Patent Application
20230039523
The present invention relates to a model update device and method, and a process control system that are suitable for application to a process control system that controls a plant where model predictive control (MPC) is introduced.
MPC is an advanced process control technology widely used in the process industry such as a chemical process and the like, and currently, more than 5,000 applications are operated all over the world. In MPC, a controller called a model predictive controller is used.
This controller (hereinafter, this controller is also referred to as an MPC) holds a model of a target process (hereinafter, this is referred to as a process model) such as a multi-input multi-output process (hereafter, this is referred to as a multiple input multiple output (MIMO) process), that is, a model for reproducing or predicting time series data of the process output from time series data of the process input.
Then, the MPC calculates an optimum input signal to bring the process output close to the reference value or hold the process output at the reference value, by using the process model of the target process and the time series data of the process input and output, and inputs the calculated input signal to the target process. The process model used at this time is obtained by inputting a test signal such as a maximum length sequence (M sequence) or the like into the process, and performing system identification by using the output obtained from the input test signal.
A general problem with the MPC is that the control performance deteriorates over time. Specifically, due to improvement and deterioration of equipment, changes in operation plans, changes in the quantity and quality of materials, and temporal changes in the target process such as debottlenecking (obstacle removal) or the like, the prediction accuracy of the process model decreases, which causes deterioration of control performance. Such deterioration of control performance causes a loss of profit and is a big problem in operation. In order to maintain good control performance, it is necessary to monitor the quality of the process model such as prediction accuracy and the like, and update the process model when necessary. In addition, like introducing MPC, updating the process model is also based on the system identification. Insertion of the test signal during operation causes a loss of profit, and enormous human cost and time cost are also required to adjust the amplitude and cycle of the test signal so as not to violate the operation constraint.
In order to address this problem, for example, JP-T-2012-528392 (PTL 1) discloses a technique of estimating a model quality for each input end and output end using the input and output data of the process and the existing process model, and automatically generating and inputting the test signal based on the model quality, thereby realizing reduction of test signals and reduction of adjustment cost at the time of model update.
PTL 1: JP-T-2012-528392
However, in the technique disclosed in PTL 1, there is a problem that the test signal is still input when the process model is updated, which causes a loss of operating profit. In addition, there is a possibility of violating the operating regulations of the plant in view of the fact that the test signal is automatically input.
Further, in the technique disclosed in PTL 1, although a method of adding the test signal to the process input is used, because MPC is a control method (closed-loop control) that determines the process input based on the measured value of the process output, the quality estimation accuracy and the identification accuracy of the model decrease due to the correlation between the test signal and the process output. In PTL 1, in order to eliminate such a correlation and improve the accuracy, an embodiment is also proposed, in which an automatic test signal generator (tester) and an MPC are integrated, but there is also a problem that the above-mentioned embodiment cannot be applied to a plant in which the existing MPC is introduced.
The present invention is made in consideration of the above issues and intends to propose a model update device and method, and a process control system, which are capable of significantly reducing the labor, time, and monetary cost required for model update and are also easily applicable to a plant in which the existing model predictive control is introduced, without causing a loss of operating profit.
In order to solve such a problem, according to the present invention, a model update device that updates a model of a target process in a model predictive control is provided, which includes: a conversion unit that converts a data format of operation data of the target process into a delay coordinate format; an update model generation unit that generates an update model reflecting secular change information of the target process by solving a regression problem including a regularization term for the operation data converted into the delay coordinate format; and a model update unit that updates the model by replacing the model with the model generated by the update model generation unit.
Further, according to the present invention, a model update method executed by a model update device that updates a model of a target process in a model predictive control is provided, which includes: a first step of converting a data format of operation data of the target process into a delay coordinate format; a second step of generating an update model reflecting secular change information of the target process by solving a regression problem including a regularization term for the operation data converted into the delay coordinate format; and a third step of updating the model by replacing the model with the generated update model.
Still further, according to the present invention, a process control system that controls a target process, includes: a control device that holds a model of the target process, calculates an input value for the target process such that an error of an output value of the target process with respect to a reference value predicted by using the model is minimized, and inputs the calculated input value to the target process to control the target process; and a model update device that updates the model held by the control unit, in which the model update device includes a conversion unit that converts a data format of operation data of the target process into a delay coordinate format; an update model generation unit that generates an update model reflecting secular change information of the target process by solving a regression problem including a regularization term for the operation data converted into the delay coordinate format; and a model update unit that updates the model by replacing the model with the update model generated by the update model generation unit.
