A control system with certain excitatioin is governed by the following mathematical equation d2xdt2-12 dxdt-118x-10-5e-4t-2e-5tThe natural time constants of the response of the system are

Natural time constant of the response depends only on poles of the system. T(s)=C(s)R(s)=1s^2+s/2+1/18 =1818s^2+9s+1=1(6s+1)(3s+1) This is in the form ...

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Control Systems

Impulse response of Second Order System

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Question

A control system with certain excitatioin is governed by the following mathematical equation

$\frac{d^{2} x}{d t^{2}} + \frac{1}{2} \frac{d x}{d t} + \frac{1}{18} x = 10 + 5 e^{- 4 t} + 2 e^{- 5 t}$

The natural time constants of the response of the system are

2s and 5s

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3s and 6s

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4s and 5s

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1/3s and 1/6s

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Solution

The correct option is B 3s and 6s
Natural time constant of the response depends only on poles of the system.

$T (s) = \frac{C (s)}{R (s)} = \frac{1}{s^{2} + s / 2 + 1 / 18}$

$= \frac{18}{18 s^{2} + 9 s + 1} = \frac{1}{(6 s + 1) (3 s + 1)}$

$T h i s i s i n t h e f o r m \frac{1}{(1 + s T_{1}) (1 + s T_{2})}$

$∴ T_{1}, T_{2} = 6 s e c, 3 s e c .$

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A control system with certain excitatioin is governed by the following mathematical equation d2xdt2+12 dxdt+118x=10+5e−4t+2e−5t The natural time constants of the response of the system are

The correct option is B 3s and 6sNatural time constant of the response depends only on poles of the system. T(s)=C(s)R(s)=1s2+s/2+1/18 =1818s2+9s+1=1(6s+1)(3s+1) This is in the form 1(1+sT1)(1+sT2) ∴T1,T2=6sec,3sec.

A control system with certain excitatioin is governed by the following mathematical equation

$\frac{d^{2} x}{d t^{2}} + \frac{1}{2} \frac{d x}{d t} + \frac{1}{18} x = 10 + 5 e^{- 4 t} + 2 e^{- 5 t}$

The natural time constants of the response of the system are