Method of collecting data for process identification of a multivariable process

Abstract

A method of collecting data for process identification of a multivariable process is provided. The method includes, for each input variable of a set of input variables of the multivariable process, performing a bi-directional excitation experiment. The bi-directional excitation experiment includes setting the input variable at an initial input value. The bi-directional excitation experiment includes performing a first excitation of the input variable, comprising setting the input variable at a first excited input value at a first time, wherein the first excited input value differs from the initial input value by a first amount. The bi-directional excitation experiment includes measuring a plurality of output variables of the multivariable process in response to performing the first excitation, wherein a respective hysteresis level is associated to each of the measured output variables. The bi-directional excitation experiment includes identifying a hysteresis exceeding output variable among the measured plurality of output variables, wherein the hysteresis exceeding output variable is an output variable having a measured value that exceeds the hysteresis level associated with the output variable. The bi-directional excitation experiment includes performing a second excitation of the input variable in response to identifying the hysteresis exceeding output variable, wherein performing the second excitation comprises setting the input variable at a second excited input value at a second time, wherein the second excited input value differs from the initial input value by a second amount, wherein the first amount and the second amount have opposite signs. The bi-directional excitation experiment includes measuring at least the hysteresis exceeding output variable in response to performing the second excitation. The bi-directional excitation experiment includes setting the input variable at a final input value at a third time after the second time.

Description

METHOD OF COLLECTING DATA FOR PROCESS IDENTIFICATION OF A MULTIVARIABLE PROCESS FIELD

[0001] Embodiments of the present disclosure relate to methods and apparatusesfor collecting data for model identificationof anindustrial process.The methods described herein involve performing experimentswherea responseof theoutput variables ofthe system to excitations of the input variables is measured, and a model ofthe process isdetermined based on said experiments. BACKGROUND

[0002] In many applications, it is important to design a mathematical model of ana priori unknown industrial process. An industrial process may have one or more inputs and one or more outputs. The inputs may be set to suitable values, which may trigger aresponseof one or more outputs of the system. For example,increasing the valueofan inputvariable maycause acorresponding increase of oneor more outputsofthe process. The mathematical relationship between thebehaviour of the outputs as a functionofthe inputs may be captured, at least approximately,by a model of theprocess.

[0003] In order to allow designing a model that correctly describes the behaviourof aprocess,data about said behaviour can be collected by performing measurements. For example, the inputs of the process maybesettoa pluralityofvalues, and the response of the outputs thereto may be measured. Basedonthe measured data, amodel of theprocessmay be constructed.

[0004] Achallenging taskin thisrespect istodesign suitable experiments thatreveal a sufficient amount of informationabout theprocessto enable the design ofan accurate model. At the same time, such experiments should not become too complex or time-consuming. That is to say, it is beneficial to design simpleexperiments that allow extracting usefulinformation about the process whileperturbing the normal operation of the process as little as possible.

[0005] Forsingle-input-single-output processes, convenient experiments havebeen designed in thepastthat reveal usefulinformationaboutthe process basedona limitedamountofmeasurements, and that henceallow constructingamodelofthe process in an efficient manner.

[0006] For processes having multiple inputs and outputs, the task in question ishowever considerably more challenging, in light of the increased number of degreesof freedominvolvedin suchsystems. Therefore, there is a need for improved methodsforgathering data for model identification of multivariableprocesses.SUMMARY

[0007] According to an embodiment, a method of collecting data forprocessidentification ofamultivariableprocess is provided. The method includes, for eachinputvariableofa setofinput variables of the multivariable process, performing abi-directionalexcitation experiment. Performing the bi-directional excitation experiment includes setting the input variable at an initial input value. Performingthebi-directionalexcitation experiment includesperforming a first excitationof theinput variable, comprisingsetting the input variable at a first excited input value atafirst time, whereinthe first excited input value differs from the initial input valueby a firstamount. Performing the bi-directional excitation experiment includes measuring a plurality of output variables of the multivariableprocessin response to performing the hrst excitation. A respective hysteresis levelisassociated to each ofthe measured output variables. Performing the bi-directional excitation experimentincludes identifying a hysteresis exceeding output variable amongthe measuredplurality of output variables, wherein thehysteresis exceeding output variable is anoutput variable havingameasured value that exceeds the hysteresis level associatedwith the output variable. Performing the bi-directional excitation experiment includes performinga second excitation of the input variable in response to identiffing the hysteresis exceeding output variable, wherein performing the second excitation comprises setting the input variable at a second excited input value at asecond time. Thesecond excited input value differs from the initial input value bya second amount. Thefirstamount andthe second amount have opposite signs.Performing the bi-directional excitation experiment includes measuringatleastthehysteresis exceeding output variableinresponsetoperformingthesecondexcitation. Performingthe bi-directional excitation experiment includes setting theinput variable at a finalinput value at a third time after the second time.

[0008] According to a further embodiment, a method of model identification of amultivariable process is provided. The method includes performingthe method ofcollecting data according to any of the embodiments described herein. The methodincludesdetermining amodel of at least aportion ofthe'multivariable process basedon measurement data obtainedfrommeasuringone ormoreoutput variables during at least one of the bi-directional excitation experiments.

[0009] According to a further embodiment, an apparatus forcollectingdataforprocessidentification of a multivariable process is provided. The apparatus includesoneormoreinput devices. The apparatus includes one or more measurementdevices. The apparatus includes a control systemconnected to theoneor more input devices and the one or more measurement devices. The apparatusis configured toperform,for each input variable of a set of input variables of the multivariableprocess,a bi-directional excitation experiment under the controlofthe controlsystem. The bi-directionalexcitation experiment includessettingthe input variable at an initialinputvalueusing an input device. The bi-directional excitationexperiment includes performing a first excitation of the input variable,comprisingsetting the input variable at a first excited input value at a first timeusing theinputdevice,wherein the first excited input value differs from the initial input value by a firstamount.The bi-directional excitation experiment includes measuring aplurality of output variables of the multivariable processinresponsetoperformingthe first excitation, wherein each output variableis measured using a measurementdevice, whereina respective hysteresis level is associated to each of the measured output variables. The bi-directional excitation experiment includes identifying ahysteresis exceeding output variable among the measuredpluralityof outputvariables, wherein thehysteresis exceedingoutput variableis an output variablehaving a measured value that exceeds the hysteresis level associated with the output variable. The bi-directional excitation experiment includesperforminga second excitation of the input variable in response to identifying the hysteresis exceedingoutput variable, whereinperformingthe secondexcitation comprises setting theinput variable at asecond excited input value at a second time using the inputdevice, wherein the second excited input value differs from the initial input value by a second amount, wherein the first amount and the second amounthave oppositesigns. The bi-directional excitationexperiment includes measuringatleast thehysteresis exceeding output variable using a measurement device in response toperforming the second excitation. The bi-directional excitation experiment includessetting the input variable at a frnal input value at a third time afterthe secondtime using the input device.

