Tutorial -3
DEPARTMENT OF MECHANICAL ENGINEERING
FACULTY OF ENGINEERING
Tutorial No-3
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2.
3.
Find the output for a unit step input for the following first order transfer
functions. Also check what happens to the output when the time goes to infinity
1
( )=
( )=
( )=
( )=
+1
Find the output for a unit step input for the following first order transfer
functions. Also check what happens to the output when the time goes to infinity.
(1)
(
)(
(2) (
)
)(
)
(3) (
If the output of a second order function is given by
)
(4) (
)
( )=
+
+
where
> 0, 0 < < 1
Show that the output for a unit step input is a decaying oscillatory function. Find
the final value when the time goes to infinity. Also show that the time to reach
the maximum peak is
where
=
1 − . Also find the maximum peak
value.
4.
Take the transfer function obtained in tutorial 2 question 3 where it is given by
1 + S(T1 + T2 ) + S2T1T2
----------------------------------1
+ S(T1 + T2 + T3) + S2T1T2
and T1, T2 and T3 are time constants that is greater than zero.
a) Show that the system will not get oscillatory output in the natural
motion.
b) Show that the system is stable.
c) Sketch the output time function for a unit step input.
5.
Find the steady state error for a unit step input, ramp input and parabolic for the
questions in Tutorial 2, question 2 and question 3.
Prepared By Dr. V P C Dassanayake
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