ProcessIt Is defined as:• Physical or chemical change of matter.• Energy conversione.g., change in pressure, temperature, speed, electricalpotential, etc.A process in a collection ofvessels, pipes, fittings, gauges etc., is built for thepurpose of producing a product or group of products.
Process ControlThe regulation or manipulation of variables influencingthe conduct of a process in such a way as to obtain aproduct of desired quality and quantity in an efficientmanner.
Input to Process: Mass or energy applied to the process.Output of Process: The product delivered by theprocess. This is a dynamic variable.Supply: Source of mass or energy input to process.Control Valve: Consists of the final actuator and finalcontrolling elements. This is the forward controllingelement which directly changes the value of themanipulated variable.Load: Anything that affects the value of the controlledvariable under a constant supply input.
Open Loop: Control without feedback. Open loop can notcope with load upsets. Example of open loop: automaticdishwasher, automatic water sprinkling system, a controlloop with the controller in manual.Primary Element: The measuring element thatquantitatively converts the measured variable energyinto a form suitable for measurement.Transmitter: A transducer which responds to a measuredvariable by means of a sensing element, and converts itto a standardized transmission signal which is a functiononly of the measured variable.
Controlled Variable: A variable the value of which issensed to originate a feedback signal. (Also known as theprocess variable.)Controller: A device which operates automatically toregulate a controlled variable.Controller Algorithm (PID): A mathematicalrepresentation of the control action to be performed.Set Point: An input variable which sets the desired valueof the controlled variable.
Error: In process instrumentation, the algebraicdifference between the real value and ideal value of themeasured signal. It is the quantity which whenalgebraically subtracted from the indicated signal givesthe ideal value.Manipulated Variable: A quantity or condition which isvaried as a function of the algebraic error signal so as tocause a change to the value of the directly controlledvariable.
Feedback Control: Control action in which a measuredvariable is compared to its desired value to produce anactuating error signal which is acted upon in such a wayas to reduce the magnitude of the error.Cascade Control: Control in which the output of onecontroller is introduced as the set point for anothercontroller.Feedforward Control: Control action in whichinformation concerning one or more conditions that candisturb the controlled variable is converted, outside ofany feedback loop, into corrective action to minimizedeviations of the controlled variable.
Open Loop ControlThe operator walked up and down a plant, looking at gaugesand opening and closing valves is effective only at the timewhen the operator moves the valve.At that instant the loop is closed.Open loop control works only when the load(s) on theprocess are constant.Any load change or supply upset can affect the productquality.
Advantages of Closed Loop ControlIncreased productivity: Automatic closed loop control allows theamount of products made in a particular process to be maximized.On Spec Products: Industrial products are produced to meetcertain purity levels.Energy and Material Conservation: A closed loop controlapplication minimizes the amount of material and energy used inproduction.Safety: Closed loop control is the first line of defense beforeEmergency Shutdown Devices (ESD) override regulatory controldevices.
Types of Control• Continuous Control is used on continuous processes. Acontinuous process is one in which process material iscontinually flowing through the process equipment.• Sequential is often referred to as on/off control. It is aseries of discrete control actions performed in a specificorder or sequence.• Batch control is a combination of sequential and continuouscontrol. A batch process is a process where the operation istime-dependent and repeatable.
Positive Feedback•It can be defined as the control action in which the error isreinforced until a limit is eventually reached.•This obviously is not a desirable outcome of control actionand should be avoided.•Imagine a tank in which level is being controlled. When thelevel exceeds the set point, the control action will increasethe level further until the tank overflows.
Negative Feedback•It can be defined as the control action in which the error isminimized, made as small as possible, depending on thealgorithm of the controller.•This obviously is a desirable outcome of the control actionand should be achieved in all feedback loops.
Direct Acting Element is one in which the value of the outputsignal increases as the value of the input signal increases.
Reverse Acting Element is one in which the value of theoutput signal decreases as the value of the input increases.
Control ValvesA control valve consists of a valve connected toan actuator mechanism. The actuator, inresponse to a signal from the controllingsystem, can change the position of a flow-controlling element in the control valve.The action of the final actuator is the first choiceand is based on “Fail-Safe Control Valve Action”.(open, closed, and in place).
TransmittersIt can be set up (calibrated) as either direct actingor reverse acting.
ProcessesIt can be either direct or reverse acting.Most processes are direct acting.Energy Flow Process1.Heat Exchanger2.RefrigerationMass Flow Process1. Level Tank2. Pipe Flow
Rule for Achieving Negative FeedbackTo achieve negative feedback in a control loop you musthave an odd number of reverse acting elements in theloop.
The odd number of reverse-acting elements fornegative feedback can be determined throughan open loop test, conducted in the followingmanner.Place the controller in manual (open loop), andstep up the output of the controller (5-10%) andobserve (record) the output of the transmitter.
Control Loop Elements AndTheir Contribution To Loop Performance
Range: The region between the limits within which a quantity is measuredis the range of that measurement.Span: The measurement span is the algebraic difference between theupper and lower range values.Minimum Span : The minimum span of measurement that the primaryelement can be used to measure within its accuracy rating.Maximum Span: The maximum span of measurement that the primaryelement can be used to measure within its accuracy rating.Rangeability (Turndown): In flow applications, rangeability is the ratio ofthe maximum flow rate to the minimum flow rate within the statedaccuracy rating.Zero Elevation and Suppression: The range at which the zero value of themeasured variable is not at the lower range value.
