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ISA Saint Louis Short Course Dec 6-8, 2010

Exceptional Process Control Opportunities - An Interactive Exploration of Process Control Improvements - Day 1

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/

http://www.modelingandcontrol.com/

Top Ten Things You Don’t Want to Hear in a Project Definition Meeting

• (10) I don’t want any smart instrumentation talking back to me• (9) Let’s study each loop to see if the valve really needs a positioner• (8) Lets slap an actuator on our piping valves and use them for control

valves• (7) We just need to make sure the control valve spec requires the

tightest shutoff• (6) What is the big deal about process control, we just have to set the

flow per the PFD• (5) Cascade control seems awfully complex• (4) The operators can tune the loops• (3) Let’s do the project for half the money in half the time• (2) Let’s go with packaged equipment and let the equipment supplier

select and design the automation system• (1) Let’s go out for bids and have purchasing pick the best deal

• “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 (the loop cannot do anything until it sees and enacts change)

• 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 system 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 system design)– Thermowells– Electrodes – Transmitter damping – Signal filters

(1) - Delay

Top Ten Concepts

• “Speed kills - (high speed processes and disturbances and low speed control systems can kill performance)”

• Fundamentals– The rate of change in 4 deadtime intervals is most important. By the end of 4 deadtimes,

the control loop should have completed most of its correction. Thus, the short cut tuning method (near-integrator) is consistent with performance objectives.

• Goals– Make control systems faster and make processes and disturbances slower

• Sources– Control system

– PID tuning settings (gain, reset, and rate)– Slewing rate of control valves and velocity limits of variable speed drives

– Disturbances– Steps - Batch operations, on-off control, manual actions, SIS, startups, and shutdowns– Oscillations - limit cycles, interactions, and excessively fast PID tuning– Ramps - reset action in PID

– Process– Degree of mixing in volumes due to agitation, boiling, mass transfer, diffusion, and migration

(2)- Speed

Top Ten Concepts

• “All is lost if nothing is gained”• Fundamentals

– Gain is the change in output for a change in input to any part of the control system. Thus there is a gain for the PID, valve, disturbance, process, and measurement. Knowing the disturbance gain (e.g. change in manipulated flow per change in disturbance) is important for sizing valves and feedforward control.

• Goals– Maximize control system gains (maximize control system reaction to change) and

minimize process and disturbance gains (minimize process reaction to change).• Sources

– PID controller gain – Inferential measurements (e.g. temperature change for composition change in distillation

column) – Slope of control valve or variable speed drive installed characteristic (inherent

characteristic & system loss curve)– Measurement calibration (100% / span). Important where accuracy is % of span– Process design– Attenuation by upstream volumes (can be estimated)– Attenuation by upstream PID loops (transfer of PV variability to controller output)

• For a discussion of unifying concepts check out Deminar #9 “Process Control Improvement Primer” Sept 8, 2010 Recording:http://modelingandcontrol.com/

(3) - Gain

Top Ten Concepts

http://modelingandcontrol.com/

(4) - Resonance

• “Don’t make things worse than they already are”• Fundamentals

– Oscillation period close to ultimate period can be amplified by feedback control

• Goals– Make oscillation period slower or control loop faster

• Sources– Control loops in series with similar loop deadtimes (e.g. multiple stage pH

control)

– Control loops in series with similar tuning and valve sticktion and backlash

– Day to night ambient changes to slow loops (e.g. column temperature control)

Top Ten Concepts

(4) - Resonance

Top Ten Concepts

1

UltimatePeriod

1

1FasterTuning

Log of Ratio ofclosed loop amplitudeto open loop amplitude

Log of ratio ofdisturbance periodto ultimate period

no attenuationof disturbances

resonance (amplification) of disturbances

amplitude ratio isproportional to ratio ofbreak frequency lag to

disturbance period

1

no better than manual worse than manual improving control

For all of you frequency response and Bode Plot Fans

(5) Attenuation

• “If you had a blend tank big enough you would not need control”• Fundamentals

– Attenuation increases as the volume of the blend tank increases and the ultimate period of the control loop decreases.

