Basic Of PID Control
&
Tuning
BASIC ON/OFF CONTROL
Inflow
START
Qin
L2
Solenoi
d
L1
S
P
P
Qou
t
Solenoid
power
supply
In On/Off control- control signal is either 0% or 100%
 Control at set point not achievable, a dead band must
be incorporated
 Useful for large , sluggish system particularly those
incorporating electric heaters
 Examples- Large tank level control
- Lube oil tank temperature control by
heaters

BASIC PROPORTIONAL
CONTROL
V1
Qin
50%
60%
Qo=50
Air to Close
SP
50kPa
40kPa
L
T
Qout
50t/h
60t/h
20-100 kPa
Qo=60
 P.C provides a control signal, proportional to the
magnitude and direction of the error signal.
 After a disturbance, P.C will provide only a new mass
balance situation. A change in control signal requires
a change in error signal, therefore offset will occur.
 P.C stabilizes an error; it does not remove it
TERMINOLOGY
M=Measure signal
k= gain
SP=set point
b=bias
e(error)= SP - M
m= controller signal output
m=ke + b
PB=proportional band
Gain(k)=

100%
PB
Proportional band is defined as that input signal span change, in
percent, which will cause a hundred percent change in output
PRACTICAL PROPORTIONAL
CONTROL
V1
Qin
50%
60%
60
%
LI
C
50kPa
L
T
40kPa
45kPa
48kPa
Qout
60t/h
50t/h
Flow
Change
Kp=
Air to Open
1
Kp=
2
Kp=
5
Kp 1
5
2
=
20-100 kPa
Loss In
Volume
Higher PB
Lower PB
Outflow
Inflow
t0
t
t0
t
Level originally SP
t1
New Level S
Offset
Offset
t1
t1
New Level SP
STEP
CHANGE
TIME
WIDE PB
OFFSET
MODERATE PB
NARROW PB
SUMMARY & OPTIMUM PB





Highly stable but sluggish system
Fast acting system with large offset
Unstable on/off system
Require bias to avoid undesirable situation because m=
ke,
so m= ke + b
Optimum setting for PB should result in the process
decaying in a ¼ decay mode
A
A/4
A/16
RESET OF INTEGRAL
ACTION
 To restore the process to the set point after disturbance
then only proportional is insufficient
 The additional inflow must replace the lost volume
Initial mass balance
Reset action
Loss in volume
Outflow
Inflow
Set point
Offset removed
Additional Control signal restores
process to set point
PHENOMENA OF RESET
ACTION
 Reset action is the Integration of the error signal to zero
 After time say ‘t’ reset action has repeated original proportional
response , it is called repeat time
 R.A is defined as either reset rate in repeats per minute (RPM) or
reset time in minutes per repeat (MPR) . MPR= 1/RPM
 Reset action will cause a ramping of the output signal to provide
the necessary extra control action.
st
Fa
se
e
R
t
r
No
t
ese
R
l
ma
t
Slow rese
Ke
Proportiona
l
Response
Exam
ple


A direct acting controller has a proportional band of 50% is subjected to
a sustained error. The set point is 50% and the measurement 55%.
After 4 minutes the total output signal from the controller has increased
by 30%. What is the reset rate setting in RPM and MPR?
Soluti
on
PB = 50%
Since ↑↑ k will be negative
gain = 100% = 2
50%
Proportional Signal = -2 x error = -2 x
-5%
+10%
Total=signal
after 4 minutes = +30%
=P+I
∴Integral Signal = +20%
i.e., integral action has repeated original proportional signal twice in 4
minutes, 1 repeats per 2 minutes or 0.5 repeats per minute.
Reset rate = 0.5 RPM or 2 MPR
SUMMAR
Y
 Mathematical expression for integral action
•
•
•
•
•
m = control signal
e = error signal (e = SP . M) ∴(+ or -)
k = controller gain (↑↑ = −) (↑↓ = +)
TR = reset time (MPR)
b = bias signal
 Reset action removes offset
 If reset action is faster than the process can respond, Reset
Windup can occur
 Reset Action makes a control loop less stable
 Do not subject process loops with reset control to sustained
errors . the control signal will be ramped to the extreme
value . reset windup will occur.
DERIVATIVE ACTION
 The proportional mode considers the present state of the
process error
 The integral mode looks at the past history of the error
 The derivative mode anticipates the future values of the
error and acts on that prediction
 Derivative is related to the rate of change of the error
signal and an anticipatory control, which provides a large
initial control signal to limit the final deviation
inpu
t
Proportiona
l action
outp
ut
Derivati
ve
action
PHENOME
NA
 Mathematical equation for PD controller
•
•
•
•
•
m = controller signal
k = controller gain
TD = derivative time
e = error
b = bias signal
 It should help reduce the time required to stabilize an error ,
derivative action ceases when the error stops
changing.
 Its use, in practice, is also limited to slow acting processes.