[0010] According to afurther embodiment, a computer program for collectingdata for process identification of a multivariable process isprovided.The computerprogram includes instructions which, when the program is executed by a computer,cause the computer toperform,for each input variable of a set ofinput variablesofthe multivariableprocess,a set ofinstructions. Theset ofinstructions includesreceiving firstmeasurement data resultingfrommeasuring aplurality ofoutputvariablesof the multivariable process in response to performing a first excitation of theinput variable, wherein performing the first excitation comprises setting theinput variable at a first excited input value at a first time, wherein the first excited input value differs from an initial input value of the input variable by a first amount, wherein a respective hysteresis level is associated to each of themeasuredoutputvariables. The set ofinstructions includesidentifyinga hysteresis exceeding outputvariable among the measured plurality of output variables based on the firstmeasurement data, wherein the hysteresis exceeding output variable is anoutputvariablehaving a measured value that exceeds the hysteresis level associated withthe output variable. The setofinstructionsincludes receiving second measurementdata resulting from measuringatleast the hysteresis exceedingoutput variable inresponse to performingasecond excitationof the input variable, whereinperformingthe second excitation comprises setting the input variable at a secondexcitedinput value at a second time in response to identifuing the hysteresisexceeding output variable, wherein the secondexcitedinputvalue differs from theinitial input value by a second amount, wherein thefirstamount andthesecondamount have opposite signs.BRIEF DESCRIPTION OF THE DRAWINGS

[0011] The components in the Figures are not necessarily to scale, insteademphasis being placed uponillustratingtheprinciplesof the invention. Moreover,inthe Figures,likereferencesignsdesignatecorrespondingparts. Theaccompanying drawings relate to embodiments of the disclosure and are described in the following: Fig.Ishowsanexampleof a multivariableprocessas considered in the present disclosure; Fig.2 illustrates the notionofhysteresisas considered in thepresentdisclosure; Fig. 3 illustrates abi-directional excitation of an input variable as considered inthepresentdisclosure;Figs.4-6 showabehaviour of output variables yby2and y: during a bi- directional excitation experiment as considered inthepresentdisclosure;Fig.7 provides a further illustration of a bi-directional excitation experiment as considered in thepresentdisclosure; andFig.8 shows an apparatus for collecting data for process identification of a multivariable process as considered in thepresentdisclosure. DETAILED DESCRIPTION

[0012] Reference willnow be made indetailto the various embodiments, one ormore examples of which are illustrated in each figure. Each example isprovidedby way of explanation and is not meant as a limitation. For example, features illustrated or described aspartof one embodiment canbe used onor in conjunction withanyother embodiment toyield yet a further embodiment. It is intended that the present disclosure includes such modifications and variations.

[0013] Within the following description of the drawings, the same referencenumbers refer to the same or to similar components. Generally, onlythedifferences with respect to the individualembodimentsaredescribed.Unlessspecifiedotherwise, the description of a part or aspect in one embodiment can apply to a corresponding part or aspect in another embodiment as well.

[0014] Fig.1 shows an example of a multivariableprocess100 havinginputvariables I l0 and outputvariables 120.

[0015] Theinput variables of a multivariable process are denoted herein as ul, u2,.... The output variablesare denoted as yr, y2,....Aninput variable may takedifferent values, such as values lying within a certain numerical range. A value taken by an input variable is sometimes referred to herein as an input value oftheinput variable, e.g. in cases where itisuseful to emphasizethatthevalue inquestionis associated with aninputvariable. Likewise,an output variable may takedifferentvalues, which may be called output values.

[0016] A multivariableprocess as described herein may be an industrial process,e.g. a process performed in an industrial plant. Embodiments described herein arenotlimited to specific examples of industrialprocess,but are generally applicable to any kindofindustrial process.

[0017] A multivariable process as described herein can beunderstoodas a processhaving N input variables and M output variables, wherein at least oneof NandMis greaterthan l. According to embodiments, the multivariable process includes apluralityofinput variablesand apluralityof output variables. The number of inputvariables of the multivariable process may be equalto or different from the numberof output variables of the multivariable process. The numberof inputvariables and / or the number of output variables may be 5 or larger, particularly 16 or larger,more particularly32 or larger. The number of input / output variables shown in the hgures is exemplary and the disclosure is not limitedthereto.

[0018] An input variable of the multivariable processmay be a variable that isadjustable or controllable. The input variable may be set at a specific value, e.g.byaninput device. Adjusting an input variable may result in a response of one or moreoutput variablesof the multivariableprocess.Theresponseof an output variablemay be measured, e.g. by a sensor. Accordingto embodiments described herein,adjusting an input variable may cause a response of several, in particularall,output variables of the multivariable process.

[0019] A multivariable process as described herein may have a behaviour, ordynamics, that is at least partiallyunknown. An aim may be to design a model describing the multivariable process, such as a mathematicalmodel desuibing arelation between the inputs and outputs of the multivariable process. A model may be designed based on measured data obtainedbyperforming oneormoreexperimentswithrespecttothe multivariableprocess.The taskofdesigning amodel can include an initial phaseof designing an initial model of theprocess.The initial model may be a crude model, or approximative model,that captures at leastsome characteristics of the process. After the initial model has been designed,theinitialmodelmay be used to construct a more detailed experiment for the process.

[0020] An initial crude model may be beneficial in many situations forthecommissioning ofamultivariable controller.A typical example is when designingan identification experiment to be used to generate data for the identification of a dynamical model.

[0021] Embodimentsdescribedherein may be beneficial for the design ofaninitial model of a multivariableprocess.Thepresent disclosure providesexperimentsthat are useful for revealing at least some characteristics of the multivariable process. The experiments inquestioninvolve exciting(asubset of) the input variables of the multivariableprocessaccording to a specifickindofexcitation andmeasuring the response of (a subset of) the output variables.100221The experiments described herein involve the notionofhysteresis. Arespective hysteresis level may be associated with at least some, particular all, output variables of the multivariableprocess.A hysteresis level associated withanoutput variable can beunderstood as awidthparameter e that determines a range,or interval, for the output variable. As long as the value of the output variableremainsinsidesaid range,itmay be the case that no reactioninterms of anadjustment of the input variables is triggered, i.e. the multivariableprocessmay continue without changing the values of the input variables. If the value of the output variable leaves said range,areaction, suchasan adjustment ofthe valuesof one ormoreinputvariables, may be triggeredinresponse thereto.

[0023] Fig.2illustrates the notionofhysteresis as considered in the presentdisclosure. A plot 250 of the behaviour an output variable yi as a function of timeisshown. The output variable yi can be any arbitrary output variable of the multivariableprocess.The horizontal axis 210 represents a timeparametert. Thevertical axis 220 represents the value of the output variable yi. A hysteresis level(225a,225b) defined by a widthparameters may be associated with theoutputvariable yi. At an initial timet:0, the value of yi may be yio. The value yto can beany suitable value depending on the context and is not limited to any specific value. The valueyiocan, for example, beareferencs value thatistargetedfor the outputvariable yiby setting a specific combinationof values of the input variables, or canbe an equilibrium value of the output variable yithatis reached whenmaintainingthe input variables atcertain values for a longer period of time. The width parametere defines an intervallyio -e,]io+ e] surrounding the value yio. When the value ofthe output variable yiis outside said interval, the hysteresis level (225a,225b) issaid to be exceeded. For example, at time 214andtime2l6,the corresponding valueof yt indicated at254 and256 is smaller than yio - t,respectivelylarger thanyiofe.Inboth cases, the hysteresislevelassociatedwithyiissaid to be exceeded. Attime 212, the corresponding valueofyiindicated at252lies inside the interval [yio-t,yio *e], so that the hysteresis level is not exceeded.10024]The respective hysteresis levelsassociated with different output variablesmay be different from each other.Afirst hysteresislevel may be associated with ahrst output variable of the multivariable process. A second hysteresislevelmay be associated with a second output variable of the multivariable process. The firsthysteresis level may bedifferent from the second hysteresis level.

