Presented at the AIChE 2013 Spring Meeting and 9th Global Congress on Process Safety meeting by Greg McMillan, CDI Process & Industrial and Hector Torres, Eastman Chemical

1. A Unified PID Control
Methodology to Meet
Plant Objectives
Greg McMillan
CDI Process & Industrial
Hector Torres
Eastman Chemical

2. ISA Books

3. Topics
 PID Basics (contribution of each mode)
 Process and Loop Dynamics
 Ultimate Limits for Disturbance Rejection
 Practical Limits for Disturbance Rejection
 PID Form and Structure Options
 Setpoint Rate Limits and Lead-Lag
 Setpoint Rise Time
 Output Tracking Opportunities
 Enhanced PID for Wireless, Analyzer, and Valve Position Control
 PID Features and Optimization with Valve Position Control
 Lambda Tuning Rules
 Misunderstood Effect of Low PID Gain
 Unified Methodology

4. Sense of Direction

5. Kick
from filtered
derivative mode
α = 1/8
∆%CO2 = ∆%CO1
∆%SP
∆%CO1
Time
(seconds)
Signal
(%)
Step from
proportional
mode Repeat from
Integral mode
No setpoint filter or lead-lag
seconds/repeat
Contribution of Each PID Mode for
Setpoint Change (Filtered Rate)
Structure of PID on error (β=1 and γ=1)
Controller in auto
Block valve closed (PV not affected)

6. Contribution of Each PID Mode for
Setpoint Change (Unfiltered Rate)
Structure of PID on error (β=1 and γ=1)
Controller in auto
Block valve closed (PV not affected)
Spike
from unfiltered
derivative mode
α = 0
∆%CO2 = ∆%CO1
∆%SP
∆%CO1
Time
(seconds)
Signal
(%)
Step from
proportional
mode
Repeat from
Integral mode
No setpoint filter or lead-lag
seconds/repeat

7. Proportional Mode Basics
Note that many analog controllers used proportional band instead of gain for the proportional mode
tuning setting. Proportional band is the % change in the process variable (∆%PV) needed to cause a
100% change in controller output (∆%CO). A 100% proportional band means a 100% ∆%PV
would cause a 100 % ∆%CO (a gain of 1). It is critical that users know the units of their controller
gain setting and convert accordingly.
Gain = 100 % / Proportional Band
 Provides an immediate reaction to magnitude of measurement change to
minimize peak error and integrated error for a disturbance
 Too much gain action causes fast oscillations (close to ultimate period) and
can make noise and interactions worse
 Provides an immediate reaction to magnitude of setpoint change for P
action on Error to minimize rise time (time to reach setpoint)
 Too much gain causes falter in approach to setpoint

8. Integral Mode Basics
Note that many analog controllers used reset settings in repeats per minute instead of reset
time for the integral mode tuning setting. Repeats per minute indicate the number of repeats
of the proportional mode contribution in a minute. Today’s reset time settings are minutes per
repeat or seconds per repeat which gives the time to repeat the proportional mode
contribution. Often the “per repeat” term is dropped giving a reset time setting in minutes or
seconds. The smooth gradual response looking only at error is in tune with operator.
Seconds per repeat = 60 / repeats per minute
 Provides a ramping reaction to error (SP-PV) to eliminate offset and minimize
integrated error if stable (since error is hardly ever exactly zero, integral action
is always ramping the controller output)
 Too much integral action causes slow oscillations (slower than ultimate period)
 Too much integral action causes an overshoot (no sense of direction)

9. Derivative Mode Basics
Nearly all derivative tuning settings are given as a rate time in seconds or minutes. The
ISA Standard Form rate time setting must never be greater than the reset time setting. The
advantages and disadvantages of the derivative mode in terms of an abrupt response and
amplification of noise are similar to that of the proportional mode except the relative
advantages are less and the relative disadvantages are greater for the derivative
mode. Derivative mode is best used to cancel out the effect of a secondary time constant.
Seconds = 60 ∗ minutes
 Provides an immediate reaction to rate of change of measurement change
to minimize peak error and integrated error for a disturbance
 Too much rate action causes fast oscillations (faster than ultimate period)
and can make noise and interactions worse
 Provides an immediate reaction to rate of change of setpoint change for D
action on Error to minimize rise time (time to reach setpoint)
 Too much rate causes fast oscillation

