CHE 185 – PROCESS
CONTROL AND DYNAMICS
PID CHARACTERISTICS AND
SIGNAL FILTERING
DIGITAL VERSIONS OF THE PID
ALGORITHM
• CONTROLLER ACTION - DIRECT AND
REVERSE
• A COMBINATION OF PROCESS GAIN AND THE TYPE
OF ACTUATOR USED. PROCESS GAIN IS A
PROCESS CHARACTERISTIC.
• WHEN PROCESS GAIN IS NEGATIVE:
– THERE IS A DECREASE IN THE VALUE OF THE
CONTROLLED VARIABLE WITH AN INCREASE IN THE
CONTROLLED PROPERTY
DIRECT LEVEL CONTROL
EXAMPLE
• PROCESS GAIN IS
POSITIVE BECAUSE WHEN
FLOW IN IS INCREASED,
THE LEVEL INCREASES.
• IF THE FINAL CONTROL
ELEMENT IS DIRECT
ACTING, USE REVERSE
ACTING PID.
• FOR REVERSE ACTING
FINAL CONTROL
ELEMENT, USE DIRECT
ACTING PID
REVERSE LEVEL CONTROL
EXAMPLE
• PROCESS GAIN IS
NEGATIVE BECAUSE
WHEN FLOW OUT IS
INCREASED, THE LEVEL
DECREASES.
• IF THE FINAL CONTROL
ELEMENT IS DIRECT
ACTING, USE DIRECT
ACTING PID.
• FOR REVERSE ACTING
FINAL CONTROL
ELEMENT, USE REVERSE
ACTING PID.
ACTUATOR DIRECTION
• BASED ON PROCESS NEEDS
• DIRECT ACTING ACTUATORS INCREASE VALUES
OF THE FINAL CONTROL ELEMENT WITH
INCREASES IN DRIVING FORCE. A DIRECT ACTING
ACTUATOR ON A VALVE (AIR-TO-OPEN OR
NORMAL CLOSED) INCREASES THE OPENING WITH
INCREASING AIR PRESSURE.
• REVERSE ACTING ACTUATORS DECREASE
VALUES OF THE FINAL CONTROL ELEMENT WITH
INCREASES IN DRIVING FORCE. A REVERSE
ACTING ACTUATOR ON A VALVE (AIR-TO-CLOSE
OR NORMAL OPEN) DECREASES THE OPENING
WITH INCREASING AIR PRESSURE
PROPORTIONAL BAND
• ANOTHER WAY TO EXPRESS THE CONTROLLER
GAIN.
• KC IN THIS FORMULA IS DIMENSIONLESS. THAT IS,
THE CONTROLLER OUTPUT IS SCALED 0-100% AND
THE ERROR FROM SETPOINT IS SCALED 0-100%.
• IN MORE FREQUENT USE 10-15 YEARS AGO, BUT IT
STILL APPEARS AS AN OPTION ON DCS’S.
CONVERSION FROM PB TO KC
• PROPORTIONAL BAND IS EQUAL TO 200%.
• THE RANGE OF THE ERROR FROM
SETPOINT IS 200 PSI.
• THE CONTROLLER OUTPUT RANGE IS 0 TO
100%.
CONVERSION FROM KC TO PB
• CONTROLLER GAIN IS EQUAL TO 15 %/ºF
• THE RANGE OF THE ERROR FROM
SETPOINT IS 25 ºF.
• THE CONTROLLER OUTPUT RANGE IS 0 TO
100%.
DERIVATION OF THE VELOCITY FORM
OF THE PID CONTROL ALGORITHM
• SEE SECTION 7.5
VELOCITY FORM OF DERIVATIVE
FROM ERROR FOR PID CONTROLLER
• NOTE THE DIFFERENCE IN PROPORTIONAL,
INTEGRAL, AND DERIVATIVE TERMS FROM
THE POSITION FORM.
• VELOCITY FORM IS THE FORM
IMPLEMENTED ON DISTRIBUTED CONTROL
SYSTEMS.
CORRECTION FOR DERIVATIVE
KICK
• DERIVATIVE KICK OCCURS WHEN A SETPOINT
CHANGE IS APPLIED THAT CAUSES A SPIKE IN THE
DERIVATIVE OF THE ERROR FROM SETPOINT.
• DERIVATIVE KICK CAN BE ELIMINATED BY
REPLACING THE APPROXIMATION OF THE
DERIVATIVE BASED ON THE ERROR FROM
SETPOINT WITH THE NEGATIVE OF THE
APPROXIMATION OF THE DERIVATIVE BASED ON
THE MEASURED VALUE OF THE CONTROLLED
VARIABLE, I.E.,
CORRECTION FOR AGGRESSIVE
SETPOINT TRACKING
• FOR CERTAIN PROCESS, TUNING THE CONTROLLER FOR
GOOD DISTURBANCE REJECTION PERFORMANCE RESULTS
IN EXCESSIVELY AGGRESSIVE ACTION FOR SETPOINT
CHANGES.
• THIS PROBLEM CAN BE CORRECTED BY REMOVING THE
SETPOINT FROM THE PROPORTIONAL TERM. THEN
SETPOINT TRACKING IS ACCOMPLISHED BY INTEGRAL
ACTION ONLY.
