1.
Fundamental Principles
of Process Control
Motivation for Automatic Process Control
• Safety First:
– people, environment, equipment
• The Profit Motive:
– meeting final product specs
– minimizing waste production
– minimizing environmental impact
– minimizing energy use
– maximizing overall production rate
“Loose” Control Costs Money
PM r o rf ei t a Pb rl oe f iOt a pb el er a Ot i op ne r a t i o n
Pro ces s : G rav ity D rain ed T an k
C o n tro ller: M an u al M o d e
operating constraint
M o re
4 .470
Pro ces s : G rav ity D rain ed T an k
C o n tro ller: M an u al M o d e
44 .2
.260
44 .0
.050
poor control means
large variability, so
the process must be
operated in a less
profitable region
33 .8
.840
33 .6
.630
3 .4
process variable
60
80
100
Tim e (m in s)
120
140
80
100
120
140
160
• It takes more material
to make
Tim e (m ina
s) product thicker, so greatest
profit is to operate as close to the minimum thickness constraint
as possible without going under
• It takes more processing to remove impurities, so greatest profit
is to operate as close to the maximum impurities constraint as
you can without going over
M o r e PM r o fr iet a Pb l re o Of i t pa eb r lae t i oO n p e r a t i o n
Tight Control = Most Profitable Operation
P ro ces s : G rav i t y D rai n ed T an k
C o n t ro l l er: M an u al M o d e
operating constraint
4 .270
P ro c e s s : G ra v i t y D ra i n e d T a n k
C o n t ro l l e r: M a n u a l M o d e
44 .2
.060
tight control permits
operation near the
constraint, which
means more profit
43 .0
.850
process variable
33 .8
.640
33 .6
.430
3 .4
80
100
120
T im e (m in s)
140
160
80
100
120
T im e (m in s)
140
160
• A well controlled process has less variability in the
measured process variable, so the process can be
operated close to the profitable constraint
Consider heating a house
set point
thermostat
controller
TC
control
signal
TT
temperature
sensor/transmitter
heat loss
(disturbance)
fuel flow
furnace
valve
Terminology 
Control Objective
Measured Process Variable
Set point
Controller Output
Manipulated Variable
Disturbances
Automatic Control is
Measurement  Computation  Action
• Is house cooler than set point?
( TSetpoint  Thouse > 0 )
Action  open fuel valve
• Is house warmer than set point?
( TSetpoint  THouse < 0 )
Action  close fuel valve
Components of a Control Loop
Home heating control block diagram
controller
error
Set Point
+
-
controller
output
signal
manipulated
fuel flow to
furnace
Thermostat
Fuel Valve
house
temperature
Home Heating
Process
Heat Loss
house temperature
measurement
signal
Disturbance
Temperature
Sensor/Transmitter
General Control Loop Block Diagram
controller
error
Set Point
+
-
controller
output
Controller
manipulated
process
variable
measured
process
variable
Final
Control
Element
Process
Disturbance
feedback
signal
Measurement
Sensor/Transmitter
Starting at the far right of the control loop
block diagram:
•
a sensor measures and transmits the current value of the process variable,
PV, back to the controller (the 'controller wire in')
•
controller error at current time t is computed as set point minus measured
process variable, or e(t) = SP – PV
•
the controller uses this e(t) in a control algorithm to compute a new
controller output signal, CO
•
the CO signal is sent to the final control element (e.g. valve, pump, heater,
fan) causing it to change (the 'controller wire out')
•
the change in the final control element (FCE) causes a change in a
manipulated variable
•
the change in the manipulated variable (e.g. flow rate of liquid or gas)
causes a change in the PV
The goal of the controller is to make e(t) = 0 (or PV = SP) in spite of
unplanned and unmeasured disturbances.
