PID Deadtime Compensation - Greg McMillan Deminar

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Demo and Seminar (Deminar) Series for Web Labs –

PID Deadtime Compensation PID Deadtime Compensation Oct 13, 2010

Sponsored by Emerson, Experitec, and MynahCreated by

Greg McMillan and Jack Ahlerswww.processcontrollab.com Website - Charlie Schliesser (csdesignco.com)

[File Name or Event]Emerson Confidential27-Jun-01, Slide 2 Slide 2

Welcome Welcome Gregory K. McMillan

– Greg is a retired Senior Fellow from Solutia/Monsanto and an ISA Fellow. Presently, Greg contracts as a consultant in DeltaV R&D via CDI Process & Industrial. 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 books on process control, his most recent being Essentials of Modern Measurements and Final Elements for the Process Industry. Greg has been the monthly “Control Talk” columnist for Control magazine since 2002. Greg’s expertise is available on the web site: http://www.modelingandcontrol.com/


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IntroductionIntroduction The first deadtime compensator to be significantly used in the process

industry was the Smith Predictor (1957)– The controller output is passed through a multiplier (process gain), filter (process time constant), and deadtime

(process deadtime) to create a model of the process with deadtime that is subtracted from PV

– The controller output is also passed through just a multiplier (process gain) and filter (process time constant) to create a model of the process without deadtime that is added to PV

– The user must adjust process gain, process time constant, and process deadtime

– The user and PID sees a PV without deadtime (special faceplate is needed to see actual PV)

Academic deadtime compensators are rarely used in industry The simplest deadtime compensator inserts a deadtime block in the

BK_CAL path (external reset) between the AO and PID blocks– Works for positive feedback integral mode (e.g. DeltaV) but not conventional integral mode (e.g. PRoVOX)

– Dynamic Reset Limit must be enabled (good idea anyway for slow valves and slow secondary loops)

– The user only needs to adjust the deadtime

– The user and PID sees the actual PV

– The external reset deadtime compensator is less sensitive than Smith Predictor to model errors

Myths exposed in this Deminar !– Deadtime is eliminated from loop

– Control is faster for existing tuning settings

– Compensator works better for loops dominated by a large deadtime

– An underestimate of the deadtime leads to instability (contrary to PID tuning calcs)

– An overestimate of the deadtime leads to sluggish response and greater stability (contrary to PID tuning calcs)


DelayDelay “Without deadtime I would be out of a job” Fundamentals

– A more descriptive name would be total loop deadtime. The loop deadtime is the amount of time for the start of a change to completely circle the control loop and end up at the point of origin. For example, an unmeasured disturbance cannot be corrected until the change is seen and the correction arrives in the process at the same point as the disturbance.

– Process deadtime offers a continuous train of values whereas digital devices and analyzers offer non continuous data values at discrete intervals, these delays add a phase shift and increase the ultimate period (decrease natural frequency) like process deadtime.

Goals– Minimize delay wherever it appears (the loop must see upset and enact a correction)

Sources – Pure delay from process deadtimes and discontinuous updates

• Piping, duct, plug flow reactor, conveyor, extruder, spin-line, and sheet transportation delays (process deadtimes set by mechanical design - remaining delays set by automation design)

• Digital device scan, update, reporting, and execution times (0.5T)• Analyzer sample processing and analysis cycle time (1.5T)• Sensitivity-resolution limits• Backlash-deadband

– Equivalent delay from lags• Mixing, column trays, dip tube size and location, heat transfer surfaces, and volumes in series

(process lags set by mechanical design - remaining lags set by automation design)• Thermowells• Electrodes • Transmitter damping • Signal filters


Time (seconds)

% Controlled Variable (CV) or

% Controller Output (CO)

CO

CV

o p2

Kp = CV CO

CV

CO

CV

Self-regulating processopen loop

negative feedback time constant

Self-regulating process gain (%/%)

Response to change in controller output with controller in manual

observed total loopdeadtime

Self-Regulating Process Open Loop Response

Self-Regulating Process Open Loop Response

oor

Maximum speedin 4 deadtimes

is critical speed


Loop Block Diagram(First Order Approximation)

Loop Block Diagram(First Order Approximation)

p1 p2 p2 Kpvp1

c1 m2 m2 m1 m1Kcvcc2

Kc Ti Td

Valve Process

Controller Measurement

Kmvvv

KLLL

Load Upset

CV

CO

MVPV

PID

Delay Lag

Delay Delay Delay

Delay

Delay

Delay

Lag Lag Lag

LagLagLag

Lag

Gain

Gain

Gain

Gain

LocalSet Point

DV

First Order Approximation: ov p1 p2 m1 m2 c

vp1m1m2c1 c2

(set by automation system design for analyzer, flow, pressure, level, speed, surge, and static mixer control)

%

%

%

Delay <=> Dead TimeLag <=>Time Constant

Ki = Kmv(Kpv / p2 ) Kcv

100% / span


Practical Limit to Loop PerformancePractical Limit to Loop Performance

ocp

x EKK

E

)1(

1

ocp

fxii E

KK

tTE

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 predictedby these equations for the PIDPlus and for a deadtime compensator cannot be better

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

Open loop error forfastest and largestload disturbance


Ultimate Limit to Loop PerformanceUltimate Limit to Loop Performance

opo

ox EE

)(

opo

oi EE

)(

2

Peak error is proportional to the ratio of loop deadtime to 63% response time

Integrated error is proportional to the ratio of loop deadtime squared to 63% response time