• Goals– Maximize attenuation by increasing volume and mixing and making loops faster

• Sources– Mixed volume size and degree of mixing

– Control loop speed

Top Ten Concepts

f

oof

tAA

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 (f) 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 a attenuated view of real world)

(5) Attenuation

Top Ten Concepts

(6) Sensitivity- Resolution

• “You cannot control what you cannot see”• Fundamentals

– Minimum change measured or manipulated - once past sensitivity limit full change is seen or used but resolution limit will quantize the change (stair step where the step size is the resolution limit). Both will cause a limit cycle if there is an integrator in the process or control system.

• Goals– Improve sensitivity and resolution

• Sources– In measurements, minimum change detected and communicated (e.g. sensor

threshold and wireless update trigger level) and quantized change (A/D & D/A)

– Minimum change that can be manipulated (e.g. valve stick-slip sensitivity and speed resolution)

Top Ten Concepts


Top Ten Concepts

o

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ActualTransmitter Response

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Top Ten Concepts

Digital Updates

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Resolution

(7) Hysteresis-Backlash

• “No problem if you don’t ever change direction”• Fundamentals

– Hysteresis is the bow in a response curve between full scale traverses in both directions. Normally much smaller and less disruptive than backlash

– Backlash (deadband) is minimum change measured or manipulated once the direction is changed - once past backlash-deadband limit you get full change

– Both Hysteresis and backlash will cause a limit cycle if there are 2 or more integrators in the process or control system.

• Goals– Minimize backlash and deadband

• Sources– Pneumatic instrument flappers, links, and levers (hopefully these are long gone)

– Rotary valve and damper links, connections, and shaft windup

– Variable speed drive setup parameter to eliminate hunting and chasing noise

Top Ten Concepts


Top Ten Concepts

Digital Updates

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0%

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Hysteresis

Hysteresis


Top Ten Concepts

Backlash (Deadband)

Deadband is 5% - 50%without a positioner !

Deadband

Signal (%)

0

Stroke (%)

Digital positionerwill force valve

shut at 0% signal

Pneumatic positionerrequires a negative % signal to close valve

(8) Repeatability-Noise

• “The best thing you can do is not react to noise”• Fundamentals

– Noise is extraneous fluctuations in measured or manipulated variables

– Repeatability is difference in readings for same true value in same direction

– Often repeatability is confused with noise

• Goals– Minimize size and frequency of noise and do not transfer noise to process

• Sources– Noise

– Bubbles– Concentration and temperature non-uniformity from imperfect mixing– Electromagnetic interference (EMI)– Ground loops– Interferences (e.g. sodium ion on pH electrode)– Velocity profile non-uniformity – Velocity impact on pressure sensors

– Repeatability– Sensitivity and resolution

Top Ten Concepts


Top Ten Concepts

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Repeatability

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Transmitter Response


Official definition of repeatabilityobtained from calibration tests


Top Ten Concepts

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0

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Transmitter Response


Practical definition of repeatabilityas seen on trend charts


Top Ten Concepts

Noise as seen on trend charts

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• There is always an offset and drift, it is matter of size and consequence• Fundamentals

– The deviation of the peak in the distribution of actual values from true value

– Drift shows up as a slowly changing offset

• Goals– Minimize offset and nonlinearity by smart transmitters and sensor matching and

smart tuned digital positioners with accurate internal closure member feedback

• Sources– Manufacturing tolerance, degradation, de-calibration, and installation effects

(process and ambient conditions and installation methods and location)

(9) Offset-Drift

Top Ten Concepts

(9) Offset-Drift

Top Ten Concepts

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(9) Offset-Drift

Top Ten Concepts

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xDrift = 1% per month

xxxxxx xxxx

Drift (Shifting Bias)

(10) Nonlinearity

• “Not a problem if the process is constant, but then again if the process is constant, you do not need a control system”

• Fundamentals– While normally associated with a process gain that is not constant, in a broader

concept, a nonlinear system occurs if a gain, time constant, or delay changes anywhere in the loop. All process control systems are nonlinear to some degree.