According to the model update device and method and the process control system of the present invention, the model can be updated to reflect a temporal change of the target process without causing a loss of operating profit or violating the target process (plant) operating regulations due to the use of the test signal. Further, the model update device and method and the process control system of the present invention can be easily applied to existing plants in which model predictive control is introduced without requiring special equipment.
According to the present invention, it is possible to implement a model update device and method, and a process control system, which are capable of significantly reducing the labor, time, and monetary cost required for model update and are also easily applicable to a plant in which the existing model predictive control is introduced, without causing a loss of operating profit.
An embodiment of the present invention will be described in detail with reference to the drawings.
A typical example of the MIMO process 2 is a chemical process. The chemical process may be used in not only the chemical industry, but also the steel industry, the food industry, the pharmaceutical industry, the paper industry, and the like. The control device 3 controls the MIMO process 2. The process model 6 is a model that simulates the MIMO process 2 on a computer.
The predictive control processing unit 5 predicts a future value of a process output POUT based on a prediction error of the process output POUT (hereafter, this may be referred to as historical data) output from the MINO process 2 and the process model 6. Then, the predictive control processing unit 5 calculates a value of a process input PIN such that an error between the predicted value of the process output POUT and a reference value 9 given by the first input and output device 7 is minimized, and inputs the calculated process input PIN to the MIMO process 2. As a result, it is possible to hold the process output POUT at the reference value 9 or bring the process output POUT close to the reference value 9.
The process input PIN is M (M is an integer of 2 or more) set values (valve opening, and the like) given to the instrumentation equipment in the MIMO process 2. Further, the process output POUT is one or both of a physical quantity (temperature, pressure, flow rate, and the like) measured by a sensor in the MIMO process 2 and a set value of the instrumentation equipment, and has P (P is an integer of 2 or more) values.
The model update device 4 calculates a difference between a dynamical property of the MIMO process 2 and a dynamical property of the process model 6 when one or both of the process input PIN of the MIMO process 2 and the reference value 9 are given as a prediction error of the process model 6, and updates the process model 6 based on the calculated prediction error. The process input PIN or the reference value 9 given at the time of calculating the prediction error is set to the process input PIN or the reference value 9 at the time of operation of the MIMO process 2.
The model update device 4 collects or accumulates time series data of the process input PIN, the process output POUT, and the reference value 9, and further, acquires a predictive control algorithm of the predictive control processing unit 5 and the process model 6 expressed in a mathematical formula from the control device 3, which are used for updating the process model 6. At this time, the model update device 4 updates the process model 6 in accordance with a temporal change of the MIMO process 2. Examples of the factor that causes the temporal change of the MIMO process 2 include improvements in equipment, deterioration over time, changes in operation plans, changes in quantity and quality of materials, debottlenecking, and the like.
The model update device 4 acquires the dynamical properties of the MIMO process 2 as input and output time series data. At this time, the model update device 4 converts the dynamical properties of the process model 6 into an input and output time series data format, to match a data format of the dynamical properties of the MIMO process 2 with a data format of the dynamical properties of the process model 6, and then calculates a prediction error.
The time series data of the process input PIN, the process output POUT, and the reference value 9 are data at the time of operation of the MIMO process 2 (hereinafter, appropriately referred to as operation data). When the MIMO process 2 is in operation, the set value given to the MIMO process 2 and the physical quantity measured in the MIMO process 2 are controlled to be held at or brought to a steady state. Then, the prediction error reflects the dynamical properties due to, among all dynamical properties of the MIMO process 2, the temporal change of the MIMO process 2.
The CPU 10 is a processor that controls the overall operation of the model update device 4. Further, the main storage device 11 is configured with a semiconductor memory and the like, for example, and is used as a work memory of the CPU 10. A process model extraction processing program 13, a prediction error calculation processing program 14, a model update data duration selection program 15, and a model update program 16, which will be described below, are loaded from the auxiliary storage device 12 into the main storage device 11 at the time of starting the model update device 4 or when necessary, and are stored and held in the main storage device 11.
