control exercise unit 4

8/11/2019 Control Exercise Unit 4

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FEEDBACK CONTROL SYSTEM

UNIT 4a. List and sketch FIVE (5) types of standard input test signal in control system.

b. Locate the positions of the poles on the s- plane for the following second order

systems:

(a) the under-damped system

(b) the over-damped system

(c) the critically damped system

c. For the following systems transfer function, identify the system order, plot the poles

on s -plane and sketch the output response.

i.10014

20)( 2 s s

sG

ii.4

2)(

s sG

d. Given a system with transfer function( )

( ) ;

i. Find ( ) when a unit step function ( ) is applied to the system,

assuming initial condition is zero.

ii. Plot pole and zero on S-plane and identify either a system is stable or not.

Why?



e. Figure 4.1 shows the output response of a first order transfer function from a

laboratory test. Consider the transfer function of a simple first order system( )

( )

( ) , where ( ) and given the output step response is

( )( )

⁄ ⁄

Figure 4.1: Laboratory results of a system step response test.

i. Find the time constant , .

ii. Calculate the value of ‘ a ’

iii. Determine the value of K.

iv. Evaluate the rise time, and settling time, .

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.05

0.1

0.15

0.2

0.25

0.3

0.35

System: sysTime (sec): 0.966Amplitude: 0.286

Step Response

Time (sec)

A m p

l i t u d e



f. Refer to Figure 2.1 as shown below, determine

i. the value of pole

ii. the system transfer function, ( ) ( ) .

Figure 2.1

g. Given a system with transfer function ( )

i. Identify the system order.

ii. Plot the pole and zero on s -plane.

-3 -2 -1 0 1 2

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Real Part

I m a g

i n a r y

P a r

t



h. Refer to Figure 6.2 , state the definition and estimate the value of :

Figure 6.2

i. Delay time,

ii. Rise time,

iii. Settling time,

iv. Peak time,

v. Percentage Overshoot,

i. Given the second order transfer function is ( )

i. Write the general equation of second order system.

ii. Find the value of natural frequency, and damping ratio, ζ.

iii. If damping ratio, ζ = 0 . What happen to the system?

Ans:

ζ ,



j. Given the transfer function ,

( )

i. Plot pole on S-plane

ii. Find peak time ( ), settling time ( ) and overshoot ( ).

(hint: ( ) )

Ans:

k. For the system shown in Figure 6.3 , find

Figure 6.3

i. the transfer function ( ) ( )

( )

ii. damping ratio ( ), Natural frequency ( )

Ans:

( ) , ,



l. A torsional mechanical system to test shaft elasticity is modelled and the transfer

function can be represented as

( ) ( )

If the values J = 3 kg-m2 and k = 27 N-m-s/rad are given, find the value of the

adjustable damper coefficient, f , such that the critically damped response can be

obtained for a unit step input.

m. For a system shown in Figure 4.27, if the transfer function, ( ) , is given as

( ) ( )

Figure 4.27

(a) Find the closed-loop transfer function of the new system.

(b) The closed-loop response is required to operate with the settling time of 1.15

seconds and 4.6% overshoot. If the values of coefficients, J and k , are 3 and

27, respectively, calculate the value of the gain, K p and the new value of

coefficient f .

control exercise unit 4

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