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# Stability Theory – 1 – 2

6. The characteristic equation 1 + G(s) R(s) = 0 of a system is given by

$s^4 + 6s^3 + 11s^2 + 6s + K = 0$

For the system to remain stable, the value of gain K should be :

(a) zero
(b) greater than zero but less than 10
(c) greater than 10 but less than 20
(d) greater than 20 but less than 30

Explanation
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7. The transfer function of a control system is given as

$\dpi{100} T(s) = k/s^2+4s+k$
where k is the gain of the system in radians/amp. For this system to be critically damped, the value of k should be :

(a) 1
(b) 2
(c) 3
(d) 4

Explanation
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8. The advantages of Nyquist stability test is/are :

(a) it guides in stabilising an unstable system
(b) it enables to predict closed loop stability from open loop results
(c) is is applicable to experimental results of frequency response of open loop system
(d) all of the above

Explanation
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9. The effect of adding poles and zeros can be determined quickly by :

(a) nicholas chart
(b) nyquist plot
(c) bode plot
(d) root locus

Explanation
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10. The root locus is a :

(a) time-domain
(b) frequency domain approach
(c) combination of both
(d) none of these