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Transcript of Matlab (1)
MATLAB Winter Training
Report
Submitted To: Submitted By:
Dr. Bhavnesh Kumar Navtej Singh Narula
ICE - II
Roll No. 492/IC/13
CERTIFICATE
This is to certify that the work presented in this report on winter training in
MATLAB, submitted by Navtej Singh Narula (Roll No. 492/IC/13) to the
Division of Instrumentation and Control Engineering, Netaji Subhas Institute
of Technology, New Delhi is a record of my own work carried out under the
supervision and guidance of Dr. S.K. Jha, ICE Dep.
(Navtej Singh Narula)Roll No. 492/IC/13
Division of Instrumentation and Control EngineeringNetaji Subhas Institute of Technology
Azad Hind Fauj Marg, Sector-3Dwarka, New Delhi-110 078
INDEX1. Develop a LV program to add all the integer number from 1 to 10.
2. Plot a sine wave having exactly 4 cycles of data points (1V, 50Hz, θ=45o.)
3. Demonstrate through the LV code the properties of the Amplitude Scaling, Time Scaling and Time Shifting for some common signals. Also include the combined operations of shifting and scaling.
4. Plot the function y = Mod( -1) on linear, semi-log and log-log plot.
5. Use 3D plot to plot your own generated data. Hint: use 2D sine wave.
6. Plot two sine waves having different amplitudes and phases on a single chart.
7. Construct any 4 × 4 matrix, calculate sum of its rows and sum of its columns. Con-struct transpose of its matrix. If 4 × 4 matrix was A and its transpose was A′, then calculate A + A′ and A × A′. Construct B matrix of 4 × 4 and calculate A + B and A × B. Calculate the determinant of the resulting matrix A + B. Now calculate the sum of its A + B diagonal elements.
8. Construct a plot between X, Y 1 and Y 2 on single plot where X = (0, 2 π) with increment of π/10
9. Create the given transfer functions.
10.Develop a MATLAB program to convert temperature reading from C to F and vice-versa.
11.Design your own problems on (Validate the results you obtained)a. Differentiationb. Integration
12.Plot all the standard signals like step, ramp, impulse and sinusoids.
13.Construct a series of numbers
14. Develop a MATLAB program to add all the integer number from 1 to 10.
15. Develop a MATLAB program to add all the odd numbers from 1 to 101, both numbers are inclusive.
16. The model of RC circuit can be found from Kirchhoff’s voltage law and conservation of change. RC × dy/dt + y = v(t). Suppose the value of RC is 0.1 second. Use a numerical method to find the free response for the case where the applied voltage v is 0 and the initial capacitor voltage is y(0) = 2 volts.
17. Consider a mechanical system with equation mx¨ + bx˙ + kx = 0 where m = 1kg, b = 3N −sec/m and k = 2N/m. Assume that at t = 0 , x(0) = 0.1m and x˙(0) = 0.05m/sec. Obtain motion of mass m subjected to initial condition.
18. Use MATLAB to compute the solution of following equation: 5¨x + 7 x˙ + 4x = sin(t)
19. Using numerical method (ODE), obtain free response of an RC circuit (RCy˙ + y = v(t))where applied voltage v is zero and initial capacitor voltage is y(0) = 2V, RC = 0.1s.
20. Use MATLAB to compute and plot the solution of following equation 10dy/dt + y = 20 + 7sin2t , y(0) = 15
21.Create a matrix of zeros with 2 rows and 4 columns. Create the row vector of odd numbers through 21,
22. Find the sum S of vector L's elements. And form the matrix.
23.Create two different vectors of the same length and add them. subtract them. Perform element-by-element multiplication on them. Perform element-by-element division on them. Raise one of the vectors to the second power. Create a 3X3 matrix and display the first row of and the second column.
24.Generate a large chunk of data and compute Mean, Standard Deviation and Variance, Mode, Moment around the mean, RMS etc.
25.Study Laplace transform and inverse Laplace transform for some standard signals using MATLAB.
26. Define the following function using syms: f ( x )=x2 ex−5 x3
Compute the integral, and the first and second derivatives of the above function symbolically. Define the following function using syms:
f ( x , y , z )=x2 e y−5 z2
Compute the integral with respect to x.
MODELS1. To convert AC into DC using Half Wave Rectifier.
2. To convert AC into DC using Full Wave Rectifier.
3. To estimate current and voltages in a DC circuit.
4. To understand the working of AND & OR logical operators when provided with two pulse wave forms.
Problem 1
Develop a LV program to add all the integer number from 1 to 10.
