Patent Application: US-26164205-A

Abstract:
a computer method and apparatus of online automated model identification of multivariable processes is disclosed . the method and apparatus carries out automatically all the four basic steps of industrial process identification : 1 ) identification test signal design and generation , 2 ) identification plant test , 3 ) model identification and 4 ) model validation . during the automated plant test , process models will be automatically generated at a given time interval , for example , every hour , or on demand ; the ongoing test can be automatically adjusted to meet the process constraints and to improve the data quality . plant test can be in open loop operation , closed - loop operations or partly open loop and partly closed - loop . in a closed - loop plant test , any type of controller can be used which include proportional - integral - derivative controllers and any industrial model predictive controller . the obtained process models can be used as the model in advanced process controllers such as model predictive control and linear robust control ; they can also be used as inferential models or soft sensors in prediction product qualities . the apparatus can be used in new mpc controller commissioning as well as in mpc controller maintenance .

Description:
fig1 shows the general block diagram of the invention . nowadays process units use distributed control systems ( dcs ) as their instrumentation and regulatory control . in the illustrations and diagrams , we will assume that the given process unit is under dcs control , although the invention can also work with other instrumentation systems , such as programmable logic control ( plc ) systems , or supervisory control and data acquisition ( scada ) systems . the computer apparatus for online automatic identification will be typically located in a personal computer ( pc ) using microsoft windows ® operating system , although it can also be located in other kind of computers using other operating systems such as linux and unix . the computer apparatus for online automatic identification consists of two parts : a testing device and a model identification device . the testing device in fig1 performs plant test by applying test signals or perturbations primarily at process mvs in order to excite process for model identification . the process mv , dv and cv data are stored in a database to be used by the model identification device . after about 25 % of the planed test time , the model identification device will be started automatically or manually ( pressing a key ). the model identification device will compute process models , calculate model step responses and frequency responses , perform model validation , and determine new desired step sizes of each test signals . all steps of identification device are performed automatically with no user intervention . the resulting models can be exported in a model format for certain mpc controller ; the new desired step sizes of test signals will be sent to the testing device for adjusting the test . before starting the test , the user needs to specify process time to steady state , or , settling time . then , test signals will be created . a typical test signal used in the invention is the summation of a generalized binary noise ( gbn ) ( tulleken , 1990 ) and a small white noise . fig2 shows the trend plot of a test signal . the guideline for designing the gbn part of the signals can be found in zhu ( 2001 , chapter 3 ). normally , the test signals are not correlated by design . however , for certain ill - conditioned processes such as high purity distillation columns , strongly correlated test signals will be used for some mvs ; see zhu ( 2001 , chapter 10 ). the user also needs to set a step size high limit for each test signals . these limits can be obtained from pre - test and from operation knowledge of the process unit . a test time t test will also be calculated for use in model validation purpose . the test time is an estimate of the test time needed for the given plant test . denote t settle as the time to steady state or settling time , m as the number of mvs in the test , the formula for calculating t test is t test = { 15 ⁢ ⁢ t settle for ⁢ ⁢ m ≤ 10 [ 1 + 0 . 