WO2024104590A1

WO2024104590A1 - Method of collecting data for process identification of a multivariable process

Info

Publication number: WO2024104590A1
Application number: PCT/EP2022/082328
Authority: WO
Inventors: Michael Lundh; Alf Isaksson
Original assignee: Abb Schweiz Ag
Priority date: 2022-11-17
Filing date: 2022-11-17
Publication date: 2024-05-23

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 apparatuses} ^{for collecting data for model identification} of an ^{industrial process.} The methods described herein involve performing experiments _where a response _{of the} output variables ofthe system to excitations of the input variables is measured, and a model of ^{the process is} determined based on said experiments. BACKGROUND _[0002] ^{In many applications, it is important to design a mathematical model of an} a 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 a ^response of one or more outputs of the system. For example, ^{increasing the value} _of ^{an input} _{variable may} ^{cause a} _{corresponding increase of one} ^{or more outputs} of ^{the process. The mathematical relationship between the} behaviour of the outputs as a function _of the inputs may be captured, at least approximately,by a model of the ^process. [0003] ^{In order to allow designing a model that correctly describes the behaviour} of a ^process, data about said behaviour can be collected by performing measurements. For example, the inputs of the process may _be set _to a plurality _of values, and the response of the outputs thereto may be measured. Based _on the measured data, amodel of the ^process may be constructed. _[0004] A ^{challenging task} in this ^{respect is} to ^{design suitable experiments that} reveal a sufficient amount of information _{about the} process _{to enable the design of} an 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 simple _{experiments that allow extracting useful} ^{information about the process while} perturbing the normal operation of the process as little as possible. _[0005] For ^{single-input-single-output processes, convenient experiments have} _{been designed in the} ^past _{that reveal useful} ^information _about ^{the process based} _on _{a limited} ^amount _of ^{measurements, and that hence} allow constructing ^a model _of the process in an efficient manner. _[0006] ^{For processes having multiple inputs and outputs, the task in question is} ^{however considerably more challenging, in light of the increased number of degrees} _{of freedom} involved _{in such} systems. Therefore, there is a need for improved methods _for gathering data for model identification of multivariable ^processes. SUMMARY _[0007] According to an embodiment, 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. Performing the bi-directional excitation experiment includes setting the input variable at an initial input value. Performing _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. Performing the bi-directional excitation experiment includes measuring a plurality of output variables of the multivariable ^process in response to performing the hrst excitation. A respective hysteresis level ^is associated to each of ^{the measured output variables. Performing 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. Performing the bi-directional excitation experiment i^{ncludes performing} a 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 a ^{second time. The} second excited input value differs from the initial input value by ^{a second amount. The} _first ^{amount and} _{the second amount have opposite signs.} Performing the bi-directional excitation experiment includes measuring _at least _the hysteresis exceeding output variable _in response _to performing _the second ^{excitation. Performing} the bi-directional excitation experiment includes setting the ^{input variable at a final} input value at a third time after the second time. [0008] ^{According to a further embodiment, a method of model identification of a} multivariable process is provided. The method includes performing _{the method of} collecting data according to any of the embodiments described herein. The method ^includes determining amodel of at least aportion ofthe'multivariable process based ^{on measurement data obtained} from ^measuring one or ^more output variables during at least one of the bi-directional excitation experiments. _[0009] ^{According to a further embodiment, an apparatus for} collecting ^data for ^process identification of a multivariable process is provided. The apparatus includes ^one or ^more input devices. The apparatus includes one or more measurement ^{devices. The apparatus includes a control system} connected to the ^one or more input devices and the one or more measurement devices. The apparatus _{is configured to} ^perform, for each input variable of a set of input variables of the multivariable ^process, a bi-directional excitation experiment under the control _of the control ^{system. The bi-directional} excitation experiment includes _setting the input variable at an initial _input value _{using an input device. 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 _{using the} input ^device, 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 each output variable} ^{is measured using a measurement} _{device, 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 using the input} device, 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 using a measurement device in response to ^{performing the second excitation. The bi-directional excitation experiment includes} setting the input variable at a frnal input value at a third time after ^{the second} time using the input device. _[0010] According to a ^{further embodiment, a computer program for collecting} data for process identification of a multivariable process is ^provided. The computer ^{program includes instructions which, when the program is executed by a computer,} _{cause the computer to} ^perform, _{for each input variable of a set of} ^{input variables} _of _{the multivariable} ^process, _{a set of} ^{instructions. The} _{set of} ^{instructions includes} _{receiving first} ^{measurement data resulting} from ^{measuring a} plurality of ^output _variables of the multivariable process in response to performing a first excitation of the ^{input variable, wherein performing the first excitation comprises setting the} input 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 the ^measured output _{variables. The set of} ^{instructions includes} _identifying ^{a hysteresis exceeding output} ^{variable among the measured plurality of output variables based on the first} measurement data, 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 set} _of ^instructions _{includes receiving second measurement} data resulting from measuring _at least the hysteresis exceeding _{output variable in} ^{response to performing} a ^{second excitation} of the input variable, wherein ^performing the second excitation comprises setting the input variable at a second ^excited input value at a second time in response to identifuing the hysteresis ^{exceeding output variable, 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.} BRIEF DESCRIPTION OF THE DRAWINGS _[0011] ^{The components in the Figures are not necessarily to scale, instead} ^{emphasis being placed upon} illustrating ^the principles _{of the invention. Moreover,} in ^{the Figures,} like ^reference signs ^designate corresponding ^{parts. The} accompanying drawings relate to embodiments of the disclosure and are described in the following: F^ig. I ^shows an ^example of a multivariable ^process as considered in the present disclosure; Fig.2 illustrates the notion _of ^hysteresis _{as considered in the} ^present disclosure; Fig. 3 illustrates abi-directional excitation of an input variable as considered iⁿ _the ^present _disclosure; F^igs.4-6 show ^a behaviour of output variables yb ^y2 and y: during a bi- directional excitation experiment as considered in _the present _disclosure; Fig.7 provides a further illustration of a bi-directional excitation experiment as considered in the ^present disclosure; and Fig.8 shows an apparatus for collecting data for process identification of a multivariable process as considered in the ^present disclosure. DETAILED DESCRIPTION _[0012] Reference will ^{now be made in} detail ^{to the various embodiments, one or} more examples of which are illustrated in each figure. Each example is ^provided by way of explanation and is not meant as a limitation. For example, features illustrated or described as ^part of one embodiment can ^{be used on} or in conjunction with ^any _{other embodiment to} yield 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 reference} numbers refer to the same or to similar components. Generally, only ^the differences with respect to the individual ^embodiments are ^described. Unless ^specified otherwise, 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 multivariable ^process 100 having ^input variables I l0 and output ^{variables 120.