• Goals– Minimize nonlinearity by process and equipment design (e.g. reagents and heat

transfer coefficients), smart transmitters and sensor matching, valve selection, signal characterization, and adaptive control

• Sources– Control valve and variable speed drive installed characteristics (flat at high flows)– Process transportation delays (inversely proportional to flow)– Digital and analyzer delays (loop delay depends upon when change arrives in

discontinuous data value update interval)– Inferred measurement (conductivity or temperature vs. composition plot is a curve)– Logarithmic relationship (glass pH electrode and zirconium oxide oxygen probe)– Process time constants (proportional to volume and density)

Top Ten Concepts

(10) Nonlinearity

Top Ten Concepts

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Good Accuracy and Good Precision2-Sigma

Bias

2-SigmaTrue and

Measured Values

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s

TrueValue

Measured Values

Good Accuracy and Poor Precision

2-Sigma 2-Sigma

Bias

True andMeasured

Values

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Measured ValuesF

requ

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Poor Accuracy and Good Precision2-Sigma

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Accuracy and PrecisionAccuracy and Precision

Top Ten Concepts

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

oor

Maximum speedin 4 deadtimes

is critical speed

Self-Regulating Process Open Loop Response

Improving Dynamics

Time (seconds)o

Ki = { [ CV2 t2 ] CV1 t1 ] } CO

CO

ramp rate isCV1 t1

ramp rate isCV2 t2

CO

CV

Integrating process gain (%/sec/%)

Response to change in controller output with controller in manual% Controlled Variable (CV)

or% Controller Output (CO)

observed total loopdeadtime


is critical speed

Integrating Process Open Loop Response

Improving Dynamics

Response to change in controller output with controller in manual

o ’p2

Noise Band

Acceleration

CV

CO

CV

Kp = CV CO

Runaway process gain (%/%)

% Controlled Variable (CV) or

% Controller Output (CO)

Time (seconds)observed total loopdeadtime

runaway processopen loop

positive feedback time constant

For safety reasons, tests are terminated after 4 deadtimes

’oor


is critical speed

Runaway Process Open Loop Response

Improving Dynamics

CV change in controlled variable (%) CO change in controller output (%) Kc controller gain (dimensionless) Ki integrating process gain (%/sec/% or 1/sec) Kp process gain (dimensionless) also known as open loop gain DV = disturbance variable (engineering units) MV manipulated variable (engineering units) PV process variable (engineering units) t change in time (sec) tx execution or update time (sec) ototal loop dead time (sec) ffilter time constant or well mixed volume residence time (sec) mmeasurement time constant (sec) p2primary (large) self-regulating process time constant (sec) ’p2primary (large) runaway process time constant (sec) p1secondary (small) process time constant (sec) Ti integral (reset) time setting (sec/repeat) Td derivative (rate) time setting (sec) to oscillation period (sec) Lambda (closed loop time constant or arrest time) (sec) fLambda factor (ratio of closed to open loop time constant or arrest time)

Nomenclature

Improving Dynamics

Phase Shift () and Amplitude Ratio (B/A)

A B

time

phaseshift

oscillationperiod To

If the phase shift is -180o between the process input A and output B, then the total shift for a control loop is -360o and the output is in phase with the input (resonance) sincethere is a -180o from negative feedback (control error = set point – process variable).This point sets the ultimate gain and period that is important for controller tuning.

Improving Dynamics

For frequency response and Bode plot fans

Basis of First Order Approximation

=Tan-1() negative phase shift(as approaches infinity, approaches -90o phase shift)

t = (-360 To time shift

B 1AR = ---- = ----------------------- amplitude ratio A [1 + (] 1/2

Amplitude ratios are multiplicative (AR = AR1AR2) and phase shifts are additive ()asis of first order approx method where gains are multiplicative and dead times are additive

Improving Dynamics

For a self-regulating process

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 flow, pressure, level, speed, surge, and static mixer pH control)

%

%

%

Delay <=> Dead TimeLag <=>Time Constant

For integrating processes: Ki = Kmv(Kpv / p2 ) Kcv

100% / span

Loop Block Diagram (First Order Approximation)

Hopefully p2 is the largest lag in the loop

Improving Dynamics

CV change in controlled variable (%) CO change in controller output (%) Kc controller gain (dimensionless) Ki integrating process gain (%/sec/% or 1/sec) Kp process gain (dimensionless) also known as open loop gain DV = disturbance variable (engineering units) MV manipulated variable (engineering units) PV process variable (engineering units) t change in time (sec) tx execution or update time (sec) ototal loop dead time (sec) ffilter time constant or well mixed volume residence time (sec) mmeasurement time constant (sec) p2primary (large) self-regulating process time constant (sec) ’p2primary (large) runaway process time constant (sec) p1secondary (small) process time constant (sec) Ti integral (reset) time setting (sec/repeat) Td derivative (rate) time setting (sec) to oscillation period (sec) Lambda (closed loop time constant or arrest time) (sec) fLambda factor (ratio of closed to open loop time constant or arrest time)

