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A Unified PID ControlMethodology to MeetPlant ObjectivesGreg McMillanCDI Process & IndustrialHector TorresEastman Chemical

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ISA Books

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Topics PID Basics (contribution of each mode) Process and Loop Dynamics Ultimate Limits for Disturbance Rejection Practical Limits for Disturbance Rejection PID Form and Structure Options Setpoint Rate Limits and Lead-Lag Setpoint Rise Time Output Tracking Opportunities Enhanced PID for Wireless, Analyzer, and Valve Position Control PID Features and Optimization with Valve Position Control Lambda Tuning Rules Misunderstood Effect of Low PID Gain Unified Methodology

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Sense of Direction

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Kickfrom filteredderivative modeα = 1/8∆%CO2 = ∆%CO1∆%SP∆%CO1Time(seconds)Signal(%)Step fromproportionalmode Repeat fromIntegral modeNo setpoint filter or lead-lagseconds/repeatContribution of Each PID Mode forSetpoint Change (Filtered Rate)Structure of PID on error (β=1 and γ=1)Controller in autoBlock valve closed (PV not affected)

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Contribution of Each PID Mode forSetpoint Change (Unfiltered Rate)Structure of PID on error (β=1 and γ=1)Controller in autoBlock valve closed (PV not affected)Spikefrom unfilteredderivative modeα = 0∆%CO2 = ∆%CO1∆%SP∆%CO1Time(seconds)Signal(%)Step fromproportionalmodeRepeat fromIntegral modeNo setpoint filter or lead-lagseconds/repeat

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Proportional Mode BasicsNote that many analog controllers used proportional band instead of gain for the proportional modetuning setting. Proportional band is the % change in the process variable (∆%PV) needed to cause a100% change in controller output (∆%CO). A 100% proportional band means a 100% ∆%PVwould cause a 100 % ∆%CO (a gain of 1). It is critical that users know the units of their controllergain setting and convert accordingly.Gain = 100 % / Proportional Band Provides an immediate reaction to magnitude of measurement change tominimize peak error and integrated error for a disturbance Too much gain action causes fast oscillations (close to ultimate period) andcan make noise and interactions worse Provides an immediate reaction to magnitude of setpoint change for Paction on Error to minimize rise time (time to reach setpoint) Too much gain causes falter in approach to setpoint

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Integral Mode BasicsNote that many analog controllers used reset settings in repeats per minute instead of resettime for the integral mode tuning setting. Repeats per minute indicate the number of repeatsof the proportional mode contribution in a minute. Today’s reset time settings are minutes perrepeat or seconds per repeat which gives the time to repeat the proportional modecontribution. Often the “per repeat” term is dropped giving a reset time setting in minutes orseconds. The smooth gradual response looking only at error is in tune with operator.Seconds per repeat = 60 / repeats per minute Provides a ramping reaction to error (SP-PV) to eliminate offset and minimizeintegrated error if stable (since error is hardly ever exactly zero, integral actionis always ramping the controller output) Too much integral action causes slow oscillations (slower than ultimate period) Too much integral action causes an overshoot (no sense of direction)

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Derivative Mode BasicsNearly all derivative tuning settings are given as a rate time in seconds or minutes. TheISA Standard Form rate time setting must never be greater than the reset time setting. Theadvantages and disadvantages of the derivative mode in terms of an abrupt response andamplification of noise are similar to that of the proportional mode except the relativeadvantages are less and the relative disadvantages are greater for the derivativemode. Derivative mode is best used to cancel out the effect of a secondary time constant.Seconds = 60 ∗ minutes Provides an immediate reaction to rate of change of measurement changeto 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 Daction on Error to minimize rise time (time to reach setpoint) Too much rate causes fast oscillation

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Proportional Only (P only)Response to Step Load DisturbancePurple PV = 0.5 x Normal GainGreen PV = 1.0 x Normal GainRed PV = 1.5 x Normal GainBrown PV = 2.0 x Normal GainPeriod = 40 secUltimate Period = 40 sec

