1. A PM DC motor is rigidly coupled to a fan; the fan load torque is described by the expression TL = 5 + 0.05ω + 0.001ω2, where torque is in Newton-meters and speed in radians per second. The motor has kaφ = kT φ = 2.42; Ra = 0.2 Q, and the inductance is negligible. If the motor voltage is 50 V, what will be the speed of rotation of the motor and fan?
2. A separately excited DC motor has the following parameters:
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Ra = 0.1 Q
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Rf = 100 Q
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La = 0.2 H
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Lf = 0.02 H
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Ka = 0.8
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Kf = 0.9
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The motor load is an inertia with J = 0.5 kg-m2 and
b = 2 N-m-s/rad. No external load torque is applied.
a. Sketch a diagram of the system and derive the (three) differential equations.
b. Sketch a simulation block diagram of the system (you should have three integrators).
c. Code the diagram, using Simulink.
d. Run the following simulations:
Armature control. Assume a constant field with Vf = 100 V; now simulate the response of the system when the armature voltage changes in step fashion from 50 to 75 V. Save and plot the current and angular speed responses. Field control. Assume a constant armature voltage with Va = 100 V; now simulate the response of the system when the field voltage changes in step fashion from 75 to 50 V. This procedure is called field weakening. Save and plot the current and angular speed responses.