Nomenclature

Improving Dynamics

opo

ox EE

)(

opo

oi EE

)(

2

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 largerthan the process time constant, the unfiltered actual process variable error can be

found from the equation for attenuation

Ultimate Limit to Loop Performance

Total loop deadtimethat is often set byautomation design

Largest lag in loopthat is ideally set bylarge process volume

Improving Dynamics

oL EeE Lo )1( /

Effect of load disturbance lag (L) on peak error can be estimated by replacing the open loop error with the exponential response of the disturbance during the loop deadtime

Disturbance Speed and Attenuation

For Ei (integrated error), use closed loop time constant instead of deadtime

Improving Dynamics

Effect of Disturbance Lag on Integrating Process

Periodic load disturbance time constant increased by factor of 10

Adaptive loop

Baseline loopAdaptive loop

Baseline loop

Primary reason why bioreactor control looptuning and performance for load upsets is anon issue!

Improving Dynamics

Accessing On-Demand and Adaptive Tuning

Click on magnifying glass to getdetail view of limits and tuning

Click on Duncan to get DeltaV Insight for “On-Demand” and “Adaptive” tuning

Improving Dynamics

Effect of Dynamics LabEffect of Dynamics Lab• Objective – Show the effect of deadtime on ultimate period and tuning

• Activities:1. Go to Main Display, select Single Loop Lab01, 2. Click on AC1-1 PID Faceplate and Click on magnifying glass icon to get Detail display 3. Click on Duncan icon for “Tune with Insight” and click on top tab “On Demand Tuning”4. Verify expert option is checked and click on “Test” for “On Demand Tuning”5. Note ultimate period and “Ziegler-Nichols - PI” tuning settings6. Update PID tuning settings and change mode from Explore to Run7. After run is finished, note metrics, and then click on any block in block diagram of loop8. Click on top tab for Process detail and increase Primary Delay from 1 to 5 sec9. Click on “Test” for “On Demand Tuning”10. Note ultimate period and “Ziegler-Nichols - PI” tuning settings11. Update PID tuning settings and change mode from Explore to Run12. After run is finished, note metrics, and decrease Primary Delay from 5 to 1 sec13. Click on top tab for Measurements detail and increase Delay from 0 to 4 sec14. Click on “Test” for “On Demand Tuning”15. Note ultimate period and “Ziegler-Nichols - PI” tuning settings16. Update PID tuning settings and change mode from Explore to Run17. After run is finished, note metrics, and decrease Measurement Delay from 4 to 0 sec18. Restore PID gain to 1.0 and reset time to 10 sec

Improving Dynamics

Top Ten Things Missing in University Courses on Process Control

• (10) Control valves with stick-slip and deadband• (9) Measurements with repeatability errors and turndown limits• (8) Volumes with variable mixing and transportation delays• (7) Process input load disturbance• (6) Control action (direct & reverse) & valve action (inc-open & inc-close)• (5) PID algorithms using percent • (4) PID structure, anti-reset windup, output limits, and dynamic reset• (3) Industry standards for function blocks and communication• (2) “Control Talk”• (1) My books

Improving Tuning - Part 1

Contribution of Each PID Mode


• Proportional (P mode) - increase in gain increases P mode contribution– 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

• Integral (I mode) - increase in reset time decreases I mode contribution– Provides a ramping reaction to error (SP-PV) to 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 of setpoint (no sense of direction)

• Derivative (D mode) - increase in rate time increases D mode contribution– 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 oscillation in approach to setpoint

Contribution of Each PID Mode


CO2 = CO1

SP

seconds/repeatCO1

Time(seconds)

Signal (%)

0

kick fromproportional

mode

bump fromfiltered

derivativemode

repeat from integralmode

Contribution of Each PID Mode for a Step Change in the Set Point

( and )

SPPVIVP

52 48 ?

TC-100Reactor Temperature

steam valveopens

watervalveopens

50%

set point

temperature

time

PV

Should steam or water valve be open ?

