1 (a)
With the help of neat block diagram, define open loop and closed loop control system.

4 M

1 (b)
For a mechanical system shown in Fig. Q1(b) obtain force voltage analogous electrical network.

8 M

1 (c)
Draw the electrical network based on torque-current analogy and give all the performance equation for the Fig Q1(c).

8 M

2 (a)
Define the following terms related to signal flow graph with a neat schematic:

i) Forward path

ii) Feedback loop

iii) Self loop

iv) Source node.

i) Forward path

ii) Feedback loop

iii) Self loop

iv) Source node.

6 M

2 (b)
Obtain the transfer function for the block diagram, shown in Fig. Q2(b). Using:

i) Block diagram reducing technique

ii) Mason's gain formula.

i) Block diagram reducing technique

ii) Mason's gain formula.

8 M

2 (c)
For the signal flow graph shown in Fig. Q2(c), find the overall transfer function by:

i) Block diagram reduction technique.

ii) Verify the result by Mason's gain formula.

i) Block diagram reduction technique.

ii) Verify the result by Mason's gain formula.

8 M

3 (a)
Define and derive the expression for: i) Rise time

ii) Peak overshoot of an under-damped second order control system subjected to step input.

ii) Peak overshoot of an under-damped second order control system subjected to step input.

6 M

3 (b)
For a unit feedback control system with \[ G(s) = \dfrac {10 (s+2)} {s^2 (s+1)} \] Find: i) The static error coefficients ii) Steady state error when the input is \[ R(s)= \dfrac {3}{8} - \dfrac {2}{s^2} + \dfrac {1}{3s^3} .\]

6 M

3 (c)
A system is given by differential equation \[ \dfrac {d^2y}{dt^2} + 4\dfrac {dy}{dt} + 8y = 8x, \] where y=output and x=input. Determine: i) Peak overshoot ii) Settling time iii) Peak time for unit step input.

8 M

4 (a)
Explain Routh-Hurwitz criterion for determining the stability of the system and mention its limitations.

6 M

4 (b)
For a system s

^{4}+22s^{2}+10s^{2}+s+k=0, find k_{mar}and ω at k_{mar}.
6 M

4 (c)
Determine the value of 'k' and 'b' so that the system whose open loop transfer function is: \[ G(s) = \dfrac {k(s+1)}{s^3+bs^2 + 3s+1} \] oscillates at a frequency of oscillations of 2 rad/sec.

8 M

5 (a)
For a unity feedback system, the open loop transfer function is given by: \[ G(s) = \dfrac {K} {s(s+2)(s^2+6s+25)} \] i) Sketch the root locus for 0≤k≤∞ ii) At what value of 'k' the system becomes unstable

ii) At this point of instability, determine the frequency of oscillation of the system.

ii) At this point of instability, determine the frequency of oscillation of the system.

15 M

5 (b)
Consider the system with \[ G(s)H(s) = \dfrac{k} {s(s+2)(s+4)} \] find whether s=-0.75 is point on root locus or not angle condition.

5 M

6 (a)
Explain the procedure for investigating the stability using Nyquist criterion.

5 M

6 (b)
For a certain control system: \[ G(s) H(s) = \dfrac {k} {s(s+2)(s+10)} . \] Sketch the Nyquist plot and hence calculate the range of value of 'k' for stability.

15 M

7 (a)
Sketch the bode plot for the open loop transfer function: \[ G(s)H(s)= \dfrac {k(1+0.2s)(I+0.025s)}{s^3 (1+0.001s)(1+0.005s)} , \] Find the range of 'k' for closed loop stability

14 M

7 (b)
Explain the following as applied to bode plots:

i) Gain margin ii) Phase margin iii) Gain and phase cross over frequency.

i) Gain margin ii) Phase margin iii) Gain and phase cross over frequency.

6 M

8 (a)
Define the following terms: i) State ii) State variable iii) State space iv) State transition.

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 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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