Solution:
Problem 2
Plot a sine wave having exactly 4 cycles of data points (1V, 50Hz, θ=45o.)
Solution
Problem 3
Demonstrate through the LV code the properties of the Amplitude Scaling, Time Scaling and Time Shifting for some common signals. Also include the combined operations of shifting and scaling.
Solution
Problem 4
Plot the function y = Mod( -1) on linear, semi-log and log-log plot.
Solution :
Problem 5
Use 3D plot to plot your own generated data. Hint: use 2D sine wave.
Solution
Problem 6
Plot two sine waves having different amplitudes and phases on a single chart.
Solution :
Problem 7
Construct any 4 × 4 matrix, calculate sum of its rows and sum of its columns. Con-struct transpose of its matrix. If 4 × 4 matrix was A and its transpose was A ′, then calculate A + A′ and A × A′. Construct B matrix of 4 × 4 and calculate A + B and A × B. Calculate the determinant of the resulting matrix A + B. Now calculate the sum of its A + B diagonal elements.
Code:1 close all 2 clear all 3 clc 4
5 A=rand(4,4); 6 disp('Matrix A:') 7 disp(num2str(A)) 8
9 sum cols = sum(A,1); 10 disp('Sum of columns:') 11 disp(num2str(sum cols)) 12
13 sum rows = sum(A,2); 14 disp('Sum of columns:') 15 disp(num2str(sum rows)) 16
17 A transpose = A'; 18 disp('Transpose of A:') 19 disp(num2str(A transpose)) 20
21 Product = A*A transpose; 22 disp('Product of A and its transpose:') 23 disp(num2str(Product)) 24
25 Sum = A+A transpose; 26 disp('Sum of A and its transpose:') 27 disp(num2str(Sum)) 28
29 B=rand(4,4); 30 disp('Matrix B:') 31 disp(num2str(B)) 32
33 sum = A+B; 34 disp('Sum of A and B:') 35 disp(num2str(sum)) 36
37 product = A*B; 38 disp('Product of A and B:') 39 disp(num2str(product)) 40
41 determinant = det(A+B); 42 disp('Determinant of A + B:') 43 disp(num2str(determinant)) 44
45 tr = trace(A+B); 46 disp('Sum of diagonal elements of A + B:') 47 disp(num2str(tr))
Output:1 Matrix A:2 0.27692 0.69483 0.43874 0.186873 0.046171 0.3171 0.38156 0.489764 0.097132 0.95022 0.76552 0.445595 0.82346 0.034446 0.7952 0.646316 Sum of columns:7 1.2437 1.9966 2.381 1.7685
8 Sum of columns: 9 1.5974
10 1.2346 11 2.2585 12 2.2994 13 Transpose of A:
14 0.27692 0.046171 0.097132 0.8234615 0.69483 0.3171 0.95022 0.03444616 0.43874 0.38156 0.76552 0.795217 0.18687 0.48976 0.44559 0.6463118 Product of A and its transpose:19 0.78689 0.49205 1.1063 0.7216420 0.49205 0.48814 0.81612 0.668921 1.1063 0.81612 1.6969 1.009422 0.72164 0.6689 1.0094 1.729323 Sum of A and its transpose:24 0.55385 0.741 0.53588 1.010325 0.741 0.6342 1.3318 0.5242126 0.53588 1.3318 1.531 1.240827 1.0103 0.52421 1.2408 1.292628 Matrix B:29 0.70936 0.6551 0.95974 0.7512730 0.75469 0.16261 0.34039 0.255131 0.27603 0.119 0.58527 0.5059632 0.6797 0.49836 0.22381 0.6990833 Sum of A and B:34 0.98629 1.3499 1.3985 0.9381435 0.80086 0.47971 0.72194 0.7448636 0.37316 1.0692 1.3508 0.9515437 1.5032 0.53281 1.019 1.345438 Product of A and B:39 0.96894 0.43974 0.80089 0.7379140 0.71028 0.3713 0.48518 0.6510141 1.3002 0.53131 0.96442 1.014242 1.2689 0.96177 1.4121 1.4816
43 Determinant of A + B: 44 −0.020018 45 Sum of diagonal elements of A + B: 46 4.1622
Problem 8Construct a plot between X, Y 1 and Y 2 on single plot where X = (0, 2 π) with increment of π/10Y 1 = sin (x)Y 2 = sin (x - 0.25)
Code:1 clear all 2 close all 3 clc 4
5 X = 0:pi/10:2*pi; 6 Y1 = sin(X); 7 Y2 = sin(X−0.25); 8
9 plot(X, Y1, X, Y2); 10 xlabel('x'); 11 ylabel('y1, y2'); 12 legend('y1', 'y2');
Output:
1y1
0.8 y2
0.6
0.4
0.2
y 2
0y 1 ,
−0.2
−0.4
−0.6
−0.8
−11 2 3 4 5 6 70
x
Plot of X,Y 1 and Y 2
Problem 9
Create the following transfer functions:
50Y1
=
s2 + 5s + 302s2 + 3s
Y2 =
4s2 + 3s
And add these two transfer functions.