[0025] According to embodiments described herein, the hysteresis levelassociated with an output variable can be determined basedona noise parameter associated with the output variable. The output variable may be subjecttonoise.The noise may causefluctuations of the output parameter. The fluctuations of theoutput variable may ariseeventhoughthe inputparametersmay be maintained at constant values. A hysteresis level maybe settocompensatefor noise fluctuationsof the output variable. For example, thewidthparameterrmaybe settobeamultiple of a standard deviation of the noise acting on the outputvariable, such as3-4 times the standard deviation, or may be a multiple of a peak noise,suchas3-4times thepeaknoise. Both the standard deviation of the noise and the peak noiseare examples of anoiseparameter asdescribed herein. By settingahysteresis levelin this manner, fluctuationsof the output variable that arecausedby noise willmostly remain inside the hysteresis level, and hencedonottrigger an adjustment ofthevaluesoftheinputvariables, in other words small fluctuations that are merely due to noise fluctuations do not cause a reaction of the system.

[0026] Embodiments desuibed herein may include maintaining at least some,particularlyall, input variables of themultivariable process at a substantiallyconstant value over a period of time. The period of time may be configured to allowat least some, particularly all, output variables to reach an equilibrium state. An equilibrium state of an output valuecan beunderstoodas a state where the valueofthe output variableremainssubstantiallyconstant apart from small fluctuations thatmay be due to noise. The method described herein may include determining a noiseparameter for at least some, particularly all, output variables. A noise parameterassociated with an output variable, suchasa standard deviationof noise or a peaknoise, may be determined byperforming oneormore measurements of the outputvariable while theinput variables at maintained at their substantially constant values. For example, the one or more measurements may involve determiningfluctuations of the output variable due to noise. A hysteresis level associated withthe output variablemay be determined based on the noise parameter, as described herein.[00271According to embodiments described herein, a set of input variables of the multivariable process is determined. The set of input variablesmayconsist of allinput variables of the multivariable process or a subset thereof. The set of inputvariables includesa pluralityofinput variables, such as 2 or more, 5 or more, or l0 ormore inputvariables, or an even higher number of input variables. For each input variable utinthe setofinput variables, an experiment isperformedin which data regarding the behaviour of the multivariableprocessisgathered.The experimentinvolvesexciting themultivariable systemby abi-directional excitation andmeasuring the response of the system to the excitation.

[0028] The method described herein may include selecting a first input variableur from the set of input variables.Thefirstinput variableurcan be any inputvariable of set of input variablesand, more generally, can be any input variableofr0140the multivariable process. With respecttothefirst input variable ur, a bi-directionalexcitation experiment may be performed.

[0029] Fig.3 illustrates a bi-directional excitation associatedwiththe input variable ur. The term "bi-directional" refers to the fact that two excitations inopposite directions (namely, the"first excitation" and theoosecondexcitation" asdescribed herein) are performed, i.e. anupward / positive excitation followed by adownward / negative excitation or vice versa, as explained in further detail below.

[0030] In Fig. 3, a plot 350 of the value of the input variable ur as a function oftime is shown. The horizontalaxis 310 represents a timeparametert. The verticalaxis 320 represents the valueofthe input variable ur.

[0031] An at initial timet:0,the input variable ur may be set at aninitialinputvalue uro, indicated at 321. The initial input value uro can be an arbitrary valuechosen forthepurposeof the experiment.

[0032] Afirstexcitation of the input variable ur isperformed.The value of theinput variable ur may be increased (e.g. accordingtoa monotonously increasingfunction, such as an exponential function) until a first excited input value u16 * A, indicated at322, is reached at a first time tr, indicatedat3l2.The first excited input value may be chosen to be a sufficiently large value, so that a response of at leastoneoutput variable of theprocesscan be expected to occur, for example in light ofa basic a prioriknowledgeof themultivariableprocess.The first excited input value uro f A differs from the initial input value uro by a firstamountA, indicatedat332.In the example shown inFig.3, thefirst amountAis apositiveamount, so that thefirstexcited input value is larger than the initial input value uro.

[0033] Insome embodiments, the input variableulmay be maintainedsubstantially at the first excited input value uro * Afromthefirst time tr to asecondtimetz indicatedat314. Thefirst excitation may end at substantially the secondtime tz. That the input variable ur is maintainedsubstantially at the first excitedinput value ulo+A may include deviations with respect to the first excited input tU40value uro+A of, for example,5-l0Yo of the valueuro +A. The timeperiod fromthe first time tr to the second time tz has a first duration 342. According to embodimentsdescribedherein, the first duration342isdetermined bya response of one or moreoutput variables, as described in more detail below.

[0034] A second excitation of the input variable ur is performed. At the secondtime tz, the input variable ur is set to a second excited input value, indicated at324.Inparticular, atthe second time tz,the value of the input variable ur may be changedfrom substantially thefirst excited input value to the second excited input value. The second excited input value may differ from the initial input value uro by asecond amount, indicated at 334. The second amount and the first amount haveopposite signs, so thatthe excitations arebi-directional.The second amount may beanegative amount,such that the second excited input value is smaller than the initial input value uro. In theparticularexample, the second excited input value is equal to rto- 24. Accordingly, the absolute value of the second amount is twice the absolutevalueofthe first amount. The disclosure is not limited thereto, and differentmagnitudes of the second amount may be considered.

[0035] Insome embodiments, the input variableulmay be maintainedsubstantiallyat the second excited input value from the second time tz to a third timetlindicated at3l6. The timeperiodfrom the second time tz to the third time t:has a second duration 344. According to embodiments described herein, the secondduration 344 is apredeterminedduration, as described in more detail below.Thesecond excitation may end atsubstantially the third time t:.

[0036] Atthethirdtime t:, the input variable ur may be set to a final input value.Inparticular, at the third time t:, the value of the input variable ur may be changed fromsubstantiallythe second excited input value to the final input value. In the example shown, the final input value may be substantially the same(allowing,for example, deviations of 5-10%) as the initial input value uro. The input variable ur may be maintained substantially at the final input value fora periodof time.

[0037] An advantage of a bi-directional excitation, as described herein, is that thesecondexcited input value, which is an excitation of the system in a directionoppositetothe first excited inputvalue, allows bringing the system back to anequilibrium state. In comparison,ifboth excitations weretobe performedin thesame direction, the system underlying the multivariable process might move awayfromequilibrium in an uncontrollable manner.

[0038] The bidirectional excitation shown in Fig. 3 is exemplary and can bemodified in several ways, including thefollowing.

[0039] The example shown in Fig. 3 involves a bi-directional excitation whereinthe value of the input variable ur is first increased to the first excited input value(positiveexcitation) and thereafter decreased to the second excited input value(negative excitation). Thedisclosure is not limited thereto. In other embodiments, a bi-directional excitation may be considered wherein the value oftheinputvariableur is first decreased and thereafter increased, so that the first excited input value issmaller thanthe initial input value(negativeexcitation) and the second excited inputvalue is largerthan the initial input value(positiveexcitation).

[0040] The example shown in Fig. 3 involves maintaining the input variable ursubstantially at the first excited input value from the first time trto the second timetz. The disclosure is not limited thereto. The value of the input variable may bechangedduring this timeperiod.The value of the input variable u1 may, forexample, be increasedduringat least a portionof theperiodfrom the first time tr tothe second time tz. In particular, the input variable ul maybeset atthefirstexcitedinput value as part of a continuous ramp-up of the inputvariableurthatstarts,forexample, shortly after the initial time t:0 and that continues after setting the inputvariable ur at the first excited input value. For example, the ramp-up may end shortly before, or substantiallyat,the second timetz.