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Proportional + Integral (PI)Response to Step Load DisturbancePurple PV = 1.5 x Normal ResetGreen PV = 1.0 x Normal ResetRed PV = 0.75 x Normal ResetBrown PV = 0.5 x Normal ResetPeriod = 65 secUltimate Period = 40 sec

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Proportional + Integral + Derivative (PID)Response to Step Load DisturbancePurple PV = 0.5 x Normal RateGreen PV = 1.0 x Normal RateRed PV = 2.0 x Normal RateBrown PV = 2.5 x Normal RatePeriod = 25 secUltimate Period = 40 sec

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Self-Regulating Process

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Integrating Process

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Runaway Process

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Origin of Loop Dynamics

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Ultimate Limit for Disturbance Rejection

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Ultimate Limit for Disturbance Rejection

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Practical Limit for Disturbance Rejection

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External Reset (Dynamic Reset Limit) Prevents PID output changing faster than a valve, VFD, or secondaryloop can respond– Secondary PID slow tuning– Secondary PID SP Filter Time– Secondary PID SP Rate Limit– AO, DVC, VFD SP Rate Limit– Slow Valve or VFD– Use PV for BKCAL_OUT– Position used as PV if valve is very slow and readback is fast– Enables Enhanced PID for Wireless Stops Limit cycles from deadband, backlash, stiction, and thresholdsensitivity or resolution limits Key enabling feature that simplifies tuning and creates moreadvanced opportunities for PID control

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ISA Standard Form with External Reset

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PID Structure Options(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)(4) PD action on error, no I action (β = 1 and γ = 1)(5) P action on error, D action on PV, no I action (β = 1 and γ = 0)(6) ID action on error, no P action (γ = 1)(7) I action on error, D action on PV, no P action (γ = 0)(8) Two degrees of freedom controller (β and γ adjustable 0 to 1)

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PID Options Effect on Setpoint Response

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Single Sided Batch Needs PD on Error

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Setpoint Rate Limits and Lead-Lag(Triple Cascade Loop)

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Setpoint Filter and Lead-Lag• PID SP filter reduces overshoot enabling tuning for load disturbances– Setpoint filter time set equal reset time• PID SP filter coordinates timing of flow ratio control– Simultaneous changes in feeds for blending and reactions– Consistent closed loop response for model predictive control• PID SP filter sets closed loop time constant• PID SP filter in secondary loop slows down cascade control systemrejection of primary loop disturbances– Secondary loop should be > 4x faster than primary loop• Primary PID must have dynamic reset limit enabled• Setpoint Lead-Lag minimizes overshoot and rise time– Lag time = reset time– Lead time = 25% lag time

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Setpoint Rate Limits• AO & PID SP rate limits minimize disruption while protectingequipment and optimizing processes– Offers directional moves suppression– Enables fast opening and slow closing surge valve– VPC fast recovery for upset and slow approach to optimum• AO SP rate limits minimize interaction between loops– Less important loops are made 10x slower than critical loops• PID driving AO SP or secondary PID SP rate limit must havedynamic reset limit enabled so no retuning is needed• PID faceplate should display PV of AO to show rate limiting

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Rise Time for Setpoint Response

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Output Tracking Opportunities• “Bang-Bang” logic for startup & batch SP changes:– For SP change PID tracks output limit until the predicted PV onedead time into future gets close to setpoint, the output is thenset at best/last startup or batch value for one dead time– Works best on slow batch and integrating processes• “Open Loop Backup” to prevent compressor surge:– When compressor flow drops below surge SP or a precipitousdrop occurs in flow, PID tracks an output that provides a flowlarge enough to compensate for the loss in downstream flow fora time larger than the loop dead time plus the surge period.• “Open Loop Backup” to prevent RCRA violation:– When an inline pH system PV approaches the RCRA pH limitthe PID tracks an incremental output (e.g. 0.25% per sec)opening the reagent valve until the pH sufficiently backs away

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Enhanced PID for Wireless• Positive feedback implementation of reset with external-resetfeedback (dynamic reset limit)• Immediate response to a setpoint change or feedforward signal ormode change• Suspension of integral action until change in PV• Integral action is the exponential response of the positive feedbackfilter to the change in controller output in elapsed time (the timeinterval since last update)• Derivative action is the PV or error change divided by elapsed timerather than PID execution• Threshold sensitivity limit is used to prevent update from noise

