Modern Control Engineering

Problems 99

B–3–9.Derive the transfer function of the electrical circuit
shown in Figure 3–38. Draw a schematic diagram of an
analogous mechanical system.

R 1 C 1

R 2

C 2

ei eo

Figure 3–38Electrical circuit.

+

• 
  

C R (^1) A
R 2
ei e
o
Figure 3–39Operational-amplifier circuit.
B–3–10.Obtain the transfer function of the
op-amp circuit shown in Figure 3–39.
Eo(s)Ei(s)

• 
  

• 
  

C A

B

R 1

R 2

R 3

ei eo

Figure 3–40Operational-amplifier circuit.

B–3–11.Obtain the transfer function of the
op-amp circuit shown in Figure 3–40.

Eo(s)Ei(s)

B–3–12.Using the impedance approach, obtain the trans-

fer function of the op-amp circuit shown in

Figure 3–41.

Eo(s)Ei(s)

+

• C

A

B

R 1

R 1

ei R 2

eo

Figure 3–41Operational-amplifier circuit.

B–3–13.Consider the system shown in Figure 3–42. An

armature-controlled dc servomotor drives a load consisting

of the moment of inertia JL. The torque developed by the

motor is T. The moment of inertia of the motor rotor is Jm.

The angular displacements of the motor rotor and the load

element are umandu, respectively. The gear ratio is

n=uum. Obtain the transfer function Q(s) Ei(s).

L R

T

n

ei Jm

JL

um

u

Figure 3–42Armature-controlled dc servomotor system.