The auxiliary storage device 12 is configured with a large-capacity non-volatile storage device such as a hard disk device, a solid state disc (SSD), or the like, for example. Various programs and various kinds of control data are stored in the auxiliary storage device 12. An operation data management table 17 and a model update data management table 18, which will be described below, are also stored and held in the auxiliary storage device 12.
Further, the communication device 19 is configured with a network interface card (NIC) or the like, for example, and performs protocol control during communication with the control device 3 or the like.
The operation data management table 17 is a table used for storing and holding operation data 24 including respective time series data of the reference value 9 of the MIMO process 2 (
The process model extraction processing unit 20 is a functional unit implemented by the CPU 10 (
The prediction error calculation processing unit 21 is a functional unit implemented by the CPU 10 executing the prediction error calculation processing program 14 (
The model update data duration selection unit 22 is a functional unit implemented by the CPU 10 executing the model update data duration selection program 15 (
Here,
As illustrated in
Meanwhile, when the reference value 9 is changed due to a change in the quantity or quality of the material, the operation data 24 is also changed greatly accordingly, such that, in the durations before and after the change of the reference value (durations B, D, F, H, . . . , in
The model update data duration selection unit 22 extracts the operation data 24 in each reference value change duration in the reference value change duration, in which the reference value 9 is changed by at least a certain magnitude (for example, by a constant multiple of the steady state deviation between the reference value 9 and the steady state operation data 24) compared to the noise, from the operation data management table 17 as a model update data candidate. At this time, a time duration (time width) when extracting the operation data 24 in the reference value change duration may be prepared in advance as a default value in accordance with the properties of the plant and the material, or may be specified by the user via the second input and output device 8.
Further, for each reference value change duration from which the operation data 24 is extracted as the model update data candidate as described above, the model update data duration selection unit 22 calculates an error (prediction error) between the actual process output POUT included in the operation data 24 in the reference value change duration and the process output POUT in the reference value change duration predicted using the process model 6, respectively. Then, the model update data duration selection unit 22 selects the operation data 24 in the reference value change duration having the calculated prediction error of a certain value or more as the model update data, and stores the selected model update data in the model update data management table 18.
Further, even for the reference value constant duration, for a duration in which the trend of the steady state properties of the MIMO process 2 changes above a certain level, the model update data duration selection unit 22 also extracts the operation data 24 of this reference value constant duration from the operation data management table 17 and stores the extracted operation data 24 in the model update data management table 18 as the model update data.
The model update unit 23 updates the process model 6 extracted by the process model extraction processing unit 20 by using the model update data stored in the model update data management table 18. Specifically, the model update unit 23 expresses the operation data 24 including the dynamical properties of the MIMO model 2 as an evolutional equation using a delay coordinate system, and solves the regression problem including the regularization term for the operation data 24 converted into the evolutional equation, to partially reflect the secular change information of the MIMO model 2 in the process model 6. The specific processing content of the model update processing executed by the model update unit 23 described above will be described below.
The date and time when the corresponding operation data 24 is acquired is stored in the acquisition date and time column 17A. The reference value 9 (
Further,
Next, specific processing content of each of various processing executed in connection with the update processing of the process model 6 as described above, by the prediction error calculation processing unit 21 (
In practice, when the prediction error calculation processing illustrated in
Then the prediction error calculation processing unit 21 reads the operation data 24 (time series data of the process input PIN and the process output POUT) in the simulation duration set in step S1 from the operation data management table 17 (S2).
Further, the prediction error calculation processing unit 21 executes a time series simulation for the process input PIN and the process output POUT of the MIMO process 2 in the simulation duration (S3) by using the read operation data 24 and the process model 6 extracted from the control device 3 by the process model extraction processing unit 20. By this time series simulation, the prediction error calculation processing unit 21 can also obtain output time series data that reproduces the process output POUT of the operation data 24 in the simulation duration as a simulation result.