[0041] The example showninFig.3involves a substantially instantaneouschange from the first excited input value to the second exitedinputvalueatthe second time tz. The disclosure is not limit thereto. The change from the first excitedinput value to the second excited input value may be a non-instantaneous change. Likewise, the change from the second excited input valueto thefinalinput valuemay be non-instantaneous.100421The example shown in Fig.3 involves a second.excited input value that istwice as large (in absolute value) as the first excited input value. The disclosure isnot limited thereto. Thesecondexcited input valuemay, for example, have the sameabsolutevalue as the first excited input value, so that the second excited input value is uro - A. Other examples can be provided. For example, the second excited inputvaluecan be any multiple of the first excited input value, or more generally anyfunction of the first excited input value.

[0043] The example shown in Fig.3 involves a final inputvaluethatissubstantially the sameas theinitialinput value uro. The disclosure is not limitedthereto. The final input value may be different from the initial input value.

[0044] The inventors have found that a bi-directional excitation experiment asdescribed above is a simple, short experiment that provides informative data, i.e.data that is useful for theidentification of a model, particularly an initial model, ofa multivariableprocess. Particularly, the bi-directional excitation experiment can be performed in a meaningful way with very minor a priori knowledge of the process.

[0045] During at least a portion of the bi-directional excitation experimentperformedwith respect to the input variable ur,a plurality of output variables maybe measured.The pluralityofoutput variables may consist ofalloutput variablesof the multivariableprocess, ora subsetthereof. For example, in somecasesit may be apparent, based e.g. on a priori considerations, that one or more output variablesare independent of the input variable ur. Such output variables may be disregarded,i.e. may not be part of the measured plurality of output variables. Thepluralityof output variables that is measured may depend on the input variable ur under consideration. For example, in a subsequent bi-directional excitationexperimentperformedwith respect to another inputvariableui, the pluralityof output variablesthat is measured may be different.

[0046] Measuring an output variable may include performing oneormoremeasurementsof the output variable, e.g. using a sensor or other measurementdevice. In some embodiments, an output variable maybe measured at apluralityof times while the bi-directional excitation in respectofan input variable is performed.Forexample,a sequenceof measurements of the output variable may be performed at regulartimeintervals.100471Accordingtoembodimentsdescribed herein, a plurality of outputvariables of the multivariable process may be measuredinresponsetoperformingthe first excitation of the input variable ur, in particular in response to settingtheinputvariable ur at the first excited input value. The plurality of output variablesmay be measured one or moretimes during the timeperiodfrom the first time tr tothe second time tz.

[0048] Figs. 4-6 show an example where three output variables yb y2andy:are measured during at least a portion of the bi-directional excitation performed inrespectoftheinputvariableur.Thatin thepresentexample a total of three outputvariables is measured is merelyfor thepurposeof illustration, and any numberof output variables may be measured.

[0049] Figs. 4-6 show horizontal axes 410, 510, 610, respectively, representingthetimeparametert, and vertical axes 420,520 and 620 representing the valueofthe output variablesytyzandyt,respectively. The first time tr, second time tz andthird time tr, which were also showninFig.3, are indicated again in Figs. 4-6. Plots450,550 and 650ofthe behaviourofthe respectiveoutput variablesasa functionof time are shown. The plots 450, 550 and 650 may be obtainedbyperformingapluralityof measurements of the output variables inquestion.

[0050] At time t:0, the output variables yb yz and yr have respective initialoutput values yrc,yzl and y:0, each being the valueof the respective output variablecorrespondingto the initial input value uro of the input variable ur. That is to say, when the input variable ur is set to the initial input value uro(fora sufftciently long time, so that equilibrium is reached, as describedherein), themultivariableprocessbehaves in amannersuchthatthecorresponding output valuesofthe output variables yby2 and yr are yro, yzo andyro,respectively. Each output variable yby2 and y: is provided with an associated hysteresis leveI425a-b, 525a-b and 625a-b,respectively, surrounding therespectiveinitial outputvalues yrc, yzl and ylo. Thehysteresis levelsmaybedetermined basedona noise parameter, as described herein.

[0051] According to embodiments described herein, the second time tz, which isthe time at which the input variable ur issetto thesecondexcitedinput value (asdescribed above withrespecttoFig.3), is not a predetermined time. The secondtimetz may depend on a response of at least one, and a priori unknown, output variable among the plurality of measured output variables triggered by the firstexcitation.

[0052] Accordingly,thefirst duration342, whichis the duration of time betweensettingthe input variable ur to the first excited input value and setting the input variable ur to the second excited input value, is not apredeterminedduration.Thefirst duration342 may depend on a response of at least one output variableamongthepluralityof measuredoutput variables triggered by the first excitation.

[0053] With respect to theexample showninFigs. 4-6, it can be seen in Fig. 4that the output variable yr shows only a mild response after the first time tr, i.e. aftersettingthe input variable ur to the first excited input value, namely a small increaseofthe valueofyr. The response does not exceed the hysteresis level425a-bassociated with the output variable yr. In Fig. 5, the response of the output variableyz is more significant. Inparticular,the value ofyz reaches the associated hysteresislevel 525a-batthe second timetz, asindicated at 552.InFig. 6,theresponse of theoutput variableyris also significant, but thevalueofyr reaches the associatedhysteresislevel625a-b substantially after the second time tz, as indicated at 652. t6140

[0054] Accordingto embodiments described herein, inresponsetoperformingthe first excitation of the input variable u1, a hysteresis exceedingoutput variableis identified among the plurality of measured output variables (in this example the output variablesVtyzandy:). The hysteresis exceeding output variable is an outputvariablethatexceedsthe associated hysteresis level in response to the firstexcitation of the inputvariable ur. Whichparticularoutput variable among thepluralityof measured output variables is the hysteresis exceeding variable is a priori unknown. The hysteresis exceeding output variable is identified by inspecting the behaviour of thepluralityof measured output variables in response to the firstexcitationofthe input variable ur.

[0055] The plurality of measured output variables may include severaloutputvariables that exceed the associated hysteresislevel inresponseto thefirstexcitation of the input variable ur. According to embodiments described herein, thehysteresisexceeding output variable may be identified to be the first(i.e.chronologically the first) output variable among the measuredoutputvariablesto exceed the associated hysteresis level. Accordingly, with respect to the example shown Figs. 4-6, the hysteresis exceeding output variable may be identified to be the output variabley2,since the output variableyzreaches the associated hysteresislevel at the secondtimeh,whereasthe output variable yr does not reach the associated hysteresis level at all andtheoutput variable y:onlyreachestheassociated hysteresis level at a time later than the second time tz.

[0056] The hysteresis exceeding output variable does not necessarily have to bethe first output variable to exceed the associated hysteresis level. In someembodiments,itmaybe the case that the first output variable to exceed theassociated hysteresis level is, for reasons that may be apparentfrom thedesignof the system, not critical for the purpose of the bi-directional excitation experimentperformedin respect of the input variable under consideration. In such a case, saidoutput variable maybe disregarded, and the hysteresis exceeding output variablemay be another output variable,for example the chronologically second outputvariable to exceed the associated hysteresis level.t7140

[0057] According toembodimentsdescribed herein, the second time tz, being thetime at which the input variable ur is set to the second excited input value, depends on, or is determined by, the time at which the hysteresis exceeding output variable exceeds the associated hysteresis level. Inparticular,both times may be substantially the same. In other words, the input variable ul may be set to the second excited input value substantially at the time when it is determined that the hysteresis exceeding output variable has reached or exceeded the associated hysteresis level. In the example desuibed with respect toFigs.4-6, the output variableyz, i.e.the hysteresis exceeding output variable, reaches the associated hysteresis level at the second time tz. Accordingly, the input variable ur may be set to the second excited input value at substantially the second time tz.

