1 (a)
Distinguish between open loop and closed loop control system, with suitable examples.

4 M

1 (b)
What are the ideal requirements of control system?

6 M

1 (c)
What is Control Action? Briefly explain proportional, proportional plus derivative and proportional plus derivative plus integral controllers, with the help of block diagrams.

10 M

2 (a)
Obtain the differential equation for the mechanical system shown in fig. Q2(a) and draw the equivalent mechanical system, also draw the analogous electrical network based on i) Force - voltage analogy ii) Force - current analogy.

10 M

2 (b)
Derive the transfer function of an armature controlled DC motor. The field current is maintained constant during operation. Assume that the armature coil has back emf \[ e_b = k_b \dfrac {d\theta} {dt} \] and the coil current produces a torque T=K

_{m}I on the rotor, K_{b}and K_{m}are the back emf constant and motor torque constant respectively.
10 M

3 (a)
Reduce the block diagram shown in fig Q3(a) to its simplest possible form and find its closed loop transfer function.

10 M

3 (b)
Using Mason's gain formula, find the gain of the following system shown in fig. Q3(b).

10 M

4 (a)
Derive an expression for the unit step response of first order system.

8 M

4 (b)
A unity feedback system is characterized by an open loop transfer function \( G(s) = \dfrac {K} {s(s+10)} \) . Determine the gain K, so that the system will have a damping ratio of 0.5. For this value of k determine peak time, setting time and peak overshoot for a unit step input.

8 M

4 (c)
Ascertain the stability of the system given by the characteristics equation S

^{5}+4S^{4}+12S^{3}+20S^{2}+30S+100=0, using R-H criteria.
4 M

5 (a)
Sketch the polar plot for the transfer function. \[ G(s) = \dfrac {10} {s(s+1)(s+2)} .\]

10 M

5 (b)
Apply Nyquist stability criterion to the system wit transfer function. \[ G(s) H(s) = \dfrac {4s+1} {s^2 (1+s)(1+2s) } \] and ascertain its stability.

10 M

6
Sketch the Bode plot for \[ G(s) H(s) = \dfrac {2} {s(s+1)(1+0.2s) }.\] Also obtain gain margin and phase margin and crossover frequencies.

20 M

7
Sketch the root locus plot for \[ G(s) H(s) = \dfrac {K} {s(s+2)(s+4)(s+6) } .\] For what values of K the system becomes unstable?

20 M

8 (a)
Explain the following: i) Lead compensator ii) Lag compensaor.

12 M

8 (b)
Determine the state controllability and observability of the system described by \[ \dot x= \begin{bmatrix}
-3 &1 &1 \\-1 &0 &1 \\0 &0 &1 \end{bmatrix}x+ \begin{bmatrix} 0 &1 \\0 &0 \\2 &1 \end{bmatrix} u \\ Y=\begin{bmatrix} 0 &0 &1 \\1 &1 &0 \end{bmatrix}x .\]

8 M

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