Response Time: An output expressed as a function of time, resultingfrom the application of a specified input (step) under specificoperating conditions.Time Constant: This is a specific measure of a response time. It is thetime required for a first order system to reach 63.2% of the totalchange when forced by a step.
Characteristic Curve (Input-Output Relationship): Acurve that shows the ideal value of an input-outputrelationship at steady state.Reproducibility: There should be a closeness ofagreement among repeated measurements of theoutput for the same value of the input made under thesame operating conditions over a period oftime, approaching from both directions.Noise: In process instrumentation noise is an unwantedcomponent of a signal or a process variable.
Flow Coefficient, CV - Is a capacity coefficient which is definedas the number of U.S gpm of 60°F water which will flowthrough a wide-open valve with a constant pressure drop of 1psi across the valve.
Valve PositionerA valve positioner is a proportional-only controller whose mainfunction is to eliminate or minimize valve hysteresis
Valve SequencingThe practical rangeability of a control valve is limited toapproximately 100/1 with most valves falling below 50/1. Theserangeability values are sufficient for most control applications.In some applications however, such as pH, the rangeabilityrequired may exceed 1000/1 and the control scheme must bedesigned to satisfy this requirement in order to achieve goodcontrol.In split ranged or sequenced strategies, the controllers outputactuates more than one valve, typically two valves.
Process Modeled Through Dead Time And Capacity
Non-self-regulating or integrating capacity (NSR)A capacity is termed non-self-regulating when a change in thecontrolled variable has no affect on the process load.
Self-Regulating-Capacity or First-Order LagIn the self-regulating-capacity process, load is not independent oflevel. When level changes in this process the load also changes.Self regulation always tries to restore equilibrium and achievesteady state.
This process operates as though it has a built-in automaticcontroller that achieves steady state by making fi = fo. In fact wewould not need to control this process if the tank was very large( ). Obviously, it is more practical to have a smaller tank and puta control loop on it.
Interacting CapacitiesInteracting capacities are identified as types of capacities inwhich the downstream capacities affect upstream capacities. C3affects C2 and C2 affects C1.
Non-Interacting CapacitiesThe non-interacting capacity can be identified as a capacity thathas no effect upstream i.e. C3 does not affect C2 and C2 does notaffect C1.
Basic Control Modes AndChoice Of Controller Algorithm
INTRODUCTIONThe effective control of a process in a feedback loopdepends on the correct choice of the controller modeor algorithm required for the given application.The controller algorithm is a mathematical expressiondescribed as the PID consisting of proportional, integraland derivative components.Each of these PID components affects the response ofthe loop and has certain advantages and limitations.
On-Off AlgorithmThe simplest and most common type of controlmode, considering home applications.Although there are multi-position discontinuouscontrollers available in industry, generally On-Off controlrefers to the two-position version.A consequence of this is that under On-Off control theloop never stabilizes.
Application of On-Off Control1) Processes where precise set point control, is notrequired e.g. some level tanks; and processes such ashome heating, cooling or refrigeration.2) Part of an emergency shutdown process (ESD). Theobjective here is not regulatory control but safeoperation.3) Large capacity processes having a low dynamic gainand a potentially small (acceptable) amplitude ofoscillation.
Advantages and Limitations of On-Off Control Advantages Limitations Extremely simple Demand not balanced by supplyInexpensive controller Loop always cyclesNo tuning required for More energy used by the start up valve Less expensive valves
Proportional AlgorithmProportional control is the minimum controlleralgorithm capable of balancing supply with the demandof the process and achieving steady state.A properly adjusted proportional controller caneliminate the oscillations that are inherently part ofOn-Off control.
Assume initially that everything is balanced.The inflow to the tank equals the outflow of the tankat 50% and the process is in a steady state condition. Fin = Fout = 50%
Also assume that at the 50% load (Fout) for thisparticular tank:Measurement = Set Point = 50% c = r = 50%If this condition persists, that is Fin = Fout @ 50%load, and c=r, the operator does not need to take anycontrol action since the supply is already balanced bythe load.
Assume in this example that suddenly the load (Fout)changes from 50% to 60%.The first indication of the load increase will be a changein the level of the tank.Acting as a proportional controller, its task is to openthe supply valve in order to stop the level fromchanging.When a balance is achieved between the supply and thedemand such that Fin = Fout = 60%, the level stopschanging.
Unfortunately, at this new steady state condition, themeasurement is at a new value below the set point.The error (r-c) is called offset. It is a steady state errorand is characteristic of all proportional controllers.The magnitude of the offset depends on the size of theload change and the capacity (size) of the tank.
The output of the proportional controller is proportional to theinput. m = GeWhen the controller is switched to automatic its output goes tozero since the error is zero. m = G (r-c) = 0As the output goes to zero the valve shuts, decreasing the Fin to0% and causing the level to decrease. The level will stopdecreasing only when the supply balances the load. This balancewill occur only if Fin becomes 50% again.If the process dictates that the gain of the controller should be 20when controlling at 50% load. The controller will operate with a2.5% error. 50 = 20 (2.5)
1. Proportional controllers always operate with an error.2. The higher the controller gain, as dictated by the process gain, the smaller the error.(It should be pointed that the controller gain can not be setarbitrarily. It is dictated by the process gain and for a given loopgain has a reciprocal relationship to the controller gain).