EXAMPL
E
Consider a simple flow control system
B
Proce
ss
Contr
ol
signa
l
A
t
Proportional
0
action
A-B
Rate
action
A-B
C
t
1
t
2
Tim
e
Rate action due to end of
Rate increase in e
action
B-C
Control signal at end of
excursion
Rate action due to end of
increase in e
Proportional
action
B-C
SUMMA
RY
 Derivative or rate action is anticipatory and will
usually reduce, but not eliminate, offset.
 Its units are minutes (advance of proportional action).
 It tends to reduce lag in a control loop.
 Its use is generally limited to slow acting processes.
PID
Response
PID Tuning
 The term tuning is used to describe methods used to select
the best controller setting to obtain a particular form of
performance.
 There are three methods that widely used for tuning
1. Process reaction
method


This method uses certain measurements made from
testing the system with the control loop open so that no
control action occurs.
A test input signal is applied to the correction unit and the
response of the controlled variable determined.


Give step input as a test signal
The graph of controlled variable is plotted against time
Final
value
Maximum
gradient
line
Measur
ed
Variabl
e
Original
value
Response of
Controlled
M
variable
Percentage
change of the
variable
per
minute
L
Start of test
signal
Tim
e
 Criteria given by Ziegler and Nichols
Type of
controll
er
Kp
P
P/ML
PI
0.9/ML
Ti
Td
3.3L
 The basis
these criteria
is 0.5L
to give a closed-loop
PID behind
1.2P/M
2L
response for theLsystem which exhibits a quarter amplitude
decay
 EXAMPLE
8
L = 5 min
0
0
5
10
15
M = 8/10 = 0.8 % / min
Kp = 1.2P / ML = 1.2 X 10/0.8 X 5
=3
Ti = 2L = 10 min
Td = 0.5L = 2.5 min
2. Ultimate cycle
method
1. Set the controller to manual operation and the plant near
to its normal operating conditions.
2. Turn off all control modes but proportional.
3. Set Kp to a low value, i.e. the proportional band to a wide
value.
4. Switch the controller to automatic mode and then
introduce a small set-point change, e.g. 5 to 10% and
observe the response.
5. Set Kp to a slightly higher value, i.e. make the proportional
band narrower.
6. Introduce a small set-point change, e.g. 5 to 10% and
observe the response.
7. Keep on repeating 6 and 7 until the response shows
sustained oscillations which neither grow nor decay.

Note the value of Kp giving this condition (Kpu) and the period
(Tu) of the oscillation.
tu
 The Ziegler and Nichols criteria controller settings to have
quarter amplitude decay is given by Table
Type of
controll
er
Kp
Ti
P
0.5 Kpu
PI
0.45
Kpu
Tu/1.2
PID
0.6 Kpu
Tu/2
Td
Tu/8
2. Quarter
Amplitude Decay
Control
led
variabl
e
 The controller is set to proportional only
 With a step input to the control system,
the output is monitored and amplitude
decay is determined
 If the amplitude decay is greater than a
quarter the proportional gain is increased
 If the amplitude decay is less than a
quarter the proportional gain is
decreased
 By method of trial & error the test input
is repeated until a quarter wave
amplitude decay is obtained
 Note this value of proportional gain
 The integral time constant is set to be
T/1.5
 The derivative time constant is T/6
Amplitude
reduced by a
quarter
T
Tim
e
Thank You!