} _[0015] The ^{input variables of a multivariable process are denoted herein as ul, u2,} _{.... The output variables} ^{are denoted as yr, y2,} _....An ^{input variable may take} different 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 of ^the input variable, e.g. in cases where it ^is useful to emphasizethatthevalue in ^question _{is associated with an} ^input _{variable. Likewise,} ^{an output variable may take} _different values, which may be called output values. _[0016] A multivariable ^{process as described herein may be an industrial process,} ^{e.g. a process performed in an industrial plant. Embodiments described herein are} ^not limited to specific examples of industrial ^process, but are generally applicable to any kind _of industrial process. _[0017] ^{A multivariable process as described herein can be} understood ^{as a process} having N input variables and M output variables, wherein at least one _{of N} and _M ^{is greater} than l. According to embodiments, the multivariable process includes a ^plurality _of ^{input variables} _{and a} ^plurality _{of output variables. The number of input} ^{variables of the multivariable process may be equal} _{to or different from the number} of output variables of the multivariable process. The number _{of input} variables and/or the number of output variables may be 5 or larger, particularly 16 or larger, ^{more particularly} 32 or larger. The number of input/output variables shown in the hgures is exemplary and the disclosure is not limited _thereto. _[0018] ^{An input variable of the multivariable process} _{may be a variable that is} adjustable or controllable. The input variable may be set at a specific value, e.g. _by ^an input device. Adjusting an input variable may result in a response of one or more ^{output variables} of the multivariable ^process. The _response of an output variable ^{may be measured, e.g. by a sensor. According} _{to embodiments described herein,} adjusting an input variable may cause a response of several, in particular _all, output variables of the multivariable process. _[0019] ^{A multivariable process as described herein may have a behaviour, or} ^{dynamics, that is at least partially} unknown. An aim may be to design a model describing the multivariable process, such as a mathematical _{model desuibing a} relation between the inputs and outputs of the multivariable process. A model may be designed based on measured data obtained _by performing one _or more ^experiments with ^respect to _{the multivariable} ^process. _{The task} of _{designing a} ^{model can include an initial phase} of designing an initial model of the ^process. The initial model may be a crude model, or approximative model, _{that captures at least} some characteristics of the process. After the initial model has been designed, _the initial ^model may be used to construct a more detailed experiment for the process. _[0020] An initial crude model may be beneficial in many situations for ^the _{commissioning of} ^a _{multivariable controller.} ^{A typical example is when designing} an identification experiment to be used to generate data for the identification of a dynamical model. _[0021] Embodiments ^described herein may be beneficial for the design of ^an initial model of a multivariable ^process. The ^{present disclosure provides} _experiments that are useful for revealing at least some characteristics of the multivariable process. The experiments in ^question involve exciting ^(a subset of) the input variables of the multivariable ^process according to a specific ^kind of _{excitation and} measuring the response of (a subset of) the output variables. ₁₀₀₂₂₁ ^{The experiments described herein involve the notion} of ^{hysteresis. A} respective hysteresis level may be associated with at least some, particular all, output variables of the multivariable ^process. A hysteresis level associated with ^an _{output variable can be} ^{understood as a} _width ^{parameter e that determines a range,} ^{or interval, for the output variable. As long as the value of the output variable} ^remains _inside ^{said range,} _it ^{may be the case that no reaction} _in ^{terms of an} adjustment of the input variables is triggered, i.e. the multivariable ^process may continue without changing the values of the input variables. If the value of the output variable leaves said range, ^a reaction, such ^as an adjustment of ^{the values} of one or ^more input ^{variables, may be triggered} in ^{response thereto.} _{[0023] Fig.}2 ^{illustrates the notion} of ^{hysteresis as considered in the present} disclosure. A plot 250 of the behaviour an output variable yi as a function of time _is shown. The output variable yi can be any arbitrary output variable of the multivariable ^process. The horizontal axis 210 represents a time ^parameter t. The ^{vertical axis 220 represents the value of the output variable yi. A hysteresis level} (225a,225b) defined by a width ^parameter s may be associated with the ^output ^{variable yi. At an initial time} t: ^{0, the value of yi may be yio. The value yto can be} any suitable value depending on the context and is not limited to any specific value. The value ^yio can, for example, be ^a referencs value that ^is targeted ^{for the output} ^{variable yiby setting a specific combination} _{of values of the input variables, or can} be an equilibrium value of the output variable yi _that is reached when _maintaining ^{the input variables at} certain values for a longer period of time. The width parameter ^{e defines an interval} lyio - ^e, ]io ^{+ e] surrounding the value yio. When the value of} ^{the output variable yi} is outside said interval, the hysteresis level (225a,225b) is ^{said to be exceeded. For example, at time 214} _{andtime2l6,the corresponding value} of yt indicated at254 and256 is smaller than yio - t _, ^respectively larger than ^yio f ^e. In ^{both cases, the hysteresis} level ^associated _with yiis _{said to be exceeded. At} ^{time 212, the corresponding value} _of ^yi _{indicated at252lies inside the interval [yio} - _t, ^{yio *} _{e], so that the hysteresis level is not exceeded.} _10024] ^{The respective hysteresis levels} associated with different output variables ^{may be different from each other.} _A ^{first hysteresis} _{level may be associated with a} hrst output variable of the multivariable process. A second hysteresis _level may be associated with a second output variable of the multivariable process. The first ^{hysteresis level may be} different from the second hysteresis level. _[0025] ^{According to embodiments described herein, the hysteresis level} associated with an output variable can be determined based _on a noise parameter associated with the output variable. The output variable may be subject _to noise. ^{The noise may cause} fluctuations of the output parameter. The fluctuations of the ^{output variable may arise} even ^though the input ^parameters may be maintained at constant values. A hysteresis level may ^{be set} _to ^compensate _{for noise fluctuations} ^{of the output variable. For example, the} _width ^parameter r ^may _{be set} to _be ^a multiple of a standard deviation of the noise acting on the output _{variable, such as} 3-4 times the standard deviation, or may be a multiple of a peak noise, _such as _3-4 times the ^peak noise. Both the standard deviation of the noise and the peak noise ^{are examples of a} noise ^{parameter as} described herein. By setting _a hysteresis level ^{in this manner, fluctuations} of the output variable that are _caused by noise will ^{mostly remain inside the hysteresis level, and hence} _do ^not _{trigger an adjustment of} _the values _of the _input variables, 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,} ^particularly _{all, input variables of the} ^{multivariable process at a substantially} ^{constant value over a period of time. The period of time may be configured to allow} at least some, particularly all, output variables to reach an equilibrium state. An equilibrium state of an output value ^{can be} understood ^{as a state where the value} of _{the output variable} ^remains _{substantially} ^{constant apart from small fluctuations that} may be due to noise. The method described herein may include determining a noise ^{parameter for at least some, particularly all, output variables. A noise parameter} associated with an output variable, such ^as a standard deviation ^{of noise or a peak} _{noise, may be determined by} ^{performing one} _or ^{more measurements of the output} _{variable while the} input variables at maintained at their substantially constant values. For example, the one or more measurements may involve determining ^{fluctuations of the output variable due to noise. A hysteresis level associated with} _{the output variable} may be determined based on the noise parameter, as described herein. _[00271 According to embodiments described herein, a set of input variables of the multivariable process is determined. The set of input variables ^may consist of all ^{input variables of the multivariable process or a subset thereof. The set of input} _{variables includes} a plurality _of input variables, such as 2 or more, 5 or more, or l0 or _{more input} variables, or an even higher number of input variables. For each input variable ut _in the set _of input variables, an experiment is ^performed in which data regarding the behaviour of the multivariable ^process is ^gathered. The experiment ^involves exciting the ^{multivariable system} by a ^{bi-directional excitation and} measuring the response of the system to the excitation. [_0028] ^{The method described herein may include selecting a first input variable} _{ur from the set of input variables.