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PID Options and Solutions ISA Mentor Program Presentation by:

Gregory 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 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/

2

http://www.controlglobal.com/blogs/controltalkblog/

http://automation.isa.org/author/gregmcmillan/

Self-Regulating Process Response

3

Near-Integrating: looks like ramp in time frame

of PID response (4 dead times)

If 4>o

o

θτ

, process is classified as Near-Integrating !

Time (seconds)

∆% CO

∆% PV

θo

Ko = ∆% PV / ∆% CO

0.63∗∆% PV

% CO

% PV

Self-regulating process primary negative feedback time constant

Open loop self-regulating process gain (%/%)

Response to change in controller output with controller in manual

observed total loop dead time

ideally τp τo

Maximum speed in 4 dead times

is critical speed

Noise Band

% P

roce

ss V

aria

ble

(%PV

) or

%

Con

trol

ler O

utpu

t (%

CO

)

o

oi

KK

τ=

Equivalent open loop integrating

process gain:

Figure 1 – Self-Regulating Process Open Loop Response

True Integrating Process Response

4

Time (seconds) θo

Ki = { [ % PV2 / ∆t2 ] − [ % PV1 / ∆t1 ] } / ∆% CO

∆% CO

ramp rate is ∆% PV1 / ∆t1

ramp rate is ∆% PV2 / ∆t2

% CO

% PV

Open loop integrating process gain (%/sec/%)


observed total loop dead time

Maximum ramp rate in 4 dead times is used to estimate integrating

process gain

% P

roce

ss V

aria

ble

(%PV

) or

%

Con

trol

ler O

utpu

t (%

CO

)

Figure 2 – True Integrating Process Open Loop Response

Continual ramp: no deceleration

and no steady state

Runaway Process Response

5


Noise Band

Acceleration !

∆% PV

∆% CO

1.72∗∆% PV

K’o = ∆% PV / ∆% CO Open loop

runaway process gain (%/%) derived from differential equations

% P

roce

ss V

aria

ble

(%PV

) or

%

Con

trol

ler O

utpu

t (%

CO

)

Time (seconds) observed total loop dead time

runaway process primary positive feedback time constant

derived from differential equations

For safety reasons, tests are terminated within 4 dead times before noticeable acceleration

τ’ o must be τ’ p θo

% PV

% CO

Figure 3 – Runaway Process Open Loop Response

Examples

• Near Integrating Processes – Continuous column composition, pH and temperature control – Continuous vessel composition, pH and temperature control

– crystallizers, evaporators, fermenters, neutralizers, reactors • True Integrating Processes

– Level and gas pressure (level or pressure doesn’t appreciably affect flow) – Batch column composition, pH and temperature control – Batch vessel composition, pH and temperature control

– crystallizers, evaporators, fermenters, neutralizers, reactors • Runaway Processes

– Polymerization reactor temperature control (highly exothermic) – Biological reactor cell concentration control (exponential growth phase) – Axial compressor speed control (precipitous drop in flow at start of surge) – Strong acid and base pH control (approach to neutral point)

6

Many Loop Objectives

• Minimum PV peak error in load response to prevent: – Compressor surge, SIS activation, relief, undesirable reactions, poor cell health

• Minimum PV integrated error in load or setpoint response to minimize: – total amount of off-spec product to enable closer operation to optimum setpoint

• Minimum PV overshoot of SP in setpoint response to prevent: – Compressor surge, SIS activation, relief, undesirable reactions, poor cell health

• Minimum Out overshoot of FRV in setpoint response to prevent: – Interaction with heat integration and recycle loops in hydrocarbon gas unit ops

• Minimum PV time to reach SP in setpoint response to minimize: – Batch cycle time, startup time, transition time to new products and operating rates

• Minimum split range point crossings to prevent: – Wasted energy-reactants-reagents, poor cell health (high osmotic pressure)

• Maximum absorption of variability in level control to prevent: – Passing of changes in input flows to output flows upsetting downstream unit ops

• Optimum transfer of variability from controlled to manipulated variable

7

FRV is Final Resting Value of PID output. Overshoot of FRV is necessary for setpoint and load response for integrating and runaway processes

Different Worlds

8

• Hydrocarbon processes and other gas unit operations with plug flow, heat integration & recycle streams (e.g. crackers, furnaces, reformers)

– Fast self-regulating responses, interactions and complex secondary responses with sensitivity to SP and FRV overshoot, split range crossings and utility interactions.

• Chemical batch and continuous processes with vessels and columns – Important loops tend to have slow near or true integrating and runaway responses

with minimizing peak and integrated errors and rise time as key objectives.

