Question

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 require an overshoot of less than 5% and a settling time of less than 0.6 seconds. (a) Use MATLAB to sketch the root locus (rlocus command) with a proportional controller and use the root locus to determine a value for K (if any) that will satisfy the design requirements (b) Design a lead compensator Ge(s) to satisfy the design specifications. You can use the mathematical approach or the trial and error approach. In any case explain your design steps. (c) Use MATLAB to sketch the new root locus (with the lead compensator designed in part b) and determine an appropriate value for K. (note that when you click on a point on the root locus plot, a small window pops up which gives the value of gain (K) that results in a closed-loop pole at that specific point) d) Plot the unit step response with the compensator designed in part b and the K value selected in part c. Verify if the required specifications are satisfied with your design Print and attach your code and the plots.

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 0.10 0.0p 0.0ち 0022 Real Axis (seconds

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 10 0.8 10 0.52 3003b 026 50 5b 600.19 0.13 008 004 10 10 Real Axis (seconds )
d) 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 Time (seconds)