} ^The _first ^{input variable} _ur ^{can be any input} _{variable of set of input variables} ^{and, more generally, can be any input variable} _of r0140 ^{the multivariable process. With respect} _to ^the _{first input variable ur, a bi-directional} excitation experiment may be performed. [_0029] Fig.3 illustrates a bi-directional excitation associated _with the input variable ur. The term "bi-directional" refers to the fact that two excitations in ^{opposite directions (namely, the} _{"first excitation" and the} ^oosecond _{excitation" as} ^{described herein) are performed, i.e. an} _{upward/positive excitation followed by a} downward/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 of} ^{time is shown. The horizontal} _{axis 310 represents a time} ^parameter _{t. The vertical} ^{axis 320 represents the value} of ^{the input variable ur.} _[0031] ^{An at initial time} t:0, ^{the input variable ur may be set at an} initial ^input value uro, indicated at 321. The initial input value uro can be an arbitrary value ^{chosen for} _the ^purpose _{of the experiment.} _[0032] A ^first excitation of the input variable ur is ^performed. The value of the ^{input variable ur may be increased (e.g. according} to ^{a monotonously increasing} function, such as an exponential function) until a first excited input value u16 * A, indicated at322, is reached at a first time tr, indicated _at3l2. The first excited input value may be chosen to be a sufficiently large value, so that a response of at least ^one output variable of the ^process can be expected to occur, for example in light of ^{a basic a priori} knowledge ^{of the} multivariable ^process. The first excited input value uro f A differs from the initial input value uro by a first _amount A, indicated _at332. ^{In the example shown in} _Fig. ^{3, the} _{first amount} ^A _{is a} ^positive _{amount, so that the} ^first excited input value is larger than the initial input value uro. _[0033] In ^{some embodiments, the input variable} ul ^{may be maintained} ^{substantially at the first excited input value uro * A} from ^the first time tr to a ^second time ^{tz indicated} at ^{314. The} first excitation may end at substantially the second ^{time tz. That the input variable ur is maintained} _{substantially at the first excited} input value ulo ⁺ A may include deviations with respect to the first excited input tU ⁴⁰ value uro ⁺ A of, for example,5-l0Yo of the value ^{uro +} A. The time ^{period from} the first time tr to the second time tz has a first duration 342. According to embodiments _described herein, the first duration ₃₄₂ ^is determined by ^{a response of one or more} output variables, as described in more detail below. _[0034] ^{A second excitation of the input variable ur is performed. At the second} time tz, the input variable ur is set to a second excited input value, indicated at324. _In particular, at _{the second time tz,} the value of the input variable ur may be changed _{from substantially the} first excited input value to the second excited input value. The second excited input value may differ from the initial input value uro by a ^{second amount, indicated at 334. The second amount and the first amount have} _{opposite signs, so that} ^{the excitations are} _{bi-directional.} ^{The second amount may be} a _{negative amount,} such that the second excited input value is smaller than the initial input value uro. In the ^particular example, the second excited input value is equal to rto- 24. Accordingly, the absolute value of the second amount is twice the absolute ^value of ^{the first amount. The disclosure is not limited thereto, and different} magnitudes of the second amount may be considered. _[0035] In ^{some embodiments, the input variable} ul ^{may be maintained} _{substantially} at the second excited input value from the second time tz to a third time _tl indicated at3l6. The time ^period from the second time tz to the third time t: ^{has a second duration 344. According to embodiments described herein, the second} duration 344 is a ^{predetermined} duration, as described in more detail below. ^The _{second excitation may end at} ^{substantially the third time t:.} _[0036] At ^the third ^{time t:, the input variable ur may be set to a final input value.} _In particular, at the third time t:, the value of the input variable ur may be changed from _{substantially} the 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 for ^{a period} of time. _[0037] ^{An advantage of a bi-directional excitation, as described herein, is that the} ^second excited input value, which is an excitation of the system in a direction ^opposite _to ^{the first excited input} _{value, allows bringing the system back to an} equilibrium state. In comparison, _if both excitations were _to be performed _{in the} same direction, the system underlying the multivariable process might move away ^from equilibrium in an uncontrollable manner. _[0038] ^{The bidirectional excitation shown in Fig. 3 is exemplary and can be} modified in several ways, including the _following. [0039] ^{The example shown in Fig. 3 involves a bi-directional excitation wherein} the value of the input variable ur is first increased to the first excited input value ^(positive excitation) and thereafter decreased to the second excited input value ^{(negative excitation). The} disclosure is not limited thereto. In other embodiments, a bi-directional excitation may be considered wherein the value of _the input _variable ur is first decreased and thereafter increased, so that the first excited input value is ^{smaller than} the initial input value ^(negative excitation) and the second excited input ^{value is larger} _{than the initial input value} ^(positive _excitation). _[0040] ^{The example shown in Fig. 3 involves maintaining the input variable ur} substantially at the first excited input value from the first time tr _{to the second time} tz. The disclosure is not limited thereto. The value of the input variable may be ^changed during this time ^period. The value of the input variable u1 may, for ^{example, be increased} _during ^{at least a portion} _{of the} ^period _{from the first time tr to} the second time tz. In particular, the input variable ul may _be set at _the first _excited input value as part of a continuous ramp-up of the input _variable ur _that starts, _for _{example, shortly after the initial time t} : _{0 and that continues after setting the input} variable ur at the first excited input value. For example, the ramp-up may end shortly before, or substantially ^at, _{the second time} ^tz. _[0041] ^{The example shown} in ^Fig.3 ^{involves a substantially instantaneous} change from the first excited input value to the second exited _input value _at the second time tz. The disclosure is not limit thereto. The change from the first excited input value to the second excited input value may be a non-instantaneous change. Likewise, the change from the second excited input value ^{to the} final ^{input value} may be non-instantaneous. ₁₀₀₄₂₁ The example shown in Fig.3 involves a second.excited input value that is ^{twice as large (in absolute value) as the first excited input value. The disclosure is} _{not limited thereto. The} ^second _{excited input value} ^{may, for example, have the same} _absolute value 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 input _value can be any multiple of the first excited input value, or more generally any ^{function of the first excited input value.} _[0043] The example shown in Fig.3 involves a final input ^value that ^is _{substantially the same} ^{as the} _initial ^{input value uro. The disclosure is not limited} thereto. The final input value may be different from the initial input value. [0044] ^{The inventors have found that a bi-directional excitation experiment as} ^{described above is a simple, short experiment that provides informative data, i.e.} _{data that is useful for the} identification of a model, particularly an initial model, of _{a multivariable} process. 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 experiment} ^performed _{with respect to the input variable ur,} ^{a plurality of output variables may} _{be measured.