•
On/Off Control – The Simplest Controller
For on/off control, the final control element is either completely
open/on/maximum or closed/off/minimum
•
To protect the final control element from wear, a dead band or upper and a lower
set point is used
•
As long as the measured variable remains between these limits, no changes in
control action are made
V a r ia b le
•
C o n t r o l l e r O u Pt pr ou ct e s s
P ro c e s s : C u s t o m P ro c e s s
56
C o n t ro l l e r: M a n u a l M o d e
upper dead band limit
54
52
50
48
46
44
lower dead band limit
55
ON
50
45
OFF
250
300
350
400
450
500
T im e ( tim e u n its )
550
600
650
700
Usefulness of On/Off Control
• On/off with dead band is useful for home appliances
such as furnaces, air conditioners, ovens and
refrigerators
• For most industrial applications, on/off is too limiting
(think about riding in a car that has on/off cruise
control)
Intermediate Value Control and PID
• Industry requires controllers that permit tighter control with less
oscillation in the measured process variable
• These algorithms:
– compute a complete range of actions between full on/off
– require a final control element that can assume intermediate
positions between full on/off
• Example final control elements include process valves, variable
speed pumps and compressors, and electronic heating elements
Intermediate Value Control and PID
• Popular intermediate value controller is
PID (proportional-integral-derivative) controller
• PID computes a controller output signal based on control error:
u (t )  ubias  KC e(t ) +
Proportional
term
KC
I

e(t )dt
Integral
term

KC D
de(t )
dt
Derivative
term
where:
y(t)
u(t)
ubias
e(t)
KC
I
D
= measured process variable
= controller output signal
= controller bias or null value
= controller error = ysetpoint – y(t)
= controller gain (a tuning parameter)
= controller reset time (a tuning parameter)
= controller derivative time (a tuning parameter)
5. P-Only => The Simplest PID Controller
The Proportional Controller
• The simplest PID controller is proportional or P-Only control
• It can compute intermediate control values between 0 –
100%
C o n tr o l S ta tio n : C a se S tu d ie s
C o n t r o l l e r O u t p uL t e v e l / S e t p o i n t
P ro c e s s : G ra v i t y D ra i n e d T a n k
C o n t ro l l e r: P ID ( P = R A , I= o ff, D = o ff )
2 .8
2 .6
2 .4
2 .2
2 .0
1 .8
60
58
56
54
52
50
10
15
20
25
30
35
T im e ( m in s )
T u n i n g : B i a s = 5 5 .2 , G a i n = 1 1 .5 , S a m p l e T i m e = 1 .0 0
40
The Gravity Drained Tanks Control Loop
• Measurement, computation and control action repeat every loop
sample time:
– a sensor measures the liquid level in the lower tank
– this measurement is subtracted from the set point level to
determine a control error
e(t) = ysetpoint – y(t)
– the controller computes an output based on this error and it
is transmitted to the valve, causing it to move
– this causes the liquid flow rate into the top tank to change,
which ultimately changes the level in the lower tank
• The goal is to eliminate the controller error by making the
measured level in the lower tank equal the set point level
P-Only Control
• The controller computes an output signal every sample time:
u(t) = ubias + KC e(t)
where
u(t)
ubias
e(t)
KC
= controller output
= the controller bias
= controller error = set point – measurement
= ysetpoint – y(t)
= controller gain (a tuning parameter)
• controller gain, KC  steady state process gain, KP
• a larger KC means a more active controller
• like KP , controller gain has a size, sign and units
Controller Gain, KC, From Correlations
• P-Only control has one adjustable or tuning parameter, KC
u(t) = ubias + KC e(t)
• KC sets the activity of the controller to changes in error, e(t)
– if KC is small, the controller is sluggish
– If KC is large, the controller is aggressive
Understanding Controller Bias, ubias
• Thought Experiment:
– Consider P-Only cruise control where u(t) is the flow of gas
