PID Control of Runaway Processes - Greg McMillan Deminar

Slide 1

Interactive Opportunity Interactive Opportunity AssessmentAssessmentInteractive Opportunity Interactive Opportunity AssessmentAssessment

Demo and Seminar (Deminar) Series for Web Labs –

PID Control of Runaway Processes PID Control of Runaway Processes Aug 25, 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

WelcomeWelcome WelcomeWelcome 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/


““Top Ten Control Room KPIs that will NOT Lead to Top Ten Control Room KPIs that will NOT Lead to Process Improvement and Should NOT be Reported”Process Improvement and Should NOT be Reported”

Courtesy of Mike Brown (September 2010 Control Talk)Courtesy of Mike Brown (September 2010 Control Talk)



(10) Number of coffee cups consumed on night shift (9) Number of chairs broken by our favorite lead Operator, “Big Bob

Gibson” (8) Average length of time an Operator can keep his eyes closed before

falling asleep (7) Shortest recorded time for Operator handover at shift change (6) Longest recorded time to bring up a DCS graphic following a control

system “upgrade” (5) Number of times the Operator gets the DCS alarm “MPC error - please

re-invert the matrix” (4) Number of Process Engineers that cannot spell PID (3) Number of instrument tuning technicians with the last name Ziegler or

Nichols (2) Number of times an Operator shouts “Bingo!”

And the Number 1 KPI NOT to be Reported:






(1) Any KPI that needs to be charted with a control range of -1000% to 1000%


IntroductionIntroduction Most important and difficult examples are highly exothermic Most important and difficult examples are highly exothermic

reactors used to produce polymers and specialty chemicalsreactors used to produce polymers and specialty chemicals – Reaction rate exponentially increases with temperature

– Tight temperature control is important for batch cycle time, production rate, and product quality (reaction rate maximization and off-spec production minimization depend on operating at maximum temperature that does not trigger side reactions)

– Tight temperature control is important for safety (a point of return can be reached where reaction heat release rate is greater than heat removal rate causing a high temperature or high pressure trip)

– Temperature control is extremely sensitive to thermal lags in heat transfer surfaces and in thermowells

– Open loop tests are deceptive and potentially a safety issue since response looks like an integrator until acceleration kicks-in

– Controller tuning settings required are unusual. Convention tuning rules can cause slow oscillations, overshoot, and potentially a trip of the safety instrument system (SIS).


IntroductionIntroduction Biological reactors in the exponential growth phase can have a Biological reactors in the exponential growth phase can have a

runaway response for cell concentration control but the time runaway response for cell concentration control but the time constant is so slow it often does not present a control problemconstant is so slow it often does not present a control problem

Strong acid and base pH control systems can exhibit a near Strong acid and base pH control systems can exhibit a near runaway response for excursions toward the neutral point due runaway response for excursions toward the neutral point due to extreme nonlinearity (orders of magnitude increase in to extreme nonlinearity (orders of magnitude increase in titration curve slope in approach to 7 pH causes acceleration) titration curve slope in approach to 7 pH causes acceleration)

An axial compressor speed control system can exhibit a severe An axial compressor speed control system can exhibit a severe extremely fast runaway response during surge due to unloading extremely fast runaway response during surge due to unloading – A speed derivative unit that tripped the compressor on high acceleration

prevented rotor damage from excessive vibration (benefits: $1,000K/yr savings in eliminating damaged rotors and need to stock multiple rotors)


Demos of Exothermic ReactorDemos of Exothermic Reactor Acceleration at high temperatures Dynamics and tuning for clean heat transfer surface

– Modified short cut open loop tuning method

– Modified ultimate oscillation closed loop tuning method Dynamics and tuning for fouled heat transfer surface

– Modified ultimate oscillation closed loop tuning method Window of allowable controller gains

– Major decrease in controller gain


Unstable ScenariosUnstable Scenarios


Runaway ResponseRunaway ResponseRunaway ResponseRunaway ResponseResponse to change in controller output with controller in manual

p p’