10. Proportional Only (P only)
Response to Step Load Disturbance
Purple PV = 0.5 x Normal Gain
Green PV = 1.0 x Normal Gain
Red PV = 1.5 x Normal Gain
Brown PV = 2.0 x Normal Gain
Period = 40 sec
Ultimate Period = 40 sec

11. Proportional + Integral (PI)
Response to Step Load Disturbance
Purple PV = 1.5 x Normal Reset
Green PV = 1.0 x Normal Reset
Red PV = 0.75 x Normal Reset
Brown PV = 0.5 x Normal Reset
Period = 65 sec
Ultimate Period = 40 sec

12. Proportional + Integral + Derivative (PID)
Response to Step Load Disturbance
Purple PV = 0.5 x Normal Rate
Green PV = 1.0 x Normal Rate
Red PV = 2.0 x Normal Rate
Brown PV = 2.5 x Normal Rate
Period = 25 sec
Ultimate Period = 40 sec

13. Self-Regulating Process

14. Integrating Process

15. Runaway Process

16. Origin of Loop Dynamics

17. Ultimate Limit for Disturbance Rejection

18. Ultimate Limit for Disturbance Rejection

19. Practical Limit for Disturbance Rejection

20. External Reset (Dynamic Reset Limit)
 Prevents PID output changing faster than a valve, VFD, or secondary
loop can respond
– Secondary PID slow tuning
– Secondary PID SP Filter Time
– Secondary PID SP Rate Limit
– AO, DVC, VFD SP Rate Limit
– Slow Valve or VFD
– Use PV for BKCAL_OUT
– Position used as PV if valve is very slow and readback is fast
– Enables Enhanced PID for Wireless
 Stops Limit cycles from deadband, backlash, stiction, and threshold
sensitivity or resolution limits
 Key enabling feature that simplifies tuning and creates more
advanced opportunities for PID control

21. ISA Standard Form with External Reset

22. PID Structure Options
(1) PID action on error (β = 1 and γ = 1)
(2) PI action on error, D action on PV (β = 1 and γ = 0)
(3) I action on error, PD action on PV (β = 0 and γ = 0)
(4) PD action on error, no I action (β = 1 and γ = 1)
(5) P action on error, D action on PV, no I action (β = 1 and γ = 0)
(6) ID action on error, no P action (γ = 1)
(7) I action on error, D action on PV, no P action (γ = 0)
(8) Two degrees of freedom controller (β and γ adjustable 0 to 1)

23. PID Options Effect on Setpoint Response

24. Single Sided Batch Needs PD on Error

25. Setpoint Rate Limits and Lead-Lag
(Triple Cascade Loop)

26. Setpoint Filter and Lead-Lag
• PID SP filter reduces overshoot enabling tuning for load disturbances
– Setpoint filter time set equal reset time
• PID SP filter coordinates timing of flow ratio control
– Simultaneous changes in feeds for blending and reactions
– Consistent closed loop response for model predictive control
• PID SP filter sets closed loop time constant
• PID SP filter in secondary loop slows down cascade control system
rejection of primary loop disturbances
– Secondary loop should be > 4x faster than primary loop
• Primary PID must have dynamic reset limit enabled
• Setpoint Lead-Lag minimizes overshoot and rise time
– Lag time = reset time
– Lead time = 25% lag time

27. Setpoint Rate Limits
• AO & PID SP rate limits minimize disruption while protecting
equipment and optimizing processes
– Offers directional moves suppression
– Enables fast opening and slow closing surge valve
– VPC fast recovery for upset and slow approach to optimum
• AO SP rate limits minimize interaction between loops
– Less important loops are made 10x slower than critical loops
• PID driving AO SP or secondary PID SP rate limit must have
dynamic reset limit enabled so no retuning is needed
• PID faceplate should display PV of AO to show rate limiting

28. Rise Time for Setpoint Response

29. Output Tracking Opportunities
• “Bang-Bang” logic for startup & batch SP changes:
– For SP change PID tracks output limit until the predicted PV one
dead time into future gets close to setpoint, the output is then
set at best/last startup or batch value for one dead time
– Works best on slow batch and integrating processes
• “Open Loop Backup” to prevent compressor surge:
– When compressor flow drops below surge SP or a precipitous
drop occurs in flow, PID tracks an output that provides a flow
large enough to compensate for the loss in downstream flow for
a time larger than the loop dead time plus the surge period.
• “Open Loop Backup” to prevent RCRA violation:
– When an inline pH system PV approaches the RCRA pH limit
the PID tracks an incremental output (e.g. 0.25% per sec)
opening the reagent valve until the pH sufficiently backs away

