1 (a)
Draw the F-V the F-I analogous circuit for the mechanical system shown in Fig Q1(a) with necessary equation.

12 M

1 (b)
For the rotational mechanical system shown draw the torque-voltage analogous circuit for Fig Q1(b).

8 M

2 (a)
Using block diagram reduction techniques for C/R for Fig Q2(a).

5 M

2 (b)
Draw the signal flow graph for the block diagram shown in Fig Q2(b) and find the TF.

8 M

2 (c)
Draw the signal flow graph and find TF Fig Q2(c).

7 M

3 (a)
Find the error coefficients K

_{p}, K_{v}and K_{a}for the system having \[ G(s)= \dfrac {10}{s^2+2s+9} \ \& \ H(s)=0.2 \]
6 M

3 (b)
Find K

_{1}so that ?=0.35. Find the corresponding time domain specifications for Fig Q3(b).

6 M

3 (c)
With respect to a second order system define the following by drawing neat response curve and expressions: i) Maximum overshoot (M

_{p}); ii) Time delay (t_{d}); iii) Time constant (T); iv) Rise time (t_{t}).
8 M

4 (a)
What are the necessary and sufficient conditions for a system to be stable according to Routh-Hurwitz criterion?

4 M

4 (b)
What value of K makes the following unity feedback system stable? \[ G(s)=\dfrac {K(s+1)^2}{s^3} \]

4 M

4 (c)
Find how many roots have real parts greater than -1 for the characteristics equation.

s

s

^{3}+7s^{2}+25s+39=0
4 M

4 (d)
How many roots of the characteristic polynomial lie in the right half of S-plane, the left half of s-plane and on jω axis. Comment on the stability of the system.

P(s)=s

P(s)=s

^{5}+2s^{4}+2s^{3}+4s^{2}+s+2
8 M

5 (a)
What are the angle and magnitude conditions that a point on root locus has to satisfy?

6 M

5 (b)
Sketch the root locus for the unity feedback control system whose open loop transfer function is \[ G(s)={1}{s(s+2)(s^2+4s+13)} \]

14 M

6 (a)
With respect to Nyquist criterion explain the following:

i) Encircle of a point

ii) Analytic function and its singularities.

iii) Mapping theorem of principle of argument

iv) Find the number of encirclements of point A in Fig Q6.1(a) and Q6.1(b)

i) Encircle of a point

ii) Analytic function and its singularities.

iii) Mapping theorem of principle of argument

iv) Find the number of encirclements of point A in Fig Q6.1(a) and Q6.1(b)

8 M

6 (b)
For the open loop TF of a feedback control system \[ G(s)H(s)=\dfrac {K(1+2s)}{s(1+s)(1+s+s^2)}. \] Sketch the complete Nyquist plot and hence find the range of K for stability using Nyquist criterion.

12 M

7 (a)
Draw the bode plot for a system having \[ G(s)=\dfrac {K(1+0.2s)(1+0.025s)}{s^3(1+0.01s)(1+0.05s)}. \] Comment on the stability of the system. Also find the range of K for stability.

12 M

7 (b)
For the plot shown determine the TF (Fig Q7(b)).

8 M

8 (a)
What are the advantages of state space analysis?

4 M

8 (b)
A system is described by the differential equation \[ \dfrac {d^3y}{dt^3}+ \dfrac {3d^2y}{dt^2}+ \dfrac {17dy}{dt}+5y=10u(t) \] Where y is the output and u is the input to the system. Determine the state space representation of the system.

6 M

8 (c)
Obtain the state equations for the electrical network shown in Fig. Q8(c).

10 M

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