Then, the prediction error calculation processing unit 21 respectively obtains differences between the output time series data acquired in step S3 and the time series data of the actual process output POUT in the simulation duration read from the operation data management table 17 in step S2, to calculate time series prediction errors of the process output POUT by the process model 6, respectively. Further, the prediction error calculation processing unit 21 writes the calculated time series prediction error of the individual process output POUT by the process model 6 into a predetermined storage area in the main storage device 11 (
Further, in step S5, the prediction error calculation processing unit 21 transmits the time series prediction error data of the process output POUT by the process model 6 calculated in step S4, the output time series data obtained by the simulation in step S3, and the operation data 24 (each time series data of the process input PIN and the process output POUT) in the simulation duration read from the operation data management table 17 in step S2 to the second input and output device 8 as screen display data (S5). As a result, based on this screen display data, a prediction error monitoring screen 30 to be described below with respect to
Subsequently, the prediction error calculation processing unit 21 calculates the least squares of the time series prediction errors of the individual process output POUT calculated in step S4, respectively, and determines whether or not at least one of these calculated least squares is equal to or greater than a threshold value preset by the user for each of these least squares (hereinafter, these are referred to as prediction error threshold values) (S6). The prediction error threshold value is the maximum value of an allowable range of the prediction error of the process model 6 with respect to the process output POUT, and is set for each time series prediction error of the individual process output POUT.
Then, when obtaining an affirmative result in this determination, the prediction error calculation processing unit 21 returns to step S2, and then repeats the processing after step S2 while sequentially switching the operation data 24 read in step S2 to the operation data 24 for the simulation duration set in step S1 including the latest operation data 24.
On the other hand, when obtaining an affirmative result in the determination of step S6, the prediction error calculation processing unit 21 transmits a notification that an alert should be displayed to the second input and output device 8 (S7), and then returns to step S2 and repeats the processing after step S2 while switching the operation data 24 to the latest one.
The current date and time is displayed in the duration width display area 31. Further, waveforms are displayed in the operation data display area 32, which are representing temporal changes of the individual process input PIN, the individual process output POUT, and the reference value 9 of these process output POUT drawn based on the operation data 24 in the simulation duration at that time read from the operation data management table by the prediction error calculation processing unit 21 in step S2 of
Note that
Further, in the simulation data display area 33, waveforms of the individual process output POUT (output time series data) in the simulation duration calculated by the simulation in step S3 of
Further, in the model update alert display area 35, a warning message (alert) urging to consider model update is displayed, because the prediction error is large when the alert display instruction notification described above is given to the second input and output device 8 from the prediction error calculation processing unit 21 in step S7 of
Meanwhile,
In practice, the model update data duration selection unit 22 starts the model update data duration selection processing of
Then, the model update data duration selection unit 22 first reads the operation data for the latest fixed period stored in the operation data management table 17 (S10), and divides the time series data of the reference value 9 of the read operation data 24 into the reference value change durations (durations B, D, F, H, . . . in
Subsequently, the model update data duration selection unit 22 reads the time series data of the process output POUT of each reference value constant duration from the operation data management table 17, respectively, and extracts trend components representing the trend (trend change) of the steady state properties of the MIMO process 2 in each reference value constant duration based on the read time series data of these process output POUT, respectively (S12).
Further, the model update data duration selection unit 22 determines whether or not there are trend changes in the steady state properties of the MIMO process 2 (whether or not the trend of the steady state properties of the MIMO process 2 decreases or increases) in any of the reference value constant durations based on the trend component of the steady state properties of the MIMO process 2 in each extracted reference value constant duration (S13). Then, when obtaining a negative result in this determination, the model update data duration selection unit 22 proceeds to step S18.
Meanwhile, obtaining an affirmative result in the determination of step S13 means that the trend of the steady state properties of the MIMO process 2 changes in any of the reference value constant durations. Then, according to the degree of the trend change in the reference value constant duration in which the trend of the steady state properties of the MIMO process 2 is changing, there is a possibility that the operation data 24 in the reference value constant duration can be used as model update data. Thus, at this time, the model update data duration selection unit 22 extracts, from each reference value constant duration, a reference value constant duration in which the influence of noises on the operation data 24 is relatively small such as, for example, a reference value constant duration in which the steady state properties of the MIMO process 2 is changed by at least a certain magnitude (for example, by a constant multiple of the steady state deviation of the MIMO process 2) compared to the noises, as a duration candidate in which the operation data 24 is used for updating the process model 6 (S14).