• Utility systems (e.g., boilers, steam headers, chillers, compressors) – Important loops tend to have fast near or true integrating responses with

minimizing peak and integrated errors and interactions as key objectives.

• Pulp, paper, food and polymer inline, extrusion and sheet processes – Fast self-regulating responses and interactions with propagation of variability into

product (little to no attenuation of oscillations by back mixed volumes) with extreme sensitive to variability and resonance. Loops (particularly for sheets) can be dead time dominant due to transportation delays unless there are heat transfer lags.

• Biological vessels (e.g., fermenters and bioreactors) – Most important loops tend have slow near or true integrating responses with

extreme sensitivity to SP and FRV overshoot, split range crossings and utility interactions. Load disturbances originating from cells are incredibly slow.

Automation System and Process Dynamics in a Control Loop

9

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)

10

Kick from filtered

derivative mode (e.g., filter = 1/8 x rate time)

∆% CO2 = ∆% CO1

∆% SP

∆% CO1

Time (seconds)

Signal (%)

Step from proportional mode Repeat from

Integral mode

No setpoint filter or lead-lag

Structure of PID on error (β=1 and γ=1)

seconds/repeat

Contribution of Each PID Mode

Why Reset Time is Set Too Small for Near-True Integrating & Runaway Processes

11

Looking at digital values humans think steam valve should be open, which is what will happen if there is more reset than gain action

Should steam or water valve be open for this liquid reactor ?

SP PV CO

52 48 ?

TC-100 Reactor Temperature

steam valve opens

water valve opens

50%

SP

Temperature

time

PV

Overshoot if steam valve is open

If integral action dominates, water valve won’t open

until error changes sign !

Peak and Integrated Error Metrics for Load Response

12

In gamesmanship, proponents of tuning methods and software show how close they get to the

optimum in simulation tests when in reality plants

are too nonlinear and non-ideal to make this realistic. The real value of figures and associated

equations is in realization of how dynamics and tuning relatively

affect loop performance.

“So Many Tuning Rules, So Little Time”, Control Global white paper: http://www.controlglobal.com/whitepapers/2014/so-many-tuning-rules-so-little-time/

The time to reversal of direction of the PV and start of the approach back to setpoint is the arrest time,

which is lambda for integrating process tuning rules.

Ratio of peak error to open loop error becomes 1 (no reduction in peak error) for dead time dominant processes and becomes dead time to time constant ratio for near integrating processes: Peak error is maximum PV excursion

Integrated error is area between PV and SP

SP

PV

http://www.controlglobal.com/whitepapers/2014/so-many-tuning-rules-so-little-time/

Rise Time, Overshoot & Undershoot Metrics for Setpoint Response

13

offci

r SPKKCOKSPT θ+

∆∗+∆∗∆

=)%)(|,%|(min

%

max

Controller gain (dimensionless)

Integrating process gain

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

Rise Time (sec) Open loop dead time

(sec)

Maximum allowable change in controller output (%)

PD on PV, I on E PID Structure

and slow reset time

The time for the PV to reach 63% of setpoint change is the closed loop time constant,

which is lambda for self-regulating process tuning rules.

Setpoint change (%)

Setpoint feedforward gain (dimensionless)

Ultimate Limit to Performance (Process Input Load Disturbance)

14

ooo

ox EE ∗

+=

)( τθθ

ooo

oi EE ∗

+=

)(

2

τθθ

Peak error is proportional to the ratio of loop deadtime 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 deadtime 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 deadtime 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

Attenuation by Process and by Automation System Time Constants

15

f

oof

tAAτπ ∗

=2

*

The attenuation of oscillations can be estimated from the expression of the Bode plot equation for the attenuation of oscillations slower than the break frequency where (τf ) is

the filter time constant, electrode or thermowell lag, or a mixed volume residence time

Equation is also useful for estimating original process oscillation amplitude from filtered oscillation amplitude to better know actual process variability (measurement lags and filters provide an attenuated view of real world)

Filtered Amplitude

Original Amplitude

Oscillation Period

Time Constant

Practical Limit to Performance (Process Input Load Disturbance)

16

oco

x EKK

E ∗∗+

=)1(

1

oco

fxii E

KKtT

E ∗∗

+∆+=

τ

Peak error decreases as the controller gain increases but is essentially the open loop error for systems when total deadtime >> process time constant

Integrated error decreases as the controller gain increases and reset time decreases but is essentially the open loop error multiplied by the reset time plus signal delays and lags for systems when total deadtime >> process time constant

Peak and integrated errors cannot be better than ultimate limit - The errors predicted by these equations for enhanced PID and deadtime compensators cannot be better

than the ultimate limit set by the loop deadtime and process time constant

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 – Control could be perfect if there is no noise or interaction

