A unity feedback system has open loop poles -2- j2 and 0- It has a single zero at -4 - j0- The angle of departure of the root locus branch starting from the poles -2 -j2is

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Center of Mass as an Average Point

A unity feedb...

Question

A unity feedback system has open loop poles ( $- 2 \pm j 2$ ) and 0. It has a single zero at $(- 4 \pm j 0$ ). The angle of departure of the root locus branch starting from the poles (-2 -j2)is

Open in App

Solution

Finding the angle of departure pole (-2 + 2j)
i.e. at $P_{2}$
$ϕ_{d (- 2 + 2 j)} = 180^{o} - (ϕ_{p 1} + ϕ_{p 3}) + (ϕ_{z 1})$
$ϕ_{p 1} = 180^{o} - t a n^{- 1} (\frac{2}{2}) = + 135^{o}$
$ϕ_{p 3} = + 90^{o}$
$ϕ_{z 1} = t a n^{- 1} (\frac{2}{2}) = + 45^{o}$
$∴ ϕ_{d (- 2 + 2 j)} = 180^{o} - (135^{o} + 90^{o}) + 45^{o}$
$= 0^{o}$
$ϕ_{d} (- 2 - 2 j) = - ϕ (- 2 + 2 j) = 0^{o}$

Suggest Corrections

Similar questions

Q. The open loop poles of a third order unity feedback system are at 0, -1, -2. Let the frequency corresponding to the point where the root locus of the system transits to unstable region be K. Now suppose we introduce a zero in the open loop transfer function at - 3, while keeping all the earlier open loop poles intact. Which one of the following is TRUE about the point where the root locus of the modified system transits to unstable region?

Q. A unity feedback system has an open loop transfer function,

G (s) = \frac{K}{s^{2}} .

Its root locus plot will be

Q. The feedback configuration and the pole-zero location of

G (s) = \frac{s^{2} - 2 s + 2}{s^{2} + 2 s + 2}

are shown below. The root locus for Negative values of

K

, i.e for

- \infty < K < 0

, has breakaway/break-in points and angle of departure at pole

P

(with respect to the positive real axis) equal to

Q. The open loop transfer fucntion of a unity feedback system is

G (s) = \frac{k (s + 2)}{(s + 1 + j 1) (s + 1 - j 1)} .

The root locus plot of the system has

A unity negative feedback system has the open-loop transfer function $G (s) = \frac{K}{s (s + 1) (s + 3)}$
The value of the gain $K (> 0)$ at which the root locus crosses the imaginary axis is

Join BYJU'S Learning Program

A unity feedback system has open loop poles (−2±j2) and 0. It has a single zero at (−4±j0). The angle of departure of the root locus branch starting from the poles (-2 -j2)is

Finding the angle of departure pole (-2 + 2j) i.e. at P2 ϕd(−2+2j)=180o−(ϕp1+ϕp3)+(ϕz1) ϕp1=180o−tan−1(22)=+135o ϕp3=+90o ϕz1=tan−1(22)=+45o ∴ϕd(−2+2j)=180o−(135o+90o)+45o =0o ϕd(−2−2j)=−ϕ(−2+2j)=0o

A unity feedback system has open loop poles ( $- 2 \pm j 2$ ) and 0. It has a single zero at $(- 4 \pm j 0$ ). The angle of departure of the root locus branch starting from the poles (-2 -j2)is