Noise Band

Acceleration

CV

CO

CV

Kp = CV CO Runaway process gain (%/%)

% Controlled Variable (CV) or

% Controller Output (CO)

Time (seconds)observed process

deadtimerunaway process

positive feedback time constant

For safety reasons, tests are terminated after 4 deadtimes


Runaway Tuning Modifications for Runaway Tuning Modifications for Near Integrator Method Near Integrator Method (Deminar #6)(Deminar #6)Runaway Tuning Modifications for Runaway Tuning Modifications for Near Integrator Method Near Integrator Method (Deminar #6)(Deminar #6)

25.11

5.0

oi

c KK

Increase gain by 25%

104 oiT

21d T

Increase reset time by factor of 10

Double rate time


Acceleration at High TemperaturesAcceleration at High Temperatures Objective – Show how runway response initially looks like

an integrating but then accelerates Activities:

– For Single Runaway Loop:• Set AC1-1 reset time = 1000 sec

• Set primary process gain = 2.2

• Set AC1-1 manual output = 25% and setpoint = 55%

• Momentarily set primary process Lag 2 to 1 sec to line out process at setpoint

• Set primary process deadtime = 8 sec

• Set primary process Lag 2 = 100 sec

• Set primary process type = Runaway

• Change in AC1-1 output from 25% to 35%

• Measure the deadtime and initial rate of change

• Note acceleration

• Stabilize process at 55% setpoint by momentarily switching back to self-regulating process with 1 sec primary process time constant and manual output of 25%

• Put AC1-1 in auto


Tuning for Today’s Example UsingTuning for Today’s Example UsingShort Cut Near Integrator MethodShort Cut Near Integrator Method

Tuning for Today’s Example UsingTuning for Today’s Example UsingShort Cut Near Integrator MethodShort Cut Near Integrator Method

sec100p sec10o

8.225.110022.0

15.025.1

15.0

oic KK

2.2p K

40010104104 oiT

42221d T

022.0%10sec/20/%8.4/)/( COtCVMaxK

Kp

pi

Fastest initial ramp rate estimated in 2 deadtime interval For safety reasons do not keep loop in manual for more than 4 deadtimes!

sec21 Process Dynamics in Single Loop Lab

Near Integrator PID Tuning Modified for Runaway Processes

Derivative action must be used to compensate for secondary lags and help prevent acceleration !


Short Cut Tuning for Clean Heat Transfer Surface

Short Cut Tuning for Clean Heat Transfer Surface

Objective – Show performance of modified short cut method for runaway and start ultimate oscillation

Activities:– For Single Runaway Loop:

• Set AC1-1 gain = 2.8, reset = 400 sec, and rate = 4

• Make setpoint change from 55% to 60%

• To create ultimate oscillations set reset time = 10,000, rate = 0, and gain = 7


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


Basis of First Order ApproximationBasis 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


Time(min)

ProcessVariable

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

Ultimate Period Tu

0

1Ku = ----------------

Kp * AR-180

Ultimate gain of controller is inversely proportional to the product of the open loop static (process) gain and the amplitude ratio at -180o phase shift,which is the starting point of resonance and instability (growing oscillations)

2 Tu = --------

n

Ultimate period of control loop occurs at natural frequency n (at -180 phase shift)

Ultimate Gain and PeriodUltimate Gain and Period


Runaway Ultimate Gain CalculationRunaway Ultimate Gain Calculation

[1 + (1u [1 + (p’Tu] 1/2

Ku = ------------------------------------------------------------------- Kp

For Tu < < (loop dominated by a large time constant), the error is negligible for the following simplification:

( p’Ku = ------------------------ Kp Tu

2


Integrating Process Data Fit from Nyquist Plots:(for osimplifies to Near-Integrating process Tu) 0.65

Tu = 4 1 + o

o

Runaway Process Data Fit from Nyquist Plots : (for p’and p’simplifies to Integrating process Tu)

N 0.65 N = (p’) p’