– Suppose velocity set point = measured velocity = 70 km/h
– Since y(t) = ysetpoint then
and P-Only controller is
e(t) = 0
u(t) = ubias + 0
– If ubias were set to zero, then the flow of gas to the engine
would be zero even though the car is going 70 km/h
• If the car is going 70 km/h, there clearly is a baseline flow of gas
• This baseline controller output is the bias or null value
Understanding Controller Bias, ubias
• In the thought experiment, the bias is the flow of gas which,
in open loop, causes the car to travel the design velocity of
70 km/h when the disturbances are at their normal or
expected values
• In general, ubias is the value of the controller output that, in
open loop, causes the measured process variable to
maintain steady state at the design level of operation when
the process disturbances are at their design or expected
values
• Controller bias is not normally adjusted once the controller
is put in automatic
Reverse Action, Direct Action
and Control Action
• If KP is positive and the process variable is too high, the
controller decreases the controller output to correct the error
=> The controller action is the reverse of the problem
When KP is positive, the controller is reverse acting
When KP is negative, the controller is direct acting
• Since KC always has the same sign as KP , then
KP and KC positive  reverse acting
KP and KC negative  direct acting
Reverse Acting, Direct Acting
and Control Action
• Most commercial controllers require you to enter
• a positive KC
• The sign (or action) of the controller is specified by
entering the controller as reverse or direct acting
• If the wrong control action is entered, the controller will
drive the valve to full open or closed until the entry is
corrected
Offset - The Big Disadvantage
of P-Only Control
• Big advantage of P-Only control:
=> only one tuning parameter so it’s easy to find “best” tuning
• Big disadvantage:
=> the controller permits offset
Offset - The Big Disadvantage
of P-Only Control
• Offset occurs under P-Only control when the set point
and/or disturbances are at values other than that used as
the design level of operation (that used to determine ubias)
u(t) = ubias + KC e(t)
• How can the P-Only controller compute a value for u(t) that
is different from ubias at steady state?
• The only way is if e(t)  0
Offset and KC
As KC increases:  Offset decreases 
Oscillatory behavior increases
Impact of KC on Offset and Oscillatory Behavior
C o n tr o lle r O u tp u t P V / S e t p o in t
P r o c e s s : G r a v ity D r a in e d T a n k
C o n tr o lle r : P I D ( P = R A , I = o f f , D = o f f )
3 .0
2 .8
2 .6
2 .4
offset
offset
2 .2
KC = 40
KC = 11.5
75
70
65
60
55
50
45
10
20
30
40
50
T im e ( m in s )
T u n in g : B ia s = 5 5 .2 , G a in = 4 0 .0 , S a m p le T im e = 1 .0 0
60
70
O pOe np eLno Lo po oPpu lSs tee pT eTset s t
C o n t r o l l e r O u t pP u r to c e s s V a r i a b l e
C o n t r o l l e r O u t pP u r to c e s s V a r i a b l e
Pulse Test
P r o Pc er os sc :e sCs u: sCt ou ms t oPmr o Pc er os sc e s s
60 60
C o nCt roonltlreor l: l eMr :a M
n uaanl uMa lo M
d eo d e
Pulse Test
55 55
50 50
60 60
55 55
50 50
0
0
5
5
10 10
T im Teim( me in( ms )in s )
15 15
20 20
• Pulse test is two step tests performed in rapid succession
• Desirable: starts from and returns to an initial steady state
• Undesirable: data generated on one side of this steady state
(which presumably is design level of operation)
P - control
Control-equation
Electrical circuit
Step-response
I - control
Control-equation
Electrical circuit
Step-response
PI - control
Control-equation
Electrical circuit
Step-response
PD - control
Control-equation
Electrical circuit
Step-response
PID - control
Control-equation
Electrical circuit
Step-response
Step response
Comparison between different types of control
Time
Block-Diagramm PID - Control
Input
Control Bias Ue
Set Value Us
Circuit -Diagramm PID - Control
P-Element
Inverting amplifier
Inverting amplifier
I-Element
Summing amplifier
D-Element