This experiment introduces MATLAB and its basic commands such as matrix operations, conditional statements, loops, and plotting.
% MATLAB Basic Commands Example
x = 5; % Assign value to variable
y = 3; % Assign value to another variable
z = x * y; % Scalar multiplication
disp(['Result of multiplication: ', num2str(z)]); % Display result
% Vector example
v = [1, 2, 3, 4, 5]; % Define a vector
disp('Vector:');
disp(v);
% Plotting example
figure;
plot(v);
title('Basic Plot');
xlabel('Index');
ylabel('Value');
This experiment involves plotting different standard signals like step, impulse, ramp, exponential, parabolic, and sinusoidal functions using MATLAB.
% Define time vector
t = 0:0.1:10;
% Unit step function
u = double(t >= 0);
% Unit impulse function
impulse = [1, zeros(1, length(t)-1)];
% Unit ramp function
ramp = t .* (t >= 0);
% Exponential function
exp_func = exp(-t);
% Parabolic function
parab = t.^2;
% Sinusoidal function
sinusoid = sin(t);
% Plotting all functions
figure;
subplot(3,2,1); plot(t, u); title('Unit Step');
subplot(3,2,2); stem(t, impulse); title('Unit Impulse');
subplot(3,2,3); plot(t, ramp); title('Unit Ramp');
subplot(3,2,4); plot(t, exp_func); title('Exponential');
subplot(3,2,5); plot(t, parab); title('Parabolic');
subplot(3,2,6); plot(t, sinusoid); title('Sinusoidal');
This experiment studies the transient response of a series RLC circuit to different types of waveforms and verifies the results using MATLAB simulations.
% RLC Circuit Transient Response
R = 1; % Resistance
L = 1; % Inductance
C = 1; % Capacitance
f = 10; % Frequency
omega = 2 * pi * f; % Angular frequency
% Define time vector
t = 0:0.001:1;
% Apply a sinusoidal voltage source
V = sin(omega * t);
% Solve for the current in the circuit using the formula
I = V / R; % Simplified for demonstration purposes
% Plot the voltage and current
figure;
subplot(2,1,1); plot(t, V); title('Voltage (V)');
subplot(2,1,2); plot(t, I); title('Current (I)');
This experiment verifies the time response of a first-order and second-order system for unit step and square wave inputs using MATLAB simulations.
% Define system transfer functions for first-order and second-order systems
sys1 = tf([1], [1, 1]); % First-order system
sys2 = tf([1], [1, 2, 1]); % Second-order system
% Time vector for simulation
t = 0:0.01:10;
% Step response for both systems
figure;
subplot(2,1,1);
step(sys1, t);
title('Step Response of First-Order System');
subplot(2,1,2);
step(sys2, t);
title('Step Response of Second-Order System');
This experiment uses MATLAB to determine the currents in various resistors connected in a network using mesh current and node voltage analysis.
% Mesh Current Analysis Example
% Define the system matrix (A) and the constant matrix (B)
A = [2, -1, 0; -1, 2, -1; 0, -1, 2];
B = [1; 0; 1];
% Solve for mesh currents
I = A \ B; % Mesh current solutions
disp('Mesh Currents:');
disp(I);
This experiment determines the Z and parameters of a given two-port network.
% Example Z parameters calculation for two-port network
% Given two-port network parameters
A = 2; B = 3;
C = 4; D = 5;
% Z-parameters
Z11 = A - (B*C)/D;
Z12 = B;
Z21 = C;
Z22 = D - (B*C)/A;
disp('Z Parameters:');
disp(['Z11: ', num2str(Z11)]);
disp(['Z12: ', num2str(Z12)]);
disp(['Z21: ', num2str(Z21)]);
disp(['Z22: ', num2str(Z22)]);
This experiment calculates the ABCD parameters of a given two-port network.
% Example ABCD parameters calculation for two-port network
% Given two-port network parameters
A = 2; B = 3;
C = 4; D = 5;
% ABCD Parameters
disp('ABCD Parameters:');
disp(['A: ', num2str(A)]);
disp(['B: ', num2str(B)]);
disp(['C: ', num2str(C)]);
disp(['D: ', num2str(D)]);
This experiment demonstrates how to fit a linear regression line through a given data set and test the goodness of fit using the mean error.