[0058] In other words, according to some embodiments, in response to setting theinputvariableur to the first excited input value (first excitation), the behaviour of a plurality of output variables is monitored, and when the first output variable amongthese monitored output variables exceeds the associated hysteresis level, the inputvariable ur is set to the second excited inputvalue (secondexcitation).

[0059] Inlightofthe above,embodiments described herein involve monitoringthe response of a plurality of output variables with respect to an excitation of one of the input variables, wherein the time at which second excitation of the input variable is started is determined by a response of an a priori unknown output variable among the measured output variables. Embodiments describedhereintherebyinvolvea "global" monitoring of the output variables during the excitation experiment. An advantage is that the most significant output variable responding to an excitation can be identified more easily. The system can in a loose manner besaid to operate under feedback, assuring that no output is allowed to grow too large.In particular, embodiments desuibed herein thereby differ from experiments where the response of a fixed,pre-selected,output variable is monitored.

[0060] As described herein, the value of the input variable under consideration,e.g. the input variable u1, may be changedfromthe second excitedinputvaluetothe final inputvalue at the third time t:. Inparticular,the input variable maybesubstantially maintained at the second excited inputvaluefromthe second time tzto the third time t:. According to embodiments, the second duration 344 of thetimeperiodfrom the second time tz to the third time t: may be a predetermined duration.In this respect,the termoopredetermined"may be understood in the sense that thesecond duration 344 may be independentof a behaviour of the output variables inresponse to setting the input variable at the second excited inputvalue.In particular, at the time tz when the input variable is set to the second excited input value, thesecondduration 344 may already be fixed.

[0061] For example, according to embodiments, the second duration 344 may beset to be equal to the first duration 342. More generally,the second duration 344may be a function of, or may be determined by, the firstduration342.100621In light thereof, the second duration 344 may be determined based on different considerations than the first duration 342. Whereas the first duration342may depend on a response of the system,itmaybe thecasethat the second duration344 does not depend on such response. For example,itmaybe thecasethat themethod according to embodiments described herein does not waituntilthehysteresisexceeding output variable exceeds the associated hysteresis level asecondtimebeforeswitching from the second excited input value to the final inputvalue. For example, as illustratedin Fig. 5, the output variableyzexceeds thehysteresis level 525a-b at a time after the third time t3, as indicatedat 554.Inother words, the input variable ul may be set to the final input value at the third time t:,before theoutput variableyzexceeds the hysteresis level 525a-b, and in particular independently thereof.

[0063] As describedherein,at the third time t:, the input variableunderconsideration is set to the final input value. The input variable maybe maintainedsubstantially at the final input value at least until the measuredoutputvariables,particularlyall output variables of the multivariableprocess,have reached a valuethat stayswithin arangehaving aprescribedwidth over aperiodof time. Theprescribedwidth associated with anoutput variable may be configured to representa stabilization ofthe output variabletoa stateofequilibrium. For example, the prescribed width may be the widthparametere of the hysteresis level associated with the respective output variable. When an output variable yi stays within arange fyi,nnar -r,]i,finar+ e] having a width e for a suffrciently long amount of time, it maybe considered that the output variable has stabilized to the valueyi,nnur. Therein,the valueyi,nnurmay be equal to the reference valuesyiobased on whichthe hysteresislevels 425a-b,525a-band 625a-b were defined, or may be a different value. The latter may be the case, for example,ifthe multivariable process is an integratingprocess.

[0064] When the output variables have reached an equilibrium state, or moregenerallywhen the outputvariables have reachedavaluewithin theabove-mentioned prescribed range, the bi-directional excitation experiment in relation to the first input variable ur may end.

[0065] The method described herein may include collecting input data during atleast aportionof the bi-directionalexcitation experiment. The input data mayinclude one or more input values of the input variable ur under consideration during the experiment. The method may include any of the following, and any combination thereof: collecting one or more input values of the input variable before the firsttime tr; collecting one or more input values of the input variable from the first timetr to the second timetz;collectingoneormore input valuesofthe input variablefromthe secondtime tz to the third time tl; md collecting one or more input values of the input variable after the third time tr.

[0066] The method described herein may include collecting measurement dataresulting from one or more measurements, particularly aplurality of measurements,performed during at least aportionof the bi-directional excitation experiment.

[0067] The method may include any of the following, and any combinationthereof:performingone or more measurements of one ormoreoutput variables oftheplurality ofoutput variables (e.g. thevariablesyvyzandy:)before the first timetr; performing one or more measurementsofone or more output variablesof saidpluralityof output variables from the first time tr to the second time tz; performing one or moremeasurementsof one or more output variables of said pluralityofoutput variables from the second time tzto the third time tr;performingone or more measurements of one or more output variablesofsaid pluralityofoutput variables after the third time tr. Measurement data resulting from the measurement(s) may be collected.

[0068] Particularly, the method may include anyof thefollowing, and anycombination thereof: performingone or moremeasurementsof thehysteresisexceeding output variable before the first timetr;performingone ormoremeasurementsof the hysteresis exceeding output variable from the first time tr to thesecondtimeb;performingone or more measursments of the hysteresisexceeding output variable fromthesecondtime tz to the third time t3;performingone or more measurements of the hysteresis exceeding output variable after thethirdtime t:. Measurement data resulting from the measurement(s) may be collected.

[0069] After the bi-directional excitation experiment relating to the input variableur has ended,themethodmayproceedby selecting a second input variable uzfromthe set of input variables and performing abi-directional excitation experiment inrespect of said second input variable, analogous to the experiment described aboveinrespectof the first input variable ur. The method may proceed accordingly byperforminga bi-directional excitation experiment for all input variables of the setof input variables. It shall be understoodthat the aspects described above for the bi-directional excitation experiment relating to the first inputvariable ur also apply toeach bi-directional excitation experiment relating to any other input variable.

[0070] Fig.7provides a further illustrationof abi-directional excitation experiment as described herein. The experiment is performed in respectofanarbitrary input variable ui. The bi-directionalexcitation of said input variable mayhave a form as described herein, e.g. asshown inFig.3. Apluralityof output2u40variables yr to yn may be measured during the experiment. The initial output value of output variable yt is denoted byyroin Fig.7,for each k ranging from 1 to n. The value of output variableyr<attime tis denotedbyyr(t). Associatedwitheachoutputvariableyrisa parameter erdefiningthe respective hysteresis level. In response to the first excitation of the input variable ui, theresponseofeachof theoutputvariablesyrtoyn may be monitored. According to embodiments described herein, as soon as one output variable among these monitored output variables exceeds the associated hysteresis level(illustratedby the OR function in Fig. 7), the secondexcitation of the input variableuimaybe started atbox702. Particularly,atsuchtime, theinput variable ui may be set to the second excited input value. Further, inan example, the duration of the second excitation(secondduration 344) may be taken to be the same as the duration of the first excitation(firstduration 342), or at least maybe apredeterminedfunctionthereof.

[0071] As described herein, the bi-directional excitation experiments accordingto the present disclosure are simple, short experiments that provide informative data that is useful for the identification of a model of a multivariableprocess.