Code:1 clear all 2 close all 3 clc 4
5 disp('Transfer Function Y1:') 6 Y1 = tf([0 0 50], [1 5 30]) 7
8 disp('Transfer Function Y2:') 9 Y2 = tf([2 3 0],[4 3 0])
10
11 disp('Transfer Function Y = Y1 + Y2:') 12 Y = Y1+Y2
Output:1 Transfer Function Y1:2
3 Transfer function: 4 50 5 −−−−−−−−−−−−−− 6 sˆ2 + 5 s + 30 7
8 Transfer Function Y2:9
10 Transfer function: 11 2 sˆ2 + 3 s 12 −−−−−−−−−−− 13 4 sˆ2 + 3 s 14
15 Transfer Function Y = Y1 + Y2:16
17 Transfer function: 18 2 sˆ4 + 13 sˆ3 + 275 sˆ2 + 240 s 19 −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− 20 4 sˆ4 + 23 sˆ3 + 135 sˆ2 + 90 s
Problem 10
Develop a MATLAB program to convert temperature reading from C to F and vice-versa.
Funtion 1 : Celsius to Fahrenheit1 function [ f ] = celsius2farh( c ) 2 % celcius2farh coverts from celsius scale to farheneit
3 % Input:4 % c : Temperature in celsius5 % Output:6 % f: Temperatutr in farheneit
7
8 f = 1.8*c + 32; 9 end
Function 2 : Fahrenheit to Celsius1 function [ c ] = farh2celsius( f ) 2 % farh2celsius coverts from farheneit scale to celsius
3 % Input:4 % f : Temperature in farheneit5 % Output:6 % c: Temperatutr in celsius
7
8 c = 5/9*(f − 32); 9 end
Code:1 clear all 2 close all 3 clc 4
5 disp(['45 degrees celsius in farheneit: ' num2str(celsius2farh(45))]) 6 disp(['113 degrees farheneit in celsius: ' num2str(farh2celsius(113))])
Output:1 45 degrees celsius in farheneit: 113 2 113 degrees farheneit in celsius: 45
Problem 11Design your own problems on (Validate the results you obtained)
1. Differentiation2. Integration
Code:1 close all 2 clear all 3 clc 4
5 syms x 6 f = exp(4*x)*sin(3*x); 7 disp('Function f: ') 8 disp(f) 9 derivative = diff(f);
10 disp('Derivative of f: ') 11 disp(derivative) 12 integral = int(f); 13 disp('Integral of f: ') 14 disp(integral)
Output:1 Function f: 2 sin(3*x)*exp(4*x) 3
4 Derivative of f: 5 3*cos(3*x)*exp(4*x) + 4*sin(3*x)*exp(4*x) 6
7 Integral of f: 8 −(exp(4*x)*(3*cos(3*x) − 4*sin(3*x)))/25
Problem 12
Plot all the standard signals like step, ramp, impulse and sinusoids.
