The forward transfer function G(s) with a H(s) feedback configuration of an uncompensated Basic Satellite Launching System is as shown in figures 1 and 2. A- in the picture  B- Compute the percent overshoot, peak time and settling time, using second order approximation through pole zero cancellation and unity feedback configuration shown in figure 2. C- Summarise the results (a) and (b) in tabular form and comment on the stability of both systems based on time response graph for (a) and computed values in (b).

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The forward transfer function G(s) with a H(s) feedback configuration of an uncompensated Basic Satellite Launching System is as shown in figures 1 and 2.

A- in the picture 

B- Compute the percent overshoot, peak time and settling time, using second order approximation through pole zero cancellation and unity feedback configuration shown in figure 2.

C- Summarise the results (a) and (b) in tabular form and comment on the stability of both systems based on time response graph for (a) and computed values in (b).

 

% a)
s = tf ('s');
a = 4; b = 2; c = 2; d = 1; e = 10; f = 4;
G = a* (s+d)/ (s * (s + c) * (s + b));
H = el (s + f);
figure()
bode (G* H)
grid on
G1 = feedback (G, H);
disp ('a')
stepinfo (G1)
figure()
step (G1)
grid on, legend ('with H (s)')
% b)
%uncompensated system
G2 = feedback (G, 1);
%u sin g
%u sin g pole zero canclellation
K = 1.678 ^2 + 1.7214^2;
G1_app = zpk ([ ], [−1. 6478 + 1. 7214i – 1. 6478 – 1. 7214i], k);
disp ('b')
stepinfo (G1_app)
figure()
step (G1_app)
grid on, legend (with unity feedback')
%c)
%comparison
Transcribed Image Text:% a) s = tf ('s'); a = 4; b = 2; c = 2; d = 1; e = 10; f = 4; G = a* (s+d)/ (s * (s + c) * (s + b)); H = el (s + f); figure() bode (G* H) grid on G1 = feedback (G, H); disp ('a') stepinfo (G1) figure() step (G1) grid on, legend ('with H (s)') % b) %uncompensated system G2 = feedback (G, 1); %u sin g %u sin g pole zero canclellation K = 1.678 ^2 + 1.7214^2; G1_app = zpk ([ ], [−1. 6478 + 1. 7214i – 1. 6478 – 1. 7214i], k); disp ('b') stepinfo (G1_app) figure() step (G1_app) grid on, legend (with unity feedback') %c) %comparison
G(s)
=
a(s+d)
s(s+c)(s+b)
H(s)
=
e
(s+f)
R(s)
G(s)
→ C(s)
H(s)
Figure 1: Uncompensated basic Satellite launching system
R(s)
G(s)
→ C(s)
Figure 2: Uncompensated basic Satellite launching system with unity feedback
Transcribed Image Text:G(s) = a(s+d) s(s+c)(s+b) H(s) = e (s+f) R(s) G(s) → C(s) H(s) Figure 1: Uncompensated basic Satellite launching system R(s) G(s) → C(s) Figure 2: Uncompensated basic Satellite launching system with unity feedback
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