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

found from the equation for attenuation

Total loop deadtimethat is often set byautomation design

Largest lag in loopthat is ideally set bylarge process volume


Fastest Practical PID Tuning Settings(For Maximum Load Disturbance Rejection)Fastest Practical PID Tuning Settings(For Maximum Load Disturbance Rejection)

op

pc KK

24.0oiT 2 1d pT

Self-Regulating Processes

oiT 5.0

For a process dominated by a process deadtime (p2 << o):

0d T

For deadtime compensatorthis factor can be increasedto 1.0 for accurate deadtime

For a process dominated by a process lag (p2 >> o):

pc KK

14.0

For deadtime compensatorthis factor can be increasedto 1.0 for accurate deadtime.Also 1.0 for PIDPlus and largeanalyzer or wireless update delay

For deadtime compensatorthe reset time can be set equal to the process lagfor accurate deadtime


Smith PredictorEmbedded Composite

PID OUT

PID PV bias

PID PV without deadtime

PID PV with deadtime

Smith Predictor Deadtime CompensatorSmith Predictor Deadtime Compensator

Three parameters to adjust (gain, time constant, and deadtime)PID PV is modeled PV without deadtime (faceplate loses actual PV)

More sensitive to errors in model (see Advanced Application Note 3)

http://www.modelingandcontrol.com/repository/AdvancedApplicationNote003.pdf


External Reset Deadtime CompensatorExternal Reset Deadtime Compensator

Simply

insert

deadtime

block

Must enable dynamic reset limit !

Just one parameter to adjust (deadtime)


Deadtime Compensation Demo 1Deadtime Compensation Demo 1(Process Lag > Process Delay)(Process Lag > Process Delay)

Deadtime Compensation Demo 1Deadtime Compensation Demo 1(Process Lag > Process Delay)(Process Lag > Process Delay)

Objective – Show improvement in loop performance by deadtime compensation and sensitivity to deadtime estimate for loop dominated by process lag

Activities:– Go to Main Display, select Single Loop Lab01, and click on any block– In Process detail, set primary Delay = 1 sec and secondary Delay = 1 sec – In Process detail, set primary Lag 2 = 10 sec and secondary Lag 2 = 1 sec – Enter tuning settings: Gain = 1.0, Reset = 10 sec, Rate = 0 sec – Enable setpoint metrics make setpoint change 50% to 60% and note metrics – In PID Detail, enable Dynamic Reset Limit and set PID Deadtime = 4 sec– Make PID setpoint change from 60% to 50% and note metrics– Click on PID faceplate and then on its Detail icon (faceplate lower left corner) – Set Gain = 2.5 make setpoint change 50% to 60% and note metrics– Set Reset = 5.0 sec make setpoint change 60% to 50% and note metrics– Set Reset = 10.0 sec (original setting)– Set PID Deadtime = 2 sec make setpoint change 50% to 60% and note metrics– Set PID Deadtime = 8 sec make setpoint change 60% to 50% and note metrics– Set PID Deadtime = 16 sec make setpoint change 50% to 60% and note metrics


Objective – Show improvement in loop performance by deadtime compensation and sensitivity to deadtime estimate for loop dominated by process delay

Activities:– Put PID in Manual with output = 50% and setpoint = 50%– In Process detail, set primary Delay = 9 sec and secondary Delay = 1 sec – In Process detail, set primary Lag 2 = 1 sec and secondary Lag 2 = 1 sec – Enter tuning settings: Gain = 0.4, Reset = 5 sec, Rate = 0 sec – Disable Dynamic Reset Limit, set PID deadtime = 0 sec, and put PID in Auto – Enable setpoint metrics make setpoint change 50% to 60% and note metrics– In PID Detail, enable Dynamic Reset Limit and set PID Deadtime = 11 sec– Make PID setpoint change from 60% to 50% and note metrics– Set Gain = 1.0 make setpoint change 50% to 60% and note metrics– Set Reset = 1.0 sec make setpoint change 60% to 50% and note metrics– Set Reset = 0.6 sec make setpoint change 50% to 60% and note metrics– Set PID Deadtime = 8 sec make setpoint change 60% to 50% and note metrics– Set PID Deadtime = 12 sec make setpoint change 50% to 60% and note metrics– Set PID Deadtime = 14 sec make setpoint change 60% to 50% and note metrics– Set PID Deadtime = 11 sec (original setting) and note stabilization of loop

Deadtime Compensation Demo 2Deadtime Compensation Demo 2(Process Delay > Process Lag)(Process Delay > Process Lag)

Deadtime Compensation Demo 2Deadtime Compensation Demo 2(Process Delay > Process Lag)(Process Delay > Process Lag)


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Summary of Deadtime CompensatorTest Results (Myth Busters)

Summary of Deadtime CompensatorTest Results (Myth Busters)

Deadtime is not eliminated by a deadtime compensator. The ultimate limit to loop performance of unmeasured load disturbances is still dictated by total loop deadtime (the loop cannot correct until it sees the upset and enacts a change that compensates for the upset).

The response of a PID with deadtime compensation will be slower unless the PID is retuned to have a much higher gain.

Improvement in performance is greater for loops where process lag > process delay (good news since few loops are deadtime dominant).

A decrease in estimated deadtime causes response to degrade to a PID without deadtime compensation.

An increase in estimated deadtime causes a jagged response. A loop dominated by a process lag is much less sensitive to a larger than needed deadtime than a loop dominated by a process deadtime.

To minimize rise time and peak error, the PID gain is increased. For loops dominated by a process lag, only the PID gain is increased. For loops dominated by a process delay, the PID gain is increased and

the reset time is decreased. The larger the process delay is compared to the process lag, the greater is the decrease in the reset time. If the reset time is not decreased, there will be severe undershoot.


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PID Deadtime Compensation - Greg McMillan Deminar

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