Reset Gives Operations What They Want


Open Loop Time Constant (controller in manual)

CO

Time(seconds)

Signal (%)

0 o

Dead Time (Time Delay)

p

Open Loop(process)

Time Constant (Time Lag)

CVSP

Controller is in Manual

Open LoopError Eo (%)

0.63Eo


Closed Loop Time Constant (controller in auto)

CO

Time(seconds)

Signal (%)

0 o

Dead Time (Time Delay)

c

Closed Loop Time Constant

(Time Lag)Lambda ()

CV

SP

Controller is in Automatic

SP (%)

0.63SP


Conversion of Signals for PID Algorithm

SensingElement

ControlValve

AOPIDSCLR

AI

SCLR

SCLR%

% %SUB

CVSP

%

CO OUT(e.u.)

ProcessEquipment

SmartTransmitterPV - Primary Variable

SV - Second Variable*TV - Third Variable*FV - Fourth Variable*

PV(e.u.)

PID

DCS

MV(e.u.)

The scaler block (SCLR) that convert between engineering units of application and % of scaleused in PID algorithm is embedded hidden part of the Proportional-Integral-Derivative block (PID)

Final Element

Measurement* - additional HART variables

PV(e.u.)

To compute controller tuning settings, the process variable and controller outputmust be converted to % of scale and time units of deadtimes and time constantsmust be same as time units of reset time and rate time settings!


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 deadtime compensators cannot be better

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

Practical Limit to Loop Performance

Open loop error forfastest and largestload disturbance


)(5.0 oi

Slow tuning (large Lambda) creates an implied deadtime where the loop performsabout the same as a loop with fast tuning and an actual deadtime equal to the

implied deadtime (i)

Implied Deadtime from Slow Tuning

For most aggressive tuning Lambda is set equal to observed deadtime(implied deadtime is equal to observed deadtime)

Money spent on improving measurement and process dynamics(e.g. reducing measurement delays and process deadtimes)

will be wasted if the controller is not tuned faster to take advantage of the faster dynamics

You can prove most any point you want to make in a comparisonof control system performance, by how you tune the PID.Inventors of special algorithms as alternatives to the PID

naturally tend to tune the PID to prove their case. For example Ziegler-Nichols tuning is often used to show excessive

oscillations that could have be eliminated by cutting gain in half


In this self-regulating process the original process delay (dead time) was 10 sec. Lambda was 20 sec and the sample time was set at 0, 5, 10, 20, 30, and 80 sec (Loops 1 - 6)

The loop integrated error increased slightly by 1%*sec for a sample time of 10 sec which corresponded to atotal deadtime (original process deadtime + 1/2 sample time) equal to the implied deadtime of 15 seconds.

http://www.modelingandcontrol.com/repository/AdvancedApplicationNote005.pdf

sample time = 0 sec

sample time = 5 sec

sample time = 10 sec




Effect depends on tuning, which leads to miss-guided generalities based on process dynamics

Effect of Implied Deadtime on Allowable Digital or Analyzer Delay


http://www.modelingandcontrol.com/repository/AdvancedApplicationNote005.pdf

Lambda Tuning for Self-Regulating ProcessesLambda Tuning for Self-Regulating Processes

CO

CVK p

)( opfp

ic K

TK

piT

Self-Regulation Process Gain:

Controller Gain

Controller Integral Time

pf Lambda (Closed Loop Time Constant)

Lambda tuning excels at coordinating loops for blending,fixing lower loop dynamics for model predictive control,

and reducing loop interaction and resonance


Lambda Tuning for Integrating ProcessesLambda Tuning for Integrating Processes

Integrating Process Gain:

Controller Gain:

Controller Integral (Reset) Time:

Lambda (closed loop arrest time) is defined in terms of a Lambda factor (f):

if K/ Closed loop arrest timefor load disturbance

CO

tCVtCVKi %

/%/% 1122

2])/[( oifi

ic KK

TK

oifi KT )/(2

Controller Derivative (Rate) Time:

pdT

To prevent slow rolling oscillations:

iic K

TK2

*

secondary lag


Fastest Possible Tuning (Lambda Tuning Method)

oic K

K

1

5.0

opf For max load rejection set lambda equal to deadtime

piT o

p

pi

KK

Substitute

)( op

ic K

TK

Into

Tuning for max disturbance rejection(Ziegler Nichols reaction curve method gain factor would be 1.0 instead of 0.5)

oiT 4

oiT 10

For setpoint response to minimize overshoot


Near Integrator Approximation (Short Cut Tuning Method)