Next, the model update data duration selection unit 22 calculates, for each reference value constant duration extracted in step S14, the prediction error of the process model 6 in the reference value constant duration as a model prediction error, respectively (S15). Specifically, the model update data duration selection unit 22 reads the time series prediction errors in the reference value constant duration thereof from the time series prediction error for the process output POUT by the process model 6 written in the predetermined area of the main storage device 11 by the prediction error calculation processing unit 21 in step S4 of
Then, the model update data duration selection unit 22 determines whether or not there is a reference value constant duration in which the value of the model prediction error calculated in step S15 is equal to or greater than a threshold value (hereafter, this is referred to as a model prediction error threshold value) set in advance for the model prediction error in the reference value constant duration extracted in step S14 (S16).
Obtaining a negative result in this determination means that there is no reference value constant duration in which the influence of noises on the operation data 24 is relatively small. Thus, at this time, the model update data duration selection unit 22 proceeds to step S18.
On the other hand, obtaining a positive result in the determination of step S16 means that there is a reference value constant duration in which the influence of noise on the operation data 24 is relatively small. Thus, at this time, the model update data duration selection unit 22 reads the operation data 24 in all the reference value constant durations, among the reference value constant durations extracted in step S14, that obtain a positive result in step S16 from the operation data management table 17, and stores the read operation data 24 in the model update data management table 18 as model update data.
Subsequently, the model update data duration selection unit 22 respectively calculates the prediction error of the process model 6 in these reference value change durations as the model prediction error, based on the operation data 24 in each reference value change duration stored in the operation data management table 17 in the same manner as in step S15 (S18).
Subsequently, the model update data duration selection unit 22 determines whether or not there is a reference value change duration, among the reference value change durations, in which the value of the model prediction error calculated in step S19 is equal to or greater than the model prediction error threshold value described above that is set in advance for the model prediction error (S19).
Obtaining a negative result in this determination means that there is no reference value change duration in which the influence of noises on the operation data 24 is relatively small. Thus, at this time, the model update data duration selection unit 22 proceeds to step S21.
On the other hand, obtaining a positive result in the determination of step S19 means that there is a reference value change duration in which the influence of noise on the operation data 24 is relatively small. Thus, at this time, the model update data duration selection unit 22 reads the operation data 24 in all the reference value change durations, among the reference value change durations, that obtain a positive result in step S19 from the operation data management table 17, and stores the read operation data 24 in the model update data management table 18 as model update data (S20).
After that, the model update data duration selection unit 22 determines whether or not a certain amount of model update data can be extracted and stored in the model update data management table 18 by the processing from steps S10 to S20 described above (S21).
Then, when obtaining a negative result in this determination, the model update data duration selection unit 22 returns to step S10, and then, in step S10, repeats the processing of steps S10 to S21 while reading the operation data for the latest fixed period including the operation data 24 newly stored in the operation data management table 17 until a positive result is obtained in step S21.
Then, when finally obtaining an affirmative result in step S22 by finishing storing at least a certain amount of model update data in the model update data management table 18, the model update data duration selection unit 22 reads the model update unit 23, and then ends the model update data duration selection processing.
When called by the model update data duration selection unit 22, the model update unit 23 starts the model update processing illustrated in
x(t+1)=A0x(t)+B0u(t) [Equation 1]
where,
In addition, in Equation (1), y(t) is a value at time t of the process output POUT forming the operation data 24, and u(t) is a value at time t of the process input PIN forming the operation data 24. Further, A0 and B0 are coefficient matrices derived from the current process model 6. Note that A0 is a (dM+dP+P) row (dM+dP+P) column, and B0 is a (dM+dP+P) row M column.
The evolutional equation form using the delay coordinate system of Equation (1) has a more redundant structure than the original process model 6 (for example, the dimension of the coefficient matrix is large). Therefore, even when the MIMO process 2 is subjected to secular change which corresponds to the change in the structure (the dimension of the state vector in the state space equation model, the order in the transfer function model, and the like) of the process model 6, it is also possible to absorb the change in the structure described above on Equation (1), which is an evolutional equation, and update the model by a simple least squares method as described below.
