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Solutions to Stop Most Oscillations Gregory K. McMillan

Presenter

• Gregory K McMillan is a retired Senior Fellow from Solutia/Monsanto and an ISA Fellow. Greg was an adjunct professor in the Washington University Saint Louis Chemical Engineering Department 2001-2004. Greg is currently a modeling and control consultant for Emerson Process Simulation.

• Greg received the ISA “Kermit Fischer Environmental” Award for pH control in 1991, the Control Magazine “Engineer of the Year” Award for the Process Industry in 1994, was inducted into the Control “Process Automation Hall of Fame” in 2001, was honored by InTech Magazine in 2003 as one of the most influential innovators in automation, and received the ISA Life Achievement Award in 2010. Greg is the author of numerous ISA books on process control, his most recent being Advances in Reactor Measurement and Control and Good Tuning: A Pocket Guide - 4th Edition. Greg has been the monthly “Control Talk” columnist for Control magazine since 2002. Greg is the founder and co-leader with Hunter Vegas of the ISA Mentor Program for users. Greg’s expertise is available on the web sites: http://www.controlglobal.com/blogs/controltalkblog/ http://automation.isa.org/author/gregmcmillan/

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Top Ten Possible Rewards for Knowledge Gained in this Presentation

• (10) Sleep like a baby before a startup (less the crying) • (9) Get back early from startups • (8) Have the plant ask what you think works best • (7) Have your CEO smile at you • (6) Inspire your children to become automation engineers • (5) Get a knowing twinkle in eyes like retired technologist • (4) Get asked by operators to special meals in control room • (3) Create a worldwide recognition of automation profession • (2) See your picture on T-shirts in Control Theory classes • (1) Become famous and regular guest on “Late Nite” TV

Topics

• Introduction • Virtual Plant Virtuosity • PID Execution Rate and Filter Time • Measurement Threshold Sensitivity • Valve Dead Band, Resolution, Sensitivity & Stroking Time • Amplification & Attenuation of Disturbance Oscillations • Window of Allowable Gains for Integrating Processes • Slow Cascade Loops & Wireless Update Rate • Automation System & Process Dynamics in Control Loop • Ultimate Limit to Performance – Dead Time is the Key • Minimizing Measurement Dead Time • PID Options & Procedure

Introduction

• The disturbances from outside influences (raw materials and weather) and internally (surface fouling and catalyst activity) tend to be so slow that reasonably good robust PID tuning can correct for them smoothly

• The disturbances from automation systems and operations are often fast and frequent with PID reactions often being late and disruptive to other loops

• Cyclic disturbances are key examples, creating abrupt changes in flows and posing additional problems in terms of propagation and resonance. Examples:

– Poor mixing, bad profiles, multiple phases (bubbles and droplets), large transportation delay – Poor sensor response time, resolution, installation, rangeability & noise & drift to bad operating pt. – Nonlinearity in slope of installed flow characteristic of valves & Variable Frequency Drives (VFD) – Sequential actions, on-off valves, manual actions, & setpoint changes – Valve or VFD dead band, resolution, and slow T86 response time (including rate limiting) – Poor positioner or actuator sensitivity, missing positioner & booster, poor VFD inverter design – PID gain too low or too high, slow filter & execution, poor PID setup, interaction & resonance

• Essential solutions include valves, VFD & sensors with good response & rangeability, good control strategies (see my ISA PC&S 2016 “Process Control Strategies to Improve Process Efficiency and Capacity), feedforward & ratio control, effective use of PID Form, Structure & Options, & good PID tuning

• All solutions were explored, discovered and detailed via a virtual plant

Use a Virtual Plant to Explore and Discover All of this and Much More

Control August 2017 Feature “Virtual Plant Virtuosity”

