1. Consider the spring mass damper system mounted on a massless moving cart.Find the mathematical model and transfer function of the system taking displacement of the cart as inut and displacement of the mass as output.

<img src='./qimages/15611-1.jpg'>

2. Find the transfer function for the block diagram reduction technique.

<img src='./qimages/15611-2.jpg'>

3. Consider the following system:

<img src='./qimages/15611-3.jpg'> Calculate and so that settling time is 2 sec. (taking tolerence) and Maximum Peak overshoot is 20% for a step input. What is the value of using the value of and obtained in

4. Using Routh stability criterion, determine the. number of closed loop poles in the left half of plane, the right half of plane and on the imaginary axis of the system whose characteristic equation is

s^6 5s^5 8s^4 10s^3 13s^2 5s 6 0.

Also comment on the stability of the system.

5. Consider the system given in the figure below

<img src='./qimages/15611-5.jpg'>

Sketch the Root locus in the graph paper as varies from 0 to infinite, showing all relevant steps and points. Also find the value of for which the closed loop system is stable.

6. Consider unity feedback system with open-loop transfer function Draw a suitable Nyquist contour with mathematical equation for each part. Sketch Nyquist plot in plane paper showing all necessary calculations. Comment on the stability.

7. An Uncompensated system is given as below

where 1/s^2;

<img src='./qimages/15611-7.jpg'>

Using Root locus analysis design a lead compensator of the form k(s such that settling time ts sec. (taking tolerance) and maximum peak overshoot Mp 516.30%.

8. A system is given by the following differential equation:

d^3x/dt^3 5d^2x/dt^2 3dx/dt 2x u1 2u2 u3
y1 4 dx/dt 3u1
y2 3 d^2x/dt^2 2u2 3u3

Obtain a state space representation of the system.

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

(a) Controllability and Observability Fuzzy Control Effect of addition of a pole to O/L transfer function