C_I_June_2011

Control & Instrumentation DCL-2-209, Exam June 2011

Page 1 of 6

Question (1) (a) Describe the functions performed by a SCADA system to monitor and control

very large systems. Describe briefly the hardware components that perform these functions.

(15 marks) (b) Describe the role of the following SCADA sensors in monitoring and protecting

a plant or facility: Humidity sensors, Motion sensors, Liquid level sensors, smoke sensors, door sensors.

(10 marks)

(5 marks) Q1 Total 25 marks

Question (2) The Transfer Function G(s) of a second-order system is as follows:

16412

)()()( 2 ++== sssU

sYsG

(a) Find the undamped natural frequency, the damping ratio and the DC gain of this

system. (6 marks)

(b) Find the poles of the system. State the type of damping that this system displays.

(6 marks) (c) Find, using the final value theorem of Laplace )(

0sYsLim

s the steady-state value

of the output of the system to a unit step input and calculate the steady-state error in following the input.

(4 marks) (d) Sketch the transient and steady-state unit step response of the system.

(4 marks) (e) Write down the second order model that approximates the step response of the

following third order system:

)164)(10(160

)()(

2 +++= ssssUsY



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Question (3)

(a) Reduce the diagram shown in figure 1 to a single transfer function block.

(8 marks)

(b) Find the transfer function given that the transmittances in figure 1 are as follows:

101=G , 2

12 += sG , 413 += sG , 11 =H , (7 marks)

(c) Write down the transfer function of the system whose dynamics are described

by the following differential equation:

)()(6.1)(6.0)(1.02

2tuty

dttdy

dttyd =++

Give one example of a physical system that may give this form of differential equation and state, with reference to your example, what determines the order of the system.


+ +G2 G3

H1

G1

Figure 1

+R(s) Y(s)


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Question (4) The transfer function G(s) of the system shown in figure 2 is given by:

36624

)()()( 2 ++== sssU

sYsG

(a) Design a simple proportional unity feedback controller, by first finding the

closed-loop transfer function of the system shown in figure 2, and then finding the gain Kp which will increase the natural frequency to 12 rad/s. Find the damping ratio at this value of Kp and find the steady state error to a UNIT STEP input.

(15 marks)

(b) Show how the proportional controller can be extended to a two term controller to give a natural frequency of 12 rad/s and a damping ratio of one.

(10 marks)

Q4 Total 25 marks

U(s) +R(s) Y(s) Kp

Figure 2

System G(s)


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Question (5) You are required to design the tracking control system shown in figure 3. It should be able to track THREE types of demand input r(t).

The demand inputs are:

A. Unit step r(t) = u(t),

B. Unit ramp r(t) = t u(t),

C. Half parabola r(t) = )(21 2 tut

(a) Find the transfer function T(s) of the closed-loop system in figure 3. Given

that the error E(s) = [1 T(s)] R(s), find an expression for E(s). (8 marks)

(b) Find the Type number of the closed-loop system.

(2 marks)

(c) Use the final value theorem of Laplace, )(0

sEsLims

, to find the values of the

steady state errors to the THREE demand inputs A, B and C.

Can the closed-loop system track the three inputs? (15 marks)

Q5 Total 25 marks

Y(s) R(s) )3(

32 +ss

E(s)

Figure 3


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Question (6) Figure 4 shows a feedback configuration to control a plant G(s). The plant transfer function G(s) and feedback compensator H(s) are given below:

Sketch the root locus of the resulting closed-loop system by finding the following:

(a) The centroid

mn = valueszerovaluespole , where n is the number of poles of GH

and m is the number of zeros of GH. (6 marks)

(b) The asymptotic angles mn360i180

= , where integer i = 0, 1, 2, etc. and n

and m are the number of poles and zeros of GH. (6 marks)

(c) The real axis segments. (3 marks)

(d) The values of gain K for which the system remains stable. (10 marks)

Q6 Total 25 marks

( )( )( ) 1)(1148)( =++++= sHjsjsssG

+G(s)

R(s) Y(s)

Figure 4

K

H(s)


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APPENDIX

Canonical Second Order System: 222

2)()(

nn

n

ssK

sUsY

++= PROPERTIES OF LAPLACE TRANSFORM

f(t) F(s) a f1(t) + b f2(t) a F1(s) + b F2(s)

dtdf sF(s) f(0)

2

2

dtfd )0()0()(

2 fsfsFs

n

n

dtfd )0()....0()0()(

121 nnnn ffsfssFs

t dttf0

)( ssF )(

)(tft )(sF

dsd

)(tfe ta )( asF )(0 tfLimt )(ssFLims )(tfLimt )(0 ssFLims

SOME LAPLACE TRANSFORM PAIRS

f(t) F(s) (t) unit impulse 1 u(t) unit step

s1

u(t-a) unit step starting at t = a saes

1

ate as +

1

( )atea

11 )(

1ass +

atet 2)(

1as +

t u(t) unit ramp 2

1s

21 t2 u(t) half parabola 3

1s

)sin(1 22

tabeab

at

bass ++ 2

12

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C_I_June_2011