The document discusses different types of compensation for linear control systems, including passive and active compensation. It describes phase-lead, phase-lag, and phase lag-lead controllers as examples of passive compensation. PID controllers are presented as a form of active compensation that can improve stability. The effects of PD, PI, and PID controllers on system properties like stability, steady-state error, and bandwidth are analyzed. Comparisons are made between passive and active compensation approaches.

1. 1
Compensation , phase–lag
compensation lag–lead
part -1
2019-2020
Dr.Ziad Saeed Mohammed

2. 2
The Compensation of the linear control systems
1. Introduction
1.1 definition of compensation
1.2 types of compensation
2. The basic controller operation analysis
2.1 phase-lead controller
2.2 phase-lag controller
2.3 phase lag-lead controller
2.4 PI D controller ---active compensation
3. Desgin compensation using method of Root loci
passive
compensation controller


3. 3
• We make the system stable by increasing a component.
• This procedure is called the compensation .
1.1Definition of the compensation:
Increasing a component ,which makes the system’s performance to
be improved, other than only varying the system’s parameters, this
procedure is called the compensation of the system.

4. 4
Compensator:
The compensator is an additional component or circuit that is
inserted into a control system to compensate for a deficient
performance.
1. Introduction
1.2 Types of the compensation
:
types
several
get
can
we
system,
the
of
structure
in the
)
(
of
location
the
to
according
and
),
(
as
designated
is
r
compensato
the
of
function
transfer
The
s
G
s
G c
c

5. 5
(1) Cascade(or series) compensation
(2) Feedback compensation
(3) Both series and feedback compensation
(4) Feed-forward compensation
(1) Cascade(or series) compensation
Features : simple but the effects to be restricted.
1. Introduction

6. 6
(2) Feedback compensation
R(s) C(s)
)
(
0 s
G
C
G
- -
R(s) C(s)
10
G 20
G
C
G
- -
Features: complicated but noise limiting, the effects are more
than the cascade compensation.
(3) Both cascade and
feedback compensation -
R(s) C(s)
-
1
C
G
2
C
G
0
G
Features: have advantages both
of cascade and feedback compensation.
1. Introduction

7. 7
(4) Feed-forward compensation
Features: theoretically we can make the error of a system to be
zero and no effects to the transient performance of the system.
1. Introduction
R(s) C(s)
+
-
C
G
10
G 20
G
C(s)
F(s)
R(s)
-
+
C
G
10
G 20
G
For input For disturbance(voice)

8. 8

9. 9
2.1 Passive compensation controllers
a
b
c
c
c
1
,
1
s
1
s
1
s
1
s
1
(s)
G
controller
lead
-
lag
phase
3)
1
s
1
s
1
(s)
G
controller
lag
-
phase
2)
1
s
1
s
1
(s)
G
controller
lead
-
phase
)
1































a
a
b
b
Types of passive compensation controller

10. 10
1
)
(
:
function
Transfer
controller
lead
-
Phase
)






 

 p
s
z
s
τs
τs
s
Gc
1
1
1
1
τ
p
τ
z

1
1


Zero and pole
2.1 Passive compensation controllers

11. 11

12. 12
Circuit diagram of the phase-lead controller
1
1
1
2
1
2
1
1
2
1
2
1








τs
τs
Cs
R
R
R
R
Cs
R
R
R
R
(s)
c
G


2
1
2
1
R
R
R
C
R


 


13. 13
1
1
1
s
1
s
)
(
:
function
Transfer
controller
lag
-
Phase
)







 



p
s
z
s
s
Gc
2
βτ
p
τ
z
1
1


Zero and pole
2.1 Passive compensation controllers

14. 14
Circuit of the Phase-lag controller
τs
τs
s
V
s
V
s
G
in
o
c





1
1
)
(
)
(
)
(
2
2
1
2
R
R
R
C β
R
τ




16. 16
1
1
)
(
:
function
transfer
controller
lead
-
lag
Phase
)







 

s
βτ
s
τ
s
ατ
s
τ
s
G
b
b
a
a
c
1
1
1
1
2
b
b τ
z
βτ
p
1
1
1
1 



a
a τ
z
τ
p
1
1
2
2 





j

1
z 1
p
2
z
2
p
Zero and pole
2.1 Passive compensation controllers

17. 17
1


Circuit of the Phase lag-lead controller

18. 18

19. 19
19
PID Controllers
PID has become almost universally used in
industrial control.
These controllers have proven to be robust and extremely
beneficial in the control of many important applications.
Proportional only:
Proportional plus Integral:
Proportional plus derivative:
Proportional, integral and
derivative:
s
K
s
K
K
s
G d
i
p
PID 


