The shunt motor in Figure P19.22 is characterized by a field coefficient k f = 0.12 V-s/A-rad, such that the back emf is given by the expression Eb = k f I f ? and the motor torque by the expression T = k f I f Ia . 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 f I f . The armature resistance is Ra = 0.75 ?, and the field resistance is R f = 60 ?. The system is perturbed around the nominal operating point VS0 = 150 V, ?0 = 200 rad/s, and Ia0 = 186.67 A.



a. Derive the dynamic system equations in symbolic form.

b. Linearize the equations you obtained in part a.


Analysis:



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