• PID tuning settings for max loop performance reduce to a function of dead time (gain inversely proportional to dead time and reset time and rate time directly proportional to dead time for near and true integrating and runway processes)

– Lambda = 0.6 x dead time for max performance for fixed and well known dynamics – Lambda = 3.0 x dead time for adverse changes in loop dynamics less than 5 – Lambda = 6.0 x dead time for adverse changes in loop dynamics less than 10 – Adverse changes are multiplicative (decreases in open loop time constant for self-

regulating and increases in open loop gain and loop dead time for all processes) • 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 oscillation periods between 2x and 10x dead time • Scan time and PID execution rates should not exceed 0.1x dead time • Oscillation periods greater than 10x dead time are indicative of too low of a PID

gain and valve problems (e.g., backlash, stiction and poor positioner designs) 17

Minimizing Measurement Dead Time

18

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)

Effect of PID Gain on Fast Disturbance Oscillations

19

Resonance results in PV amplitude in automatic greater than in manual

Filtering by process lag

Effect of PID Gain on Slow Disturbance Oscillations

20

Hi PID gain can effectively eliminate slow oscillation

Effect of Hi PID Gain on Near-Integrating Processes

21

Effect of Hi PID Gain on True Integrating Processes

22

Effect of Hi PID Gain on Runaway Processes

23

The Question

• If a loop is oscillating, should we decrease the PID gain?

24

Effect of Lo PID Gain on Near-Integrating Processes

25

Same scales as for Hi PID gain tests to show increases in oscillation period and amplitude

Effect of Lo PID Gain on True Integrating Processes

26


Effect of Lo PID Gain on Runaway Processes

27


Effect of Backlash Deadband in Integrating Processes

28


Window of Allowable PID Controller Gains

29

iic TK

K∗

>2

controller gain (dimensionless)

reset time (sec)

iic TK

K∗

>5.0

oic K

Kθ∗

=8.0

integrating process gain

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

dead time (sec)

oic K

Kθ∗

<6.1

To prevent the start of significant fast oscillations:

To prevent severe fast oscillations:

oic K

Kθ∗

<2.1

Maximum gain for smooth response:

To prevent the start of significant slow oscillations:

To prevent severe slow oscillations:

Simple Solution – Lambda Tuning for Integrating Processes

30

oiT θλ +∗= 2

2)( oi

ic K

TKθλ +∗

=

maximum dead time

(sec)

control objective arrest time

(sec)


reset time (sec)

Use Lambda Integrating Process Tuning Rules for Near-Integrating, True Integrating, and Runaway Processes

(All tuning rules shown are for ISA Standard Form PID)

[ ]),5.0(,25.0 soid MaxTMinT τθ∗∗=rate time (sec)

Setting reset time first and then controller gain per above tuning rules prevents violation of

low gain limit & prevents violation of high gain limit if arrest time is greater than maximum dead time !

Tuning for Level Control

31

max

max

FLAt fsr ∆

∆∗∗=

ρ level span (m)

flow span (kg/sec)

full scale residence time

(sec)

arrest time (sec)

Maximum allowable level change (%)

∆∆

∗=max

max

%%,

COPVtMax fsroθλ

Maximum allowable PID output change (%)

For level control by manipulation of liquid inlet or outlet flow the theoretical process dead time would be small. The actual total loop deadtime can be much larger. Sources of large level loop dead time is the time till correct response in boiling liquids due to inverse response, time it takes level rate of change to get through sensor noise or resolution or threshold sensitivity limit, heat transfer surface lags from manipulation of heat input, and time it takes PID output rate of change to get through VFD or valve deadband and resolution.

Modified Lambda Tuning Rules Self-Regulating Processes

32

[ ]ooi MaxT τθ ,4.0 ∗=

)( oo

ic K

TKθλ +∗

=

oo

oc K

Kθ

τ∗

∗= 5.0

[ ]),5.0(,25.0 soid MaxTMinT τθ∗∗=

A low limit is added to traditional equations to prevent a reset time smaller than ¼ the dead time for loops where time constant is very small compared to dead time to provide some gain action:

For maximum unmeasured disturbance rejection, a lambda equal to the dead time is used yielding equation seen in most other tuning methods (gain about ½ Ziegler Nichols Reaction Curve gain):

If the primary time constant is greater than ½ the dead time, derivative action may be beneficial

Closed loop time constant

(sec)

reset time (sec)


rate 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

• Setpoint rate limits: Provides directional move suppression to reduce split range crossings and 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 33

Advantages of PID Proportional Mode Gained through PID Options

• PID gain: – Provides a more immediate response whose magnitude decreases as the PV

approaches setpoint and stops changing if process variable has settled – Essential for minimizing peak error and rise time – Essential for missing self-regulation and overdriving output past final resting value