Tu = 4 1 + o

D D = (p’) (p’o) o

As either oro approach ’, D approaches zero, Tu approaches infinity, and the

controller is unstable for all tuning settings (window of allowable gains is closed)

Equations to Estimate Ultimate PeriodSource: Tuning and Control Loop Performance - My First Book and Creative Work (1984)Equations to Estimate Ultimate Period

Source: Tuning and Control Loop Performance - My First Book and Creative Work (1984)

Self-Regulating Process Data Fit from Bode Plots:(for near-integrating process Tu o) 1 0.65

Tu = 2 1 + o

po


For a Proportional plus Integral plus Derivative (PID) controller:

Kc = 0.4Ku 0.5*1.25 x Ziegler-Nichols (0.64) controller gain factor

Ti = 10 Tu 20 x Ziegler-Nichols (0.5) integral time factor

Td = 0.125 Tu Ziegler-Nichols (0.125) integral time factor

Ultimate Oscillation Tuning Modified for Runaway Process

Ultimate Oscillation Tuning Modified for Runaway Process

Manual methods pose a safety risk, so damped small rather than large equal amplitude oscillations are used

Auto and adaptive tuners are preferred that maintain or use closed loop control

The relay method on-demand auto tuner will automatically compute theUltimate Period and Ultimate Gain

Window of Allowable Controller Gains1/ Kp > Kc < Ku


Ultimate Oscillation Tuning for Clean Heat Transfer Surface


Objective – Show how Ziegler-Nichols tuning settings are modified for runaway


• Measure ultimate period and note ultimate gain

• Compute tuning settings by factoring ultimate period and ultimate gain



Kc = 0.4Ku

Ti = 10 Tu

Td = 0.125 Tu




Loop Block DiagramLoop Block Diagram(First Order Approximation)(First Order Approximation)

Loop Block DiagramLoop Block Diagram(First Order Approximation)(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

%

%

%

Delay => Dead TimeLag =>Time Constant

Ki = Kmv(Kpv / p2 ) Kcv

100% / span

Positive Feedback Time Lag


CV change in controlled variable (%) CO change in controller output (%) Kc controller gain (dimensionless)

Ki integrating gain (%/sec/% or 1/sec)

Kp process gain (dimensionless) also known as open loop gain MV manipulated variable (engineering units) PV process variable (engineering units) t change in time (sec)

ototal loop dead time (sec)

mmeasurement time constant (sec)

pprocess time constant (sec) also known as open loop time constant

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)

NomenclatureNomenclature NomenclatureNomenclature


Dynamics and Tuning for Fouled Heat Transfer Surface

Dynamics and Tuning for Fouled Heat Transfer Surface

Objective – Show increase in ultimate period due to fouling of heat transfer surface


• Increase secondary process Lag2 from 2 to 20 sec

• To create ultimate oscillations set reset time = 10,000, rate = 0, and gain = 4


For Runaway Process:

N 0.65 N = (p’) p’ = 120*100*20 = 240,000

Tu = 4 1 + o

D D = (p’) (p’o) o= 80*90*10 = 72,000

(N/D) 0.65 = (240,000/72,000) 0.65 = 2.2

Tu = 4 1 + 115 sec

Ultimate Period for Fouled Heat Transfer Surface

Ultimate Period for Fouled Heat Transfer Surface

pure deadtime (secondary lag taken as )


Tuning for Fouled Heat Transfer Surface

Tuning for Fouled Heat Transfer Surface

Objective – See extreme effect of secondary lag on ultimate period of runaway process


• Measure ultimate period and note ultimate gain



Kc = 0.4Ku

Ti = 10 Tu

Td = 0.125 Tu

Ultimate Oscillation Tuning for Fouled Heat Transfer Surface

Ultimate Oscillation Tuning for Fouled Heat Transfer Surface


Window of Allowable Controller GainsWindow of Allowable Controller Gains Objective – Show effect of controller gain below low gain

limit (process diverges from setpoint and goes off scale) Activities:

– For Single Runaway Loop:• Decrease AC1-1 gain to 0.2


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PID Control of Runaway Processes - Greg McMillan Deminar