To accommodate zero error situations m = Ge + BiasThe Bias term has a fixed value and does not have the ability tochange. The Bias is the output of the controller whenever theerror is zero. m = Bias , if e = 0Apply this algorithm to the previous example.Assume that we put the controller in manual and adjust all thesignals to 50%: r = c = Fin = Fout = 50%. When we place thecontroller in automatic: m = Ge + Bias m = 0 + Bias = BiasA typical Bias setting being 50%, m = 50%
If the load changes an error will occur once again. m = Ge + Bias 60 = 20(e) + 50 20(e) = 10 e = 0.5%Some manufacturers write the expression m = (100/PB) e + BiasProportional band is defined as the change in input required toproduce a full range change in output due to proportional controlaction.It may also be seen as the change in measurement required tochange the output 100% or to fully stroke the valve.
Proportional Offset m = (100/PB)e + Bias Offset = e = (m - Bias)(PB/100)There are two conditions which can make the offset equal tozero or a very small value.1) Small values of PB or high gains on the controller. Remember that the process dictates the controller gain or PB. It is not an arbitrarily assigned value.2) If (m = bias): in this situation, when the load is equal to theBias, there will be no offset. Since the Bias is fixed this impliesthat the load is also fixed.
Application of Proportional-Only ControlProportional-only control is not a common control application.1) Processes where precise control at the set point is not required. Processes where offset can be tolerated.2) Processes where the load changes are infrequent (seasonal).This allows matching load with Bias to eliminate or minimize theoffset.3) Low gain processes. Typically these are large capacityprocesses with low process gains. The low gain of the processallows a high gain on the controller minimizing the offset.
Advantages and Limitations of Proportional-Only Control Advantages Limitations Immediate response Offset Easy to tuneGood period of response Simple
Integral AlgorithmThe error in proportional algorithm could be eliminated ifthe two terms in the parenthesis were made to equal eachother. Offset = e = (m - Bias) PB/100Since the output of the controller m is directly related to theload our only choice is to vary the Bias term by making theBias = m and thus eliminating the error.The integral mode fulfills this requirement by providing thevariable Bias capability that automatically achieves this loadbalancing task while eliminating errors at steady state.
mI=(1/I) edt + mo mI = Ti edt + mowhereI = min./repTi = rep./min.mI : is the output of the integral-only controller.I : is the gain adjustment for the integral-only controller knownas the integral or reset time.mo : is the controller output at the time integration starts
Application of Integral-Only ControlWhenever the integral mode is required in an application it iscustomary to have a small amount of proportional along with it.The integral mode eliminates the offset at a cost of slower loopresponse.Integral can be justified and should be the major contributor forthe following applications.1. Slow loops designed to produce slow corrective action.2. The integral mode is the major contributor in fast flow control applications usually with a minor contribution from the proportional controller.
WindupSaturation of the integral mode of a controllerdeveloping during times when control cannot beachieved, which causes the controlled variable toovershoot its setpoint when the obstacle to control isremoved.
Advantages and Limitations of Integral-Only Control Advantages Limitations Eliminates offset Slows the response Easy to tune Potential windup or saturationReduces integrated error Unstable with NSR capacity. (Always oscillates with NSR)
Proportional Plus Integral AlgorithmThe need for precise control with zero error at steadystate brought the integral mode in the picture.The integral mode eliminated the error at steady statebut at an unacceptable cost of a slow loop response.Combining the two modes in a PI controller is a veryeffective compromise suitable for most processapplications.
The following observations should be made:1) Integral mode is a must for precise control.2) The cost of integration is a slower response.3) If unable to eliminate the error at steady state thepotential exists for loss of control through what isknown as windup or saturation.
The PI is by far the most common algorithm used inprocess control applications.In most plants the PI controller is used in excess of 80%of the time.The reason for its popularity is due to the fact that thealgorithm benefits by getting an instantaneous responsedue to error from the proportional mode and theelimination of steady state error from the integral mode.
Advantages and Limitations of PI Control Advantages Limitations No offset More difficult to tune Can minimize integrated Windup or saturation error potentialReasonably good period of response
Derivative Algorithm• In some applications the increased period of responsedue to the integral mode is not acceptable• Especially if we recognize that after an upset it takesabout 3 cycles for a loop to settle down and reachsteady state.• Furthermore in approximately 10% of the processesthe natural period of the loop is rather long and thepenalty of even longer periods due to the need ofhaving integral is not desirable.
•The natural period of a distillation column is typicallyseveral hours.•If a given column has a natural period of 4 hoursand, assuming a penalty of a 50% longer period due tothe integral mode.•It would take approximately 18 hours (4 x 3 x 1.5 = 18)for this loop to reach steady state.•The problem gets further aggravated if other upset(s)occurs before steady state is reached.
Proportional plus Derivative Algorithm•Remember that derivative-only controllers do notexist.•The derivative mode must be combined with aproportional or a proportional plus integral controllerand the phase will be limited to some value less than+90%.
The older version with the Derivative on error m = 100/PB ( e + Dde/dt ) + Bias
The newer version with the Derivative on measurement m = 100/PB ( e - Ddc/dt ) + Bias
Application of Proportional plus Derivative ControllersThe proportional plus derivative controller is not a frequentchoice in process control applications.Its major limitation is its inability to eliminate offset orsteady state error.To apply the derivative mode we have to make sure that thecontrolled variable is free of noise.
Regarding offset it has the same problem as theproportional-only controller.The addition of derivative however produces animprovement in the speed of response.PD controllers are recommended for large capacityprocesses where precise (set point) control is notrequired.The major application of this controller is in batchprocesses where because of the nature of the process(integrating process) it may not be desirable to use theintegral mode.