[0072] According to embodiments desuibed herein, a model of at least a portionof the multivariableprocess may be determined. The model may be based on inputdata andmeasurement data fromatleast one of the bi-directional excitationexperiments. The model may be an initial model as described herein.

[0073] According to some embodiments desuibed herein, the model may include,for at least one, particularly each, input-outputpair (ui, y.;)consisting of an input variable ui and an output variabley;of the multivariableprocess,anassociatedtransfer function. The output variableyjmaybethehysteresis exceeding outputvariableidentified in the bi-directional excitation experiment performed with regard to theinputvariable ui, or may be any other output variable.

[0074] The transfer function may be a first order transfer functionwitha delaySuch a transfer function may have the form:;61 K G;r(s)e -s / , where K, L and T are a priori unknown parametersofthe transferfunction. TheparametersK, L and T may depend on i andj,but this dependency is not shown inthe above formulafor ease ofpresentation.Theparametersin question may beestimated based on the measurement datacollected in the respective excitationexperiment(s). The set of transfer functionsQi(s)may formaninitialmodel of themultivariableprocess.The initial model may form the basis for determining a moredetailed model, by performingfurther measurements of the process.

[0075] The model,such a model involving transfer functions of the kind described above, may be determined from the measurementdata using a pluralityof commercially known techniques. For exampl e,the delayest andarmaxtoolsfromtheMatlab System Identification toolbox may be used for this purpose.

[0076] In the following, an example of one possible approach for determining atransfer functionG:i(s) isprovided.Thedisclosureisnotlimited thereto, and it shallbe understood that several other approaches are possible.100771For determining the transfer functionQi(s),itisbeneficial toconsideracorrespondingdiscrete time transfer function Fli(q). The transfer function I{:i(q) has the formwhereQ-1is the backwards shift operator,dis the delayinsamples,and bp and aare parameters. There are threeb-paramters to compensatefor apotential inaccurateestimationof the delay d. Evidently, once Fli(q) is determined, G;i(s) can bedetermined as wellsince both transfer functions can be mapped to each other.

[0078] The bi-directional excitation experiment relating to the input variable ui,as well as the measurement data obtained during said excitationexperiment, areconsidered.The excitation experiment may involve the input data sequence(wheretheindex i is omitted for ease of presentation) u(k)u(k + tt) u(k + 2h) u(k +Ntt),where kmay be a time shortly before the first time tr(wheretr is the time when theinputvariable is set to the first excited input value), h is a sampling interval and Nis a constant such that k + Nh representsa time near the end of the experimentrelating to theinput variable ui.

[0079] Themeasurement datathat isconsideredmay involve a plurality of measurementsof theoutput variable yj performed during the experiment, represented by an output data sequence(wheretheindex j is omitted)y(k)y(k+ tt)y(k+ 2h)y(k+Nh)

[0080] The output variableyjmay be thehysteresis exceeding output variableidentified insaidexperiment, ormay be a different output variable. The outputsequencs may be assumed to be noisy and may be filtered through a non-casual filter with zerophasedistortion to keep the waveform.

[0081] The modeling may be done in two steps using the input and the output datasequences.

[0082] First, the timedelay may be estimated. This may be performed using thefunctiondelayest from Matlab's System Identification toolbox. This provides thevalue of the parameter d in the discrete time transfer functionEi(q).

[0083] Further, the parametersaand by of the function functionf!i(q)may beidentified using the function armax from Matlab's SystemIdentification toolbox.An estimate of the uncertainty of theparameters may also be provided.

[0084] In light of the above, according to anembodiment, a method of collectingdata forprocessidentification ofa multivariable process is provided. The methodincludes, for eachinputvariable ofa setofinput variablesofthe muitivariabieprocess, performinga bi-directional excitation experiment. Performing the bi- directional excitation experiment includes settingtheinput variableatan initial input value. Performing the bi-directional excitation experiment includesperforminga first excitation of the input variable, comprising setting the inputvariable atafirstexcitedinputvalue at ahrsttime, wherein the first excited inputvalue differs from the initial input valueby a first amount. Performing the bi-directional excitation experiment includes measuring a plurality of output variables of the multivariableprocessin response to performing the first excitation. Arespective hysteresislevel is associated to each of the measured output variables.Performingthe bi-directional excitation experiment includes identifuing a hysteresis exceeding output variable among the measured pluralityofoutput variables, wherein the hysteresis exceeding output variable is an output variablehaving ameasured value that exceeds the hysteresis level associated with the output variable.Performingthe bi-directional excitation experiment includesperforminga second excitation of the input variable in responsetoidentifying the hysteresisexceeding output variable, wherein performing the second excitation comprises setting the input variable at a second excited input value at a second time. Thesecondexcitedinputvalue differs from the initial input value by a second amount. The first amount and the second amount have opposite signs.Performingthebi-directional excitation experiment includes measuringatleast the hysteresisexceeding output variable in response to performing the second excitation.Performingthe bi-directional excitation experiment includes setting the inputvariableat afrnalinput value at athird timeafter the secondtime.

[0085] That the pluralityof outputvariablesismeasuredinresponse toperforming the first excitationofthe input variable under consideration can be understood in the sense that the output variables in question are measured after the first excitationhasstarted, inparticularafter the input variable has been set to thefirstexcited input value (in otherwords after the first time tr).

[0086] According toembodiments, the measured pluralityofoutput variablesmay consist of all output variables of the multivariable process. Accordingly, all output variables may be measured inresponsetoperformingthe first excitation.

[0087] According to embodiments, the hysteresis exceeding output variable maybean a priori unknown output variable among the plurality of measured outputvariables. Identi$ing the hysteresis exceeding output variable may include determining which output variable among the plurality of measured outputvariables is the hysteresis exceedingoutput variablebased onmeasured valuesobtained by the measuring of the plurality of output variables.

[0088] According to embodiments, the time period from the second time to thethirdtime may have apre-determinedduration.

[0089] According to embodiments, the timeperiodfrom the first time tothesecond time has a first duration and the pre-determined duration of the time period from the second time to the third time is a second duration, wherein the secondduration may be a function of the first duration. Particularly, the second durationmay be substantially equal tothefirst duration.

[0090] According to embodiments, the hysteresis exceeding output variable maybe thefirst output variable among the measured plurality of output variables to exceed the associated hysteresis level in response to performing the first excitation.

[0091] According to embodiments, the input variable under consideration may bemaintained substantially at the final input value at least until each output variable of themeasuredplurality of output variables stays within a range havingaprescribedwidth overaperiod of time.

[0092] According toembodiments, the method may include,for eachoutputvariableofa setofoutput variables of the multivariable process, determining thehysteresis level associated with the output variable based on a noise parameter.

[0093] According to embodiments, the method may include maintaining the inputvariable under considerationat substantially thefirstexcited input value from thefirst time to the second time. Additionally or alternatively, the method may include maintaining the input variable at substantially the second excited input value from the second time to the third time.

[0094] According to embodiments, the second amount may be a function of thefirst amount.

[0095] According to a further embodiment, a methodofmodelidentification ofamultivariableprocessis provided. The method includes performing the methodofcollecting data according to any of the embodiments described herein. The methodincludes determining a modelof at leasta portionof the multivariableprocessbasedon measurement data obtained from measuring one ormore output variables duringat least one of the bi-directional excitation experiments.

[0096] According to embodiments, the model may include, for at least one input-outputpairconsisting of an input variable and an output variable of themultivariable process,afirstorder transfer functionwitha delay. Determining themodel may include determining at least one parameterof thefirstordertransfer function based on the measurement data.

