transfer_function_analysis.m

clc
clear
close all

% Cruise control function example
s = tf('s');                % Define Laplace transform
sysG = 0.001/(s^2+0.05*s);  % Transfer function

p = pole(sysG);             % Compute poles
[z,k] = zero(sysG);         % Compute zeros and gain

fprintf('Example 1\n');
disp('Poles: ');
disp(p);
disp('Zeros: ');
disp(z);
disp('Gain: ');
disp(k);

% Cruise control example 2
sysG2 = (3*s+9)/(s^2+6*s+25);

p2 = pole(sysG2);
[z2,k2] = zero(sysG2);

fprintf('\nExample 2\n');
disp('Poles: ');
disp(p2);
disp('Zeros: ');
disp(z2);
disp('Gain: ');
disp(k2);

% Satellite example 3
sysS = 0.0002/s^2;
t = 0:0.01:10;  % set up time vector with dt = 0.01 sec

u1 = [zeros(1, 500),...
      25*ones(1, 10),...  % pulse of 25N, at 5 sec, for 0.1 sec duration
      zeros(1, length(t) - 500 - 10)];  % pulse input

[y1] = lsim(sysS, u1, t);   % linear simulation
ff = 180/pi;                  % conversion factor from radians to degrees
y1 = ff * y1;                 % output in degrees
figure;
subplot(2, 1, 1);
plot(t, u1);                  % plot input signal
title('Input Signal');
xlabel('Time (s)');
ylabel('Amplitude');

subplot(2, 1, 2);
plot(t, y1);                  % plot output response
title('Output Response');
xlabel('Time (s)');
ylabel('Output (Degrees)');

% Cruise control example 3
sysG3 = 100/(s^3 + 10.1*s^2 + 101*s);

p3 = pole(sysG3);
[z3, k3] = zero(sysG3);

fprintf('\nExample 3\n');
disp('Poles: ');
disp(p3);
disp('Zeros: ');
disp(z3);
disp('Gain: ');
disp(k3);

poles_3 = repmat("pole", 3, 1);
disp(poles_3);
figure;
plotComplex(p3, poles_3);

% Plotting satellite poles and zeros
poles_sat = repmat("pole",[size(pole(sysS))]);
[z_sat,k_sat] = zero(sysS);
zeros_sat = repmat("zero",[size(z_sat)]);
figure(Name="First Sat Plot")
plotComplex(pole(sysS),poles_sat)