Advantages and Limitations of PD Controllers Advantages LimitationsGood response period OffsetFastest to reach steady Can not handle noise stateEasier to tune than PID Insufficient benefit on fast processes
PID AlgorithmThis three-mode controller has the attributes of all themodes along with their limitations.In summary the PID uses the immediate response of theproportional mode followed by the integral modes ability toeliminate the offset.The slowing down of the response due to integration iscompensated for by the derivative mode.
To justify the application of the PID controller theprocess should satisfy the following conditions:1. The controlled variable should be free of noise.2. The process should have a large capacity for optimumbenefit.3. The slower response due to the integral mode is notacceptable for good control.
Advantages and Limitations of PID Controllers Advantages LimitationsGood period of response Noisy measurementCompensates for the slow Difficult to tune integral Minimizes integrated Windup concerns errors Optimizes control loops
Procedure for Determining Process Characteristics1. Let the system stabilize.2. Open the loop by placing the controller in manual.3. Make sure the system is at steady state, the outputand the controlled variable maintaining their values.4. Introduce a small disturbance by stepping up theoutput of the controller.5. Record the reaction of the controlled variable.6. Bring the output back to the normal operating pointand switch to auto.
Steady State Gains of ElementsSteady state gain is simply the slope of the input-output relationship of the elements response curvewhen both the input and output are time invariant (donot vary with time).
Linearization For Constant Loop GainInstead of tuning at the highest gain condition to be onthe safe side, a better solution to the non-linearityproblem is to use a complementary linearizing elementin the loop through either the valve or other element.The objective of good control is to make the loop gainindependent of the operating point as much aspossible.
THE STEADY STATE GAIN OFMEASURING ELEMENTS/TRANSMITTERS
Flow TransmittersThe most common industrial flow applications involve one of thefollowing measuring Devices. LINEAR DEVICES NON LINEAR DEVICES Magnetic Flow Meters Orifice Positive Displacement Meters Venturi Vortex Meters Flow Nozzle Turbine Meters Elbow Meters Ultrasonic Target Meters Rotameter Weirs Coriolis Flumes
Linearizing With A Compensating ResponseIt is possible to linearize the differential producer (orificeplate) with a complementary response curve.To find a curve (b) type function from one of the otherelements in the loop, i.e. the valve.The advantage of this approach is the elimination of theneed for a square root extractor.The disadvantage is that the loop will be operating with(Flow)2 information.
Non-Linear ControllersAs electronic controllers were introduced, it was possible tobuild non-linear PID controllers.In some applications it is not desirable to have a constantgain controller.Non-linear controllers were designed to handle processeswith variable gain.They were set up to have low gain in the high-gain region ofthe process and high gain in the low-gain region of theprocess.
Linearizing Process Characteristic with a Non-Linear Controller
Acceptable Tuning Criteria Used in the Process Industry
• If safety is the primary concern, speed and efficiencycan be sacrificed and a critically damped response mightbe the best choice.• If the objective is to eliminate the error and achievesteady state as quickly as possible after an upset, thensome form of underdamped response will be the choice.Generally most of the better tuning techniques lead toan underdamped response, with some decay ratio and aspecific speed of response (period.)
Tuning Criteria Using Error Minimization ApproachesThe objective of a well-tuned loop is to eliminate theerror as quickly as possible by bringing themeasurement equal to the set point.
Quarter Amplitude Decay Criteria(QAD) is one of the most common under-damped responsecriteria.The controller gain is adjusted so that the amplitude of eachsuccessive cycle is one quarter of the previous amplitude.Unfortunately, this criteria does not completely define theresponse.Beyond an amplitude decay ratio, it gives no otherinformation as to what the optimum period of the responseshould be.
There is no mathematical justification for the QAD response. Itspopularity and acceptance are due to its open loop gain, whichbetween 0.5 and 0.6 seems to be a reasonable compromise indamping and period.
The main criticism of QAD as a criterion is that it gives noinformation about speed of response, or period of aloop, and as such, it does not indicate an optimumresponse.In two or three mode controllers such as PI or PID thereare an infinite number of settings that will give you aQAD response, only one of which will have the correctperiod for optimum response.
Tuning Criteria Using Integral Error MinimizationThese techniques are especially useful if energy is used to makethe product.Minimization of the area (error) under the curve leads to lessenergy consumption and higher efficiency.There are various error minimization criteria, each having certainadvantages and limitations, and different PID settings.
Integrated Error (IE) IE = e dtIntegral Absolute Error (IAE) IAE = e dtIntegrated Squared Error (ISE) ISE = e2 dtIntegrated Time Absolute Error (ITAE) ITAE = e t dt
Robustness•A loop tuned to particular criteria raises the question ofloop stability when process conditions change.• A robust control loop, has a safety factor built in to thecontroller tuning settings, allowing the loop to maintainstability even if the process undergoes moderatechanges in gain or dead time.
• A robustness plot allows an analysis of how safely a loop istuned. The gain ratio is the ratio of the current process gain to the original process steady-state gain. The delay ratio is the ratio of the process dead time to the dead time existing when the process was tuned.
Making PID Adjustments and Observing their Effect on Loop Response
To change the response of the loop, adjust only with:PB or Gain. Decrease the loop gain to less than one inorder to dampen the response.The obvious choices of response for this controllerwould range from an overdamped response to aQuarter Amplitude Decay response (QAD).To get a QAD response the Proportional Band wouldhave to be doubled (2 x PBu) to drive the loop gain to0.5.
