Question

The operating region of the developed torque \( T_{em} \) and speed \( \omega \) of an induction motor drive is given by the shaded region OQRE in the figure. The load torque \( T_L \) characteristic is also shown. The motor drive moves from the initial operating point O to the final operating point S. Which one of the following trajectories will take the shortest time? 

• A. \( O \rightarrow Q \rightarrow R \rightarrow S \)
• B. \( O \rightarrow P \rightarrow S \)
• C. \( O \rightarrow E \rightarrow S \)
• D. \( O \rightarrow F \rightarrow S \)

Hint:

To minimize transition time in motor drive trajectories, always follow the path that allows maximum accelerating torque \( (T_{em} - T_L) \) throughout the motion.

Answer 1

The Correct Option is A

To minimize the transition time from point O to S, the motor must operate with the maximum possible accelerating torque at every stage. The accelerating torque is the difference T_em - T_L. The shaded region defines the maximum torque that can be applied at any given speed.

Path O → Q → R → S:

• Applies maximum torque (T_em) throughout, which gives maximum acceleration.
• Hence, this path results in the shortest travel time.

Other paths involve applying less than maximum available torque or moving through regions with smaller torque margins, thus resulting in slower acceleration and longer time.