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

6 M

1 (b)
Write the differential equations of performance for the mechanical system shown in Fig. Q1 (b). Draw its F-V analogous circuit.

6 M

1 (c)
Obtain the transfer function of an armature controlled DC servomotor.

6 M

2 (a)
Obtain the transfer function of the block diagram shown below, using block diagram reduction technique.

10 M

2 (b)
Obtain the closed loop transfer function C(s)/R(s) for the signal flow graph of a system shown in Fig. Q2(b) by use of Mason's gain formula.

10 M

3 (a)
Derive expression for peak response time t

_{p}and maximum overshoot M_{p}of an under damped second order control system subjected to step input.
6 M

3 (b)
A second order control system is represented by a transfer function given below: \[ \dfrac {0_0(s)}{T(s)}= \dfrac {1}{Js^2+Fs+K} \] where ?

i) Maximum overshoot is 6%

ii) Peak time is 1 sec

iii) The steady state value of the output is 0.5 radian.

Determine the values of J, F and K.

_{0}is the proportional output and T is the input torque. A step unit of 10 N-m is applied to the system and test results are given below:i) Maximum overshoot is 6%

ii) Peak time is 1 sec

iii) The steady state value of the output is 0.5 radian.

Determine the values of J, F and K.

8 M

3 (c)
For a unity 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 transform is \[ R(s)= \dfrac {3}{s}- \dfrac {2}{s^2}- \dfrac {1}{3s^2} \]

i) The static error coefficients

ii) Steady state error when the input transform is \[ R(s)= \dfrac {3}{s}- \dfrac {2}{s^2}- \dfrac {1}{3s^2} \]

6 M

4 (a)
Explain Routh-Hurwitz's criterion for determining the stability of a system and mention any three limitations of R-H criterion.

10 M

4 (b)
A unity feedback control system is characterized by the open loop transfer function: \[ G(s) = \dfrac {K(s+13)} {s(s+3)(s+7)} \] i) Using the Routh's criterion, calculate the range of values of K for the system to be stable.

ii) Check if for K=1, all the roots of the characteristic equation of the above system are more negative than -0.5.

ii) Check if for K=1, all the roots of the characteristic equation of the above system are more negative than -0.5.

10 M

5 (a)
Sketch the root locus for a unity feedback control system with open loop transfer function: \[ G(s)= \dfrac {K(s+2)(s+3)}{s(s+1)} \]

12 M

5 (b)
Show that the root Loci for unity feedback control system with \[ G(s)=\dfrac {K(s^2 +6s +10)}{(s^2+2s+10)} \] are the areas of circle of radius √10 and centred at the origin.

8 M

6 (a)
Sketch the Bode plot of a unity feedback system whose open loop transfer function is given by \[ G(s)= \dfrac {K}{s(1+0.1s)(s+0.05s)} \] i) Find the value of K for a gain margin of 10dB.

ii) Find the value of K for a phase margin of 30°.

ii) Find the value of K for a phase margin of 30°.

14 M

6 (b)
Determine the open loop transfer function of a system whose approximate plot is shown below.

6 M

7 (a)
State and explain Nyquist stability criterion.

6 M

7 (b)
Sketch the Nyquist plot for a system whose open loop transfer function is \[ G(s)H(s)= \dfrac {K(4s+1)}{s(2s-1)} \] Determine the range of K for which the system is stable.

14 M

8 (a)
Define state variable and state transition matrix. List the properties of the state transition matrix.

8 M

8 (b)
Obtain the state model of the electrical network shown in below, by choosing V

_{1}(t) and V_{2}(t) as state variables.

12 M

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