1 ⁢ ( m - 10 ) ] ⁢ 15 ⁢ t settle for ⁢ ⁢ m & gt ; 10 ( 1 ) the testing device , when turned on , applies the designed test signals at process mvs and possibly some cv setpoints or cv limits in a real time manner that works at a constant sampling time , say , 1 minute . this testing sampling time can be the equal or greater than the mpc controller sampling time . fig3 shows the flow diagram of the testing task for each tested mv at a sampling interval . one important feature of the current invention is that many mvs are tested ( moved ) simultaneously . this number can be 10 , 20 , 30 or more than 50 . another advantage of the present invention is its ability to use closed - loop test as well as open test . in an open loop plant test , all cvs of the mpc controller are in open loop mode , namely , none of the cvs is controlled . in an open loop test , test signals are applied at mvs . fig4 shows the connection between the testing device and the process unit in an open loop test . in an open loop test , the testing device writes the full values to the tested mvs . in a partial closed - loop test , pid controllers control some sensitive cvs ; the rest of the cvs are in open loop . in a partial closed - loop test , test signals are applied at open loop mvs ; for those closed - loop cvs , the test signals are usually applied at cv setpoints . fig5 shows the connection between the testing device and the process unit in a partial closed - loop test where cv1 is controlled by a pid controller using mv1 . during an mpc closed - loop plant test , an mpc controller controls part or all the cvs . in an mpc closed - loop test , test signals are usually applied at mvs . test signals can also be applied to some cv setpoints and / or cv limits . fig6 shows the connection between the testing device and the process unit in an mpc closed - loop test . for understanding various test types , it is useful to distinguish two parts of an mv value : 1 ) mean value or nominal value , the mv value without applying the test signal , 2 ) test signal , the perturbation added to the mv during the test . during the test , the relation is : when an mv is in open loop mode , the testing device will write the full mv value ; see fig4 . when an mv is in mpc closed - loop , the testing device will write the test signal only and the mpc controller will write the mean value . the full mv value is obtained using a summer block ; see fig6 . when a cv is in pid closed - loop control , the test device will write the full value of the cv setpoint ; see fig5 . because the testing device is connected directly to the dcs or plc , it is independent of the mpc controller and can work with any given mpc controller . it should be clear that we could also use mixed pid and mpc closed - loop test where some process cvs are controlled by an mpc controller and some by pid controllers . when an mv is in closed - loop control , its movement consists of the test signal and controller action . because the controller action of one mv can be correlated to the unmeasured disturbances and to other mvs , mvs in a closed - loop test will be , in general , correlated with each other and with unmeasured disturbances . the current invention can use correlated mv data in model identification . in plant test , one needs to strike a balance between two conflicting gaols : 1 ) to excite the process for generating informative data about the process dynamic behaviour , and 2 ) to minimize disturbance caused by the test signals . the ability of using closed - loop test and closed - loop identification by the invention plays a key role in solving the two problems , because : 1 ) it is well know that closed - loop test can reduce disturbance to the process unit operation , and 2 ) it can also be shown that process data from a closed - loop test can lead to better models for closed - loop control ; see hjalmarsson et . al . ( 1996 ), koung and macgregor ( 1993 ), jacobsen ( 1994 ) and zhu ( 2001 , chapter 10 ). besides , the testing device uses several other intelligent testing functionalities to meet the two goals , which are explained here . control action during plant test . if a cv is under closed - loop control , the underline controller will control it during the test . however , the testing device can also do some control in order to stabilize unit operation as follows : 1 ) control for slow cv drifts . this is only done for open loop cvs . if an open loop cv is drifting away and is outside its high ( low ) limit , find its strong mv &# 39 ; s according to the expectation matrix and change their average values in order to bring it back ( according to the signs of the expectation matrix ). the amount of change for each mv is perform this action once each 0 . 3 * t settle until the cv is back within the limit . here t settle is the process time to steady state . 2 ) control for bumping cvs . this is for both open loop and closed - loop cvs . if a cv is bumping around and hits both high and low limits , find its strong mv &# 39 ; s and reduce their step sizes . the amount of step size reduction for each mv is perform this action once each 0 . 