The proportional band or gain adjustment can besummarized as follows: • Changing gain or PB affects only the damping of the response. • Increasing the PB setting decreases gain while the period stays roughly the same.
Any change of period length over n is of minorconsequence. The amount depending on the processcharacteristics.•For dead-time only processes there would be no periodchange at all.•For dead-time plus capacity processes the period mightincrease by 10 - 15% over the natural period n.It is best to consider the proportional adjustment as again adjustment with no significant effect on the periodof response.
PID AdjustmentSuppose we find our damping to be acceptable, butthe period of response, o is too long.We need to maintain our loop gain constant, but toeither increase derivative action or decrease integralaction.Changing either one alone will not only change o, butwill also change the gain vector which will in turnaffect loop gain.
The correct procedure in this case would be to increasederivative gain GD, by increasing derivative time D,while at the same time to decrease integral gain GI byincreasing integral time I.This will tend to increase derivative action whilemaintaining the length of the PID vector constant.As a result, damping will remain unchanged whileresponse period o is decreased.
Interacting And Noninteracting PIDThere are at least two ways in which three-mode PIDcontrollers can be built.The PID algorithm discussed so far is an ideal noninteractingcontroller algorithm.The noninteracting controller is designed such that itsderivative and integral modes are in a parallel path and actindependently of each other.The interacting PID controller is designed such that theintegral and derivative modes interact.
Effective PID values in terms of the actual settings
Reasons for Tuning MethodsOver the years many tuning methods or approacheshave been developed and used with varying degrees ofsuccess.There is no general agreement as to what method is thebest to use, the preferred choice usually being theone, that the individual has the most experience with.
• Some of the methods are trial and error solutions tofinding the desired response; others rely onmathematical relationships.• The preferred tuning method might be, it is desirableto have the capability to apply more than one approach.• In some cases, process or operational constraintsdictate the method to use.• With experience, you develop a feel of what approachworks best for a given application, and tune accordingly.
Keep in mind that any tuning method, will give you onlypreliminary settings, which require fine tuning later foroptimum response.The various tuning methods can be grouped into closed-loop and open-loop categories.
The main distinction between the two is as follows: •In the closed-loop methods, adjustments are made and tested with the controller in automatic. •In the open-loop methods, preliminary settings are calculated by an open loop test, with the controller in manual. These preliminary adjustments are introduced in the controller and tuning is continued with the controller in automatic.
Summary of making PID adjustments and observing their effect on loop responseThe table is designed to assist the user in deciding which direction the adjustments should be made.
Procedure for Trial and Error Constant Cycling Method P-Only Controller1. Place controller in manual.2. Increase proportional band to a safe wide value3. Place controller in automatic.4. Make a 5 - 10% set point change around the operating point.5. Reduce PB until constant amplitude cycling occurs.6. Double PB for QAD. Controller is tuned.7. Make a small upset and observe the response. Measurement will not be at set-point at steady state.
P + I Controller1. Increase I-time to maximum min/rep or minimum rep/min. (This eliminates the integral action.)2. Tune as a P-Only Controller.3. Increase Integral gain until constant amplitude cycling occurs.4. Double the I-time in min/rep for QAD. (Halve the I-time if in rep/min.)5. Make upset and observe the response. Measurement should reach set-point at steady state.
PID Controller (Interacting Types)1. Adjust the integral time min/rep and proportional band to highvalues.2. Adjust derivative time to a very low value.3. Reduce PB until constant amplitude cycling just occurs.4. Double PB for QAD.5. Controller is now tuned as P-Only.6. Increase derivative time until constant amplitude cycling occurs.7. Cut derivative time by 1/2 for QAD.8. Set integral time to a value of 2 to 4 times that of the derivativetime.9. Make upset and observe the response. Measurement should beat the set-point at steady state.10. Readjust PB, I, and D small amounts to get desired response.
Procedure for Ziegler-Nichols and Cohen-Coon Constant Amplitude Cycling Method1. With the controller in manual, remove the Derivative and Integral modes. (Remove or turn off Derivative action. Set Integral to its lowest gain value, by setting to maximum min/rep or minimum rep/min.) Set the Proportional Band or gain to a safe value depending on the process.Examples of safe values of PB or Gain: · Flow PB 300-500 % or Gain 0.2 to 0.3 · Temperature PB 100 % or Gain 1.0At this point, you have a low-gain, Proportional-only controller.
2. Switch the controller to automatic, put a small upset byintroducing a 5-10% set-point change around the operating pointand observing the response. You should get a safe sluggishresponse.3. Increase the gain or decrease the Proportional Band and repeatstep (2) until uniform or sustained oscillations occur as shown incurve (C). If the gain is too low such as curve (A) increase the gainor lower the PB. Avoid unstable responses such as curve (B). Recordthe following information at uniform oscillation. Make sure theoscillation is due to the loop gain and not due to a limit cycle. (e. g.,Valve hitting the stops produces what looks like uniform oscillationbut the gain > 1).
Procedure for Obtaining a Process Reaction Curveand Optimum PID Settings from Ziegler-Nichols or Cohen-Coon Process Reaction Method
1. Let the system stabilize at the normal operating point (set pointand load at normal.)2. Open the loop by placing the controller in manual. The outputshould hold at the same value as in step (1).3. Make sure the system is at steady state with the output and thecontrolled variable maintaining their values.4. Introduce a small disturbance by stepping up the output of thecontroller. The resulting output change should have enoughresolution for analysis.5. Record the reaction of the controlled variable. This is where afast speed recorder at the output of the transmitter (in the order 1in./min) comes in handy.6. Bring the output back to the normal operating point and switchcontroller back to auto.
