Module 5
Second – Order System,
Time-Domain Response
(2 hours)
Ramp response
Harmonic response
Transient response as a function of the
location of the poles
5,1
5.2 Impulse Response
22
2
2
)(,1)(
nn
n
ss
sCsR



Assume,10
01s i n
1
)( 2
2

tntn tetc n

0)(e
t
)(tc 10
1
5.3
5.4 Relationship between System Poles and
Transient Response (P79)
The characteristic equation and the characteristic
roots are:
02 22 nn ss
dnnn jjss
2
21 1,

211 1 tgtg
n
d
Transient response as a function of the location of the
poles
Recall the unit step response for
tetetc dt
d
n
d
t nn?
s inc o s1)(
c o s?
Step Response from Various Poles on the
Complex Plane
Underdamped Undamped
Negative
damped
Overdamped Criticaldamped
Time-Domain Performance Specifications
Instructional objectives:
At the end of this lecture students should be able to
calculate the time response of SISO system
sketch the phase and amplitude plots of a
SISO sys.
apply the formulas for the %Overshoot,rise
time,settling time; peak time and steady
state error.