Closed Loop Transfer Function

% clear the console, workspace and close all open figures
clc; clear; close all;
% define s variable for s-domain transfer function
s = tf('s');
% Open loop trasfer function (OLTF)
G_1 = 1/(1+0.5*s);
% Step response of OLTF
figure(1);
step(G_1), grid;
title('1^{st} Order Open Loop Transfer Function');
disp('G_1: ');
disp(stepinfo(G_1));
saveas(gcf,'FO_OLTF.png');
% Closed loop transfer function (CLTF) with unity feedback (H(s) = 1)
T_11 = feedback(G_1, 1);
% Step response for unity feedback CLTF
figure(2);
step(T_11), grid;
title('1^{st} Order Closed Loop Transfer Function (Unity Feedback)');
disp('T_11: ');
disp(stepinfo(T_11));
saveas(gcf,'FO_CLTF_Unity.png');
% Closed loop transfer function (CLTF) with H(s) = 0.5
T_12 = feedback(G_1, 0.5);
% Step response for feedback CLTF, H(s) = 0.5
figure(3);
step(T_12), grid;
title('1^{st} Order Closed Loop Transfer Function (H(s) = 0.5)');
disp('T_12: ');
disp(stepinfo(T_12));
saveas(gcf,'FO_CLTF_0.5.png');
% Second order system
G_2 = 101.20/(s^2 + 2*s + 40.48);
% Step response of OLTF
figure(4);
step(G_2), grid;
title('2^{nd} Order Open Loop Transfer Function');
disp('G_2: ');
disp(stepinfo(G_2));
saveas(gcf,'SO_OLTF.png');
% Closed loop transfer function (CLTF) with unity feedback (H(s) = 1)
T_21 = feedback(G_2, 1);
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% Step response for unity feedback CLTF
figure(5);
step(T_21), grid;
title('2^{nd} Order Closed Loop Transfer Function (Unity Feedback)');
disp('T_21: ');
disp(stepinfo(T_21));
saveas(gcf,'SO_CLTF_Unity.png');
% Closed loop transfer function (CLTF) with H(s) = 0.5
T_22 = feedback(G_2, 0.5);
% Step response for feedback CLTF, H(s) = 0.5
figure(6);
step(T_22), grid;
title('2^{nd} Order Closed Loop Transfer Function (H(s) = 0.5)');
disp('T_22: ');
disp(stepinfo(T_21));
saveas(gcf,'SO_CLTF_Unity.png');
G_1:
RiseTime: 1.0985
SettlingTime: 1.9560
SettlingMin: 0.9045
SettlingMax: 1.0000
Overshoot: 0
Undershoot: 0
Peak: 1.0000
PeakTime: 5.2729
T_11:
RiseTime: 0.5493
SettlingTime: 0.9780
SettlingMin: 0.4523
SettlingMax: 0.5000
Overshoot: 0
Undershoot: 0
Peak: 0.5000
PeakTime: 2.6365
T_12:
RiseTime: 0.7323
SettlingTime: 1.3040
SettlingMin: 0.6030
SettlingMax: 0.6666
Overshoot: 0
Undershoot: 0
Peak: 0.6666
PeakTime: 3.5153
G_2:
RiseTime: 0.1857
SettlingTime: 3.6395
SettlingMin: 1.5835
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SettlingMax: 4.0150
Overshoot: 60.6008
Undershoot: 0
Peak: 4.0150
PeakTime: 0.5066
T_21:
RiseTime: 0.0935
SettlingTime: 3.7596
SettlingMin: 0.2938
SettlingMax: 1.2623
Overshoot: 76.7258
Undershoot: 0
Peak: 1.2623
PeakTime: 0.2639
T_22:
RiseTime: 0.0935
SettlingTime: 3.7596
SettlingMin: 0.2938
SettlingMax: 1.2623
Overshoot: 76.7258
Undershoot: 0
Peak: 1.2623
PeakTime: 0.2639
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