In the motor given in the figure, 0, is the motor angle; w(t) is the motor speed; ea(t) is the input voltage; ia(t) is the armature current; v(t) is a back-emf voltage; and Tm (t) is the mechanical torque. In this model, ignore the field as it is kept at a constant voltage. The Transfer Function G(p) wm(t) ea(t) N(p) D(P) when the armature inductance is negligible, that is, La ≈0, was developed from the Ra La field elle Rotor Armature v(t) circuit Tm(1) ia(1) - ed(1) 0m(1) block diagram: ea ia Tm 1 Kt Ra Kbwm Kb Gm(p)= wm(t) K₁ Rajm N(p) ea(t) P+ + P KK + D(p) m Ralm 1 Tm p+Tm Dm Wm Noticed a typo: β p+Tm ea(t) wm(t) G(p) B = 4 × 10-4 Nm/(rad/sec) P1. Use Laplace Transforms to find the motor speed wm (t) for a step input ea (t) = A us(t) Obtain a plot of ea(t) and wm (t) on the same graph. Select appropriate initial conditions and step magnitude.

In the motor given in the figure, 0, is the motor angle; w(t) is the motor speed; ea(t) is the input voltage; ia(t) is the armature current; v(t) is a back-emf voltage; and Tm (t) is the mechanical torque. In this model, ignore the field as it is kept at a constant voltage. The Transfer Function G(p) wm(t) ea(t) N(p) D(P) when the armature inductance is negligible, that is, La ≈0, was developed from the Ra La field elle Rotor Armature v(t) circuit Tm(1) ia(1) - ed(1) 0m(1) block diagram: ea ia Tm 1 Kt Ra Kbwm Kb Gm(p)= wm(t) K₁ Rajm N(p) ea(t) P+ + P KK + D(p) m Ralm 1 Tm p+Tm Dm Wm Noticed a typo: β p+Tm ea(t) wm(t) G(p) B = 4 × 10-4 Nm/(rad/sec) P1. Use Laplace Transforms to find the motor speed wm (t) for a step input ea (t) = A us(t) Obtain a plot of ea(t) and wm (t) on the same graph. Select appropriate initial conditions and step magnitude.

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter12: Power System Controls

Section: Chapter Questions

Problem 12.4P

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