Code:1 close all 2 clear all 3 clc 4
5 t = −10:0.01:10;6
7 y1 = heaviside(t); 8 h=figure; 9 plot(t, y1);
10 xlabel('t'); ylabel('y1'); 11 title('Step Response'); 12 axis([−10 10 −1 2]); 13 saveas(h, 'Q7 fig1.eps', 'eps'); 14
15 y2 = sin(t); 16 h=figure; 17 plot(t, y2); 18 xlabel('t'); ylabel('y2'); 19 title('Sine Curve'); 20 axis([−10 10 −1.5 1.5]); 21 saveas(h, 'Q7 fig2.eps', 'eps'); 22
23 y3 = t; 24 h=figure; 25 plot(t, t); 26 xlabel('t'); ylabel('y3'); 27 title('Ramp Function'); 28 axis([−10 10 −15 15]); 29 saveas(h, 'Q7 fig3.eps', 'eps'); 30
31 t=[−2:1:2]; 32 y4 = zeros(size(t)); 33 y4(3)=1; 34 h=figure; 35 stem(t,y4); 36 xlabel('t'); ylabel('y4'); 37 title('Impulse Function'); 38 axis([−2.5 2.5 −1 1.5]); 39 saveas(h, 'Q7 fig4.eps', 'eps');
Output:y1
Step Response2
1.5
1
0.5
0
−0.5
−1−8 −6 −4 −2 0 2 4 6 8 10−10t
Step Signal
Sine Curve1.5
1
0.5
y2 0
−0.5
−1
−1.5−8 −6 −4 −2 0 2 4 6 8 10−10
t
Sinusoidal Signal
y3y4
15
10
5
0
−5
−10
−15−10
1.5
1
0.5
0
−0.5
−1−2.5
Ramp Function
−8 −6 −4 −2 0 2 4 6 8 10t
Ramp Signal
Impulse Function
−2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5t
Impulse Signal
Problem 14
Construct a series of numbers:
A = 1 3 5 7 9 11 13 15 17 19 21
B = 50 48 46 44 42......................2
Code:1 close all 2 clear all 3 clc 4
5 A = [1:2:21]; 6 B = [50:−2:2]; 7
8 disp('A =') 9 disp(num2str(A))
10
11 disp('B =') 12 disp(num2str(B))
Output:1 A =2 1 3 5 7 9 11 13 15 17 19 213 B =4 50 48 46 44 42 40 38 36 34 32 30 28 26 24 22 20 18 16 145 12 10 8 6 4 2
Problem 15
Develop a MATLAB program to add all the integer number from 1 to 10.
Code:1 clear all 2 close all 3 clc 4
5 s = sum(1:10); 6 disp('Sum of numbers from 1 to 10:') 7 disp(num2str(s))
Output:1 Sum of numbers from 1 to 10: 2 55
Problem 16
Develop a MATLAB program to add all the odd numbers from 1 to 101, both numbers are inclusive.
Code:1 close all 2 clear all 3 clc 4
5 s = sum(1:2:101); 6 disp('Sum of odd numbers from 1 to 101:') 7 disp(num2str(s))
Output:1 Sum of odd numbers from 1 to 101: 2 2601
Problem 17
The model of RC circuit shown in figure 1 can be found from Kirchhoff’s voltage law and conservation of change. RC × dy/dt + y = v(t). Suppose the value of RC is 0.1 second. Use a numerical method to find the free response for the case where the applied voltage v is 0 and the initial capacitor voltage is y(0) = 2 volts.
Code:1 close all 2 clear all 3 clc 4
5 sol = dsolve('0.1*Dy+y = 0', 'y(0)=2', 't');6 disp('Solution is:')7 disp(sol)8 h=figure;9 ezplot(sol);
10 saveas(h, 'Q11 fig1.eps', 'eps');
Output:1 Solution is:
2 2/exp(10*t)
23 2/exp(10 t)x 10
10
9
8
7
6
5
4
3
2
1
0
−6 −5 −4 −3 −2 −1 0t
Figure 7: Solution Plot
Conclusion: The free response of the RC circuit has been obtained.
Problem 18Consider a mechanical system with equation mx¨ + bx˙ + kx = 0 where m = 1kg, b = 3N −sec/m and k = 2N/m. Assume that at t = 0 , x(0) = 0.1m and x˙(0) = 0.05m/sec. Obtain motion of mass m subjected to initial condition.
