Question

A dc motor whose parameters are given in example 2.3 is started directly from a 220⋅V dc supply with no load. Find its starting speed response and the time taken to reach 100rad/sec.

Solution
ω(s) / V(s) ​= Gωv​(s)= Kb / s²(JLₐ​) + s(B₁​L₃​+Jₐ)+(B₁Rₐ​+Kb² = 15.968 / s² + 167s + 12874
​ω(s) = 3.512×10⁶ / s(s²+167 s+12874)
ω(t)=272.8(1−1.47e⁻⁸³.⁵ᵗ sin (76.02t+0.744))​
The time to reach 100rad/sec is evaluated by equating the left-hand side of the above equation to 100 and solving for t. giving an approximate value of 10/ms.

Answer 1

The question requires using DC motor parameters to calculate its starting speed response and the time taken to reach a specific angular velocity, using principles of electromechanical systems and calculus.

Step-by-step explanation:

The question involves mathematical equations related to the operation of a direct current (DC) motor and its starting speed response. An understanding of DC motor parameters, such as back electromotive force (back emf), armature resistance, and angular acceleration, is crucial for solving the problem. The student is expected to apply their knowledge of electromechanical systems and calculus to determine the motor's behavior at startup and calculate specific operational characteristics like the time taken to reach 100 rad/sec.