True or False? In a system whose root locus is given below, it is possible to de

Question

True or False?

In a system whose root locus is given below, it is possible to design a closed-loop system that operates at a damping ratio of 0.707 without compensation (i.e. via gain adjustment). Consider a unity feedback system shown below where H(s) = 1, and denote the closed-loop transfer function C(s)/R(s) = T(s). If T(s) is marginally stable, the gain margin of G(s) is zero. The phase frequency response for G(s) = 1 - 5s/1 + 5s is 0 for all omega. The magnitude frequency response for G(s) = 1 - 5s/1 + 5s is 1 for all omega.

Explanation / Answer

5) True

Open loop Transfer function assuming gain K is,

G(s) = K(s+3)(s+4) / (s+1)(s+2)

G(s) = K(s+3)(s+4) / (s2 + 3s + 2)

Comapring this transfer function with

T.F. = wn2 / s2 +2Ewns + Wn2

E = damping ratio

We see that 2Ewn = 3 & wn = K1/2    ................1

Therefore from 1 damping ratio E can be 0.707 without compensation

6) False

T(s) is marginally stable if gain margin is zero or phase margin is zero or both gain and phase margin is zero. Hence if T(s) is marginally stable doesn't mean that gain margin of G(s) is zero.

7) False

Phase angle for G(s) for any w can be given as,

theta = -tan-1 5w - tan-1 5 w            .................2

from 2 it is clear that phase frequency response is not zero for all w

8) True

Magnitude response M is given by,

M = ( 1 + (5w)2 )1/2 / ( 1 + (5w)2 )1/2  

M = 1                                   .....................3

From 3 it is clear that magnitude response for G(s) is 1 for all w.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.