1. Derive the transfer function of the system shown in Figure k being the amplifier gain. <img src='./qimages/11536-1.jpg'>
2. Determine the transfer functions C1 R1, C2 R2, C1 R2 and C2 R1 from the block diagram shown in Figure using block diagram reduction technique. <img src='./qimages/11536-2.jpg'> <br><br>

3. Write short notes on any four of the following: Potentiometer
Synchros
AC Servomotor
Tachogenerators
Pneumatic Controller

4. A unity feedback system is characterized by the open-loop transfer function

G(s) /s(0·5s (0·2s

Determine the steady-state errors for unit step, unit ramp and unit acceleration inputs. Also determine the damping ratio and natural frequency of the dominant roots.

5. The open-loop transfer function of a unity feedback system is given by 1)

Sketch the polar plot and determine the gain margin and phase margin.

6. The open-loop transfer function of a unity feedback system is given by

G(s) 10)

Determine the value of k so that the system is stable with a phase margin> and gain crossover frequency as large as possible.

7. Sketch the root-loci for the system shown in Figure 3. <img src='./qimages/11536-7.jpg'> Construct a state model for the following transfer function
5 Derive the transfer function corresponding to the following state model <img src='./qimages/11536-8b.jpg'>