Second – Order System,
Disturbance Rejection and
Rate Feedback
( 1 hour )
Module 6
6.1 Open- and Closed-loop Disturbance Rejection
Open-loop control system with disturbance D:
CR R
D
1G 2G
H
C
D
O p enD es i r ed CCDGRGGC 221
)(.,0 2 DDGCDCRW h e n O p e n
Closed-loop control system with disturbance D:
R
CK
D
C
1G 2G
H
E*R
O p e nC l o s e d CGGC
211
1
C l o s e dD e s i r e d CCDGG
GR
GG
GGC

*
21
2*
21
21
11
C
D
Closed loop
Open loop
21
*
*
1 GG
CC
D e sire d ** CCK D e sire dC
H=1
6.2 Effect of Velocity Feedback (Rate Feedback)
6.2.1 Second-Order System without Velocity
Feedback
CE
)1(?Tss
K
HK
R
HH KKsTs
K
KKTss
K
R
C
2)1(
The characteristic Equation is:
02 HKKsTs
or:
012 TKKsTs H
HT K K
1
2
1
T
KK H
n
T2
1?
The characteristic roots are:
HT K KTTs 412
1
2
1
2,1
HT K K
1
2
1
T
KK H
n
o v e r s h o o tTKK H?,,)1(
–– disadvantage
)()2( eK
–– advantage
6.2.2 Second-Order System with Velocity
Feedback
C
)1(?Tss
K
ER
HK
sKv
1E
]1[)1( vv KKTss
K
sKKTss
K
E
C

Open-loop Transfer
Function
Compare with the open-loop transfer function without
velocity feedback:
)1( Tss
K
E
C
We can find that:
)1( vv KK
where,? – without velocity feedback
v?
– with velocity feedback
T
KK H
n
no change
The characteristic
Equation is:
0)1(2 Hv KKsKKTs
n
overshoot
6.2.3 Other forms of velocity feedback system
C
)1(?Tss
K
ER
HK
sKv
1E
CER
HK
1E
1?Ts
K
vK
s
1
C
)1(?Tss
K
ER
sKK vH?
Sample Problem,(P101 Fig.6.11)
Sample Problem
0
0
At the end of this lecture students should be
able to
select control strategies to (i) minimize
steady state error (ii) reduce/ eliminate the
influence of a disturbance (iii) reduce the
response time (rise time)
apply the partial fraction expansion for
arbitrary T,F.
Predict overshoot,rise time.
Instructional objectives: