A system with transfer function 1- s-1- subjected to a step input takes 10 seconds to reach 50

The response of a first order system for unit step input is, θ (t)=θ_o[1 e^ t/τ] θ_02=θ _0[1 e^ 10/τ] 12=1 e^ 10/τ e^ 10τ=12 10τ= 0.693 ∴ nbsp; τ =14.4 sec ...

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Step Response of First Order System

A system with...

Question

A system with transfer function $\frac{1}{τ s + 1}$ , subjected to a step input takes 10 seconds to reach 50% of the step height. The value of $τ$ is

6.9 s

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10 s

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14.4 s

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20 s

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Solution

The correct option is C 14.4 s
The response of a first order system for unit step input is,
$θ (t) = θ_{o} [1 - e^{- t / τ}]$
$\frac{θ_{0}}{2} = θ_{0} [1 - e^{- 10 / τ}]$
$\frac{1}{2} = 1 - e^{- 10 / τ}$
$e^{\frac{- 10}{τ}} = \frac{1}{2}$
$\frac{- 10}{τ} = - 0.693$
$∴ τ = 14.4$ sec

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A system with transfer function 1τs+1, subjected to a step input takes 10 seconds to reach 50% of the step height. The value of τ is

The correct option is C 14.4 sThe response of a first order system for unit step input is, θ(t)=θo[1−e−t/τ] θ02=θ0[1−e−10/τ] 12=1−e−10/τ e−10τ=12 −10τ=−0.693 ∴ τ=14.4 sec

A system with transfer function $\frac{1}{τ s + 1}$ , subjected to a step input takes 10 seconds to reach 50% of the step height. The value of $τ$ is

The correct option is C 14.4 s
The response of a first order system for unit step input is,
$θ (t) = θ_{o} [1 - e^{- t / τ}]$
$\frac{θ_{0}}{2} = θ_{0} [1 - e^{- 10 / τ}]$
$\frac{1}{2} = 1 - e^{- 10 / τ}$
$e^{\frac{- 10}{τ}} = \frac{1}{2}$
$\frac{- 10}{τ} = - 0.693$
$∴ τ = 14.4$ sec