} The plurality _of output variables may consist of _all output variables _{of the multivariable} process, or ^{a subset} thereof. For example, in some ^cases it may be apparent, based e.g. on a priori considerations, that one or more output variables ^{are 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. The ^plurality of output variables that is measured may depend on the input variable ur under consideration. For example, in a subsequent bi-directional excitation ^experiment ^performed with respect to another input _variable ui, the plurality _{of output variables} that is measured may be different. [_0046] ^{Measuring an output variable may include performing one} or ^more ^measurements of the output variable, e.g. using a sensor or other measurement ^{device. In some embodiments, an output variable may} be measured at a ^plurality of times while the bi-directional excitation in respect _of an input variable is performed. ^For example, ^{a sequence} of measurements of the output variable may be performed at regular _time intervals. ₁₀₀₄₇₁ ^According to ^embodiments described herein, a plurality of output ^{variables of the multivariable process may be measured} in ^response to ^performing the first excitation of the input variable ur, in particular in response to setting _the ^input variable ur at the first excited input value. The plurality of output variables ^{may be measured one or more} _{times during the time} ^period _{from the first time tr to} the second time tz. _[0048] ^{Figs. 4-6 show an example where three output variables yb y2} and ^y: are measured during at least a portion of the bi-directional excitation performed in ^respect _of ^the _input ^variable _ur. ^That _{in the} ^present _{example a total of three output} ^{variables is measured is merely} _{for the} ^purpose _{of illustration, and any number} of output variables may be measured. _[0049] ^{Figs. 4-6 show horizontal axes 410, 510, 610, respectively, representing} ^the time ^parameter t, and vertical axes 420,520 and 620 representing the value _of ^{the output variables} yt ^yz and ^yt, respectively. The first time tr, second time tz and ^{third time tr, which were also shown} _in ^Fig. _{3, are indicated again in Figs. 4-6. Plots} 450, ^{550 and 650} of ^{the behaviour} of ^{the respective} _{output variables} ^as _{a function} ^{of time are shown. The plots 450, 550 and 650 may be obtained} by ^performing a ^plurality of measurements of the output variables in ^question. _{[0050] At time t} : _{0, the output variables yb yz and yr have respective initial} ^{output values yrc,yzl and y:0, each being the value} _{of the respective output variable} _{corresponding} to 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 ^(for a sufftciently long time, so that equilibrium is reached, as described ^{herein), the} multivariable ^process _{behaves in a} manner _such that _the corresponding output values _of the output variables yby2 and yr are yro, yzo and ^yro, respectively. Each output variable yby2 and y: is provided with an associated hysteresis leveI425a-b, 525a-b and 625a-b, _{respectively, surrounding the} ^respective _{initial output} ^{values yrc, yzl and ylo. The} _{hysteresis levels} may _be determined based _on a noise parameter, as described herein. _[0051] ^{According to embodiments described herein, the second time tz, which is} the time at which the input variable ur is ^set to the ^second excited ^{input value (as} _{described above with} respect _to Fig.3), is not a predetermined time. The second _time tz 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 first ^excitation. _[0052] Accordingly, ^the first duration342, which ^{is the duration of time between} _setting the input variable ur to the first excited input value and setting the input variable ur to the second excited input value, is not a ^{predetermined} duration. ^The first duration342 may depend on a response of at least one output variable ^among the ^plurality of measured ^{output variables triggered by the first excitation.} _[0053] With respect to the ^{example shown} in ^{Figs. 4-6, it can be seen in Fig. 4} that the output variable yr shows only a mild response after the first time tr, i.e. after _setting the input variable ur to the first excited input value, namely a small increase _of the value _of yr. The response does not exceed the hysteresis level ^425a-b ^{associated with the output variable yr. In Fig. 5, the response of the output variable} _{yz is more significant. In} ^particular, _{the value of} ^{yz reaches the associated hysteresis} level 525a-b _at the second time _{tz, as} indicated at 552.In ^{Fig. 6,} the ^{response of the} _{output variable} ^yr _{is also significant, but the} ^value _of ^{yr reaches the associated} _hysteresis level625a-b substantially after the second time tz, as indicated at 652. t6140 _[0054] ^According to embodiments described herein, in ^response to ^performing the first excitation of the input variable u1, a hysteresis exceeding _{output variable} is identified among the plurality of measured output variables (in this example the output variables _Vtyz andy:). The hysteresis exceeding output variable is an output ^variable that ^exceeds the associated hysteresis level in response to the first ^{excitation of the input} _{variable ur. Which} ^particular _{output variable among the} ^plurality of measured output variables is the hysteresis exceeding variable is a priori unknown. The hysteresis exceeding output variable is identified by inspecting the behaviour of the ^plurality of measured output variables in response to the first ^excitation of ^{the input variable ur.} _[0055] ^{The plurality of measured output variables may include several} output ^{variables that exceed the associated hysteresis} level in ^response to the ^first excitation of the input variable ur. According to embodiments described herein, the ^hysteresis exceeding output variable may be identified to be the first ^(i.e. ^{chronologically the first) output variable among the measured} output ^variables to 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 variable ^y2, since the output variable ^yz reaches the associated hysteresis ^{level at the second} time _h, ^whereas the output variable yr does not reach the associated hysteresis level at all and _the output variable y: _only reaches _the associated hysteresis level at a time later than the second time tz. [0056] ^{The hysteresis exceeding output variable does not necessarily have to be} the first output variable to exceed the associated hysteresis level. In some ^embodiments, it ^may be the case that the first output variable to exceed the ^{associated hysteresis level is, for reasons that may be apparent} from the ^design of the system, not critical for the purpose of the bi-directional excitation experiment ^performed in respect of the input variable under consideration. In such a case, said ^{output variable may} be disregarded, and the hysteresis exceeding output variable ^{may be another output variable,} _{for example the chronologically second output} ^{variable to exceed the associated hysteresis level.} t7140 _[0057] ^{According to} embodiments ^{described herein, the second time tz, being the} time 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. In ^particular, 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 to ^Figs.4-6, the output variable ^{yz, 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 the} input _variable ur to the first excited input value (first excitation), the behaviour of a plurality of output variables is monitored, and when the first output variable among ^{these monitored output variables exceeds the associated hysteresis level, the input} variable ur is set to the second excited input ^{value (second} excitation). _[0059] ^In light ^of the above, ^{embodiments described herein involve monitoring} the 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 described ^herein thereby _involve a "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 be ^{said 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 changed ^from the second excited ^input value ^to ^{the final input} value at the third time t:. In ^particular, the input variable may _be substantially maintained at the second excited input _value from _{the second time tz} to the third time t:. According to embodiments, the second duration 344 of the _time ^period from the second time tz to the third time t: may be a predetermined duration. ^{In this respect,} the term ^{oopredetermined"} may be understood in the sense that the ^{second duration 344 may be independent} _{of a behaviour of the output variables in} response to setting the input variable at the second excited input _value. In particular, at the time tz when the input variable is set to the second excited input value, the ^second duration 344 may already be fixed. _[0061] ^{For example, according to embodiments, the second duration 344 may be} set to be equal to the first duration 342. More generally, _{the