[0097] According to a further embodiment, and as illustrated in Fig. 8, anapparatus 800for collecting data forprocessidentification of a multivariable process 100 is provided. The apparatus 800 includesone ormoreinput devices 810.The apparatus includes oneormore measurement devices 820. The apparatus includes a control system 850 connected to the one or more input devices 810 and the one or more measuremsnt devices 820. The apparatus 800 is configured toperform,for each input variable of a set of input variables of the multivariableprocess,a bi-directional excitation experiment under the control of the control system 850. The bi-directional excitation experiment includessetting the inputvariable at an initial input value using an input device 810. The bi-directional excitation experiment includesperforminga first excitation of the input variable,comprising setting the input variable at a first excited input value at a hrst time using the input device 810, wherein the first excited input value differs from the initial input value by afirstamount.Thebi-directionalexcitation experimentincludes measuring a plurality of output variables of the multivariable process in response to performing the first excitation, wherein each output variable is measured using a measurement device 820, whereinarespective hysteresis levelisassociatedtoeachofthe measured output variables. The bi-directional excitation experiment includes identifying a hysteresis exceeding output variable among the measured plurality of output variables, wherein the hysteresis exceeding output variable is an output variable having a measured value that exceeds thehysteresislevel associatedwiththe output variable. The bi-directional excitation experiment includes performingasecond excitationofthe input variable in response to identifying the hysteresis exceeding output variable, whereinperformingthe second excitation comprises setting the input variable at a second excited input value atasecond time usingthe input device 810, wherein the second excited input valuediffersfrom the initial input value by a second amount, wherein the first amount and the second amount have opposite signs. The bi-directional excitation experiment includes measuring atleastthehysteresisexceeding outputvariableusing ameasurement device 820 in response to performing the second excitation.The bi-directional excitation experiment includes setting the input variable at a finalinput value at a third time after the second time using the input device.

[0098] The apparatus may be configured forperformingany aspect or combination of aspects of the methods described herein.

[0099] An input device as described herein can be any input device suitable forsetting or adjusting one or more input variables to a specified value. An input devicecanbe aninputactuator.

[0100] A measurement device as described herein can be any measurementdevice,such as a sensor, detector or the like, for measuring a value of one or more output variables.

[0101] The controlsystem, or controller, may beasingle system or a distributed system including aplurality of individual controllers. Acontrolsystem may include one or more computers or processors for processing data supplied to the control system.

[0102] Accordingtoembodiments,the control system may be configured, foreach output variableofa setof outputvariablesofthemultivariableprocess,fordetermining the hysteresis level associated with the output variable based on a noise parameter.

[0103] According to embodiments, the apparatus may be configured, e.g. underthecontrolof the control system, for: maintaining the input variable under consideration at substantially the first excited input value from the firsttime tothe second time; and / or maintaining the input variableatsubstantially the second excited input value from the second time to the third time.

[0104] According to embodiments, the apparatus, and inparticularthe controlsystem, may beconfiguredfordetermining a model of atleastaportionof the multivariable process based on measurement data obtained from measuringone ormore output variables duringatleast oneofthe bi-directional excitation experiments.

[0105] Accordingtoafurtherembodiment,a computerprogramfor collectingdata for process identification of a multivariable process is provided. Thecomputer program includes instructions which, when the program is executed by a computer, cause the computer toperform,for each input variable of a set of input variablesofthe multivariableprocess,a set of operations. The set of operations includesreceivingfirstmeasurementdata resulting from measuring apluralityof outputvariables of the multivariable process in responsetoperforming afirst excitation of the input variable, wherein performing the firstexcitationcomprises setting the input variable at a first excited input value at a first time, wherein the first excitedinput valuediffers from an initial input value of the input variable by a first amount,wherein a respective hysteresis level isassociated to each of the measured outputvariables. The set of operations includes identifying a hysteresis exceeding output variable among the measured plurality of output variables based on the first measurement data,wherein thehysteresis exceeding output variable is an output variable having a measured value that exceeds the hysteresis level associated withthe output variable. The set of operations includes receiving second measurementdata resulting from measuring at least the hysteresis exceeding output variable inresponse toperformingasecondexcitationof the inputvariable,whereinperforming the second excitation comprises setting the input variable at a second excited input value at a second time in response to identiffing the hysteresis exceeding output variable, wherein the second excitedinputvalue differsfromtheinitial input valueby a second amount, wherein the f,rrst amount and the second amount have opposite signs.

[0106] The computerprogrammay be configured toperformany computer- implementable aspect or combination of aspects of themethodsdescribedherein.

[0107] The computerprogrammay includeinstructionswhich, whentheprogram is executed by a computer, cause the computer to perform, for each input variable of a set of input variables of the multivariableprocess,any one the following operations, or any combination thereof: determining the initial input value of the input variable; determining the first excitedinputvalue of theinputvariable;determining the first time; determining the second excited input valueofthe input variable; determining the second time; determining the hnal input value of the input variable; and determining the third time.

[0108] Thecomputer programmay includeinstructionswhich, whentheprogram is executed by a computer, cause the computer, for each output variable of a set of output variables of the multivariableprocess,to determine the hysteresis level associated with the output variablebasedona noise parameter.

[0109] .Thecomputerprogrammay include instructions which, whentheprogramisexecutedbya computer, cause the computer to determine a model of atleast a portion of the multivariable processbased on at least the first measurementdata and the second measurement data.

[00110] As used herein, the terms "computer", "processor" and"controller",andrelated terms,are not limited tojustthose integrated circuits referred to in the art asa computer, but broadly refersto a microcontroller, a microcomputer, an analogcomputer,aprogrammablelogic controller(PLC),an application specific integrated circuit (ASIC), and other programmable circuits, and thesetermsare used interchangeably herein. In the embodiments described herein,"memory"mayinclude, but is not limitedto,acomputer-readable medium, such as a random-accessmemory (RAM),a computer-readable non-volatile medium, such as a flash memory. Alternatively, a floppy disk, a compact disc -readonly memory(CD-ROM), a magneto-optical disk (MOD), and / or a digital versatiledisc(DVD)mayalso be used.Also, in the embodiments described herein, additional input channelsmay be, but are not limitedto, computerperipheralsassociated with an operatorinterface such as a touchscreen,amouse,and a keyboard. Altematively, other computerperipheralsmay also be used that may include, forexample, but notbe limited to, a scanner. Furthermore, in the example embodiment, additional outputchannels may include,but not be limited to, an operator interface monitor or heads-up display. Some embodimentsinvolve the use of one or more electronic or computing devices. Such devices typically include a processor, processingdevice,or controller, such as a general-purpose central processing unit (CPU), a graphicsprocessingunit(GPU),a microcontroller, a reduced instruction set computer(RISC) processor,an ASIC, aprogrammablelogic controller (PLC), a fieldprogrammable gate array (FPGA), a digital signal processing (DSP)device, andlorany other circuit or processing device capableof executing the functions described herein. The methods described herein may be encoded as executable instructions embodied inacomputer readable medium, including, without limitation, a storagedevice and / or amemorydevice.Such instructions, when executed by aprocessingdevice, cause the processing devicetoperformat least aportionof the methodsdescribed herein. The above examples are notintendedto limit in any waythedefinition and / ormeaningofthetermprocessor and processing device.

