VII - P, PI PID Controllers
VII - P, PI PID Controllers
VII - P, PI PID Controllers
CONTROLLERS
APPROACHES TO SYSTEM DESIGN
3
Control Configurations
4
Feedback Control
Heat exchanger
TT Sensor
Final (Temperature
control Transmitter)
element Controller
steam
The advantage of feedback control is that it is
a very simple technique that compensates for
all disturbances. Any disturbance affects the
controlled variable and once this variable
deviates from set point , the controller changes
its input in such a way as to return the
temperature to the set point.
The feedback loop does not know, nor does it
care, which disturbance enters the process. It
tries only to maintain the controlled variable at
set point and in so doing compensates for all
disturbances.
The disadvantage of feedback control is that it
can compensate for a disturbance only after the
controlled variable has deviated from set point.
That is, the disturbance must propagate
through the entire process before the feedback
control scheme can initiate action to
compensate it.
Feed forward Control
Sensor
(Temperature
Controller TT Transmitter)
Heat exchanger
Final
control
element
steam
The objective of feed forward control is to measure the
disturbances and compensate for them before the
controlled variable deviates from set point. If applied
correctly, the controlled variable deviation would be
minimum.
Suppose that in heat exchanger example the major
disturbance is the inlet temperature. To implement feed
forward control the disturbance first must be measured
and then a decision is be made how to manipulate the
steam to compensate for this change.
The complements of process control to
engineering implies that for a good control
design is important and is a result of a
hierarchy of control objectives which depend
on the operating objectives for the plant.
We would like processes to run at the designed
steady state, however processes would not.
In designing control systems or strategies
the dynamic behavior of the process is very
important, therefore we should have
knowledge about process dynamics and
modeling.
Example 1
hs
Fi, Ti
Level Measuring
Device
F, T
Fi, Ti
FT
Controller
F, T
For this example;
input variables are: Fi, Ti and Fst (which denote
the effect of surroundings on the process)
output variables are: F, V and T (which denote
the effect of process on the surroundings)
Controll er Type
20
21
Controll er Type
22
The current situation
K
U (
s )
Kp
i
K
s
dE
(s
)
s
In the time domain:
de
(
t
) t
u
(
t
)Ke
p(
t
)K
i
0
e
(
t)
dtK
d
dt
proportional gain integral gain derivative gain
PID Controller
v in
i1
R
dv
i2 C o
dt
Applying KCL at the inverting input
i1+i2 = 0
dv o v in
C 0
dt R
1
vo
RC v in dt v o (initial )
Op-Amp Differentiator Circuit
Op-Amp Differentiator Cont
Since the inverting input is at virtual ground
dv in
i1 C
dt
vo
i2
R
Applying KCL at the inverting input
i1+i2 = 0
dv in v o
C 0
dt R
dv in
v o RC
dt
Differentiators are avoided in practice as they amplify noise
PID structures
Proportional only:
dV (
t)
V
(
outRC
) in
dt
Integrating Op-Amp
C
Vin
Vin R V-
- 1
dt
Vout RC
R V+ +
Vou
t
1
t
V V
out
ind
RC0
PID Controller System Block Diagram
VSENSOR
Sensor
System to control
Adjust Change
Kp RP1, RP2
Ki RI, CI
Kd RD, CD
VERR VERROR
OR PID
41
42
43
44
45
46
47
48
49
50
51
52
Controller Effects
This corresponds to a
steady-state error of 95%,
quite large!
F
(
s) K s2
10
s(20
K)
1 p p
s2
10
s20
Ex (contd): Proportional
control
Let Kp 300
F
(
s) K K 2
s s(
10K)
s(
20
K)
1 p d d p
2
s10
s20
Ex (contd): PD control
p
Let K 300
,K
d 10
F
(
s) K Ki/
s s
3 2
10
s(
20
K )
sK
1 p p i
2
s10s20
Ex (contd): PI Controller
Let Kp30
,Ki70
K
pKs
dKi/s
d
2
X
(
s) s
2
10
s20 K
s K sK
p i
) K
F
(
s KsK /
3
ss(d
10
K)
s2
(
20
K )
sK
1p d i p i
s2
10
s20
Ex (contd): PID Controller
p i
Let K 350
,K 300
,
d
K 5500
P PD
PI PID
PID Controller Functions
Output feedback
from Proportional action
compare output with set-point
Anticipation
From Derivative action
react to rapid rate of change before errors grows too big
Effect of Proportional,
Integral & Derivative Gains on
the
Dynamic Response
Proportional Controller
Pure gain (or attenuation) since:
the controller input is error
the controller output is a proportional gain
E
(
s)
KpU
(
s
) u
(
t
) K
e
p(
t)
Change in gain in P controller
Increase in gain:
Upgrade both
steady-
state and transient
responses
Reduce steady-state
error
Reduce stability!
P Controller with high gain
Integral Controller
Integral of error with a constant gain
increase the system type by 1
t
K
E
(
s)i
s
U(
s
) u
(
t
)K
i
0
e
(
t)
dt
Change in gain for PI controller
Increase in gain:
Do not upgrade
steady-
state responses
Increase slightly
settling time
Increase
oscillations
and overshoot!
Derivative Controller
Differentiation of error with a constant gain
detect rapid change in output
de
(
t
)
E
(
s)
Kd
sU(
s
) u
(
t
)Kd
dt
Effect of change for gain PD
controller
Increase in gain:
Upgrade transient
response
Decrease the peak
time
and rise time
Increase overshoot
and settling time!
Changes in gains for PID
Controller