After obtaining the Process Reaction Curve, proceed to determineP, PI, or PID settings using either Ziegler-Nichols or Cohen and Coonequations as shown.
Procedure and Summary of Integral Criteria- Driven Open-Loop MethodObtain a process reaction curve
•If the load (Fw) suddenly increases, the temperature (T2)decreases.•The controller senses this and acts on this error through itsalgorithm.•In two to three cycles, the loop stabilizes.
Cascade Control may be defined as, "control in which the outputof one controller is the set point for another controller."The set point to the flow controller defines the amount of flowrequired. On an upset in flow, the controller repositions the valveto bring the flow to the set point, r.
These cascade loops are known as the primary andsecondary loops.The loop closest to the controlled variable is the primaryloop and the loop manipulating the valve is the secondaryloop.The primary loop is known also as the master loop, outerloop, or the slower loop.The secondary loop may be called the slave loop, the innerloop, or the faster loop.
The purpose of cascading is to have the secondary loopcompensate for any supply upsets that may occurbefore they can influence the primary controlledvariable.A supply upset to the primary loop is in effect a loadupset to the secondary loop, and a fast-actingsecondary can immediately correct for it.
Results and ConsiderationsIn order for the cascaded control scheme to functionwithout adversely affecting the gain of the primary loop,The 1/ 2 ratio must exceed 4.The higher the ratio, the easier it is to cascade.
Advantages of Cascade1. Cascade control eliminates the effects of supply upsets.2. Quicker return to set point in the primary loop and lessintegrated absolute error (IAE).3. The secondary loop is more responsive to the demands ofthe primary.4. The primary loop sets the amount of supply input ratherthan valve position. Thus, the effects of valve characteristics(including non-linearities) are minimized, and effectivelyremoved.
Limitations of Cascade1. More expensive because of additional hardware needs.2. The primary loop must be substantially slower than thesecondary loop.3. In some applications it is difficult to break the process intoa primary and secondary loop and identify the supplyvariable.4. Compared to a feedback loop, it is more difficult to start upand tune a cascade loop.
Specific Cascade ApplicationsValve PositionerThe primary reason for having a positioner is to remove hysteresisfrom the valve.
Limit CyclingLimit cycling can be another consequence of hysteresis, or deadband. The limit cycle is a clipped sine wave of the manipulatedvariable. Controller adjustments (tuning) cannot eliminate theseoscillations. Widening PB will increase the amplitude and theperiod of oscillation, while decreasing integral action reducesamplitude and increases the period.Recognizing a limit cycle wave (clipped sine wave) can eliminatesome frustrating and unsuccessful tuning effort. The only solutionsto a limit cycle are as follows:• Use a valve positioner or other cascade application.• Remove integral action from the controller.
Temperature On Flow Cascade ControlTemperature on flow is a good candidate for cascade control. Thesupply is well defined and the flow and temperature processeshave significantly different natural periods allowing a good cascadewithin the natural period ratio criteria.
Temperature-On-Temperature Cascade Control Of An ExothermicReactorThe idea here is to keep the temperature inside the reactor (T1) atthe desired value by controlling the temperature of the jacket (T2)by manipulating cooling water flow to the jacket.
Flow as the Inner LoopThe secondary loop is frequently a flow loop as seen inthe various temperature cascades.The benefits are that the flow loop protects the primaryloop from supply upsets;overcomes non-linear valve characteristics;and, reduces the effect of valve friction on the primarycontrolled variable.
Level on Flow (Valve Positioner) CascadeA level application requiring precise control and unableto attain it due to valve hysteresis or frequent supplyupsets.It is a good candidate for level valve position cascade.A cascade through either a valve positioner or a flowloop can be used since the level loop (primary) is mostlikely four times slower than the valve position loop, sothat the criteria 1/ 2 > 4 is not violated.
Integral Windup Preventing Measures in CascadedLoopsIf in attempting to eliminate a sustained error, thecontroller output goes beyond 0 to 100%, the controlleris wound up.Windup occurs if the error persists, with the valve fullyopen and the controller output at 100%.The controller becomes saturated, with loss of control.
Windup Prevention MeasuresPlace controller in manual.The operator can intervene to get any controller(analog on digital) out of the windup state by puttingit in manual.This is a simple solution, but not practical in mostapplications.Sooner or later this approach fails.
1. Place the primary controller in manual and the secondary controller to the local set point.2. Tune the secondary controller as if it were the only controlloop present.3. Return the secondary controller to remote set point andplace the primary controller in auto.4. Now tune the primary loop as if it were the only controlloop present.Remember, when tuning the primary controller that thereshould be no interaction between the primary and secondaryloops.
Feedback Loop Advantages• Does not require extensive knowledge of the process.• Easy to implement (start up and tune).• Requires minimal amount of hardware (leastexpensive control strategy.)• Can be successfully implemented most of the time.(Feedback is sufficient 80 -90 % of the time.)• Reasonably good control.
Feedback Loop Disadvantages• Process characteristics dictate the response.• Response is oscillatory.• Cannot handle frequent load upsets.• Trial and error solution to valve position consumesmore energy.
If in addition to the load upsets the process was alsosubject to frequent supply upsets, cascade control wasthe solution.