[0111] While the foregoing is directed to embodiments, other and furtherembodiments may be devised without departing from the basic scope,andthescopeis determined by the claims that follow. REFERENCE NUMERALS multivariable process 100 input variable 110output variable120 horizontal axis 210 time 2t2 time 214 time 2t6vertical axis220 plot 250 horizontal axis 310 vertical axis 320initialinput value321final input value321 first excited input value 322 second excited input value 324 first amount 332 second amount 334first duration342 second duration 344 plot 3s0 horizontal axis 410 vertical axis 420hysteresis level 425a-b plot 450 horizontal axis 510 vertical axis s20hysteresis level525a-b plot 550 horizontal axis 610 vertical axis 620 hysteresis level 625a-bplot650 box 702 apparatus 800 input device 810 measurement device 820control system850

Claims

CLAIMS 1. Amethodofcollecting data for process identification of a multivariableprocess(100), comprising: for each input variable (l10)ofa setof input variables of themultivariableprocess, performing abi-directionalexcitation experiment, comprising: setting the input variable at an initial input value (321); performing a first excitation of the input variable, comprising setting the input variable at a first excited input value(322)aI a firsttime(tr),whereinthe firstexcitedinput value differs from the initial input value by a first amount (332); measuring a plurality of output variables (yt yz, y:) of the multivariable process in response toperformingthe first excitation, wherein arespective hysteresislevel(425a-b,525a-b,625a-b) isassociated to each of the measured output variables; identifying a hysteresis exceeding output variable(yz)among the measured plurality of output variables, wherein thehysteresisexceeding output variableis anoutput variablehaving a measured value that exceedsthe hysteresis level associated with the output variable; performing a second excitation of the input variable in response to identifying the hysteresis exceeding output variable, whereinperformingthe second excitation comprises setting the input variable at a second excited input value(324) at a secondtime(tz),wherein thesecond excitedinputvalue differsfromtheinitialinputvaluebya second amount (334),whereinthe first amount and the second amount have opposite signs; measuring at least the hysteresis exceeding output variable in response to performing the second excitation; and setting the input variable at a final input value at a third time(tr)after the second time.2.The methodofclaim 1,wherein the timeperiod (344)from the second time to the third time has a pre-determined duration. 3.The methodof claim 2, wherein the time period (342) from the first timeto the second time has a first duration,wherein thepre-determinedduration of thetime period from the second time to the thirdtimeis a second duration,whereinthe second duration is a function of the first duration, particularly wherein thesecondduration is substantially equal to the first duration. 4.The methodofanyofthe precedingclaims, wherein the hysteresis exceeding output variable is the first output variable among the measured plurality of output variables to exceed the associated hysteresis level in response to performing thefirstexcitation. 5.The method of any of the preceding claims, wherein theinputvariable ismaintained substantially at the final input value at least until each output variable of themeasured pluralityof output variables stays within a range having a prescribed width over a periodof time.6.The method of any of the preceding claims, further comprising:for each output variable of a set of output variables of the multivariableprocess, determining the hysteresislevel associated with the output variable basedon a noise parameter. 7.The method of any of the preceding claims, furthercomprising:maintaining the input variable at substantially the first excited input valuefromthefirsttime to the second time; and / or maintainingtheinputvariable at substantially the second excited input value from the second time to the third time.8.The method of any of the preceding claims, wherein the second amount isa function of the hrst amount.

9. A method of modelidentificationof amultivariable process (100),comprising: performing the method of collectingdataaccording to any oftheprecedingclaims; and determininga model of at least a portion of the multivariable process basedonmeasurement data obtained from measuring one or more output variables during at least one of the bi-directional excitation experiments. 10.The methodof claim9, wherein the model includes, for at least one input-outputpair consistingofan input variable and an output variable of the multivariableprocess,a first order transfer function with a delay,andwherein determining the model comprises: determiningat least one parameter of the first order transfer function based on the measurement data. 11.An apparatus (800) for collecting data for process identification of amultivariableprocess (100), comprising:oneor more input devices (810); one or more measurement devices(820);a control system(850)connected to the one or more input devicesand theone or more measurement devices, wherein the apparatus is configured toperform,foreach input variable(110)of a set of input variables ofthe multivariable process, a bi-directionalexcitation experimentunder thecontrol of the controlsystem, the bi-directionalexcitation experimentcomprising:setting the input variable at an initial input value(321)using an input device of the one or more input devices;performing a first excitationof the input variable, comprisingsetting the input variable at a first excited input value (322) at afirst time(tr) usingthe input device, wherein the first excited input value differs from the initial inputvalue byafirst amount(332);measuringapluralityofoutput variables(yuyz,y:) ofthemultivariable processinresponsetoperformingthefirstexcitation,wherein each output variable is measured using a measurement deviceofthe oneormore measurementdevices, wherein a respective hysteresislevel (425a-b, 525a-b,625a-b) is associatedto each of the measured outputvariables; identifying a hysteresis exceeding outputvariable(yz) among the measured pluralityof output variables, wherein the hysteresis exceeding output variable is an output variablehaving a measured valuö that exceedsthe hysteresis level associatedwiththe output variable;performinga second excitation of the input variable in responsetoidentifying the hysteresis exceeding output variable, wherein performing the secondexcitation comprises setting the input variable at a second excited input value (324)at a second time(tz)using the input device,wherein the second excited input value differs fromthe initial input valuebya second amount(334),wherein the first amount and the second amount haveopposite signs; measuring at least the hysteresisexceeding output variable using ameasurement device of the one or moremeasurement devices in responsetoperformingthe second excitation; and setting the input variable at a final input value (321) atathird time(t:) after the secondtime using the input device.12.The apparatus of claim 11, wherein thetimeperiod (344)from the second time to the third time has a pre-determined duration.

13. The apparatus of claim12, wherein the time period (342) from the firsttime tothe second time has a first duration, wherein thepre-determinedduration of the time period from the second time to the third timeisa secondduration,wherein the second durationis afunctionof thefirstduration,particularly whereintheseconddurationis substantially equal to the first duration. 14.The apparatus of any of claims 11 to 13, wherein the hysteresis exceedingoutput variable is the first output variableamong the measured plurality of outputvariables to exceed theassociated hysteresis level in response to setting the input variable at the first excited input value. 15.A computer program for collecting data for process identification of amultivariableprocess (100), the computer program comprising instructionswhich, whenthe program is executed by a computer, cause the computer to perform, for each input variable(110)of a set of input variables ofthemultivariableprocess,the followingoperations :receiving firstmeasurement data resulting from measuring a pluralityofoutput variables(yt,yz, y:) of the multivariable process in response toperformingafirst excitation of the input variable, whereinperformingthe first excitationcomprises setting the input variable at a first excited input value (322) at a firsttime(tr),wherein the first excitedinput valuediffersfrom an initial input valueofthe input variable by a firstamount (332), wherein a respective hysteresis level(425a-b,525a-b,625a-b) is associated to each of the measured output variables; identifyingahysteresis exceeding output variable(yz)amongthemeasured pluralityofoutput variables based on the first measurement data,wherein thehysteresis exceedingoutput variableisanoutput variable having ameasured value that exceeds the hysteresis levelassociatedwith theoutputvariable; and receiving secondmeasurement data resulting from measuring at least thehysteresis exceeding output variable in response to performing a second excitationoftheinputvariable, wherein performing the second excitation comprises settingthe input variable at a second excited input value (324) at a secondtime(tz)inresponseto identifying the hysteresis exceeding output variable, wherein thesecond excited input value differs fromthe initial input value by a second amount(334),wherein the first amount and the second amount haveopposite signs.

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