second duration 344} may be a function of, or may be determined by, the first _duration342. ₁₀₀₆₂₁ In light thereof, the second duration 344 may be determined based on different considerations than the first duration 342. Whereas the first duration342 ^{may depend on a response of the system,} _it ^may _{be the} ^case _{that the second duration} 344 does not depend on such response. For example, _it may _{be the} case _{that the} method according to embodiments described herein does not wait _until ^the ^hysteresis exceeding output variable exceeds the associated hysteresis level a ^second time ^before switching from the second excited input value to the final input ^{value. For example, as illustrated} _{in Fig. 5, the output variable} ^yz _{exceeds the} hysteresis level 525a-b at a time after the third time t3, as indicated _{at 554.In} other words, the input variable ul may be set to the final input value at the third time t:, ^{before the} output variable ^yz exceeds the hysteresis level 525a-b, and in particular independently thereof. _[0063] As described ^herein, at the third time t:, the input variable ^under consideration is set to the final input value. The input variable may _{be maintained} substantially at the final input value at least until the measured _output variables, ^particularly all output variables of the multivariable ^process, have reached a value ^{that stays} _{within a} ^range _{having a} ^prescribed _{width over a} ^period _{of time. The} prescribed _{width associated with an} output variable may be configured to represent _{a stabilization of} the output variable _to a state _of equilibrium. For example, the prescribed width may be the width ^parameter e 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 may} be considered that the output variable has stabilized to the value ^{yi,nnur. Therein,} the value ^yi,nnur may be equal to the reference values ^yio based on which ^{the hysteresis} levels 425a-b, _525a-b and 625a-b were defined, or may be a different value. The latter may be the case, for example, _if the multivariable process is an integrating ^process. [0064] ^{When the output variables have reached an equilibrium state, or more} ^generally _{when the output} ^{variables have reached} _a ^value _{within the} ^above- 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 at} _{least a} ^portion _{of the bi-directional} ^{excitation experiment. The input data may} include 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 first ^{time tr; collecting one or more input values of the input variable from the first time} _{tr to the second time} ^tz; _collecting ^one _or ^{more input values} _of ^{the input variable} from _{the second} time 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 data} ^{resulting from one or more measurements, particularly aplurality of measurements,} performed during at least a ^portion of the bi-directional excitation experiment. _[0067] The method may include any of the following, and any combination _thereof: performing _{one or more measurements of one or} more _{output variables of} ^the plurality of ^{output variables (e.g. the} _variables yvyz _and y:) _{before the first time} tr; performing one or more measurements _of one or more output variables _{of said} ^plurality of output variables from the first time tr to the second time tz; performing one or more ^measurements of one or more output variables of said plurality _of ^{output variables from the second time tz} to the third time tr; ^performing one or more measurements of one or more output variables _of said plurality _of output variables after the third time tr. Measurement data resulting from the measurement(s) may be collected. _[0068] ^{Particularly, the method may include any} of the ^{following, and any} ^{combination thereof: performing} one or more ^measurements of the ^hysteresis exceeding output variable before the first time _tr; performing _{one or} ^more ^measurements of the hysteresis exceeding output variable from the first time tr to the ^second time _b; ^performing one or more measursments of the hysteresis ^{exceeding output variable from} _the ^second _{time tz to the third time t3;} ^performing one or more measurements of the hysteresis exceeding output variable after the _third time t:. Measurement data resulting from the measurement(s) may be collected. _[0069] ^{After the bi-directional excitation experiment relating to the input variable} ^{ur has ended,} _the ^method _may ^proceed _{by selecting a second input variable uz} from ^{the set of input variables and performing a} _{bi-directional excitation experiment in} ^{respect of said second input variable, analogous to the experiment described above} in ^respect of the first input variable ur. The method may proceed accordingly by ^performing a bi-directional excitation experiment for all input variables of the set ^{of input variables. It shall be understood} _{that the aspects described above for the bi-} directional excitation experiment relating to the first input _{variable ur also apply to} ^{each bi-directional excitation experiment relating to any other input variable.} _[0070] Fig.₇ provides a further illustration _{of a} bi-directional excitation experiment as described herein. The experiment is performed in respect _of an ^{arbitrary input variable ui. The bi-directional} _{excitation of said input variable may} have a form as described herein, e.g. as _{shown in} Fig._{3. A} plurality _{of output} 2u ⁴⁰ variables yr to yn may be measured during the experiment. The initial output value of output variable yt is denoted by ^yro in Fig.7 _, for each k ranging from 1 to n. The value of output variable ^yr< _at time t _{is denoted} by ^{yr(t). Associated} with _each ^output _variable yr _is a parameter er _defining the respective hysteresis level. In response to the first excitation of the input variable ui, the ^response of ^each of the ^output _variables yr _to yn may be monitored. According to embodiments described herein, as soon as one output variable among these monitored output variables exceeds the associated hysteresis level ^(illustrated by the OR function in Fig. 7), the second _{excitation of the input variable} ^ui _may ^{be started at} _box ^{702. Particularly,} _at ^such time, the ^{input variable ui may be set to the second excited input value. Further, in} an example, the duration of the second excitation ^(second duration 344) may be taken to be the same as the duration of the first excitation ^(first duration 342), or at least may _{be a} predetermined _function thereof. _[0071] ^{As described herein, the bi-directional excitation experiments according} to the present disclosure are simple, short experiments that provide informative data that is useful for the identification of a model of a multivariable ^process. _[0072] ^{According to embodiments desuibed herein, a model of at least a portion} _{of the multivariable} process may be determined. The model may be based on input _{data and} measurement data from _at least one of the bi-directional excitation ^{experiments. 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-output ^{pair (ui, y.;)} consisting of an input variable ui and an output variable ^y; of the multivariable ^process, an ^associated _{transfer function. The output variable} ^yj _may ^be _the ^{hysteresis exceeding output} _variable identified in the bi-directional excitation experiment performed with regard to the _input variable ui, or may be any other output variable. _[0074] ^{The transfer function may be a first order transfer function} with ^{a delay} Such a transfer function may have the form :;61 K G_;r(s) e -s/, where K, L and T are a priori unknown parameters _of the transfer _{function. The} ^parameters K, L and T may depend on i and ^j, but this dependency is not shown in ^{the above formula} _{for ease of} ^{presentation.} _The ^parameters _{in question may be} ^{estimated based on the measurement data} collected in the respective excitation ^{experiment(s). The set of transfer functions} _Qi(s) ^{may form} _an ^initial _{model of the} multivariable ^process. The initial model may form the basis for determining a more ^{detailed model, by performing} _{further measurements of the process.} _[0075] ^{The model,} such a model involving transfer functions of the kind described above, may be determined from the measurement _{data using a plurality} of commercially known techniques. For exampl e,the delayest and _armax tools _from ^the Matlab System Identification toolbox may be used for this purpose. [0076] ^{In the following, an example of one possible approach for determining a} transfer function ^{G:i(s) is} provided. ^The disclosure ^is not _{limited thereto, and it shall} ^{be understood that several other approaches are possible.} ₁₀₀₇₇₁ ^{For determining the transfer function} _Qi(s), it ^is beneficial to ^consider a ^{corresponding} discrete time transfer function Fli(q). The transfer function I{:i(q) has the form

