Question

6. Given the unity feedback system with the forward transfer function KG)H(s + 2)(s + 10) a) b) c) d) e) Sketch the root locus Find the breakaway point Find the gain at the breakaway point If one of the poles of the closed-loop system is at s--11, find the other poles and k Are there two dominant poles so that we can find the transient response using second order approximation? If we have dominant poles, find the percent overshoot and settling time using second order approximation. Find the steady state error for unit ramp using the value of K obtained in partd f) g) 4. Repeat the above problem using MAT LAB as follows: Display Root locus and Pause Draw a close-up of the root locus where the axes range from -5 to +5 on the real axis and -5 to+5 on the imaginary axis Overlay 10% line on the closed-loop root locus. Find the gain , poles and percent overshoot at the point where the 10% line crosses the root locus. a. b. d. Use the value of K and obtain the step response for the third order system e. Approximate this by second order system f. Obtain step response for the approximate second order system g. Show both plots obtained in part d and f and compare

Can someone help me with problem 4? You dont need to find the answers for problem 6. Just use the transfer function from problem 6 to do problem 4.

Answer 1

4.

a) & b) matlab code:

s=tf('s');
g=1/(s*(s+2)*(s+10));
rlocus(g)
axis([-5 5 -5 5])
c)

d) K = 21.5

s=tf('s');
g=21.5/(s*(s+2)*(s+10));
step(feedback(g,1))
e) &f) second order approximation:

g =

2.085
---------------------
s^2 + 1.746 s + 2.085

s=tf('s');
g=2.04/((s+0.873+1.15i)*(s+0.873-1.15i));
step(feedback(g,1))