COtCVMaxK

Kp

pi /)/(

For “Near Integrating” gain approximation use maximum ramp rate divided by change in controller output

The above equation can be solved for the process time constant by taking the process gain to be 1.0 or for more sophistication as the

average ratio of the controlled variable to controller output

Tuning test can be done for a setpoint change if the PID gain is > 2 and the PID structure is

“PI on Error D on PV” so you see a step change in controller output from the proportional mode


Fastest Controller Tuning (ultimate oscillation method*)

Kc Ku

Ti = 1.0 * u

Td = 0.1 u

For integrating processes or for self-regulating processes where p >> o,

double the factor for reset time (0.5 => 1.0) and add rate time if the process noise is negligible.

The oscillations associated with quarter amplitude decay is about ½ the ultimate gain. Thus if we use quarter amplitude decaying oscillations for the test, we take ½ of the controller gain that caused these oscillations to get ¼ of the ultimate gain

These tuning equations provide maximumdisturbance rejection but will cause

some overshoot of setpoint response


* - Ziegler Nichols method closed loop modifiedto be more robust and less oscillatory

op

pc K

K

24.0oiT 4 1d pT

For runaway processes:

For self-regulating processes:

oic K

K

1

5.0oiT 4 1d pT

oic K

K

1

6.0

oiT 40 1d 2 pT

For integrating processes:

op

pc K

K

2'6.0

oic K

K

1

4.0

Near integrator (p2 >> o):

oiT 5.0

Near integrator (’p2 >> o):

Deadtime dominant (p2 << o):

0d Tp

c KK

14.0


Fastest Controller Tuning (reaction curve method*)

These tuning equations provide maximumdisturbance rejection but will cause

some overshoot of setpoint response

* - Ziegler Nichols method closed loop modifiedto be more robust and less oscillatory

Ultimate Period and Ultimate Gain

Time(min)

Measurement (%)

Ultimate Gain is Controller Gain that Causedthese Nearly Equal Amplitude Oscillations (Ku)

Set Point

Ultimate Period Tu

0

If po then Tu If po then u


Set Point

Time(min)

Measurement (%)

Offset

110% of o

Quarter Amplitude Period Tq

0

Damped Oscillation - (Proportional Only Control)


1. Put the controller in auto at normal setpoint. 2. Choose largest step change in controller setpoint that is safe. Increase the reset

time by a factor of 10x for test.3. Add a PV filter to keep the controller output fluctuations from noise within the valve

deadband.4. Step the controller setpoint. If the response is non-oscillatory, increase the

controller gain and step the controller setpoint in opposite direction. Repeat until you get a slight oscillation (ideally ¼ amplitude decay). Make sure the controller output is not hitting the controller output limits and is on the sensitive part of the control valve’s installed characteristic.

5. Estimate the period of the oscillation. Reduce the controller gain until the oscillation disappears (½ current gain), set the reset time equal to ½ the period, and the rate time equal to ¼ of the reset time. If the oscillation is noisy or resembles a square wave or the controller gain is high (e.g. > 10), set the rate time to zero. The factors are ½ the ultimate period and twice the ultimate gain factors because the controller gain that triggered the ¼ amplitude oscillation is about ½ the ultimate gain and the ¼ amplitude period is larger than the ultimate period.

6. If a high controller gain is used (e.g. > 10) use setpoint rate of change (velocity) limits if a big kick in the controller output for setpoint changes from proportional action on error ( > 0) is disruptive to operations.

7. Make setpoint changes across the range of operation to make sure an operating point with a higher controller gain or larger process deadtime does not cause oscillations. Monitor the loop closely over several days of operation.

Damped Oscillation Tuning Method


Traditional Open Loop Tuning Method 1. Choose largest step change in controller output that is safe.

2. Add a PV filter to keep the controller output fluctuations from noise within the valve deadband.

3. Make a change in controller output in manual.

4. Note the time it take for the process variable to get out of the noise band as the loop deadtime.

5. Estimate the process time constant as the time to reach 63% of the final value.

6. Estimate the process gain as final change in the process variable (%) after it reaches a steady state divided by change in the controller output (%).

7. To use reaction curve tuning, set the controller gain equal to ½ the process time constant divided by the product of the process gain and deadtime.