Code:1 close all 2 clear all 3 clc 4
5 sol = dsolve('D2y + 3*Dy + 2*y = 0', 'y(0)=0.1', 'Dy(0) = 0.05', 't'); 6 disp('Solution is:') 7 disp(sol) 8 h=figure; 9 ezplot(sol,[0 10]);
10 saveas(h, 'Q14 fig1.eps', 'eps');
Output:1 Solution is:
2 1/(4*exp(t)) − 3/(20*exp(2*t))
1/(4 exp(t)) − 3/(20 exp(2 t))
0.1
0.08
0.06
0.04
0.02
0
0 1 2 3 4 5 6 7 8 9 10t
Figure 8: Solution Plot
Problem 19
Use MATLAB to compute the solution of following equation:5¨x + 7 x˙ + 4x = sin(t)
Code:1 close all 2 clear all 3 clc 4
5 y=dsolve('d*D2x + 7*Dx +4*x = sin(t)','t'); 6 disp('Solution is:') 7 disp(y)
Output:1 Solution is: 2 C2*exp((t*((49 − 16*d)ˆ(1/2) − 7))/(2*d)) + 3 C3*exp(−(t*((49 − 16*d)ˆ(1/2)+ 7))/(2*d)) + 4 (exp((7*t + t*(49 − 16*d)ˆ(1/2))/(2*d))*exp(−(t*((49 − 16*d)ˆ(1/2) + 7))/5 (2*d))*(cos(t) − (sin(t)*((49 − 16*d)ˆ(1/2) + 7))/(2*d)))/ 6 ((49 − 16*d)ˆ(1/2)*(((49 − 16*d)ˆ(1/2) + 7)ˆ2/(4*dˆ2) + 1)) − 7 (exp((7*t − t*(49 − 16*d)ˆ(1/2))/(2*d))*exp((t*((49 − 16*d)ˆ(1/2) − 7))/ 8 (2*d))*(cos(t) + (sin(t)*((49 − 16*d)ˆ(1/2) − 7))/ 9 (2*d)))/((49 − 16*d)ˆ(1/2)*(((49 − 16*d)ˆ(1/2) − 7)ˆ2/(4*dˆ2) + 1))
Problem 20Using numerical method (ODE), obtain free response of an RC circuit (RCy˙ + y = v(t))where applied voltage v is zero and initial capacitor voltage is y(0) = 2V ,RC = 0.1s.
Code:1 close all 2 clear all 3 clc 4
5 sol = dsolve('0.1*Dy+y = 0', 'y(0)=2', 't');6 disp('Solution is:')7 disp(sol)8 h=figure;9 ezplot(sol);
10 saveas(h, 'Q11 fig1.eps', 'eps');
Output:1 Solution is:
2 2/exp(10*t)
23 2/exp(10 t)x 10
10
9
8
7
6
5
4
3
2
1
0
−6 −5 −4 −3 −2 −1 0t
Figure 9: Solution Plot
Problem 21
Use MATLAB to compute and plot the solution of following equation
10dy/dt + y = 20 + 7sin2t , y(0) = 15
Code:1 clear all 2 close all 3 clc 4
5 sol = dsolve('10*Dy + y = 20 + 7*sin(2*t)','y(0) = 15','t'); 6 disp('Solution is:') 7 disp(sol) 8 h=figure; 9 ezplot(sol);
10 saveas(h, 'Q17 fig1.eps', 'eps');
Output:1 Solution is:
2 (7*sin(2*t))/401 − 1865/(401*exp(t/10)) − (140*cos(2*t))/401 + 20
(7 sin(2 t))/401 − 1865/(401 exp(t/10)) −...+ 2018
17
16
15
14
13
12
11
−6 −4 −2 0 2 4 6t
Figure 10: Solution Plot
Problem 22a) Create a matrix of zeros with 2 rows and 4 columns.b) Create the row vector of odd numbers through 21,L = 1 3 5 7 9 11 13 15 17 19 21(Use the colon operator)
Solution:a)
b)
Problem 23a) Find the sum S of vector L's elements.b) Form the matrixA = 2 3 2
1 0 1
Solution: a)
b)
Problem 24a) Create two different vectors of the same length and add them.b) Now subtract them.c) Perform element-by-element multiplication on them.d) Perform element-by-element division on them.e) Raise one of the vectors to the second power.f) Create a 3X3 matrix and display the first row of and the second column on the screen.
Solution:a)
b)
c)
d)
e)
f)
Problem 25Generate a large chunk of data and compute Mean, Standard Deviation and Variance, Mode, Moment around the mean, RMS etc. Solution:Code: a=0:10;sum=0;for i=1:10sum=sum+a(i);endfor i=1:10;s=(a(i)-mean)^2;endmean=sum/11sd=sqrt(s/10)variance=sd^2
Output :
Problem 26
a) Define the following function using syms:f ( x )=x2ex−5 x3
b) Compute the integral, and the first and second derivatives of the above function symbolically.c) Define the following function using syms:
f ( x , y , z )=x2 e y−5 z2
Compute the integral with respect to x .
Solution:
Model – 1
To convert AC into DC using Half Wave Rectifier.
Model – 2
To convert AC into DC using Full Wave Rectifier.
Model – 3
To estimate current and voltages in a DC circuit.
Model – 4
To understand the working of AND & OR logical operators when provided with two pulse wave forms.