• SEE EQN 7.5.5
SUMMARY OF 3 VERSIONS OF THE
PID ALGORITHM OFFERED ON DCS’S
• (1) THE ORIGINAL FORM IN WHICH THE
PROPORTIONAL, INTEGRAL, AND
DERIVATIVE TERMS ARE BASED ON THE
ERROR FROM SETPOINT
• EQN. 7.5.4
SUMMARY OF 3 VERSIONS OF THE
PID ALGORITHM OFFERED ON DCS’S
• (2) THE FORM IN WHICH THE
PROPORTIONAL AND INTEGRAL TERMS
ARE BASED ON THE ERROR FROM
SETPOINT WHILE THE DERIVATIVE-ONMEASUREMENT IS USED FOR THE
DERIVATIVE TERM
• EQN. 7.5.2
SUMMARY OF 3 VERSIONS OF THE
PID ALGORITHM OFFERED ON DCS’S
• (3) THE FORM IN WHICH THE
PROPORTIONAL AND DERIVATIVE TERMS
ARE BASED ON THE PROCESS
MEASUREMENT AND THE INTEGRAL IS
BASED ON THE ERROR FROM SETPOINT.
• EQN. 7.5.5
SIGNAL FILTERING
• FILTERS ARE USED TO REMOVE SOME OF
THE NOISE FROM LOOPS AND OPERATE
WITH AVERAGED VALUES FOR VARIABLES.
• THE SIMPLEST FILTERS AVERAGE N
PREVIOUS VALUES TO OBTAIN THE ONE
ACTUALLY SENT TO THE CONTROLER.
• FILTERS ARE LOCATED AFTER THE
SENSOR SIGNAL IN THE BLOCK DIAGRAM
FEEDBACK LOOP WITH SENSOR
FILTERING
FILTERING THE PROCESS
MEASUREMENT
• FILTERING REDUCES THE EFFECT OF
SENSOR NOISE BY APPROXIMATING A
RUNNING AVERAGE.
• FILTERING ADDS LAG WHEN THE FILTERED
MEASUREMENT IS USED FOR CONTROL.
• NORMALLY, USE THE MINIMUM AMOUNT OF
FILTERING NECESSARY.
• f- FILTER FACTOR (0-1)
EFFECT OF FILTERING ON
CLOSED LOOP DYNAMICS
FILTERING EXAMPLE USING 50
DATA POINTS
• INITIAL DATA ARE SHOWN AS OUTPUT
FILTERING EXAMPLE USING 50
DATA POINTS
• FILTERED DATA ARE AVERAGED VALUES
FOR THE PREVIOUS 5 DATA POINTS
• CUMULATIVE VALUES ARE THE AVERAGES
STARTING FROM THE FIRST POINT.
• RESULTING GRAPH (NEXT PAGE) SHOWS
SIGNAL SENT TO COMPARATOR
• ALSO SEE FIGURE 7.8.1
FILTERING EXAMPLE USING 50
DATA POINTS
Noise Filtering Function
25.000
24.000
23.000
22.000
21.000
Output
Signal 20.000
Filtered
cum Mean
19.000
18.000
17.000
16.000
15.000
1
3
5
7
9
1
1
3
1
5
1
7
1
9
1
1
2
3
2
5
2
7
2
Point
9
2
1
3
3
3
5
3
7
3
9
3
1
4
3
4
5
4
7
4
9
4
FILTERING EXAMPLE USING 50
DATA POINTS
• THE BALANCE REQUIRED IS TO MINIMIZE
THE NOISE SO A RELATIVELY STABLE
SIGNAL CAN BE SENT TO THE
CONTROLLER.
– TOO FEW DATA POINTS IN THE AVERAGE
LEAVES A RESIDUAL THAT CAN HAMPER
CONTROL
– TOO MANY DATA POINTS RESULTS IN VALUES
THAT CAN LAG THE ACTUAL VALUES
• DERIVATIVE ACTION IS THE PROPERTY
THAT IS MOST AFFECTED BY NOISE
ANALYSIS OF EXAMPLE
• τf IS EQUAL TO Δt (1/f-1) AS f
BECOMES SMALL, τf BECOMES LARGE.
• AS τf IS INCREASED, τp WILL
INCREASE.
• CRITICAL ISSUE IS RELATIVE
MAGNITUDE OF τf COMPARE TO τp.
EFFECT OF THE AMOUNT OF FILTERING ON
THE OPEN LOOP RESPONSE
AN EXAMPLE OF TOO MUCH
AND TOO LITTLE FILTERING
FILTER FACTOR (f), THE RESULTING
REPEATABILITY REDUCTION RATIO (R)
AND THE FILTER TIME CONSTANT (τf)
KEY ISSUES FOR SENSOR
FILTERING
• TO REDUCE THE EFFECT OF NOISE (I.E., R
IS INCREASED), f MUST BE REDUCED,
WHICH INCREASES THE VALUE OF τf.
FILTERING SLOWS THE CLOSED-LOOP
RESPONSE SIGNIFICANTLY AS tf BECOMES
LARGER THAN 10% OF τp.
• THE EFFECT OF FILTERING ON THE
CLOSED-LOOP RESPONSE CAN BE
REDUCED BY INCREASING THE
FREQUENCY WITH WHICH THE FILTER IS
APPLIED, I.E., REDUCING Δtf.