30 A shunt motor in Figure P14.30 is characterized by a field coefficient kf = 0.12 V-s/A-rad, such that the back emf is given by the expression E, = kfIfw and the motor torque by the expression T = kçI,Iq. The motor drives an inertia/viscous friction load with parameters J = 0.8 kg-m² and b= 0.6 N-m-s/rad. The field equation may be approximated by Vs = R;IF. The armature resistance is R, = 0.75 2, and the field resistance is Rp = 60 2. The system is perturbed around the nominal operating point V5p = 150 V, wn = 200 rad/s, Io = 186.67 A, respectively. %3D a. Derive the dynamic system equations in symbolic form. b. Linearize the equations you obtained in part a. Ia ll La Ra Vs ER
30 A shunt motor in Figure P14.30 is characterized by a field coefficient kf = 0.12 V-s/A-rad, such that the back emf is given by the expression E, = kfIfw and the motor torque by the expression T = kçI,Iq. The motor drives an inertia/viscous friction load with parameters J = 0.8 kg-m² and b= 0.6 N-m-s/rad. The field equation may be approximated by Vs = R;IF. The armature resistance is R, = 0.75 2, and the field resistance is Rp = 60 2. The system is perturbed around the nominal operating point V5p = 150 V, wn = 200 rad/s, Io = 186.67 A, respectively. %3D a. Derive the dynamic system equations in symbolic form. b. Linearize the equations you obtained in part a. Ia ll La Ra Vs ER
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Transcribed Image Text:30 A shunt motor in Figure P14.30 is characterized
by a field coefficient kf = 0.12 V-s/A-rad, such that
the back emf is given by the expression E, = kfIfw
and the motor torque by the expression T = kçI,Iq.
The motor drives an inertia/viscous friction load with
parameters J = 0.8 kg-m² and b= 0.6 N-m-s/rad.
The field equation may be approximated by
Vs = R;IF. The armature resistance is R, = 0.75 2,
and the field resistance is Rp = 60 2. The system is
perturbed around the nominal operating point
V5p = 150 V, wn = 200 rad/s, Io = 186.67 A,
respectively.
%3D
a. Derive the dynamic system equations in symbolic
form.
b. Linearize the equations you obtained in part a.
Transcribed Image Text:Ia
ll
La
Ra
Vs
ER
Expert Solution
Step 1
Applying KVL
By ohm’s law
Step 2
As given machine is exciting by a dc voltage
Expression for torque
Step 3
Expression of torque under dynamic condition
Substituting value of T in the above expression
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