The transfer function of the system described by d2ydt2-dydt-dudt-2u with u as input and y as output is

D^2ydt+dydt=dudt+2u ⇒ s^2Y(s)+sY(s)=sU(s)+2U(s) ∴Y(s)U(s)=s+2(s^2+s) ...

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Control Systems

Definition of Transfer Function

The transfer ...

Question

The transfer function of the system described by $\frac{d^{2} y}{d t^{2}} + \frac{d y}{d t} = \frac{d u}{d t} + 2 u$ with u as input and y as output is

\frac{(s + 2)}{(s^{2} + s)}

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\frac{(s + 1)}{(s^{2} + s)}

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\frac{2}{(s^{2} + s)}

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\frac{2 s}{(s^{2} + s)}

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Solution

The correct option is A $\frac{(s + 2)}{(s^{2} + s)}$
$\frac{d^{2} y}{d t} + \frac{d y}{d t} = \frac{d u}{d t} + 2 u$

$\Rightarrow s^{2} Y (s) + s Y (s) = s U (s) + 2 U (s)$

$∴ \frac{Y (s)}{U (s)} = \frac{s + 2}{(s^{2} + s)}$

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The transfer function of the system described by d2ydt2+dydt=dudt+2u with u as input and y as output is

The correct option is A (s+2)(s2+s)d2ydt+dydt=dudt+2u ⇒s2Y(s)+sY(s)=sU(s)+2U(s) ∴Y(s)U(s)=s+2(s2+s)

The transfer function of the system described by $\frac{d^{2} y}{d t^{2}} + \frac{d y}{d t} = \frac{d u}{d t} + 2 u$ with u as input and y as output is

The correct option is A $\frac{(s + 2)}{(s^{2} + s)}$
$\frac{d^{2} y}{d t} + \frac{d y}{d t} = \frac{d u}{d t} + 2 u$

$\Rightarrow s^{2} Y (s) + s Y (s) = s U (s) + 2 U (s)$

$∴ \frac{Y (s)}{U (s)} = \frac{s + 2}{(s^{2} + s)}$