Feedforward or calculation control is the alternativecontrol strategy when we are unwilling or unable toaccept an oscillatory type of response in a givenapplication, or if the load upsets are very frequent (<3 n) the controlled variable does not have a chance tosettle out.
Feedforward Advantages• Can handle processes with frequent load upsets (< 3tn).• Potentially perfect control without oscillations.• Response virtually independent of processcharacteristics.• Minimum integrated errors (IE, IAE) can approach zero.• Avoiding a trial error search of valve position conservesenergy.
Feedforward Disadvantages• Requires more knowledge of the process.• Requires additional engineering effort and time.• Requires additional hardware for implementation.• More expensive than feedback control.• Economic justification to implement feedforward is madeconditionally.
Feedback Trim LoopsThe feedforward model attempts to predict the effect ofsteady state and dynamic loads on the product beingmade.It is not feasible to include all the loads that affect theproduct, in order to have a perfect feedforward model.It is impossible to come up with a perfect feedforwardrequiring the need to have a corrective feedback loopknown as the feedback trim loop.
Mass Flow Processes @ S.S. LEVEL = CONSTANTas dh/dt = 0Thus the steady state calculation in this example will simply make theflow input equal to the flow output. @ S.S. Fin = FoutTherefore Fin = Fout
•For negative feedback, an odd number of reverse-actingelements is needed.•The final actuator, process and transmitter are all direct-actingelements.•The controller is put in a reverse-acting mode for negativefeedback.
•In open-loop test to check, it is found that as the steam flowor load increases, the level in the drum initially increases(instead of decreasing as expected.)•Typically, the level will go up initially and then come down asshown, temporarily creating a positive feedback situation andloss of control.•This happens because as the load increases due to moresteam flow, the pressure in the drum decreases, causing theliquid in the drum to temporarily increase or swell.
Two-Element Feedforward Drum Level Application•During steady state operation the steam flow (load)information is used to control the feed water flow on apound-to-pound basis responding immediately to anyload changes.•The drum-level feedback trim loop provides thenecessary slow corrections to bring measurement backto the set point.•This configuration assumes a linear and repeatablerelationship between the load and the feed water valve.•If this is true then two-element control is sufficient.
Energy Flow Feedforward Applications• Energy flow processes vary in their complexity.• These processes must be sufficiently well definedbefore attempting feedforward control.• For a given process there may be several loads thataffect the product from the steady state point of view.
• Some of these load contributions are nonlinear and insome cases difficult to evaluate and implement in themodel.• These are the type of processes that consist of multiplelags and long dead-times which make them difficult tocontrol with a feedback loop and thus good candidatesfor a feedforward strategy.
Simple Energy Flow Example•To implement this in a feedforward loop, measure Qout and putan equal amount of Qin.•If succeed, the temperature in the vessel will stay constant.
Recognize that this equation is:1. Steady state without any dynamic considerations.2. Only the major loads are represented in the model.3. Minor loads are not accounted for. These include: • losses to ambient, • measuring element and transmitter accuracy, • change in efficiency due to fouling (scaling) or change in operating point, • heat lost in condensate.4. Supply variations relating to the energy of the steam (enthalpy) are notaccounted for. This might dictate cascade for supply upsets, not uncommon inthis type of application.
Applying A Feedback Trim Loop To The Feedforward
Trim Loop Characteristics:• Use a P + I controller tuned for a slow response, noQAD.• Typical settings require wide proportional bands (lowgain) and relatively long integral times in min/rep (i.e. 2-5 min/rep), no derivative action.• The idea is to take slow corrective action withoutaffecting the major feedforward scheme.• Do not introduce non-linear elements that affect thegain versus operating point relationship of the loop.
• Remember, if unable to linearize for constant loopgain, tune at the highest gain, sluggish response isacceptable in this case.• If the feedforward model is reasonably accurate, thetrim controllers output should be 50% during normaloperation.• If this is not the case, i.e., output of trim either high orlow, there is a good chance that the model does notaccurately represent all major loads.
Ratio Control Scheme• Ratio is a rudimentary form of feedforward where onevariable is controlled in ratio to another.• It is used in processes where two components aremixed together in a certain proportion or ratio.• The controlled variable in effect is the ratio.
Protection of Equipment (Safety)Parallel Metering Combustion SchemeIn boiler applications the furnace control system mustsatisfy various needs:•Maintenance of safe furnace conditions•Maintenance of safe furnace pressure in balanceddraft units•Satisfaction of the energy demand•Maintenance of correct air/fuel ratios
Pumping Station On a PipelineThe system should provide protection against the following:• Cavitation. If the suction pressure drops below apredetermined low value, the valve starts closing to bringsuction pressure up and avoid cavitation.• Motor Load. As the motor draws a current exceeding themotor specifications, the valve starts closing to protect themotor.• Downstream Pressure. If the discharge pressure attempts toexceed the maximum recommended downstream pressure, thevalve closes to prevent overpressurizing process piping.
Tuning Selective Loops• Tune each loop and testing the system forfunctionality.• When all loops are tuned, check schemeperformance.• Control should alternate smoothly, without a"bump," automatically transferring from onecontroller to another through the selective system.
•The word adapt means to change or fit by modification to newconditions.•An adaptive control system may be defined as a system whoseparameters automatically change in response to changing processcharacteristics.•The automatic change of the control parameters allowscompensation for the changes in the process characteristics andthe maintenance of a constant loop gain.•A simple linearization to achieve constant steady state is notconsidered adaptation since all the controller functions remain thesame.
