1. Determine the transfer function for the
system given in the Figure 1 using block diagram reduction techniques. <img src='./qimages/8844-1.jpg'> <br><br>

2. For the unity feedback system having open-loop transfer function as K(s 7s 12) determine type of the system, error constants Kp, Kv and Ka, and steady state error for parabolic input.

3. Determine the overshoot and the time to reach peak overshoot for the system shown in Figure when a unit step input is applied.

<img src='./qimages/8844-3.jpg'>
4. Consider the closed-loop feedback control system shown in Figure 3. <img src='./qimages/8844-4.jpg'>

Using Routh-Hurwitz criterion, determine the range of K for which the system is stable. Also find the number of roots of the characteristic equation that are in the right half of s-plane for 0.5.

5. A unity feedback system has an open-loop transfer function Using Nyquist criterion, determine whether the closed-loop system is stable or not.

6. For a closed-loop unity feedback system whose
open-loop transfer function is given by 10/s(s 1)(0.1s 1)
Draw the Bode diagram. Obtain the phase margin and gain margin.

7. Sketch the root locus diagram for Determine the gain and the phase margin for K =10.

8. Determine the state space representation in phase variable form for the system whose closed-loop transfer function is given by 24 9s^2 26s 24.

9. Check whether the following system is completely state controllable and completely observable

<img src='./qimages/8844-9.jpg'>

10. Write short notes on any two of the following:

(a) Neural Network Based Control
Fuzzy Logic Control
Asymptotic and Conditional Stability