http://www.controlglobal.com/articles/2017/virtual-plant-virtuosity/

Explore, Discover, Prototype, Justify, Deploy, Test, Train, Commission, Maintain

Effect of PID Execution Rate (∆tx) on Actual PV for Self-Regulating Process

PID ∆tx = 0.5 sec

PID ∆tx = 10 sec

PID ∆tx = 20 sec

PID ∆tx = 40 sec

Dead Time = 10 sec Load Upset = 10%

PID ∆tx = 0.5 sec

PID ∆tx = 10 sec

PID ∆tx = 20 sec

PID ∆tx = 40 sec

Dead Time = 10 sec Load Upset = 10%

Effect of PID Execution Rate (∆tx) on Actual PV for Near-Integrating Process

Effect of PID Filter Time (τf ) on Actual PV for Self-Regulating Process

PID τf = 0 sec

PID τf = 5 sec

PID τf = 10 sec

PID τf = 20 sec

Dead Time = 10 sec Load Upset = 10%

Effect of PID Filter Time (τf ) on Actual PV for Near-Integrating Process

PID τf = 0 sec

PID τf = 5 sec

PID τf = 10 sec

PID τf = 20 sec

Dead Time = 10 sec Load Upset = 10%

Effect of Measurement 0.5%Threshold Sensitivity for Self-Regulating Process

PID Tuning = Aggressive

PID Gain = 0.5 x Max

PID Reset = 2.0 x Min

PID Rate = 0 sec

Dead Time = 10 sec Load Upset = 10%

Effect of Measurement 0.5%Threshold Sensitivity for Near-Integrating Process

PID Tuning = aggressive

PID Gain = 0.5 x Max

PID Reset = 2.0 x Min PID Rate =

0 sec

Dead Time = 10 sec Load Upset = 10%

Flow Open Loop 0.2% Step Response for 2% Shaft Backlash Dead Band

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2% Backlash

Dead Band (Lost Motion)

Signal

Flow

Flow Closed Loop 10% Load Response 0,10% Backlash: 0.2,0.05 PID Gain

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Lower PID Gain causes delayed slower recovery

Level Closed Loop 10% Load Response 10% Backlash: 4.4,8.8,0.88 PID Gain

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10% Backlash 8.8 PID Gain

External Reset Off

10% Backlash 4.4 PID Gain

External Reset Off

10% Backlash 0.88 PID Gain

External Reset Off

Higher PID Gain reduces amplitude & period

Level

Signal

Level Closed Loop 10% Load Response 10% Backlash: 4.4,8.8 PID Gain & ERF Off => On

17

Higher PID Gain & External-Reset Feedback (ERF) help

Flow Open Loop 0.2% Step Response for 1% Shaft Stiction Resolution

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1% Stiction

Resolution

Signal

Flow

Flow Closed Loop 10% Load Response 6% Stiction: 0.2,0.05 PID Gain & ERF Off => On

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Lower PID Gain increase limit cycle period External-Reset Feedback (ERF) stops cycle with offset

Level Closed Loop 10% Load Response 6% Stiction: 4.4,8.8,0.88 PID Gain

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Higher PID Gain reduces amplitude and period

Flow Open Loop 0.1% Step Response for Poor Positioner Sensitivity

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Variable T86 response time that increases as step size decreases and doubles for change in direction

Flow Closed Loop 10% Load Response Poor Positioner: 0.2 PID Gain

22

Irregular cycling due to variable dead time

Flow Closed Loop 10% Load Response Poor Positioner: 0.4 PID Gain & 30 sec Reset

23

Higher PID gain & larger reset time stops cycles

Flow Closed Loop 10% Load Response Poor Positioner: 0.8 PID Gain & ERF On

24

External-Reset Feedback (ERF) gives big improvement

Flow Open Loop 20% Step Response for Large Actuator

25

Signal

Flow

0.6%/sec Slew Rate

Flow Closed Loop 20% Load Response Large Actuator: 0.2 PID Gain & ERF Off => On

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External-Reset Feedback (ERF) can stop cycles

Level Closed Loop 20% Load Response Large Actuator: 4.4 PID Gain & ERF Off => On

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External-Reset Feedback (ERF) can stop cycles

Control March 2016 White Paper “Valve response: Truth or Consequences”

Please, please, please use valve bodies, actuators and smart positioners that minimize deadband, resolution and 86%

response time for small (e.g., 0.25%) and large (e.g., 25%) step changes maximizing valve response rather than minimizing leakage!

Tight shutoff valves have really bad stiction and often backlash. Use on-off valves for

isolation and use throttling valves for control. Better loop performance and lower life cycle costs will more than pay for valve cost.

Finally, turn off integral action

in the positioner and tune for more gain action. Integral action makes

open loop tests look better by eliminating offset but plays

havoc with closed loop control!

http://www.controlglobal.com/articles/2016/how-to-specify-valves-and-positioners-that-dont-compromise-control/

Effect of PID Gain on Fast Disturbance Oscillations

Disturbance oscillation amplification by

feedback action for fast disturbance period ¼ to 4x ultimate period

worse for higher PID gains. Cutoff period for Lambda

tuned loops is 2 ∗ π ∗ λ

Resonance results in PV amplitude in automatic greater than in manual

Filtering by process lag

Effect of PID Gain on Slow Disturbance Oscillations

Disturbance oscillation attenuation by

feedback action for slow disturbance period

> 10x ultimate period better for higher PID gains

Effect Low PID Gain on Near-Integrating Processes

Oscillation amplitude is 4x and period is 10x larger for low PID gain than for high PID gain!

Disturbance oscillation amplitude and persistence

more problematic (larger and slower) for lower PID gains as process loses

self-regulation but oscillations eventually

decay (damped)

iic TK

K∗

>2

reset time (sec)

To prevent the start of slow oscillations:

controller gain (dimensionless)

integrating process gain

(%/sec/% => 1/sec)

Lambda tuning ensures inequality is met if

λ > dead time

Effect Low PID Gain on True Integrating Processes

Oscillation amplitude is 4x and period is 10x larger for low PID gain than for high PID gain!

