# WBUT Question Papers EC Control Systems B Tech Fifth Sem 2011 12

# WBUT Question Papers EC

## Control Systems B Tech Fifth Sem 2011 12

Time Allotted ; 3 Hours

The figures in the margin indicate full marks.

Candidates are required to give their answers in their own words

as far as practicable.

GROUP-A ( Multiple Choice Type Questions )

1. Choose the correct alternatives for any ten of the following :

10 x 1 – 10

x) If the maximum overshoot is 100%, the damping ratio is

a) 1

t

c) 0;5

ii) If the, characteristic equation of a system is s^{2} .+ 8s + 25 = 0 , the value of £ _{n} and co_{n} will be

b) 0-8, 0*5 rad/s

d) 5, V8 rad/s.

iii) Addition of a pole to the close loop transfer function

a) increases rise time b) decreases rise time

c) increases overshoot d) has no effect.

iv) The transfer function of a system having a gain of 9 and a pole zero map as in figure below is

—*—A—– o

-3 -I

| |||||||||||||

| |||||||||||||

| |||||||||||||

| |||||||||||||

| |||||||||||||

| |||||||||||||

| |||||||||||||

v) The TF of a network —–P.*^{5 s} i_{s} known

2 + s

a) High pass system

b) Lead network

c) Lag network

d) Proportional controller.

vi) If the Nyquist plot of a certain feedback system crosses the negative real axis at -0*1 point, the gain margin of the system is given by

b) 10

d) none of these.

xi) The root locus is symmetrical w.r.t.

a) negative real axis

b) positive real axis

c) imaginary axis

d) positive & negative real axis.

xii) A feedback control system is basically

a) high pass filter b) band pass filter

c) low pass filter d) none of these.

GROUP -B

( Short Answer Type Questions )

Answer any three of the following 3×5= 15

- Consider the following mechanical translational system shown in figure below. F denotes force, x denotes displacement, M denotes mass and B denotes friction coefficient and K denotes spring constan

i) Write down the differential equation(s) governing the above system.

ii) Draw the corresponding electrical equivalent circuit using force-voltage analogy.

- Using Routh criterion investigate the stability of the unity

feedback control system whose open loop transfer function is

For what value of Twill the system be stable ?

- A system is represented by

-3 | -2 | X + | Y |

-1 | – 2 | 1 |

Y = [ 1 2] X

Find the poles of the system. Assume D = 0.

- Find the Z-transfer function of the system defined by

y ( n) – 0 • 5y ( n -1) = x ( n – 2)- 5x ( n – 2) + £>x ( n) where y ( n ) and x ( n) denote output and input sequences respectively.

- For the system defined by G (s) =

approximate root-^{f}locus diagram.

- Using Mason’s Gain formula, determine the transfer function

of the system.

- Obtain the Z-transform for a unit-step function.

**GROUP -C **( Long Answer Type Questions )

Answer any three of the following. 3 x 15 = 45

- a) A unity feedback control system has an open loop

transfer function

G (s) = -j-————-

(s^{2} + 8s+ 32)

• Sketch the root locus of the system and deduce how the

peak overshoot varies with increasing k if the loop is closed. 5 + 5

b) What kind of controller would you recommend for this system ? 5

- Prove that for a standard second order system defined by

W

G(s)=—7z – 7T, the peak overshoot due to a step

s +2^W s + W

^ n n

input depends on £, only. Prove further that the constant lines pass through the origin of the ( cr i j co ) plane. 10 + 5

9 f *

- a) Derive the transfer function for a zero-order hold. 5

b) A continuous function y (t) is sampled by an impulse sampler as shown below :

Ct’)

TyopvO rf

“k

Obtain the Laplace transform for y (t ) 5

c) Obtain the Z-transform for x[n]- |a|^{M} and comment on the ROC. 5

- The open-loop transfer function of a unity feedback control system is given by

s + 0•25

s (s + l)(s + 0-5)

Determine the closed-loop stability by applying Nyquist criterion.

1,3. Sketch the Bode Plot for the transfer function defined by

2 (s + 0 • 2)

G{s)H{s)

s^{2} +-(s 4 l)(s 4 0 – 5)

Determine

a) phase cross-over frequency

b) gain cross-over frequency

c) gain margin

d) phase margin.

14. a) Determine tl^e transfer matrix for a system whose A, B, C matrices are :

“1 | – 2 | ~2 | ||

A ~ | , B – | |||

4 | ~5 | 1 |

b) Is the system stable ?

c) Is the system controllable ? Assume D = 0.