)
(
s
K
K
s
G i
p
PI 

)
(
s
K
K
G d
p
PD 

p
P K
s
G 
)
(

20. 20
2. Operation analysis of the basic compensators
2.2 Active Compensation
PID controller － active “compensator”.
Transfer function:
D
p
D
I
p
I
D
I
p
D
I
p
c
K
K
K
K
s
K
s
K
K
s
τ
s
τ
K
(s)
G











;
)
(
1
1
1
stability.
improving
controller
al
differenti
-
-
D
.
clearing
controller
g
integratin
-
-
I
y.
sensitivit
promoting
controller
al
proportion
-
-
P



ss
e

21. 21
PD controller )
(
:
function
transfer s
K
K
s
G D
p
c 

C(s)
G(s)
R(s)
－
＋
p
K
s
KD
＋
＋
)
(s
GC
)
2
(
)
(
:
Assuming
2
n
n
s
s
s
G




)
2
(
)
(
)
(
)
(
:
is
system
d
compensate
the
of
function
transfer
loop
open
The
2
n
D
P
n
c
s
s
s
K
K
s
G
s
G






D
P
K
K
s 

 :
at
zero
loop
open
a
adding
to
equivalent
is
controller
PD
the
that
shows
It

22. 22
Effects of PD controller:
2) PD controller improve the system’s stability (to increase
damping and reduce maximum overshoot);
3) PD controller reduce the rise time and settling time;
4) PD controller increase BW(Band Width) and
improve GM(Kg),PM(γc), and Mr .
1) PD controller does not alter the system type;
2 . Operation analysis of the basic compensators
－ bring in the noise !

23. 23
PI controller
s
K
K
s
G I
p
c
1


)
(
:
function
Transfer
)
2
(
)
(
:
Assuming
2
n
n
s
s
s
G




C(s)
G(s)
R(s)
－
＋
p
K
s
KI
1
＋
＋
)
(s
GC
2. Operation analysis of the basic compensators
)
2
(
)
(
)
2
(
)
1
(
)
(
)
(
:
is
system
d
compensate
the
of
function
transfer
loop
open
The
2
2
2
n
I
P
n
n
I
P
n
c
s
s
K
s
K
s
s
s
K
K
s
G
s
G











0
s
:
at
pole
a
and
:
at
zero
loop
open
a
adding
to
equivalent
is
controller
PI
the
that
shows
It




P
I
K
K
s

24. 24
Effects of PI controller:
1) Increase the system’s type－clear the steady-state error ;
2) reduce BW(Band Width) and GM(Kg), PM(γc) and Mr ;
2. Operation analysis of the basic compensators
beneficial to the noise limiting ,
not beneficial to the system’s stability.

25. 25
G(s)
R(s) C(s)
- +
p
K
s
KI
1
s
KD
)
(s
GC
PID controller
2. Operation analysis of the basic compensators
Transfer function: s
K
s
K
K
(s)
G D
I
p
c 


1
PID controller have advantages both of PI and PD.

26. 26
Circuits of PID
_
+
C
R1
ur
u0
PI controller
R2
_
+
C
R1
ur
u0
PD controller
R2
_
+
C1
R1
ur
u0
PID controller
C2
R2
)
(
)
(
)
(
Cs
R
R
R
U
U
s
R
s
2
1
2
0 1
1

)
(
)
(
)
(
s
C
R
R
R
U
U
s
R
s
1
1
1
2
0 1

?
)
(
)
(

s
R
s
U
U0

27. 27
2.3 Comparing active compensation controllers and
passive compensation controllers
)
1
)(
1
(
)
1
)(
1
(
:
lead
lag
phase
)
1
(
)
1
1
(
:
PID
1
1
:
lag
phase
)
1
(
)
1
1
(
:
PI
1
1
:
lead
phase
)
(1
:
PD
2























s/α
τ
s
ατ
s
τ
s
τ
s
s
s
K
s
τ
s
τ
K
s
s
s
s
K
s
τ
K
s
s
s
τ
K
b
a
b
a
I
I
D
I
p
D
I
p
I
I
p
I
p
D
p











28. THANKS
28