^where _Q-1 ^{is the backwards shift operator,} d ^{is the delay} in ^samples, and bp and a ^{are parameters. There are three} _{b-paramters to compensate} for apotential inaccurate ^estimation of the delay d. Evidently, once Fli(q) is determined, G;i(s) can be ^{determined as well} since 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 excitation _{experiment, are} _considered. The excitation experiment may involve the input data sequence ^(where _the index i is omitted for ease of presentation) u_(k) u(k + tt) u(k + 2h) u(k + ^Ntt), _{where k} may be a time shortly before the first time tr ^(where tr is the time when the _input variable is set to the first excited input value), h is a sampling interval and N _{is a constant such that k + Nh represents} ^{a time near the end of the experiment} _{relating to the} ^{input variable ui.} _[0079] The ^{measurement data} that is ^considered may involve a plurality of measurements _{of the} output variable yj performed during the experiment, represented by an output data sequence ^(where the ^{index j is omitted)} y(k) ^y(k + tt) ^y(k + 2h) ^y(k + ^Nh) _[0080] The output variable ^yj may be the ^{hysteresis exceeding output variable} _{identified in} ^said _{experiment, or} ^{may be a different output variable. The output} sequencs may be assumed to be noisy and may be filtered through a non-casual filter with zero ^phase distortion to keep the waveform. _[0081] ^{The modeling may be done in two steps using the input and the output data} sequences. _[0082] First, the time ^{delay may be estimated. This may be performed using the} _function delayest from Matlab's System Identification toolbox. This provides the ^{value of the parameter d in the discrete time transfer function} _Ei(q). _[0083] ^{Further, the parameters} a ^{and by of the function function} f!i(q) ^{may be} identified using the function armax from Matlab's System ^{Identification toolbox.} _{An estimate of the uncertainty of the} ^{parameters may also be provided.} [_0084] In light of the above, according to an ^{embodiment, 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 muitivariabie} ^{process, performing} a bi-directional excitation experiment. Performing the bi- directional excitation experiment includes setting _the input variable _at an initial input value. Performing 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 ^hrst time, wherein the first excited input ^{value differs from the initial input value} _{by a first amount. Performing the bi-} directional excitation experiment includes measuring a plurality of output variables of the multivariable ^process in response to performing the first excitation. A ^{respective hysteresis} level is associated to each of the measured output variables. ^Performing the bi-directional excitation experiment includes identifuing 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. ^Performing 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. The ^second excited ^input value differs from the initial input value by a second amount. The first amount and the second amount have opposite signs. _Performing the _bi- ^{directional excitation experiment includes measuring} at ^{least the hysteresis} exceeding output variable in response to performing the second excitation. ^Performing the bi-directional excitation experiment includes setting the input ^variable _{at afrnal} ^{input value at a} _{third time} ^{after the second} _time. _[0085] ^{That the plurality} of output ^variables is ^measured in ^{response to} performing the first excitation _of the input variable under consideration can be understood in the sense that the output variables in question are measured after the first excitation ^has started, in ^particular after the input variable has been set to the _first ^{excited input value (in other} _{words after the first time tr).} _[0086] According to ^{embodiments, the measured plurality} of ^{output variables} may consist of all output variables of the multivariable process. Accordingly, all output variables may be measured in ^response to ^performing the first excitation. _[0087] ^{According to embodiments, the hysteresis exceeding output variable may} be ^{an a priori unknown output variable among the plurality of measured output} variables. Identi$ing the hysteresis exceeding output variable may include determining which output variable among the plurality of measured output _{variables is the hysteresis exceeding} ^{output variable} _{based on} ^{measured values} obtained by the measuring of the plurality of output variables. _[0088] ^{According to embodiments, the time period from the second time to the} third _{time may have a} ^{pre-determined} _duration. _[0089] According to embodiments, the time ^period from the first time to ^the second 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 second ^{duration may be a function of the first duration. Particularly, the second duration} may be substantially equal to ^the first duration. _[0090] ^{According to embodiments, the hysteresis exceeding output variable may} _{be the} first 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 be} maintained substantially at the final input value at least until each output variable of the ^measured plurality of output variables stays within a range having ^a prescribed _{width over} ^a period of time. _[0092] According to ^{embodiments, the method may include,} for each ^output ^variable of ^{a set} of ^{output variables of the multivariable process, determining the} hysteresis level associated with the output variable based on a noise parameter. _[0093] ^{According to embodiments, the method may include maintaining the input} ^{variable under consideration} _{at substantially the} first _{excited input value from the} first 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 the} first amount. _[0095] ^{According to a further embodiment, a method} of ^model identification of ^a multivariable ^process is provided. The method includes performing the method _of collecting data according to any of the embodiments described herein. The method ^{includes determining a model} _{of at least} ^{a portion} _{of the multivariable} ^process _based ^{on measurement data obtained from measuring one or} _{more output variables during} at least one of the bi-directional excitation experiments. _[0096] ^{According to embodiments, the model may include, for at least one input-} output ^pair consisting of an input variable and an output variable of the ^{multivariable process,} _a ^first _{order transfer function} with _{a delay. Determining the} model may include determining at least one parameter _{of the} first _order transfer function based on the measurement data. _[0097] ^{According to a further embodiment, and as illustrated in Fig. 8, an} ^{apparatus 800} for collecting data for ^process identification of a multivariable process 100 is provided. The apparatus 800 includes _{one or} more _{input devices 810.} The apparatus includes one _or more 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 to ^perform, for each input variable of a set of input variables of the multivariable ^process, a bi-directional excitation experiment under the control of the control system 850. The bi-directional excitation experiment includes _{setting the input} variable at an initial input value using an input device 810. 