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Static Mixer pH Setpoint Response

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Static Mixer pH Load Response

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Static Mixer pH Failure Response

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Optimization of Batch Reactor byValve Position Control (VPC)

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Optimization Examplesby Valve Position Control (VPC)Optimization VPC PID PV VPC PID SP VPC PID OutMinimize PrimeMover EnergyReactor FeedFlow PID OutputMaximum ThrottlePositionCompressor or PumpPressure SPMinimize BoilerFuel CostSteam Flow PID Output Maximum ThrottlePositionBoilerPressure SPMinimize BoilerFuel CostEquipment TemperaturePID OutputMaximum ThrottlePositionBoilerPressure SPMinimize Chilleror CTW EnergyEquipment TemperaturePID OutputMaximum ThrottlePositionChiller or CTWTemperature SPMinimize PurchasedReagent or Fuel CostPurchased Reagent orFuel Flow PID OutputMinimum ThrottlePositionWaste ReagentOr Fuel Flow SPMinimize Total ReagentUseFinal NeutralizationStage pH PID OutputMinimum ThrottlePositionFirst NeutralizationStage pH PID SPMaximize ReactorProduction RateReactor or CondenserTemperature PID OutputMaximum ThrottlePositionFeed Flow or ReactionTemperature SPMaximize ReactorProduction RateReactor VentPressure PID OutputMaximum ThrottlePositionFeed Flow or ReactionTemperature SPMaximize ColumnProduction RateReboiler or CondenserFlow PID OutputMaximum ThrottlePositionFeed Flow or ColumnPressure SP

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PID Features for Valve Position ControlPID Feature Function Advantage 1 Advantage 2Directional VelocityLimitsLimit VPC Action SpeedBased on DirectionPrevent Running Outof ValveMinimize Disruptionto ProcessDynamic ResetLimitLimit VPC Action Speedto Process ResponseDirectional VelocityLimitsPrevent Burst ofOscillationsAdaptive Tuning Automatically Identifyand Schedule TuningEliminate ManualTuningCompensation ofNonlinearityFeedforward Preemptively Set VPCOut for UpsetPrevent Running Outof ValveMinimize DisruptionEnhanced PID Suspend Integral Actionuntil PV UpdateEliminate Limit Cyclesfrom Stiction &BacklashMinimize Oscillationsfrom Interaction &Delay

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Self-Regulating Process Lambda Tuning

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Integrating Process Lambda Tuning

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Often Misunderstood Low PID Gain EffectLag Dominant Self-Regulating ProcessPeriod = 400 secUltimate Period 40 sec

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Often Misunderstood Low PID Gain EffectIntegrating ProcessPeriod = 400 secUltimate Period 40 sec

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Often Misunderstood Low PID Gain EffectRunaway ProcessPeriod = 400 secUltimate Period 40 sec

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Low PID Gain and Reset Time Limit

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Unified Methodology - 1 Add a flow measurement to every important process and utilitystream to enable a secondary flow loop for cascade control.– A secondary flow loop isolates pressure disturbances, and nonlinearitiesof the installed characteristic of control valve and variable speed drivesfrom the control of a higher process variable.– Flow measurement enable flow feedforward control and the possibility ofchanging production rates by moving plant flows in unison per PFD.– Flow measurements enable closing material and energy balancesleading to process knowledge eliminating uncertainties from pressureflow relationships and valve backlash and stiction.– Control valves and VSD normally have a greater rangeability than adifferential head or vortex meter. When this occurs, a calculated flowbased on the installed characteristic should be substituted for themeasurement flow before the signal becomes too noisy or in the case ofthe vortex meter the signal drops out. An automatic pressure drop biasenables smooth transition from measured to calculated flow

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Unified Methodology - 2 Set the output limits to keep the manipulated setpoints in thedesired operating range. For variable speed drives set the processPID low output limit so the speed cannot cause the discharge head toapproach the static head in order to prevent excessive sensitivity topressure and to prevent reverse flow. In general, set the anti-resetwindup limit to match the output limit. If the output scale isengineering units, the output limits and anti-reset windup must bebased on the output scale range and units. Choose the best structure for your application. Generally the bestchoice is structure 2 with PI on error and D on PV. For a singledirection response (e.g. batch heating or neutralization), use structure4 or structure 5 so that there is no integral action. For a highlyexothermic reaction, you might want structure 5 to help prevent arunaway from integral action. Set the signal filter noise just large enough to keep the controlleroutput fluctuations from exceeding the resolution limit or deadband ofthe final control element.

