Reg. No. :

B.E./B.Tech. DEGREE EXAMINATION, NOVEMBER/DECEMBER 2010

Fourth Semester

Electronics and Communication Engineering

EC 2255 — CONTROL SYSTEMS

(Regulation 2008)

Time : Three hours Maximum : 100 Marks

(Graph Sheets, Semi log sheets and polar charts are to be provided)

Answer ALL questions

PART A — (10 × 2 = 20 Marks)

1. Give the comparisons between open loop system and closed loop system.

2. Define the transfer function of a system.

3. What is meant by peak overshoot?

4. What is meant by steady state error?

5. List the advantages of Nichol's Chart?

6. What are the specifications used in frequency domain analysis?

7. What is meant by BIBO stability?

8. Using Routh criterion, determine the stability of the system represented by the

characteristic equation 0516188 234 =++++ SSSS . Comment on the location

of the roots of characteristics equation.

9. What is meant by sampling theorem?

10. Mention the need for state variables?

Question Paper Code : 64027

64027 2

PART B — (5 × 16 = 80 Marks)

11. (a) (i) The transfer function of a system is given by,

( ) ( )( )( )( )12752

62 ++++

+=

sSsss

sKsT Determine

(1) Poles

(2) Zeros

(3) Characteristics equation

(4) Pole-zero plot in s-plane. (8)

(ii) Find ( )( )sR

sCfor the signal flow graph shown below. (8)

Or

(b) (i) Reduce the block diagram to its canonical form and obtain

( ) ( ).sRsC (10)

(ii) Give the comparison between block diagram and signal flow graph

methods. (6)

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12. (a) The open loop transfer function of a unity feedback system is given by

( ) ( )1+= sTsKsG , where K and T are positive constant. By what factor

should the amplifier gain K be reduced, so that the peak overshoot of unit

step response of the system is reduce from 75% to 25%. (16)

Or

(b) Explain in detail the system response with, PI, PD and PID controllers.

(16)

13. (a) Sketch Bode plot for the following transfer function and determine the

system gain K for the gain cross over frequency to be 5 rad/sec

( )( )( )

2

1 0.2 1 0.02

KsG s

s s=

+ +. (16)

Or

(b) The open loop transfer function of a unity feedback system is given by

( )( )( )sss

sG211

12 ++

= . Sketch the polar plot and determine the gain

margin and phase margin.

14. (a) Sketch the root locus of the system whose open loop transfer function is

( ) ( )( )42 ++=

sss

KsG . Find the value of K, so that the damping ratio of the

closed loop system is 0.5. (16)

Or

(b) Construct the Nyquist plot for a system whose open loop transfer

function is given by ( ) ( ) ( )3

21

S

SKsHsG

+= . Find the range of K for

stability. (16)

15. (a) (i) Explain in detail the state space representation for continuous time

systems. (8)

(ii) Explain in detail the state space representation for discrete time

systems. (8)

Or

(b) Determine the state controllability and observability of the system

described by uxx

+

−

−

=

12

00

10

100

101

113

xy

=

011

100. (16)

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Reg. No.

Question Paper Code: 55336

B.E./B.Tech. DEGREE EXAMINATIONS, NOV./DEC. 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. What is meant by ‘block diagram’ of a control system? What are the basic com-ponents of a block diagram?

3. The damping ratio and natural frequency of oscillation of a second order system is0.5 and 8 rad/sec respectively. Calculate resonant peak and resonant frequency.

4. With reference to time response of a control system, define ‘Rise time’.

5. Name the parameters which constitute frequency domain specifications.

6. Write the MATLAB command for plotting Bode diagramY (s)

U(s)=

4s+ 6

s3 + 3s2 + 8s+ 6.

7. State any two limitations of Routh-stability criterion.

8. Define stability of a system.

9. What are the advantages of State-Space approach?

10. What is ‘alias’ in sampling process?

Part B - (5 x 16 = 80 marks)

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

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

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

OR

11. (b) (i) For the signal flow graph shown below, find C(s)/R(s) by using Mason’sgain formula. (10)

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(ii) Find the transfer functionC(S)

R(S)of block diagram shown below. (6)

12. (a) (i) Derive an expression to find steady state error of a closed loop controlsystem. (6)

(ii) The closed loop transfer function of a second order system is given by

T(s) =100

s2 + 10s+ 100. Determine the damping ratio, natural frequency

of oscillations, rise time, settling time and peak overshoot. (10)

OR

12. (b) Consider a unity feedback system with open-loop transfer function, G(s) =75

(s+ 1)(s+ 3)(s+ 8). Design a PID controller to satisfy the following specifi-

cations :

(i) The Steady-State error for unit ramp input should be less than 0.08

(ii) Damping ratio = 0.8 and

(iii) Natural frequency of oscillation = 2.5 rad/sec.

State the expressions for the transfer function of the PID controller and for theopen loop transfer function of the compensated system. (16)

13. (a) (i) Sketch the Bode magnitude plot for the transfer functionG(s) =100(1 + 0.1s)

(1 + 0.01s)(1 + s).

(8)

(ii) Draw the polar plot for the following Transfer functionG(s) =10(s+ 2)

s(s+ 1)(s+ 3).

(8)

OR

13. (b) A unity feedback control system has, G(S) =10

S(S + 1). Design a lead compen-

sator such that the closed loop system will satisfy the following specifications:Static velocity error constant = 20 sec.Phase margin = 50◦

Gain margin ≥ 10 dB.Draw the Bode plots and explain. (16)

14. (a) (i) A certain unity negative feedback control system has the following open

loop transfer function G(s)H(s) =K

s(s+ 2)(s2 + 2s+ 5). Find the break-

away points and draw Root Locus for 0 ≤ ω ≤ ∞. (12)

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(ii) List the advantages of Routh’s array method of examining stability of acontrol system. (4)

OR

14. (b) Sketch the Nyquist plot for a system with open loop transfer function

G(s)H(s) =K(1 + 0.4s)(s+ 1)

(1 + 8s)(s− 1)and determine the range of K for which the

system is stable. (16)

15. (a) (i) Find the state variable equation for a mechanical system (spring-mass-damper system) shown below. (8)

(ii) A LTI system is characterized by the state equation[x1

x2

]=

[1 01 1

] [x1

x2

]+

[01

]u

where u is a unit step function. Compute the solution of these equation

assuming initial condition x0 =

[10

]. Use inverse Laplace transform

technique. (8)

OR

15. (b) A sampled data control systems is shown in the figure below:

Find the open loop pulse transfer function, if the controller gain is unity withsampling time 0.5 seconds. (16)

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