•A nonlinear controller typically used in a pH applicationoperates at different gains based on the loop operating point.•This controller is not considered adaptive since its controllerfunctions are fixed.
•If the titration curve drifts (changes shape) the linearization loses itseffectiveness and there is nothing the controller can do to take care of theproblem.•Therefore, this is strictly nonlinear control. Remember, to be adaptive, thecontroller must change its parameters in order to accommodate thechanging process parameters.•To accomplish this requires a more capable controller as well as additionalcommunication between the process and the controller.
Approaches to AdaptationA few approaches have been used to implementadaptive control strategies:• Gain scheduling or programmed adaptation - basedon a change in a process variable i.e. the set point.• Feedforward adaptation - based on a change in load.• Feedback adaptation - based on a change in thecontrolled variable (measurement.)
Example of Programmed Adaptation Using Process Variable Information
Process Equations: C1 = K11g11m1 + K12g12m2 C2 = K21g21m1 + K22g22m2Changing m1 affects both C1 and C2.Changing m2 affects both C2 and C1.
Simultaneous Control of Pressure and Flow•This involves the simultaneous control of pressure and flow with thefact that both valves affect both the flow and the pressure.•The first consideration is to decide which valve should be assigned tocontrol a particular variable.•The second consideration is whether a control system can be designedto cancel the interaction between two loops.
AI - Analog InputThe Analog Input block takes the input data from the Transducer block, selected bychannel number, and makes it available to other function blocks at its output.266
DI - Discrete InputThe DI block takes the manufacturer’s discrete input data, selected by channelnumber, and makes it available to other function blocks at its output.267
PUL – Pulse InputThe Pulse Input Block provides analog values based on a pulse (counter) transducer input.There are two primary outputs available. An accumulation output is intended to beconnected to an integrator block for differencing, conversion, and integration. This is mostuseful when the count rate is low relative to the block execution rate. For high countrates, the accumulated count of pulses per block execution can be interpreted as ananalog rate (vs. accumulation) value and can be alarmed. 268
PID - PID ControlThe PID block offers a lot of control algorithms that use the Proportional, integral andderivative terms. 269
EPID – Enhanced PID ControlThe EPID block has all parameters of the PID block. Additionally it provides 4 types forbumpless transference from Manual mode to Auto mode, and also a special treatmentfor tracking outputs.APID – Advanced PID ControlThe advanced PID function block provides the following additional features comparingto the standard PID algorithm and the enhanced PID:• Selection of the terms (proportional, integral, derivative) calculated on error orprocess variable• PI Sampling algorithm• Adaptive gain• Configurable Limits of anti reset wind-up• Special treatment for the error• Discrete output to indicate the actual mode 270
ARTH - ArithmeticThe ARTH block can be used in calculating measurements from combinations of signalsfrom sensors. It is not intended to be used in a control path, so it does not supportcascades or back calculation. It does no conversions to percent, so scaling is notsupported. It has no process alarms. 271
SPLT-SplitterThe Splitter block provides the capability to drive multiple outputs from a singleinput, usually a PID. This block would normally be used in split ranging or sequencing ofmultiple valve applications. Included in the block features are the capability to openvalves as part of a predetermined schedule and leave open or closed a given valve afterthe controller has transitioned off the valve. The splitter supports two outputs. Since thisblock will participate in the control path after a PID block, back calculation support isincluded. 272
CHAR - Signal Characterizer•The block calculates OUT_1 from IN_1 and OUT_2 from IN_2, according to a curvegiven by the points: [x1 ;y1 ], [x2 ; y2 ]..............[x21 ; y21]Where x corresponds to the Input and y to the Output.•OUT_1 is related to IN_1 and OUT_2 is related to IN_2 using the same curve, but thereis no correlation between IN_1 and IN_2 or between OUT_1 and OUT_2. 273
INTG – Integrator•The Integrator Function Block integrates a variable in function of the time oraccumulates the counting of a Pulse Input block. The integrated value may goup, starting from zero, or down, starting from the trip value (parameter SP). The blockhas two inputs to calculate flow.•This block is normally used to totalize flow, giving total mass or volume over a certaintime, or totalize power, giving the total energy. 274
OSDL - Output Signal Selector and Dynamic LimiterThe output signal selector and dynamic limiter block (OSDL) provides two differentalgorithms types.•As Output Selector the cascade input may be routed for one of two outputs based onthe value of the OP_SELECT input parameter.•As Dynamic Limiter the cascade input is transferred to both output, but it is limited bythe secondary inputs multiplied by a gain, plus a bias. The Dynamic LIMITER is extremelyuseful in one of its most important applications: combustion control with double crosslimits. 275
FMTH – Flexible Mathematical BlockThis block provides mathematical expression execution with inputs, outputs andauxiliary variables generated by the user, and also including conditional expressions.The FMTH block has the following characteristics:• It allows execute several mathematical expressions “customized” by user with inputand output values, and also using auxiliary variables in these expressions.• Friendly edition of the mathematical expressions, similar to the Microsoft Excel.276
• It allows the usage of the following operations described in the table below: 277
AO - Analog OutputThe Analog Output Block is a function block used by devices that work as outputelements in a control loop, like valves, actuators, positioners, etc. The AO block receivesa signal from another function block and passes its results to an output transducer blockthrough an internal channel reference. 278
DO - Discrete OutputThe DO block converts the value in SP_D to something useful for the hardware found atthe CHANNEL selection. 279