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 hrst time using the input device 810, 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 each output variable is measured using a measurement device 820, 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 using ^{the input device 810, 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 _{using a} measurement device 820 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 using the input device. _[0098] The apparatus may be configured for ^performing any aspect or combination of aspects of the methods described herein. _[0099] ^{An input device as described herein can be any input device suitable for} ^{setting or adjusting one or more input variables to a specified value. An input device} _can ^{be an} _input ^actuator. [00100] ^{A measurement device as described herein can be any measurement} _device, such as a sensor, detector or the like, for measuring a value of one or more output variables. _[00101] ^{The control} system, or controller, may be ^a single system or a distributed system including aplurality of individual controllers. A _control system may include one or more computers or processors for processing data supplied to the control system. _[00102] ^According to ^embodiments, the control system may be configured, for ^{each output variable} of ^{a set} _{of output} ^variables _of ^the _{multivariable} ^process, _for determining the hysteresis level associated with the output variable based on a noise parameter. _[00103] ^{According to embodiments, the apparatus may be configured, e.g. under} the ^control of the control system, for: maintaining the input variable under consideration at substantially the first excited input value from the first _{time to} the second time; and/or maintaining the input variable _at substantially the second excited input value from the second time to the third time. _[00104] According to embodiments, the apparatus, and in ^particular the control ^{system, may be} configured ^for determining a model of at ^least a ^portion of the multivariable process based on measurement data obtained from measuring _{one or} more output variables during _at least one _of the bi-directional excitation experiments. _[00105] ^According to ^a further ^embodiment, a computer ^program for collecting ^{data for process identification of a multivariable process is provided. The} computer program includes instructions which, when the program is executed by a computer, cause the computer to ^perform, for each input variable of a set of input variables _of the multivariable ^process, a set of operations. The set of operations includes ^receiving _first ^measurement _{data resulting from measuring a} ^plurality _{of output} ^{variables of the multivariable process in response} to ^{performing a} first excitation of the input variable, wherein performing the first _excitation comprises setting the input 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 the measured output} variables. 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 the} hysteresis exceeding output variable is an output variable having a measured value that exceeds the hysteresis level associated with ^{the output variable. The set of operations includes receiving second measurement} data resulting from measuring at least the hysteresis exceeding output variable in _{response to} performing _a ^second excitation _{of the input} variable, ^wherein performing 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 excited ^input value differs ^from the _{initial input value} by a second amount, wherein the f,rrst amount and the second amount have opposite signs. _[00106] The computer ^program may be configured to ^perform any computer- implementable aspect or combination of aspects of the ^methods described ^herein. _[00107] The computer ^program may include ^instructions which, when ^the program is executed by a computer, cause the computer to perform, for each input variable of a set of input variables of the multivariable ^process, any one the following operations, or any combination thereof: determining the initial input value of the input variable; determining the first excited ^input value of the ^input _variable; ^{determining the first time; determining the second excited input value} _of the input variable; determining the second time; determining the hnal input value of the input variable; and determining the third time. _[00108] The ^{computer program} may include ^instructions which, when ^the program is executed by a computer, cause the computer, for each output variable of a set of output variables of the multivariable ^process, to determine the hysteresis level associated with the output variable ^based on ^{a noise parameter.} _[00109] ^.The computer ^program may include instructions which, when ^the program _is executed _by a computer, cause the computer to determine a model of at ^{least a portion of the multivariable process} _{based on at least the first measurement} data and the second measurement data. [_00110] ^{As used herein, the terms "computer", "processor" and} "controller", _and ^{related terms,} are not limited to ^just those integrated circuits referred to in the art as ^{a computer, but broadly refers} to a microcontroller, a microcomputer, an analog ^computer, a ^programmable logic controller ^(PLC), an application specific integrated circuit (ASIC), and other programmable circuits, and these _terms are used interchangeably herein. In the embodiments described herein, _"memory" may ^{include, but is not limited} _to, ^a _{computer-readable medium, such as a random-access} ^{memory (RAM),} a computer-readable non-volatile medium, such as a flash memory. Alternatively, a floppy disk, a compact disc - ^read _{only memory} ^(CD- ROM), a magneto-optical disk (MOD), and/or a digital versatile _disc (DVD) _may ^{also be used.} Also, in the embodiments described herein, additional input channels ^{may be, but are not limited} _{to, computer} ^peripherals _{associated with an operator} ^{interface such as a touchscreen,} a ^mouse, and a keyboard. Altematively, other computer ^peripherals may also be used that may include, for _{example, but not} be limited to, a scanner. Furthermore, in the example embodiment, additional output ^{channels may include,} but not be limited to, an operator interface monitor or heads- ^{up display. Some embodiments} involve the use of one or more electronic or computing devices. Such devices typically include a processor, processing _device, or controller, such as a general-purpose central processing unit (CPU), a graphics ^processing unit ^(GPU), a microcontroller, a reduced instruction set computer ^{(RISC) processor,} _{an ASIC, a} ^programmable _{logic controller (PLC), a field} programmable gate array (FPGA), a digital signal processing (DSP) _{device, andlor} ^{any other circuit or processing device capable} of executing the functions described herein. The methods described herein may be encoded as executable instructions embodied in ^a computer readable medium, including, without limitation, a storage ^{device and/or a} _memory ^device. _{Such instructions, when executed by a} ^processing ^{device, cause the processing device} _to ^perform _{at least a} portion _{of the methods} described herein. The above examples are not ^intended to limit in any way ^the _{definition and/or} ^meaning of ^the _term ^{processor and processing device.} _[00111] ^{While the foregoing is directed to embodiments, other and further} embodiments may be devised without departing from the basic scope, ^and the ^scope is determined by the claims that follow. REFERENCE NUMERALS multivariable process 100 input variable 110 ^{output variable} 120 horizontal axis 210 time 2t2 time 214 time 2t6 ^{vertical axis} 220 plot 250 horizontal axis 310 vertical axis 320 _initial ^{input value} 321 ^{final input value} 321 first excited input value 322 second excited input value 324 first amount 332 second amount 334 ^{first duration} 342 second duration 344 plot 3s0 horizontal axis 410 vertical axis 420 hysteresis level 425a-b plot 450 horizontal axis 510 vertical axis s20 ^{hysteresis level} 525a-b plot 550 horizontal axis 610 vertical axis 620 hysteresis level 625a-b ^plot 650 box 702 apparatus 800 input device 810 measurement device 820 ^{control system} 850

