1. Consider the coupled tank system as shown below. Find the transfer function of the system taking as input and as output. (All notations are having their usual meaning)

<img src='./qimages/13285-1.jpg'>

2. Find the transfer function C for the block diagram, using block reduction technique.

<img src='./qimages/13285-2.jpg'>

3. Define Rise Time, Settling Time and Maximum Peak Overshoot for a standard 2nd order underdamped system and indicate them in the step response of a system. Also derive their mathematical expression .in terms of system parameters. (Use standard notation)

4. Using R-H stability criterion, determine the number of poles in the left half, right half and on the imaginary axis of s-plane for a system whose characteristic equation is:

s^7 4s^6 10s^5 14s^4 10s^3 14s^2 9s +10 0.

Also comment on the stability of the system.

5. For the given system, sketch the root locus in the graph paper as varies from 0 to 00, showing all relevant steps and calculations

<img src='./qimages/13285-5.jpg'>

Calculate the value of approximately (mathematically or graphically) for which the close-loop system response gives 16·3% overshoot.

6. Sketch the bode plot of the open-loop transfer function in a semi-log paper and show the gain margin, phase margin, gain crossover frequency and phase crossover frequency.

7. Consider the following system:

<img src='./qimages/13285-7.jpg'>

Using-the root locus method, design a suitable lag-lead compensator so that the following specifications are met

Mp 16.3%; ts 2 sec (taking tolerance) and Kv 30.

Phase margin is correlated to which time domain specification and how?

An experiment is carried out on an open-loop stable minimum phase LTI system and the following steady state inputs and outputs are noted:

Input Output
3 sin (l·4lt) 1·5 sin (l·4lt
3 sin (0·9t) 2 sin (0·9t
3 sin (0·45t) 3 sin (0·45t
3 sin (0·25t) 3·5 sin (0·25t

Calculate the phase crossover frequency, gain crossover frequency, gain margin and phase margin of the system.

If the system is made close-loop with unity feedback., will the close-loop system be stable? Justify the answer.

Define state variables and state space.

What are the advantages of state space analysis over transfer function analysis

Define controllability and observability.

Determine the controllability and observability of the following system

X. X 1 u
1 0

y

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

M-Circle and N-Circle

PID Control

Fuzzy Logic Based Control