% Linear regression fitting
x = [1, 2, 3, 4, 5]; % Independent variable
y = [2, 4, 5, 4, 5]; % Dependent variable
% Perform linear regression
p = polyfit(x, y, 1); % Fit a first-degree polynomial (linear)
y_fit = polyval(p, x); % Evaluate the fitted polynomial
% Plot the data and the fitted line
figure;
plot(x, y, 'o', x, y_fit, '-');
title('Linear Regression Fit');
xlabel('x');
ylabel('y');
legend('Data points', 'Fitted line');
% Calculate mean error
mean_error = mean(abs(y - y_fit));
disp(['Mean Error: ', num2str(mean_error)]);
This experiment demonstrates how to perform multiple linear regression (MLR) on a given data set and test the goodness of fit using the mean error.
% Multiple Linear Regression (MLR)
x1 = [1, 2, 3, 4, 5]; % First independent variable
x2 = [5, 4, 3, 2, 1]; % Second independent variable
y = [2, 3, 4, 5, 6]; % Dependent variable
% Create design matrix for MLR
X = [ones(length(x1), 1), x1', x2']; % Add column of ones for intercept
b = X \ y'; % Solve for regression coefficients
% Compute the fitted values
y_fit = X * b;
% Plot the data and fitted values
figure;
scatter3(x1, x2, y, 'filled');
hold on;
% Plot the fitted regression surface
[X1, X2] = meshgrid(min(x1):0.1:max(x1), min(x2):0.1:max(x2));
Y = b(1) + b(2)*X1 + b(3)*X2;
surf(X1, X2, Y);
title('Multiple Linear Regression Fit');
xlabel('x1');
ylabel('x2');
zlabel('y');
% Calculate mean error
mean_error = mean(abs(y - y_fit));
disp(['Mean Error: ', num2str(mean_error)]);
This experiment demonstrates how to solve a Linear Programming Problem (LPP) with three variables using the Simplex Method.
% Example LPP: Maximize z = 3x + 2y + 4z
% Subject to constraints:
% x + y + z <= 10
% 2x + y + 2z <= 15
% x, y, z >= 0
% Coefficients of the objective function
f = [-3, -2, -4]; % Negative for maximization
% Coefficients of the constraints
A = [1, 1, 1; 2, 1, 2]; % Constraint matrix
b = [10; 15]; % Right-hand side
% Solve the LPP using the Simplex method
options = optimset('Display', 'off');
[x, fval] = linprog(f, [], [], A, b, zeros(3,1), [], options);
disp('Optimal Solution:');
disp(x);
disp('Optimal Value of Objective Function:');
disp(-fval); % Change sign to get maximized value
This experiment demonstrates how to solve a transportation problem involving three variables using optimization techniques.
% Example Transportation Problem
% Supply: [30, 40, 50]
% Demand: [20, 40, 60]
% Cost matrix:
% C1 C2 C3
% S1 8 6 10
% S2 9 7 4
% S3 3 2 5
supply = [30, 40, 50]; % Supply
demand = [20, 40, 60]; % Demand
cost = [8, 6, 10; 9, 7, 4; 3, 2, 5]; % Cost matrix
% Solve the transportation problem using linprog
f = reshape(cost', [], 1); % Flatten the cost matrix into a vector
A_eq = [kron(eye(length(supply)), ones(1, length(demand))); kron(ones(1, length(supply)), eye(length(demand)))];
b_eq = [supply'; demand'];
x = linprog(f, [], [], A_eq, b_eq, zeros(length(f),1), []);
disp('Optimal transportation plan:');
disp(reshape(x, length(supply), length(demand)));
This experiment demonstrates how to solve an assignment problem of three variables using optimization techniques.
% Example Assignment Problem
% Cost matrix for assignments
% A1 A2 A3
% P1 9 2 7
% P2 6 4 3
% P3 3 8 6
cost = [9, 2, 7; 6, 4, 3; 3, 8, 6]; % Cost matrix
% Solve the assignment problem using Hungarian algorithm
[x, fval] = munkres(cost);
disp('Optimal assignment solution:');
disp(x);
disp('Total cost of assignment:');
disp(fval);