(FRV) for integrating and runaway processes – Essential in valve positioner to give immediate response – Reduces dead time and oscillations in PID controllers from valve backlash and

stiction and from measurement sensitivity and resolution limit – Judicious signal filter (e.g., 0.2 deadtime) prevents valve movement from gain action

on noise (PID output fluctuations kept less than valve deadband and resolution)

• External Reset Feedback turned on with BKCAL that is fast readback of manipulated variable PV (e.g., flow or valve position) enables:

– Suppression of oscillations from violation of cascade rule – Directional move suppression by setpoint rate limits on valve or secondary loop

– Prevention of unnecessary crossings of split range point – Gradual optimization and fast get away for valve position control and surge control – Suppression oscillations and optimize the transfer of variability from the controlled to the

manipulated variable achieving tight PV control with minimal upset to other loops – PID gain to be inverse of dead time dominant open loop self-regulating gain 34

Procedure

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

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

• For noise, use small PV filter time less than 0.2x dead time. • Choose PID options accordingly (e.g., use PID structure with no gain

or rate action on SP to minimize 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. 35

PID Structure

36

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) {equivalent to setpoint filter equal to reset time }

4. PD action on error (β = 1 and γ = 1) (no I action)

5. P action on error, D action on PV (β = 1 and γ = 0) (no I action)

6. ID action on error (γ = 1) (no P action)

7. I action on error, D action on PV (γ = 0) (no P action)

8. Two degrees of freedom controller (2DOF) (β and γ adjustable 0 to 1)

The β and γ factors do not affect the load response!

Effect of Beta on PID %PV Response in 2DOF Structure for Setpoint Change

37

Beta = 1 Beta = 0.5 Beta = 0.25

Beta = 0

Effect of Beta on PID %CO Response in 2DOF Structure for Setpoint Change

38

Beta = 1

Beta = 0.5

Beta = 0.25

Beta = 0

Series (Real) Form

39

Σ

∗

%SP

β

∆ proportional

integral

derivative

∗

Gain

∗

∗ ∗

∗

Inverse Reset Time

∗

Rate Time

∆

∆

γ

%CO

filter

filter

%PV filter

Filter Time = α ∗ Rate Time

Σ

Switch position for no derivative action

All signals are % of scale in PID algorithm but inputs and outputs are in engineering units

Most books show a more concise generic Laplace Transform Block Diagram - simpler

than this Time Domain Block Diagram

Series Form in analog controllers and early DCS available as a choice in most modern DCS

Settings are interactive in time domain but non-interactive in frequency domain

Parallel (Independent) Form

40

Parallel Form in a few early DCS and many PLC and in many control theory textbooks

Σ

∗

%SP

β

∆ proportional

integral

derivative

∗

Proportional Gain Setting

∗

∗

∗

∆

∆

γ

%CO filter

%PV filter

Integral Gain Setting

Derivative Gain Setting


ISA Standard Form

41

Σ

∗

%SP

β

∆ proportional

integral

derivative

∗

Gain

∗

∗ ∗

∗

∗

∆

∆

γ

%CO

filter

filter

%PV filter

Filter Time = α ∗ Rate Time


Rate Time

Default ISA Standard Form in most modern DCS

Inverse Reset Time

ISA Standard Form with External Reset Feedback

42

Gain

E-R is external reset (e.g. secondary % PVs)

Σ

% SP

β

derivative

∗

∗

∗ ∗ ∗

∆

∆

γ

% CO

filter

filter

% PV filter Filter Time = α ∗ Rate Time

Σ

filter

Filter Time = Reset Time

E-R

Positive Feedback


Out1

Out2 D

*P

∗

−

+

−

+

∆ +

−

*P = (β −1) ∗ Gain ∗ % SP

Rate Time

Switch position for external

reset feedback feedback

∆

For zero error Out1 = 0

For reverse action, Error = % SP − % PV

I

PI

Bias

Bias is used as input to Reset time filter block when there is “no integral action”. Bias is the PID output when the error is zero and is filtered by the reset time whose best setting is reduced to be about the dead time.

∆

Σ

Smart Preload

For structures with “No P action”: this Gain is zero for proportional mode, this Gain is one for integral mode and this Gain is equal to PID block gain setting for the derivative mode

This is the only known Time Domain Block Diagram showing positive feedback implementation of integral mode with external reset feedback for

ISA Standard Form

General and Specific PID Solutions

43

Standards

Certification

Education & Training

Publishing

Conferences & Exhibits

Questions?

pid options and solutions€¦ · dead time . maximum ramp rate . in 4 dead times is used . to...

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