Consider a negative unity feedback system with the forward path transfer function s2-s-1s3-2s2-2s-k- where K is a positive real number- The value of K for which the system will have some of its poles on the imaginary axis is

CE is 1 + G(s) H(s) = 0 ⇒ 1+s^2+s+1s^3+2s^2+2s+K=0 ⇒ s^3+3s^2+3s+(1+K)=0 R.H. criteria: . s^3 nbsp; s^2 nbsp; s^1| 1 amp;3 3 nbsp; nbsp; am ...

You visited us 2 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Electric Potential at a Point in Space Due to a Point Charge Q

Consider a ne...

Question

Consider a negative unity feedback system with the forward path transfer function $\frac{s^{2} + s + 1}{s^{3} + 2 s^{2} + 2 s + k},$ where K is a positive real number. The value of K for which the system will have some of its poles on the imaginary axis is

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A 8
CE is
$1 + G (s) H (s) = 0$

$\Rightarrow 1 + \frac{s^{2} + s + 1}{s^{3} + 2 s^{2} + 2 s + K} = 0$

$\Rightarrow s^{3} + 3 s^{2} + 3 s + (1 + K) = 0$

R.H. criteria:

$\begin{matrix} s^{3} s^{2} s^{1} \end{matrix} ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & 3 3 & (1 + K) 9 - (1 + K) & 0 \end{matrix}$

For marginal stability,

$9 - (1 + K) = 0$

$\Rightarrow K = 8$

Suggest Corrections

Similar questions

The forward path transfer function of a unity negative feedback system is given by $G (s) = \frac{K}{(s + 2) (s - 1)}$
The value of $K$ which will place both the poles of the closed-loop system at the same location is

Q. Consider a unity feedback system with forward path transfer function G(s) =

\frac{K (s + 3) (s + 5)}{(s - 2) (s - 4)}

The range of K to ensure stability is

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

Q. A system with the open loop transfer function:

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

is connected in a negative feedback configuration with a feedback gain of unity. For the closed-loop system to be marginally stable, the value of k is

Consider a unity feedback system, as in the figure shown, with an integral compensator $\frac{K}{s}$ and open-loop transfer function
$G (s) = \frac{1}{s^{2} + 3 s + 2}$
where $K > 0$ . The positive value of $K$ for which there are exactly two poles of the unity feedback system on the $j ω$ is equal to (rounded off to two decimal places)

Join BYJU'S Learning Program

Consider a negative unity feedback system with the forward path transfer function s2+s+1s3+2s2+2s+k, where K is a positive real number. The value of K for which the system will have some of its poles on the imaginary axis is

The correct option is A 8CE is 1+G(s)H(s)=0 ⇒1+s2+s+1s3+2s2+2s+K=0 ⇒s3+3s2+3s+(1+K)=0 R.H. criteria: s3s2s1∣∣ ∣ ∣∣133(1+K)9−(1+K)0 For marginal stability, 9−(1+K)=0 ⇒K=8

Consider a negative unity feedback system with the forward path transfer function $\frac{s^{2} + s + 1}{s^{3} + 2 s^{2} + 2 s + k},$ where K is a positive real number. The value of K for which the system will have some of its poles on the imaginary axis is