30. Enhanced PID for Wireless
• Positive feedback implementation of reset with external-reset
feedback (dynamic reset limit)
• Immediate response to a setpoint change or feedforward signal or
mode change
• Suspension of integral action until change in PV
• Integral action is the exponential response of the positive feedback
filter to the change in controller output in elapsed time (the time
interval since last update)
• Derivative action is the PV or error change divided by elapsed time
rather than PID execution
• Threshold sensitivity limit is used to prevent update from noise

31. Static Mixer pH Setpoint Response

32. Static Mixer pH Load Response

33. Static Mixer pH Failure Response

34. Optimization of Batch Reactor by
Valve Position Control (VPC)

35. Optimization Examples
by Valve Position Control (VPC)
Optimization VPC PID PV VPC PID SP VPC PID Out
Minimize Prime
Mover Energy
Reactor Feed
Flow PID Output
Maximum Throttle
Position
Compressor or Pump
Pressure SP
Minimize Boiler
Fuel Cost
Steam Flow PID Output Maximum Throttle
Position
Boiler
Pressure SP
Minimize Boiler
Fuel Cost
Equipment Temperature
PID Output
Maximum Throttle
Position
Boiler
Pressure SP
Minimize Chiller
or CTW Energy
Equipment Temperature
PID Output
Maximum Throttle
Position
Chiller or CTW
Temperature SP
Minimize Purchased
Reagent or Fuel Cost
Purchased Reagent or
Fuel Flow PID Output
Minimum Throttle
Position
Waste Reagent
Or Fuel Flow SP
Minimize Total Reagent
Use
Final Neutralization
Stage pH PID Output
Minimum Throttle
Position
First Neutralization
Stage pH PID SP
Maximize Reactor
Production Rate
Reactor or Condenser
Temperature PID Output
Maximum Throttle
Position
Feed Flow or Reaction
Temperature SP
Maximize Reactor
Production Rate
Reactor Vent
Pressure PID Output
Maximum Throttle
Position
Feed Flow or Reaction
Temperature SP
Maximize Column
Production Rate
Reboiler or Condenser
Flow PID Output
Maximum Throttle
Position
Feed Flow or Column
Pressure SP

36. PID Features for Valve Position Control
PID Feature Function Advantage 1 Advantage 2
Directional Velocity
Limits
Limit VPC Action Speed
Based on Direction
Prevent Running Out
of Valve
Minimize Disruption
to Process
Dynamic Reset
Limit
Limit VPC Action Speed
to Process Response
Directional Velocity
Limits
Prevent Burst of
Oscillations
Adaptive Tuning Automatically Identify
and Schedule Tuning
Eliminate Manual
Tuning
Compensation of
Nonlinearity
Feedforward Preemptively Set VPC
Out for Upset
Prevent Running Out
of Valve
Minimize Disruption
Enhanced PID Suspend Integral Action
until PV Update
Eliminate Limit Cycles
from Stiction &
Backlash
Minimize Oscillations
from Interaction &
Delay

37. Self-Regulating Process Lambda Tuning

38. Integrating Process Lambda Tuning

39. Often Misunderstood Low PID Gain Effect
Lag Dominant Self-Regulating Process
Period = 400 sec
Ultimate Period 40 sec

40. Often Misunderstood Low PID Gain Effect
Integrating Process
Period = 400 sec
Ultimate Period 40 sec

41. Often Misunderstood Low PID Gain Effect
Runaway Process
Period = 400 sec
Ultimate Period 40 sec

42. Low PID Gain and Reset Time Limit

43. Unified Methodology - 1
 Add a flow measurement to every important process and utility
stream to enable a secondary flow loop for cascade control.
– A secondary flow loop isolates pressure disturbances, and nonlinearities
of the installed characteristic of control valve and variable speed drives
from the control of a higher process variable.
– Flow measurement enable flow feedforward control and the possibility of
changing production rates by moving plant flows in unison per PFD.
– Flow measurements enable closing material and energy balances
leading to process knowledge eliminating uncertainties from pressure
flow relationships and valve backlash and stiction.
– Control valves and VSD normally have a greater rangeability than a
differential head or vortex meter. When this occurs, a calculated flow
based on the installed characteristic should be substituted for the
measurement flow before the signal becomes too noisy or in the case of
the vortex meter the signal drops out. An automatic pressure drop bias
enables smooth transition from measured to calculated flow

