1 (a)
Compare the linear and non-linear control system.

4 M

1 (b)
For the two port network shown below, obtain the transfer functions, \[ i) \ \dfrac {V_2(s)}{V_1(s)} \ and \ ii) \ \dfrac {V_1 (s)}{1_1(s)} \]

8 M

1 (c)
For the rotational system shown in below, i) Draw the mechanical network ii) Write the differential equations iii) Obtain torque to voltage analogy.

8 M

2 (a)
Illustrate how to perform the following, in connection with block diagram reduction reules:

i) Shifting a take-off after a summing point.

Shifting a take-off point before a summing point.

i) Shifting a take-off after a summing point.

Shifting a take-off point before a summing point.

4 M

2 (b)
The performance equations of a controlled system are given by the following set of linear algebraic equations:

i) Draw the block diagram

ii) Find the overall transfer function C(s)/R(s) using block diagram reduction technique. \[ E_1(s)=R(s)-H_2(s)C(s); \ E_2(s)=E_1(s)-H_1(s)E_4(s); \ E_2(s)=G_1(8)E_2(8)-H_2(s)C(s) E_4(s)=G_2(s)E_2(s); \ C(s)=G_2(s)E_4(s) \]

i) Draw the block diagram

ii) Find the overall transfer function C(s)/R(s) using block diagram reduction technique. \[ E_1(s)=R(s)-H_2(s)C(s); \ E_2(s)=E_1(s)-H_1(s)E_4(s); \ E_2(s)=G_1(8)E_2(8)-H_2(s)C(s) E_4(s)=G_2(s)E_2(s); \ C(s)=G_2(s)E_4(s) \]

8 M

2 (c)
Draw the corresponding signal flow graph for the given block diagram is shown in below, and obtain the overall transfer function by Mason's gain formula.

8 M

3 (a)
Derive the expression for peak time.

4 M

3 (b)
The loop transfer function of a feed back control system is given by, \[ G(s)H(s)= \dfrac {100}{s^2(s+4)(s+12)} \] i) Determine the static error co-efficients

ii) Determine the steady state error for the input r(t)=2t

ii) Determine the steady state error for the input r(t)=2t

^{2}+5t+10
8 M

3 (c)
A system is given by differential equation, \[ \dfrac {d^2 y(t)} {dt^2}+4\dfrac {dy(1)}{dt}+ 8y(t)=8x(t) \] Where y(t)=output and x(t)=input

Determine

i) Peak time

ii) Peak over shoot

iii) Settling time

iv) expression of the output response.

Determine

i) Peak time

ii) Peak over shoot

iii) Settling time

iv) expression of the output response.

8 M

4 (a)
Define the term stability applied to control system and what is the difference between absolute stability and relative stability.

4 M

4 (b)
Using Routh's criterion determine the stability of following systems:

i) Its open loop transfer function has poles at s=0, s=-1, s=-3 and zero at s=-5. Gain K=10.

ii) It is a type one system with an error constant of 10 sec

i) Its open loop transfer function has poles at s=0, s=-1, s=-3 and zero at s=-5. Gain K=10.

ii) It is a type one system with an error constant of 10 sec

^{-1}and poles at s-3 and s=-6
8 M

4 (c)
Using RH criterion determine the stability of the system having the characteristics equation, s

^{4}+10s^{2}+36s^{2}+70s+75=0 has roots more negative than s=-2.
8 M

5 (a)
The open-loop transfer function of a feed back control system in \[ G(s)H(s)= \dfrac {K}{(s+1)(s+2)(s+3)} \] check whether the following points are on the root locus. IT so, find the value of K at these points, i) s=-1.5 ii) s=0.5+j2

6 M

5 (b)
Sketch the root locus plot for a negative feed back control system characterized by an open loop transfer function, \[ G(s)H(s)= \dfrac {K}{s(s+3)(s^2+3s+11.2s)} \] Comment on stability.

14 M

6 (a)
State the advantages and limitations of frequency domain approach.

6 M

6 (b)
Determine the transfer function of a system whose asymptotic gain plot is shown in below.

10 M

6 (c)
List the effect of lead compensation.

4 M

7 (a)
Draw polar plot of \[ G(s)H(s)= \dfrac {100}{(s+2)(s+4)(s+8)} \]

4 M

7 (b)
Explain Nyquist stability criterion.

6 M

7 (c)
Sketch the Nyquist plot for, \[ GH(s)= \dfrac {k}{s(s+1)(s+2)} \] Then find the range of K for closed loop stability.

10 M

8 (a)
Define the following terms: i) state ii) state variables iii) state space.

6 M

8 (b)
List the advantages of state variable analysis.

4 M

8 (c)
Obtain the state transition matrix for, \[ A=\begin{bmatrix} 0 &-1 \\2 &-3 \end{bmatrix} \]

10 M

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