The range of the controller gains ( $K_{p}, K_{i}$ ) that makes the closed loop control system (shown in the following figure) stable is given as

K_{i} < 0 a n d K_{p} < \frac{K_{i}}{12} - 20

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

K_{i} > 0 a n d K_{p} > 0

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

K_{i} < 0 a n d K_{p} > \frac{K_{i}}{12} - 20

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

K_{i} > 0 a n d K_{p} > \frac{K_{i}}{12} - 20

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

Open in App

Solution

The correct option is D $K_{i} > 0 a n d K_{p} > \frac{K_{i}}{12} - 20$
Characteristic equation $1 + G (s) H (s) = 0$

$1 + (\frac{k_{p} s + k_{I}}{s}) (\frac{1}{(s + 2) (s + 10)}) = 0$

$1 + \frac{(k_{p} s + k_{I})}{s (s + 2) (s + 10)} = 0$

$s^{3} + 12 s^{2} + (20 + k_{p}) s + k_{I} = 0$

According to R-H array;
For stability criteria to be satisfied,

$\frac{12 K_{p} + 240 - K_{I}}{12} > 0 a n d K_{I} > 0$

$o r K_{p} > \frac{k_{I}}{12} - 20 a n d k_{I} > 0$

Suggest Corrections

Similar questions

\begin{matrix} s^{3} & 1 & (2 k + 3) s^{2} & 2 K & 4 \end{matrix}

K

K = 1

ω_{d}

K_{P}

K_{D}

G_{c} (s)

G_{p} (s)

Join BYJU'S Learning Program