Reg. No. · 2019. 3. 5. · EC2255 — CONTROL SYSTEMS (Regulation 2008) Time: Three hours Maximum: 100 Marks Answer ALL Questions PART A — (10 × 2 = 20 Marks) 1. Compare the open

Reg. No. :

B.E./B.Tech. DEGREE EXAMINATION, APRIL/MAY 2010

Fourth Semester

Electronics and Communication Engineering

EC2255 — CONTROL SYSTEMS

(Regulation 2008)

Time: Three hours Maximum: 100 Marks

Answer ALL Questions

PART A — (10 × 2 = 20 Marks)

1. Compare the open loop system with closed loop system.

2. Draw the analogous electrical network for the mechanical system in Figure 1

using force-voltage analogy.

Figure 1

3. The block diagram shown in the Figure 2 represents a heat treating oven. The

set paint is 1000° C. What is the steady-state temperature?

Figure 2

Question Paper Code: E3080

E 3080 2

4. Determine error coefficients for the system having

( ) ( ) ( )( ) ( )sss

ssHsG

2.015.01

2

+++

= .

5. Determine the frequency domain specification of a second order system when

closed loop transfer function is given by

( )( ) 6410

642 ++

=sssR

sC.

6. Derive the transfer function of a lead compensator network.

7. What are the effects of addition of open loop poles?

8. State Nyquist stability criterion.

9. Write the properties of state transition matrix.

10. Determine the controllability of the system described by the state equation.

PART B — (5 × 16 = 80 Marks)

11. (a) (i) Determine the transfer function for the system having the block

diagram as shown in Figure 3.

Figure 3

(ii) Determine the transfer function of the network in Figure 4.

Figure 4

Or

E 3080 3

(b) Determine the transfer function of the transistor’s hybrid model shown in

Figure 5 using signal flow graph. (16)

Figure 5

12. (a) (i) Determine K to limit the error of a system for input 2

2

1881 tt ++ to

0.8 having ( ) ( )( ) ( )412 ++

=sss

KsHsG . (8)

(ii) The forward path transfer function of an unity feed back control

system is given by ( )( )32

+=

sssG . Obtain an expression for unit

step response of the system. (8)

Or

(b) An unity feed back control system is shown in Figure 6 below. By using

derivative control the damping ratio is to be made to 0.8. Determine the

value of dT and compare the rise time, peak time and maximum

overshoot of the system.

(i) Without derivative control

(ii) With derivative control.

The input to the system being unit set p. (16)

Figure 6

13. (a) A unity feed back control system has ( )( )( )104 ++

=sss

KsG . Draw the

Bode plot. Find K when phase margin = 30°. (16)

Or

(b) A unity feed back control system has ( )( )( )21

10

++=

ssssG . Draw the

Nyquist plot and comment on closed loop stability.

E 3080 4

14. (a) Draw the root locus for the open-loop transfer function of a unity

feedback control system give below and determine.

(i) the value of K for G = 0.5

(ii) the value of K for marginal stability

(iii) the value of K at S = –4.

( )( )( )31 ++

=sss

KsG .

Or

(b) (i) Using Routh criterion, investigate the stability of a unity feedback

control system whose open-loop transfer function is given by

( )( )2+

=−

ss

esG

st

.

(ii) A Closed loop control system has the characteristic equation given

by 05.15.35.4 23 =+++ sss .

15. (a) (i) Using cascade method decompose the transfer function

( )( ) ( )( )21

3

+++

=ss

s

sU

sY and obtain the state model.

(ii) Obtain state space representation for the electrical network shown

in Figure 7 below.

Figure 7

Or

(b) (i) Determine the transfer matrix from the data given below:

−

−=

10

13A [ ] 011

1

1==

= DCB .

(ii) The transfer function of a control system is given by

( )( ) 24269

223 +++

+=

sss

s

sU

sY.

Check for controllability.

———————

Reg. No.

