GATE Electrical Engineering (EE) 2020 Solved Paper

Question : 55 of 65

Marks: +1, -0

Consider a permanent magnet dc (PMDC) motor which is initially at rest. At

t=0, a d c

voltage of

5 {V}

is applied to the motor. Its speed monotonically increases from0 rad/s to

6.32

rad/s in

0.5 {sec}

and finally settles to

10

rad/s. Assuming that the armature inductance of the motor is negligible, the transfer function for the motor is

Solution:

{T}( {s})=\;{ {K}}/{( {ts}+1)}

r(t)=5 u(t)

R(s)=\;{5}/{s}

{C}( {s})= {T}( {s}) ⋅ {R}( {s}) \;\; =\;{ {K}}/{(τ {s}+1)} × \;{5}/{ {s}}

{C}(∞)=\lim ↙{ {s} → 0} {sC}( {s}) \;\; =\lim ↙{ {s} → 0} {s} \;{5 {K}}/{ {s}( {ts}+1)}

=5 {K}

According to question

C(∞)=10

5 K=10 ⇒ K=2

Time constant

τ=0.5

{T}( {s})=\;{ {K}}/{( {Ts}+1)}

=\;{2}/{(0.5 {s}+1)}

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