Claims

CLAIMS 1. A ^method of ^{collecting data for process identification of a multivariable} process ⁽¹00), comprising: for each input variable (l ¹⁰⁾ of ^{a set} of input variables of the ^{multivariable} process, performing a _{bi-directional} excitation 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 first ^time (tr), _wherein the first _excited input 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 to ^performing the first excitation, wherein a ^{respective hysteresis} level ^(425a-b, 525a-b, ^{625a-b) is} associated to each of the measured output variables; identifying a hysteresis exceeding output variable ^(yz) among the measured plurality of output variables, wherein the ^hysteresis exceeding o_{utput variable} ^{is an} _{output variable} ^{having a measured value that exceeds} the hysteresis level associated with the output variable; 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 e_{xcited input value} ^{(324) at a second} _time ^(tz), _{wherein the} ^{second excited} input _{value differs} from ^the _initial input ^value _by ^{a second amount (334),} w_herein the 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 method} of ^{claim 1,} wherein the time ^{period (344)} from the second time to the third time has a pre-determined duration.

3. ^{The method} of claim 2, wherein the time period (342) from the first time ^{to the second time has a first duration,} _{wherein the} ^{pre-determined} _{duration of the} time period from the second time to the third _time is a second duration, _wherein the second duration is a function of the first duration, particularly wherein the ^second duration is substantially equal to the first duration.

4. ^{The method} of ^any of ^{the preceding} claims, 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 the _first excitation.

5. ^{The method of any of the preceding claims, wherein the} _input ^{variable is} maintained substantially at the final input value at least until each output variable of the ^{measured plurality} of output variables stays within a range having a prescribed width over a period _{of time.}

6. ^{The method of any of the preceding claims, further comprising:} for each output variable of a set of output variables of the multivariable ^{process, determining the hysteresis} _{level associated with the output variable based} on a noise parameter.

7. ^{The method of any of the preceding claims, further} _comprising: maintaining the input variable at substantially the first excited input value ^from the ^first time to the second time; and/or m^aintaining the ^input variable 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 is} a function of the hrst amount.

9. A method of model ^{identification} of a ^{multivariable process (100),} comprising: performing the method of collectingdataaccording to any ofthe ^preceding claims; and d_etermining a model of at least a portion of the multivariable process based _on measurement data obtained from measuring one or more output variables during at least one of the bi-directional excitation experiments.

10. ^{The method} of claim ^{9, wherein the model includes, for at least one input-} _output pair consisting _of an input variable and an output variable of the multivariable ^process, a first order transfer function with a delay, ^and wherein determining the model comprises: d_etermining at 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 a} _{multivariable} ^{process (100), comprising:} o_ne or more input devices (810); one or more measurement devices ^(820); a control system ⁽⁸⁵⁰⁾ connected to the one or more input devices ^{and the} one or more measurement devices, w_{herein the apparatus is configured to} ^perform, _for ^{each input variable} ⁽¹¹⁰⁾ _{of a set of input variables of} ^{the multivariable process, a bi-directional} _{excitation experiment} ^{under the} _{control of the control} ^{system, the bi-directional} _{excitation experiment} ^comprising: setting the input variable at an initial input value ⁽³²¹⁾ using an input device of the one or more input devices; ^{performing a first excitation} _{of the input variable, comprising} setting the input variable at a first excited input value (322) at a _{first time} (^{tr) using} the input device, wherein the first excited input value differs f^{rom the initial input} _{value by} ^a _{first amount} ^(332); ^measuring a ^plurality of _{output variables} (yu ^yz, y:) of _the m^{ultivariable process} in ^response to ^performing _the first _excitation, wherein each output variable is measured using a measurement device _of t^{he one} or ^{more measurement} _{devices, wherein a respective hysteresis} l^{evel (425a-b, 525a-b,625a-b) is associated} _{to each of the measured output} variables; identifying a hysteresis exceeding output _variable (yz) among the m^{easured plurality} of output variables, wherein the hysteresis exceeding o^{utput variable is an output variable} _{having a measured valuö that exceeds} t^{he hysteresis level associated} with _{the output variable;} p^erforming a second excitation of the input variable in response _to identifying the hysteresis exceeding output variable, wherein performing t^{he second} excitation comprises setting the input variable at a second e^{xcited input value (324)} _{at a second time} ^(tz) _{using the input device,} wherein the second excited input value differs from _{the initial input value} b^y a second amount ^(334), wherein the first amount and the second amount h^ave opposite signs; m^{easuring at least the hysteresis} _{exceeding output variable using a} m^{easurement device of the one or more} _{measurement devices in response} to ^performing the second excitation; and setting the input variable at a final input value (321) ata _{third time} (^{t:) after the second} _{time using the input device.}

12. ^{The apparatus of claim 11, wherein the} time ^{period (344)} from the second time to the third time has a pre-determined duration.

13. The apparatus of claim ^{12, wherein the time period (342) from the first} _{time to} the second time has a first duration, wherein the ^{pre-determined} duration of the time period from the second time to the third time ^is a second ^duration, _{wherein the second duration} ^{is a} function ^{of the} first ^duration, particularly wherein _the second _duration is substantially equal to the first duration.

14. ^{The apparatus of any of claims 11 to 13, 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 setting the input variable at the first excited input value.

15. ^{A computer program for collecting data for process identification of a} _{multivariable} process (100), the computer program comprising instructions _{which, when} the program is executed by a computer, cause the computer to perform, for each input variable ⁽¹¹⁰⁾ of a set of input variables of ^the _{multivariable} ^process, _{the following} ^{operations :} r_{eceiving first} ^{measurement data resulting from measuring a plurality} of _{output variables} (yt,yz, y:) of the multivariable process in response to ^performing _a first excitation of the input variable, wherein ^performing the first excitation ^{comprises setting the input variable at a first excited input value (322) at a first} _time ^(tr), _{wherein the first excited} ^{input value} _differs ^{from an initial input value} of _{the input variable by a first} ^{amount (332), wherein a respective hysteresis level} (425a-b,525a-b,625a-b) is associated to each of the measured output variables; identifying _a hysteresis exceeding output variable ^(yz) among ^the ^{measured plurality} of ^{output variables based on the first measurement data,} wherein the _{hysteresis exceeding} output variable ^is _an ^{output variable having a} measured value that exceeds the hysteresis level ^associated with the ^output variable; and r_{eceiving second} measurement data resulting from measuring at least the ^{hysteresis exceeding output variable in response to performing a second excitation} o_f the _input variable, wherein performing the second excitation comprises setting the input variable at a second excited input value (324) at a second _time (tz) _in ^response to identifying the hysteresis exceeding output variable, wherein the ^{second excited input value differs from} _{the initial input value by a second amount} ^(334), wherein the first amount and the second amount have _{opposite signs.}