Match the transfer function of the second-order system with the nature of the system given below-Transfer function Nature of system P- 15s2-5s-15 I-Overdamped Q- 25s2-10s-25 II- Critically damped R- 35s2-18s-35 III- UnderdampedCodes-

P = 15s^2+5s+15 ω _n = √(15) = 3.872 rad/sec. 3ξ× nbsp;3.872 = 5 ξ = 52 × nbsp;3.872 = 0.64 (Underdamped) Q = 25s^2+10s+25 ω _n = √(25) = 5rad/sec. 2ξ ...

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Control Systems

Types of Second Order Systems

Match the tra...

Question

Match the transfer function of the second-order system with the nature of the system given below.

$\begin{matrix} T r a n s f e r f u n c t i o n & N a t u r e o f s y s t e m P . \frac{15}{s^{2} + 5 s + 15} & I . O v e r d a m p e d Q . \frac{25}{s^{2} + 10 s + 25} & I I . C r i t i c a l l y d a m p e d R . \frac{35}{s^{2} + 18 s + 35} & I I I . U n d e r d a m p e d \end{matrix}$

Codes:

P-I, Q-II, R-III

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P-II, Q-I, R-III

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P-III, Q-II, R-I

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P-III, Q-I, R-II

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Solution

The correct option is C P-III, Q-II, R-I
$P = \frac{15}{s^{2} + 5 s + 15}$

$ω_{n} = \sqrt{15}$ = 3.872 rad/sec.

$3 ξ \times 3.872 = 5$

$ξ$ = $\frac{5}{2 \times 3.872} = 0.64$
(Underdamped)

$Q = \frac{25}{s^{2} + 10 s + 25}$

$ω_{n} = \sqrt{25} = 5 r a d / s e c .$

$2 ξ \times 5 = 10$

$\Rightarrow ξ = 1$
(Critically damped)

Observing all the options, option (c) is correct.

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Match the transfer function of the second-order system with the nature of the system given below. Transfer functionNature of systemP.15s2+5s+15I.OverdampedQ.25s2+10s+25II.CriticallydampedR.35s2+18s+35III.Underdamped Codes:

The correct option is C P-III, Q-II, R-IP=15s2+5s+15 ωn=√15 = 3.872 rad/sec. 3ξ×3.872=5 ξ = 52×3.872=0.64 (Underdamped) Q=25s2+10s+25 ωn=√25=5rad/sec. 2ξ×5=10 ⇒ξ=1 (Critically damped) Observing all the options, option (c) is correct.