44. Unified Methodology - 2
 Set the output limits to keep the manipulated setpoints in the
desired operating range. For variable speed drives set the process
PID low output limit so the speed cannot cause the discharge head to
approach the static head in order to prevent excessive sensitivity to
pressure and to prevent reverse flow. In general, set the anti-reset
windup limit to match the output limit. If the output scale is
engineering units, the output limits and anti-reset windup must be
based on the output scale range and units.
 Choose the best structure for your application. Generally the best
choice is structure 2 with PI on error and D on PV. For a single
direction response (e.g. batch heating or neutralization), use structure
4 or structure 5 so that there is no integral action. For a highly
exothermic reaction, you might want structure 5 to help prevent a
runaway from integral action.
 Set the signal filter noise just large enough to keep the controller
output fluctuations from exceeding the resolution limit or deadband of
the final control element.

45. Unified Methodology - 3
 For near-integrating, true integrating, and runway processes use
the lambda integrating process tuning rules. To maximize the
transfer of variability from the process variable to the manipulated
variable, set the lambda (arrest time) equal to the maximum possible
dead time* and use the largest integrating process gain for all
operating conditions in the tuning. To maximize the absorption of
variability (e.g. surge tank level) use the minimum arrest time
computed from paper Equations 1 through 10 for all possible
operating conditions. If you decrease the PID gain, proportionally
increase the PID reset time to prevent slow rolling oscillations.
 For self-regulating processes with the open loop time constant
less than 4 times the dead time, use the lambda self-regulating
tuning rules. To maximize the transfer of variability from the process
variable to the manipulated variable set the lambda (closed loop time
constant) equal to the maximum possible dead time* and use the
largest process gain and smallest time constant for all operating
conditions in the tuning (worse case is often lowest production rate).
* Due to unknowns a more practical lambda is twice the max dead time

46. Unified Methodology - 4
 Turn on external reset feedback. Make sure the external reset
feedback signal is correctly propagated back to the PID (e.g. BKCAL
signal) especially if there are split range, signal characterizer, or
signal selector blocks on the PID output.
 For final control elements that are slow or that have deadband
or resolution limit, use a fast readback of the valve position or
variable frequency drive speed as the external reset feedback to
prevent a burst of oscillations from the PID output changing faster
than the final control element can respond.
 For final control elements that create limit cycles from
resolution limits and deadband, use a fast readback of the valve
position or variable frequency drive speed to stop the limit cycles
 For cascade control, use the PV of the secondary loop as the
external reset feedback to prevent a burst of oscillations from
violation of the cascade rule where the secondary loop must be
significantly faster than the primary loop.

47. Unified Methodology - 5
 For setpoint filters of secondary loops for coordination of flow
loops, use the PV of the secondary loop as the external reset
feedback to prevent the need to retune the PID.
 For setpoint rate limits use the PV of the analog output block or
secondary loop as the external reset feedback to prevent the
need to retune the PID. Add setpoint rate limits to minimize the
interaction between loops and in valve position control and to provide
directional move suppression to enable a fast getaway for abnormal
conditions and a slow approach to optimum. For valve position
control, use an enhanced PID developed for wireless with a threshold
sensitivity limit to ignore insignificant changes in the valve position to
be optimized.
 Add output tracking for equipment protection and a full throttle
(bang-bang control) strategy for the fastest possible time to reach
setpoint on startup and for batch operations.
 Use valve position control for simple and quick optimization by
just a PID configuration.

48. Unified Methodology - 6
 Add output tracking logic to momentarily track an output that
insures equipment and environmental protection. For compressor
surge protection track a sufficiently large opening of the surge valves.
To prevent a RCRA pH violation, track a rapidly incrementing reagent
valve position to prevent an effluent excursion < 2 pH or > 12 pH.
 Add feedforward control for large and fast measured
disturbances. For flow feedforward, use a ratio and bias station so
the operator can enter a desired flow ratio and see the actual flow
ratio. Setup the PID to provide a bias correction to the manipulated
flow. Add dynamic compensation (dead time and lead-lag blocks) to
the feedforward so the manipulated flow arrives at the same point in
the process at the same time as the measured disturbance.
 For wireless devices or analyzers (discontinuous PV update
delay) use an enhanced PID to eliminate the need to retune the
controller to prevent oscillations. If the delay is much larger than the
63% process response time, the PID gain can be set as large as the
inverse of the maximum open loop gain for self-regulating processes.