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GATE 2020 EE – Question 44

Control Systems · Mathematical modelling and representation of systems, Feedback principle, Transfer function, Block diagrams and Signal flow graphs · 2 marks · Multiple choice

Consider a permanent magnet dc (PMDC) motor which is initially at rest. At $t=0$, a dc voltage of 5 V is applied to the motor. Its speed monotonically increases from 0 rad/s to 6.32 rad/s in 0.5 s and finally settles to 10 rad/s. Assuming that the armature inductance of the motor is negligible, the transfer function for the motor is

  1. $\dfrac{10}{0.5s+1}$
  2. $\dfrac{2}{0.5s+1}$
  3. $\dfrac{2}{s+0.5}$
  4. $\dfrac{10}{s+0.5}$

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Correct answer: (B) $\dfrac{2}{0.5s+1}$

Explanation

With negligible armature inductance the motor is a first-order system. The steady-state speed per volt is $\frac{10}{5}=2$ rad/s per V. The speed reaches 63.2% of its final value ($6.32$ of 10 rad/s) in one time constant, so $\tau=0.5$ s. So $G(s)=\frac{2}{0.5s+1}$.