Disturbance oscillation amplitude and persistence

more problematic (larger and slower) for lower PID gains as process loses

self-regulation but oscillations eventually

decay (damped)

iic TK

K∗

>2

reset time (sec)

To prevent the start of slow oscillations:

controller gain (dimensionless)

integrating process gain

(%/sec/% => 1/sec)

Lambda tuning ensures inequality is met if

λ > dead time

Cascade Control Slow Secondary Loop Lower Loop Lambda = 0.1x Primary Time Constant

External-Reset Feedback Off

Setpoint Change Upper Loop Metrics Overshoot = 2.69 % Undershoot = 0.73 % Rise Time = 36 sec Settle Time = 144 sec

Upper Loop PID SP

Upper Loop PID PV

Lower Loop PID PV

Lower Loop PID SP Lower Loop

PID Output

SP Step = +10%

Cascade Control Slow Secondary Loop Lower Loop Lambda = 0.1x Primary Time Constant

External-Reset Feedback On

Setpoint Change Upper Loop Metrics Overshoot = 1.59 % Undershoot = 0.26 % Rise Time = 41 sec Settle Time = 122 sec

Upper Loop PID SP

Upper Loop PID PV

Lower Loop PID PV

Lower Loop PID SP

Lower Loop PID Output

SP Step = +10%

Cascade Control Slow Secondary Loop Lower Loop Lambda = 0.2x Primary Time Constant

External-Reset Feedback Off

Setpoint Change Upper Loop Metrics Overshoot = 3.88 % Undershoot = 1.49 % Rise Time = 42 sec Settle Time = 235 sec

Upper Loop PID SP

Upper Loop PID PV

Lower Loop PID PV

Lower Loop PID SP

Lower Loop PID Output

SP Step = +10%

Cascade Control Slow Secondary Loop Lower Loop Lambda = 0.2x Primary Time Constant

External-Reset Feedback On

Setpoint Change Upper Loop Metrics Overshoot = 1.96 % Undershoot = 0.39 % Rise Time = 47 sec Settle Time = 149 sec

Upper Loop PID SP

Upper Loop PID PV

Lower Loop PID PV

Lower Loop PID SP Lower Loop

PID Output

SP Step = +10%

Cascade Control Slow Secondary Loop Lower Loop Lambda = 0.4x Primary Time Constant

External-Reset Feedback Off

Upper Loop PID SP Upper Loop

PID PV

Lower Loop PID PV

Lower Loop PID SP

Lower Loop PID Output

Setpoint Change Upper Loop Metrics Overshoot = 6.23 % Undershoot = 3.87 % Rise Time = 61 sec Settle Time = 836 sec

SP Step = +10%

Cascade Control Slow Secondary Loop Lower Loop Lambda = 0.4x Primary Time Constant

External-Reset Feedback On

Setpoint Change Upper Loop Metrics Overshoot = 2.04% Undershoot = 0.42 % Rise Time = 58 sec Settle Time = 190 sec

Upper Loop PID SP

Upper Loop PID PV

Lower Loop PID PV

Lower Loop PID SP

Lower Loop PID Output

SP Step = +10%

Cascade Control Slow Secondary Loop Lower Loop Lambda = 0.8x Primary Time Constant

External-Reset Feedback Off

Upper Loop PID SP Upper Loop

PID PV

Lower Loop PID PV

Lower Loop PID SP

Lower Loop PID Output

Setpoint Change Upper Loop Metrics Overshoot = 6.23 % Undershoot = 3.87 % Rise Time = 61 sec Settle Time = 836 sec

SP Step = +10%

Cascade Control Slow Secondary Loop Lower Loop Lambda = 0.8x Primary Time Constant

External-Reset Feedback On

Setpoint Change Upper Loop Metrics Overshoot = 1.71 % Undershoot = 0.30 % Rise Time = 78 sec Settle Time = 258 sec

Upper Loop PID SP

Upper Loop PID PV

Lower Loop PID PV

Lower Loop PID SP

Lower Loop PID Output

SP Step = +10%

Wireless Reagent Flow Loop Pressure Upset (16 sec Update Rate)

Step Load

= + 20%

Wireless Inline pH Loop Influent Upset (60 sec Update Rate)

Step Load

= + 20%

Effect of Feedforward Lag Mismatch on PID PV for Self-Regulating Process

FF Lag Mismatch − 10 sec

Inverse Response !