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Unified Methodology - 3 For near-integrating, true integrating, and runway processes usethe lambda integrating process tuning rules. To maximize thetransfer of variability from the process variable to the manipulatedvariable, set the lambda (arrest time) equal to the maximum possibledead time* and use the largest integrating process gain for alloperating conditions in the tuning. To maximize the absorption ofvariability (e.g. surge tank level) use the minimum arrest timecomputed from paper Equations 1 through 10 for all possibleoperating conditions. If you decrease the PID gain, proportionallyincrease the PID reset time to prevent slow rolling oscillations. For self-regulating processes with the open loop time constantless than 4 times the dead time, use the lambda self-regulatingtuning rules. To maximize the transfer of variability from the processvariable to the manipulated variable set the lambda (closed loop timeconstant) equal to the maximum possible dead time* and use thelargest process gain and smallest time constant for all operatingconditions in the tuning (worse case is often lowest production rate).* Due to unknowns a more practical lambda is twice the max dead time

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Unified Methodology - 4 Turn on external reset feedback. Make sure the external resetfeedback signal is correctly propagated back to the PID (e.g. BKCALsignal) especially if there are split range, signal characterizer, orsignal selector blocks on the PID output. For final control elements that are slow or that have deadbandor resolution limit, use a fast readback of the valve position orvariable frequency drive speed as the external reset feedback toprevent a burst of oscillations from the PID output changing fasterthan the final control element can respond. For final control elements that create limit cycles fromresolution limits and deadband, use a fast readback of the valveposition or variable frequency drive speed to stop the limit cycles For cascade control, use the PV of the secondary loop as theexternal reset feedback to prevent a burst of oscillations fromviolation of the cascade rule where the secondary loop must besignificantly faster than the primary loop.

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Unified Methodology - 5 For setpoint filters of secondary loops for coordination of flowloops, use the PV of the secondary loop as the external resetfeedback to prevent the need to retune the PID. For setpoint rate limits use the PV of the analog output block orsecondary loop as the external reset feedback to prevent theneed to retune the PID. Add setpoint rate limits to minimize theinteraction between loops and in valve position control and to providedirectional move suppression to enable a fast getaway for abnormalconditions and a slow approach to optimum. For valve positioncontrol, use an enhanced PID developed for wireless with a thresholdsensitivity limit to ignore insignificant changes in the valve position tobe optimized. Add output tracking for equipment protection and a full throttle(bang-bang control) strategy for the fastest possible time to reachsetpoint on startup and for batch operations. Use valve position control for simple and quick optimization byjust a PID configuration.

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Unified Methodology - 6 Add output tracking logic to momentarily track an output thatinsures equipment and environmental protection. For compressorsurge protection track a sufficiently large opening of the surge valves.To prevent a RCRA pH violation, track a rapidly incrementing reagentvalve position to prevent an effluent excursion < 2 pH or > 12 pH. Add feedforward control for large and fast measureddisturbances. For flow feedforward, use a ratio and bias station sothe operator can enter a desired flow ratio and see the actual flowratio. Setup the PID to provide a bias correction to the manipulatedflow. Add dynamic compensation (dead time and lead-lag blocks) tothe feedforward so the manipulated flow arrives at the same point inthe process at the same time as the measured disturbance. For wireless devices or analyzers (discontinuous PV updatedelay) use an enhanced PID to eliminate the need to retune thecontroller to prevent oscillations. If the delay is much larger than the63% process response time, the PID gain can be set as large as theinverse of the maximum open loop gain for self-regulating processes.