8. If the process lag is much larger than the loop deadtime, set the reset time setting equal to 4x the deadtime and set the rate time setting equal to the deadtime. If process lag is much smaller than the loop deadtime, set the reset time to 0.5x the loop deadtime and the rate time to zero.

9. If a high controller gain is used (e.g. > 10) use setpoint rate of change (velocity) limits if a big kick in the controller output for setpoint changes is disruptive to operations (for PID structures with > 0).



Short Cut Ramp Rate Tuning Method

1. Choose largest step change in controller output and setpoint that is safe. If the test is to be made in auto, increase the reset time by factor of 10x for test.

2. Add a PV filter to keep the controller output fluctuations from noise within the valve deadband. Measure the initial rate of change of the process variable (PV1/t).

3. Make a either a change in controller output in manual or change in set point in auto4. Note the time it take for the for the process variable to get out of the noise band as

the loop deadtime.

5. Estimate the rate of change of the process variable (PV2/t) over successive deadtime intervals (at least two). Choose the largest rate of change. Subtract this from initial rate of change of the process variable and divide the result by the step change in controller output to get the integrating process gain.

6. To use reaction curve tuning, set the controller gain equal to 0.4 the inverse of the product of integrating process gain and loop deadtime (Equation 7). • If the inverse of the integrating gain is much larger than the loop deadtime, set the reset time

setting equal to 4x the process deadtime and set the rate time setting equal to the process deadtime, otherwise set the reset time to 0.5x the process deadtime and the rate time to zero

7. If a high controller gain is used (e.g. > 10) use setpoint rate of change (velocity) limits if a big kick in the controller output for setpoint changes is disruptive to operations (for PID structures with > 0)



Manual Tuning LabManual Tuning Lab

• Objective – Gain experience with manual tuning methods to appreciate auto tuning

• Activities:1. Go to Main Display, and select Single Loop Lab01

2. Click on any block in block diagram

3. In Process detail, set Primary Process Lag 2 = 30 sec for Inc and Dec

4. Click on AC1-1 PID Faceplate and Click on magnifying glass icon to get Detail display

5. Tune PID with damped oscillation method and note tuning settings

6. Tune PID with traditional open loop method and note tuning settings

7. Tune PID with short cut tuning method and note tuning settings


On-Demand Tuning Algorithm

Time(min)

Ultimate Period Tu

0

Set Point

d

a

Ultimate Gain 4 d Ku = e

n

e = sq rt (a2 - n2) If n = 0, then e = aalternative to n is a filter to smooth PV

Signal (%)


Adaptive Tuning Algorithm


Pure Gain Process

K

Estimated Gain

Multiple Model Interpolation with Re-centering

K

Estimated Gain

Multiple Model Interpolation with Re-centering

Changing Process Input

2( ) ( ( ) ( ) ) iE t y t Yi t

For each iteration, the squared error is computed for every model I each scan

Where:is the process output at the time tis i-th model output

A norm is assigned to each parameter value k = 1,2,….,m in models l = 1,2,…,n.

if parameter value is used inthe model, otherwise is 0

For an adaptation cycle of M scans

( ) y t( ) Yi t

1

( ) ( ) N

klkl i

i

Ep t E t

= 1kl

klp

1

( )M

kl kl

t

sumEp Ep t

1kl

kk

Ff sumF

1kl kl

FsumEp

11( ) ... ...k k kl kn

k kl knp a p f p f p f

Initial Model Gain = G1

G2-Δ G2 G2+ΔG2-Δ G2 G2+Δ

G3-Δ G3 G3+ΔG3-Δ G3 G3+Δ

Multiple iterations per

adaptation cycle

The interpolated parameter value is


TC 1-4aTC

1-4a

TT 1-4a

AC 1-1AC 1-1

AT 1-1

LT 1-2

LC 1-2LC 1-2

TT 1-3

TC 1-3TC 1-3

RSP

Reactor

Coolant

Discharge

FC 1-5FC 1-5

FT 1-5

Slurry

Base

HeatExchanger A

RSP

FF 1-1FF 1-1

FF 1-2FF 1-2

FF 1-3FF 1-3

HydrocloneFeed Flow

Multiplied byFractional

Splitter Time

Feedforward

Feedforward

Feedforward

Dryer

Centrifuge

Splitter

HydrocloneFeed Flow

Multiplied byFractional

Splitter TimepH

ReactorTemperature

Level

Product Flow

RecirculationTemperature

Pensacola Reactor Adaptive Control Beta Test


Pensacola Reactor Adaptive Control Beta Test

pH

Level

Temperature

Slurry Feed

Reactor Control “Before”

pH

LevelTemperature

Slurry Feed

Reactor Control “After”

