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3. Consider the tilt control block diagram shown below R(s) DesiredG(s) 12 s(s+10)(s+70) Y(s) Tilt tilt Design specifications

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Answer #1

a) root locus of uncompensated system:

clc;

clear all;

s=tf('s');

g=12/(s*(s+10)*(s+70));% plant transfer function

rlocus(g);grid % locus of uncompensated system

Root Loeus 022 0.11 0025 005 0022 30 20 06. Gain 263 463 Damping: 0.693 Oversrud (%): 487 Frequency trade: 6 68 06 20 022 0.1

for 5% overshoot the system is not meeting the design requirements.

b) lead controller

ans he -24.499 454

The compensator gain found by magnitude criteria at the dominant pole is K=459.7012

c) compensated system root locus:

clc;

clear all;

s=tf('s');

g=12/(s*(s+10)*(s+70));% plant transfer function

gc=(s+7.9364)/(s+11.4403)% compensator transfer function

rlocus(g*gc);grid % locus of compensated system

Root Locus 038 026 0.T8 0.13 008 20052 System: untriled Gain 747 Damping: 0.517 Ouersnat (%): 15 FIequancy (rads) : 1 1.5 10d) step response

clc;

clear all;

s=tf('s');

g=12/(s*(s+10)*(s+70));% plant transfer function

gc=(s+7.9364)/(s+11.4403)% compensator transfer function

k=459.7012;

step(feedback(k*g*gc,1));grid

Step Response Systam untitied Peak ampinude: 1.02 Overshootやsk 2.34 nem Altime tseconds):o.b525 seconds): 0.586 02 0.4 12 Tim

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