3 * t settle until the cv stopped bumping against high / low limits . here t settle is the process time to steady state . test signals step size adjustment . model identification device will not only produce process models , it will also provide information for step size changes for the ongoing plant test . for a given mv , if all its expected models are with good quality , the mv step size can be reduced in order to reduce disturbance to process unit ; if some model quality will not be good enough at the end of the test , the mv step size will be increased in order to improve signal to noise ratio in the data . the text on model identification device will explain how to determine model quality . the testing device will implement the step changes , provided that they do not violate mv limits . step changes can also be done manually . test signal switch time adjustment . the frequency content or power spectrum of a test signal is mainly determined by the average switch time , or , average step length of the gbn signal . increasing the average switch time will increase the signal power at lower frequencies and hence improve model quality at lower frequencies . similarly , decreasing the average switch time will increase the signal power at higher frequencies and hence improve model quality at higher frequencies . hence , for an mv , if the corresponding model quality needs to be improved only at lower frequencies , the testing device will increase the average switch time , typically , double it ; if the corresponding model quality needs to be improved only at higher frequencies , the testing device will decrease the average switch time , typically , halve it . test signal switch time can be adjusted automatically by the testing device , or , manually . model identification device performs model identification , model validation and other related computations using most recent mv , dv and cv data available . fig7 shows the flow diagram of model identification device . the identification algorithms used in the device is based on the asymptotic method ( asym ) developed in zhu ( 1998 , 2001 ). the following gives a description of the methodology . given a multivariable process with m mvs and p cvs . dvs will be treated as mvs in model identification . assume that a linear discrete - time process generates the data as y ( t ) = g o ( z − 1 ) u ( t )+ h o ( z − 1 ) e ( t ) ( 3 ) where u ( t ) is an m - dimensional input vector , y ( t ) is a p - dimensional output vector , g o ( z − 1 ) is the true process model and z − 1 is the unit time delay operator . h o ( z − 1 ) e ( t ) represents the unmeasured disturbances acting at the outputs , and e ( t ) is a p - dimensional white noise vector . denote the data sequence that is collected from an identification test as z n :={ u ( 1 ), y ( 1 ), u ( 2 ), y ( 2 ) , . . . , u ( n ), y ( n )} ( 4 ) the model to be identified is in the same structure as in ( 3 ): y ( t ) = g ( z − 1 ) u ( t ) + h ( z − 1 ) e ( t ) ( 5 ) the process model g ( z − 1 ) and noise filter h ( z − 1 ) will be parametrized in matrix fraction description ( mfd ); see zhu ( 2001 ) for details . the model will be calculated by minimizing the prediction error cost function ; see ljung ( 1985 ). the frequency response of the process and that of the model are denoted as t o ( e iω ):= col [ g o ( e iω ) , h o ( e iω )] { circumflex over ( t )} n ( e iω ):= col [ ĝ n ( e iω ), ĥ n ( e iω )] where n is the degree of the polynomials of the model , col (.) denotes the column operator . under some conditions of model order and structure and test signals , the following asymptotic results on the model properties in the frequency domain can be shown ( ljung , 1986 and zhu , 1989 ) { circumflex over ( t )} n ( e iω )→ t o ( e iω ) as n →∞ ( consistence ) ( 6 ) the errors of { circumflex over ( t )} n ( e iω ) follow a gaussian distribution , with covariance as cov [{ circumflex over ( t )} n ( e iω )≈ n / nφ − t ( ω ) φ v ( ω ) ( 7 ) where φ ( ω ) is the spectrum matrix of inputs and prediction error residual col [ u t ( t ), ξ t ( t )], φ v , ( ω ) is spectrum matrix of unmeasured disturbances , denotes the kronecker product and − t denotes inverse and then transpose . this theory holds for data created by both open loop tests and closed - loop tests . in the following , we will outline the model identification method using the asymptotic theory . â n ( z − 1 ) y ( t )={ circumflex over ( b )} n ( z − 1 ) u ( t )+ ê ( t ) ( 8 ) where â n ( z − 1 ) is a diagonal polynomial matrix and { circumflex over ( b )} n ( z − 1 ) is full polynomial matrix , both with degree n polynomials . denote ĝ n ( z − 1 ) as the high order arx model of the process , and ĥ n ( z − 1 ) as the high order model of the disturbance . the high order model in ( 8 ) is unbiased , provided that the process behaves linear around the working point . the variance of this model is high due to its high order . here we intend to reduce the variance by perform a model reduction on the high order model . using the asymptotic result of ( 6 ) and ( 7 ), one can show that the asymptotic negative log - likelihood function for the reduced process model is given by ( wahlberg , 1989 , zhu and backx , 1993 ) v = ∑ i = 1 p ⁢ ∑ j = 1 m ⁢ ∫ - π π ⁢  {  g ^ ij n ⁡ ( ω ) - g ^ ij ⁡ ( ω )  2 ⁢ 1 [ φ - 1 ⁡ ( ω ) ] ij ⁢ φ v i ⁡ ( ω ) }  ⁢ ⁢ ⅆ ω ( 9 ) the reduced model ĝ ( z − 1 ) is thus calculated by minimizing ( 9 ) for a fixed order . the same can be done for the