Solve the following:

1.5 Mathematical modeling of electromechanical systems (Unsolved

Problems - Home work)

1.12 Find the transfer function of the system X(s)/Ea(s) for the system shown in figure 1.16.

Figure 1.16

1.13 A dc motor develops 50 N-m of torque at a speed of 500 rad/s when 10 volts are

applied. It stalls out at this voltage with 100N-m of torque. If the inertia and damping of the

armature are 5 kg-m2 and 1N-m-s/rad respectively, find the transfer function

G(s)=θL(s)/Ea(s) of this motor if it drives an inertia load of 100kg-m2 through a gear train as

shown in figure 1.17.

Figure 1.17

1.14 For the motor, load and torque speed curve shown in Figure 1.18 find the transfer

function G(s) = θL(s)/Ea(s).

Figure 1.18

1.15. For the combined translational and rotational system shown in figure 1.19, find the

transfer function G(s) =X(s)/T(s).

Figure 1.19.

1.16 Derive the transfer function of an AC servo motor.

References:

1. Control Systems Engineering, Norman S. Nise, Wiley, 2003, ISBN: 0471445770