Question Paper Code: 11287

B.E./B.Tech.Degree Examinations, April/May 2011Regulations 2008

Fourth Semester

Electronics and Communication Engineering

EC 2255 Control Systems

Time: Three Hours Maximum: 100 marks

Answer ALL Questions

Part A - (10 x 2 = 20 marks)

1. Define open-loop and closed-loop control systems.

2. Write down the transfer function of the system whose block diagram is shown below.

3. How a control system is classified depending on the value of damping?

4. Why derivative controller is not used in control system?

5. What is meant by ‘Corner frequency’ in frequency response analysis?

6. Draw the circuit of lead compensator and draw its pole zero diagram.

7. State the rule for obtaining the breakaway point in root locus.

8. Define stability of a system.

9. Name the methods of state space representation for phase variables.

10. What is meant by quantization?

Part B - (5 x 16 = 80 marks)

11. (a) (i) Consider the mechanical system shown below. Identify the variables and writethe differential equation. (6)

(ii) Draw the torque-voltage electrical analogous circuit for the following mechanicalsystem shown . (4)

(iii) Obtain the transfer function of the following electrical network. (6)

2 11287

OR

11. (b) (i) A block diagram shown below.

Construct the equivalent Signal Flow Graph and obtainC

Rusing Mason’s formula.

(8)

(ii) For the block diagram shown below, find the output C due to R and disturbanceD. (8)

12. (a) (i) The unity feedback system is characterized by an open loop transfer function

G(s) =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 settling time, peak overshoot andtime to peak overshoot for a unit step input.

(8)

(ii) A unity feedback system has the forward transfer function G(s) =K1(2s + 1)

s(5s + 1)(1 + s)2.

The input r(t) = (1+6t) is applied to the system. Determine the minimum valueof K1, if the steady error is to be less than 0.1. (8)

OR

12. (b) With suitable block diagrams and equations, explain the following types of controllersemployed in control systems:(1) Proportional controller (4)(2) Proportional-plus-integral controller (4)(3) PID controller (4)(4) Integral controller (4)

3 11287

13. (a) Given G(s) =Ke−0.2s

s(s + 2)(s + 8), find K for the following two cases:

(i) gain margin equal to 6 db(ii) Phase margin equal to 45◦.

(16)

OR

13. (b) The open loop transfer function of a unity feedback control system is

Gf (s) =k

s(s + 1)(s + 2).

Design a suitable lag-lead compensator so as to meet the following specifications:Static velocity error constant Kv = 10 sec−1, phase margin = 50◦ and Gain margin≥ 10 dB. (16)

14. (a) (i) A unity feedback system is characterized by the open-loop transfer function,

G(s) =k

(s + 2)(s3 + 10s2 + 49s + 100).

Using Routh-Stability criterion, calculate the range of values of K for system tobe stable. Determine the value of K, which will cause sustained oscillations inthe closed loop system. Also determine the frequency of sustained oscillations.(10)

(ii) State the rules for construction of the Root-locus for a feedback system.(6)

OR

14. (b) Draw the Nyquist plot for the system whose open loop transfer function is

G(s)H(s) =K

s(s + 2)(s + 10).

Determine the range of K for which the closed loop system is stable. (16)

15. (a) The state space representation of a system is given below:

x1

x2

x3

=

−2 1 00 −3 1−3 −4 −5

x1

x2

x3

+

001

u

y =(

0 1 0)

x1

x2

x3

Obtain the transfer function. (16)

4 11287

OR

15. (b) Write the state equations for the system shown below in which x1, x2 and x3 constitutethe state vector.

Determine whether the system is completely controllable and observable. (16)

5 11287

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Reg. No. · 2019. 3. 5. · EC2255 — CONTROL SYSTEMS (Regulation 2008) Time: Three hours Maximum: 100 Marks Answer ALL Questions PART A — (10 × 2 = 20 Marks) 1. Compare the open