FF Lag Mismatch

0 sec

FF Off

FF Lag Mismatch + 10 sec

Step Load

= + 10%

Automation System and Process Dynamics in a Control Loop

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Y fraction of small lag that is equivalent dead time is a logarithmic function of the ratio of the small to largest lag (Y = 0.28, 0.88 for ratios = 1.0 and 0.01, respectively)

Ultimate Limit to Performance (Process Input Load Disturbance)

45

ooo

ox EE ∗

+=

)( τθθ

ooo

oi EE ∗

+=

)(

2

τθθ

Peak error is proportional to the ratio of loop dead time to 63% response time (Important to prevent SIS trips, relief device activation, surge prevention, and RCRA pH violations)

Integrated error is proportional to the ratio of loop dead time squared to 63% response time (Important to minimize quantity of product off-spec and total energy and raw material use)

For a sensor lag (e.g. electrode or thermowell lag) or signal filter that is much larger than the process time constant, the unfiltered actual process variable error can be

found from the equation for attenuation

Total loop dead time that is often set by automation design

Largest lag in loop that is ideally set by large process volume

Open loop error for fastest and largest load disturbance

Dead Time is the Key

• Without Dead Time, I would be Out of a Job – Controller would immediately see and correct for load upsets and setpoint change – No high limit to maximum controller gain and no low limit as to minimum reset time

• PID tuning settings for best loop performance are a function of dead time – Gain, phase margin = 3, 61o (λ = 1 ∗ θ) for max load rejection for fixed well known dynamics – Gain, phase margin = 6, 76o (λ = 3 ∗ θ) to deal with adverse changes in loop dynamics < 5 – Gain, phase margin = 9, 81o (λ = 5 ∗ θ) to reduce resonance and interaction

• Ultimate Period is 2x to 4x dead time for self-regulating processes and is 4x dead time for other processes using first order plus dead time approximation

• Resonance can occur for disturbance oscillation periods 2x => 10x dead time • PID execution & filter time should be < 0.2x & 0.1x dead time, respectively • Oscillation periods < 4x dead time are indicative of gain or rate too high • Oscillation periods 5x => 10x dead time are indicative of reset time too fast • Oscillation periods > 10x dead time are indicative valve and VFD problems

(e.g., deadband, slow stroking or rate limiting & poor sensitivity & resolution)

Minimizing Measurement Dead Time

47

mxmmmmawm YY θθθττθθθ +++∗+∗++= 2121

wireless dead time

(sec)

analyzer dead time

(sec)

sensor lag

(sec)

transmitter damping

(sec)

transport delay (sec)

sensor delay (sec)

resolution or sensitivity delay

(sec)

wxw t∆∗= 5.0θ

wireless update rate

(sec)

azaxa tt ∆∗+∆∗= 5.05.1θ

analyzer cycle time

(sec)

tPVSm

mx ∆∆=

/%θ

sensor resolution or threshold sensitivity

(%)

PV rate of change (%/sec)

88.028.0 =>≅YMeasurement

dead time (sec)

analyzer multiplex time

(sec)

PID Options

• Integral Deadband: stops integral action when error is within deadband • External-Reset Feedback: Prevents integral mode output from changing

faster than the response of the secondary loop PV or valve position – is the key feature for suppressing oscillations from backlash, stiction, and cascade rule violation, enabling move suppression and enhanced PID

• PID & AO Setpoint rate limits: Provides directional move suppression to reduce split range crossings & to provide smooth optimization with fast recovery for abnormal conditions (e.g., surge and valve position control)

• Enhanced PID: Prevents integral mode from changing output if PV has not updated (critical for wireless update rates and analyzer cycle times)

• PID Structure: Enables user to specify what modes are active and if active, whether they act only changes in PV or also on changes in SP

• Anti Reset Windup Limits: Normally set equal to output limits but can be set inside output limits to provide faster recovery from heat transfer limit and to get valve open when there is solids buildup or high seal stiction

• Feedforward control: Flow and speed ratio control corrected by PID 48

Procedure

• Determine loop objective(s) with operators and process engineers. • With PID in manual track down and mitigate noise & oscillations. For

remaining oscillation amplitude and period determine if limit cycle, low PID gain limit violation, noise amplification or if resonance can occur.

• For noise, use small PV filter time less than 0.1x dead time. • Choose PID options accordingly (e.g., use PID structure no gain & no

rate action on SP to minimize SP overshoot). Use ISA Standard Form. • Use signal characterization in DCS to help linearize system. • Identify dynamics for different production rates, weather, products,

fouling, catalyst activity etc. (identify dead time, open loop process gain, open loop (primary) time constant for self-regulating processes, secondary time constant, and lead time). Find the worst case and determine if process should be treated as integrating or runaway.

• Tune for loop objectives(s) using adaptive control as needed making sure the PID window of allowable gains is open enough for changes and unknowns. First test load response by momentarily putting PID in manual making output change and finally test setpoint response. 49

General and Specific PID Solutions

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