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.
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)
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
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
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 !
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