Broadley-James Corporation Bioreactor Setup


• Hyclone 100 liter Single Use Bioreactor (SUB)

• Rosemount WirelessHART gateway and transmitters for measurement and control of pH and temperature. (pressure monitored)

• BioNet lab optimized control system based on DeltaV

Bioreactor Adaptive Control Performance


Bioreactor Adaptive Tuning Setup


Bioreactor Adaptive Model Viewing


Bioreactor Adaptive Learning Setup


Output comes off high limit at 36.8 oC

0.30 oC overshoot

Bioreactor Adaptive Tuning Gain 40 Reset 500



0.12 oC overshoot

Bioreactor Adaptive Tuning Gain 40 Reset 5,000


0.13 oC overshoot




0.20 oC overshoot




0.11 oC overshoot




Integrating and Runaway Process Tuning

• It is difficult to prevent overshoot in processes without self-regulation• Controller gain adds self-regulation via closed loop response• Examples of integrating processes (ramping response) are

– Liquid and solids level – furnace, column, or vessel pressure – batch composition, pH, or temperature

• Examples of runaway processes (accelerating response) are – exothermic reactor temperature– strong acid - strong base pH– exponential growth phase biomass– compressor speed during surge

• An overdrive of the controller output beyond its resting value is needed to reach a set point or compensate for a disturbance (achieved by high controller gain)

• The maximum allowable controller gain for many integrating processes is well beyond the comfort level of most users. Measurement noise and resolution often sets the practical high limit to the controller gain rather than process dynamics

• Too much reset action (too small of a reset time) cause severe overshoot• A higher controller gain creates more overdrive for small setpoint changes and gets

controller off it’s output limit sooner for large setpoint changes• There is a window of allowable controller gains.

– Instability from too high of a controller gain (not likely for industrial processes)– Slow rolling oscillations from too low of a controller gain (common case) that slowly decay for

integrating processes but can grow for runaway processes till it hits physical limits


MIT Anna India University Lab MIT Anna India University Lab Setup


http://www.controlglobal.com/articles/2010/LevelControl1002.html

http://www.controlglobal.com/articles/2010/LevelControl1002.html


Gravity discharge flow makes the level response self-regulating (increase in level head increases flow through discharge valve)

Increase in cross sectional area with level increases process time constantmaking process response slower

Conical Tank Detail


Conical Tank Linear Level Controller Performance


Conical Tank Adaptive Level Controller Models


Conical Tank Adaptive Level Controller Performance

Nonlinear Control Valve LabNonlinear Control Valve Lab


Equal PercentageFlow Characteristic



click on PID tagand then Tune



Process gain isapproximatelyproportionalto flow for

equal percentageflow characteristic



IdentificationOut Limit thatsets deadzoneshould be setapproximatelyequal to valvedeadband and stick-slip near

closed position

• Objective - Show adaptive control of fast nonlinear self-regulating processes (fast loop with equal percentage valve)

• Activities:1. Go to Main Display, select Cascade Loop Lab022. Click on any block, in Control Valve detail set Equal % Characteristic in Table3. Click on secondary loop AC1-2 PID Faceplate and put PID in Auto 4. Click on magnifying glass icon to get Detail display 5. Click on Duncan icon for “Tune with Insight” 6. Run “On-Demand Tuner” (set Ziegler-Nichols - PI factors: 0.2*Ku and 0.6*Tu)7. In “Models Viewing”, set number of regions = 5 and state parameter as “OUT”8. Go to settings, and set boundaries for each region

1. Region 1 0 => 35%2. Region 2 35 => 60%3. Region 3 60 => 75%4. Region 3 75 => 90%5. Region 3 90 => 100%

9. In “Adaptive Tuner”, set Lambda time = reset time10.With Adaptive Mode “Off” make 2 setpoint changes in each region11.Review “Adaptive Control” screen12.Review “Model Viewing” screen13.Review “Simulate” screen14.With Adaptive Mode “Partial” make same setpoint changes in each region

