM-10
OBJECT : PLOT THE GRAPH OF e -x -
MATLAB PROGRAM :
T=linspace(0,200);
X=exp(-t);
Semilogx(x,y),grid

PROGRAM-11
OBJECT: TWO VECTORS ARE GIVEN-
U=4i+9j-5k&V=-3i+6j-7k. CALCULATE THE DOT PRODUCT?
MATLAB PROGRAM:
U= [4;9;-5];
V=[-3 6 -7];
X= U*V
X=77

PROGRAM-12
OBJECT : DETERMINE CURRENT IN EACH REGISTER USING KVL-
AFTER APPLYING KVL
10=3I 1 -5I 2 -7I 3
0=-5I 1 +21I 2 -6I 3
7=-7I 1 -6I 2 +16I 3
X= ; A= ; B=
MATLAB PROGRAM:
A=[13 -5 -7;-5 21 -6;7 -6 16];
B=[10;0;7];
A\B
X= 2.0668
0.9805
1.7094
i1=2.0668
i2=0.9805
i3=1.7094