Total marks: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary


1(a) Define relative,absolute and robust stability of the system.
5 M
1(b) What is gain and phase margin?Explain how to find gain phase margin by using polar plot.
5 M
1(c) Differentiate open loop and closed loop system.
5 M
1(d) What is damping ratio? Show the location of roots in s plane for different values of damping ratio.
5 M

2(a) Derive the transfer function of electromechanical system shown in fig:

10 M
2(b) Find the transfer function of the electrical network in figure

10 M

3(a) Find the closed loop transfer of the system whose block diagrams is given in figure;

10 M
3(b) State and prove properties of state transition matrix.
5 M
3(c) What is optimal control?Why optimal control is needed?
5 M

4(a) Construct a state model of the system shown infig

10 M
4(b) Predict the controllability and observability for the system
[x=egin{bmatrix} 0 & 1 & 0\ 3& 0& 2\ -12&-7 &-6 end{bmatrix}x +egin{bmatrix} 0\ 0\ 0 end{bmatrix}u\]
y=[1 2 0]dx
10 M

5(a) Construct the root locus for the system having following open loop transfer function:
[G(s)H(s)=dfrac{k}{(s+3)(s+5)(s^{2}+2s+2)}
10 M
5(b) Construct the bode plot for the following transfer function:
[G(s).H(s)=dfrac{10(s+10)}{s(s+10)(s+5)}\]
10 M

6(a) What is adaptive control? Explain one method of adaptive control.
7 M
6(b) Explain how the stability of the system can be analysed Using Nyquist Criterion.
7 M
6(c) Explain the time domain specifications.
6 M



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