disturbance model ĥ n ( z − 1 )= 1 / â n ( z − 1 ). the best order of the reduced model is determined using a frequency domain criterion asyc ; see zhu ( 1994 ) for the motivation and evaluation . the basic idea of this criterion is to equalise the bias error and variance error of each transfer function in the frequency range that is important for control . let [ 0 , ω 2 ] defines the frequency band that is important for the mpc application , the asymptotic criterion ( asyc ) is given by : asyc = ∑ i = 1 p ⁢ ∑ j = 1 m ⁢ ∫ 0 ω 2 ⁢  [  g ^ ij n ⁡ ( ω ) - g ^ ij ⁡ ( ω )  2 - n n ⁡ [ φ - 1 ⁡ ( ω ) ] jj ⁢ φ v i ⁡ ( ω ) ]  ⁢ ⁢ ⅆ ω ( 10 ) delays often exist in process units . good delay estimation can improve model accuracy . delays are estimated by trying various delays in model identification for a fix order . the delays that minimize the simulation error loss function will be used . the loss function for selecting the best delays is ∑ i = 1 p ⁢  y i ⁡ ( t ) - y ^ i ⁡ ( t )  2 ( 11 ) according to the result ( 4 ) and ( 5 ), a 3σ bound can be derived for each transfer function of the high order model as follows :  g ij o ⁡ ( ⅇ i ⁢ ⁢ ω ) - g ^ ij n ⁡ ( ⅇ iω )  ≤ bnd ij = 3 ⁢ n n ⁡ [ φ - 1 ⁡ ( ω ) ] jj ⁢ φ v i ⁡ ( ω ) ⁢ ⁢ w . p ⁢ . 99 ⁢ . 9 ⁢ % ( 12 ) we will also use this bound for the reduced model because the model reduction will in general improve model quality . the upper bound will be used to quantify the quality of each model . grade the model according to the relative size of the error bound and the model frequency response over the low and middle frequencies . a model is graded as ‘ a ’ ( very good ), if bound ≦ 30 % model , ‘ b ’ ( good ), if 30 % model & lt ; bound ≦ 60 % model , ‘ c ’ ( marginal ), if 60 % model & lt ; bound ≦ 90 % model , and ‘ d ’ ( poor , or , no model ), if bound & gt ; 90 % model . this grading system can be adjusted for the given class of applications . the above grading is suitable for mpc application for the refining and petrochemical industries . if most , say 80 %, of the expected models are with ‘ a ’ and ‘ b ’ grades , the rest of the expected models are with c grade , models can be used in the mpc controller and identification test can be stopped . if the above condition is not met , continue the test and , possibly , adjust the ongoing test . as mentioned before , test adjustment includes change mv step sizes , average switch time of gbn signals . the required changes are obtained using the so - called future upper bounds , the estimated upper bounds at the end of the test . denote n test as the number of samples at the end of the test , the future upper bound for a model is bnd ij future = 3 ⁢ n n test ⁡ [ φ - 1 ⁡ ( ω ) ] jj ⁢ φ v i ⁡ ( ω ) ( 13 ) the grading results using the future upper bounds will be called future grades . for a given mv , if the future grades of the expected models are mostly ‘ a ’ and ‘ b ’, the mv step size is proper . no change is needed . for a given mv , if the future grades of many expected models are ‘ c ’ and ‘ d ’, increase its step sizes so that they become ‘ a ’ or ‘ b ’ grade . for a given mv , if the future grades of many expected models are ‘ c ’ and ‘ d ’, increase the mv step size so that the future grades become ‘ a ’ or ‘ b ’ grade . the corresponding upper bound is inversely proportional to the mv step size ; see zhu ( 2001 , chapter 6 and 7 .) for a given mv , if the future grades of many expected models are ‘ c ’ and ‘ d ’ and the mv step size already at its high limit , increase the average switch time of the mv test signal ; usually double it . for a given mv , if the future grades of the expected models are mostly ‘ a ’, the mv step size can be reduced somewhat ; usually 30 to 50 %. the computation of the test adjustments is done in the model identification device and the results are passed to the testing device for implementation . the expectation matrix provides information about the locations of models between mvs and cvs . when using the expectation matrix in identification , only expected models between certain mvs and cvs will be identified ; unexpected models corresponding to the empty elements of the expectation matrix will be excluded . compared with identifying the full models between all mvs and all cvs , the use of expectation matrix will reduce the number of parameters considerably , which can lead to higher model accuracy and can also increase the speed of computation . the use of expectation matrix in model identification is optional . when an expectation matrix is not available or not reliable , the full models will be identified . note that an expectation matrix can be created or modified using the identification results of full models . hjalmarsson , h ., m . gevers , f . de bruyne ( 1996 ). for model - based control design , closed - loop identification gives better performance . automatica , vol . 32 , no . 12 , pp . 1659 - 1673 . jacobsen , e . w . 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