Hereinafter, a method of converting the process model 6 into an evolutional equation will be described. In Equation (1), the first to Pth rows of A0 and B0 have the same structure as the so-called ARX model. According to Minh Q. Phan, Ryoung K. Lim, and Richard W. Longman, in “Unifying input-output and state-space perspectives of predictive control,” Department of mechanical and aerospace engineering technical report No.3044, Prenceton University, 1998. (hereinafter, this is referred to as Non-PTL 1), when the process model 6 is a state equation of discrete time, the process model 6 can be analytically converted into an ARX model. When the process model 6 is not represented by a discrete time state space equation, such as when the process model 6 is represented by a continuous time state space equation including dead time, for example, a numerical simulation of the output y(t) when the input u(t) is used as test signals such as an M sequence or the like is performed based on the process model 6, and from the obtained simulation data, an ARX model is identified by a sparse optimization technique such as least absolute shrinkage and selection operator (LASSO) regression or the like while avoiding over fitting, and these are designated as the first to Pth rows of A0 and B0. Note that the elements from the (P+1)th row to the (dM+dP+P)th row of A0 and B0 are fixed values of 0 or 1 regardless of the original process model 6, and thus do not need to be calculated.
Subsequently, the model update unit 23 converts an expression format of each model update data stored in the model update data management table 18 into an expression format of the delay coordinate system (S31).
Next, the model update unit 23 estimates ΔA, which is a secular change of the coefficient matrix A0 in the MINO model 2 (
[Equation 2]
[ΔA, ΔB]=ΔA,ΔBargminΣt=t
Note that, in Equation (2), the part expressed by
[Equation 3]
(x(t+1)−A0x(t)−B0u(t)) (3)
represents a prediction error at each time t, the part expressed by
[Equation 4]
(ΔAx(t)+ΔBu(t)) (4)
is a correction term for a secular change component, and the part expressed by
[Equation 5]
λ∥[ΔA ΔB]∥1,2 (5)
is a term for ensuring sparsity and preventing over fitting. In Equation (5),
[Equation 6]
∥[ΔA ΔB]∥1,2 (6)
is L1 or the Frobenius norm of the matrix [ΔA ΔB].
Hereinafter, the purpose and effect of the estimation method of ΔA and ΔB will be described, and then the corresponding processing of steps S32 and S33 will be described.
The regularization term of Equation (5) is necessary to suppress the influence of the observed noise included in the process inputs PIN and POUT and to reflect the secular change of the MIMO process 6 in the process model 2 as much as possible. In general, a process input PIN contains only a limited time scale change component as compared to the test signals such as an M sequence and the like. Therefore, when ΔA and ΔB are estimated without the regularization term described above, in the time scale not covered by the fluctuation component described above, the influence of the observed noises included in the PIN and POUT is reflected in ΔA and ΔB instead of the secular change of the MIMO process 6. Further, since the observed noises included in POUT are fed back to the prediction processing unit 5 and used for determining the PIN, when ΔA and ΔB are estimated without the regularization term described above, the properties of the predictive control processing unit 5 are reflected in ΔA and ΔB. From the above, it is difficult to obtain ΔA and ΔB accurately representing the secular change of MIMO process 6 even by using the general least squares method (not including the regularization term). On the other hand, in the least squares method including the regularization term of Equation (2), by providing a penalty according to the size of the elements of ΔA and ΔB, it is possible to prevent ΔA and ΔB from over fitting with the properties of the noise and the prediction processing unit 5, and to obtain ΔA and ΔB that accurately represent the secular change of the MIMO process 6.
Prior to the estimation of ΔA and ΔB described above, the model update unit 23 first determines the regularization parameter λby cross validation. Specifically, among the delay coordinate system format data converted in step S31, by using one or both of a dataset when two or more different reference values are changed at different times, a pair of a dataset when the reference values are changed, and a dataset when the reference values are constant, a cross validation error of Equation (2) is calculated, and λ that minimizes the cross validation error is adopted (S32).
After that, the model update unit 23 estimates ΔA and ΔB according to Equation (2) using the regularization parameter λ adopted above (S33).
As described above, it is possible to reflect the secular change of the MIMO process 6 included in the operation data 24 to ΔA and ΔB as much as possible without over fitting to a specific valve or time scale in the process input PIN.
Then, the model update unit 23 generates an updated model of the process model 6 (hereinafter, this is referred to as an update model) according to the following equation by using ΔA and ΔB estimated in step S33 (S34).
[Equation 7]
x(t+1)=(A0+ΔA)x(t)+(B0+ΔB)u(t) (7)
Hereinafter, the contents of the related literature regarding the delay coordinate system and regularization, and the difference between the related literature and the model update unit 23 will be described below.
The idea of the delay coordinate system used in the model update unit 23 itself is widely used in the analysis and control of the chaos generated in the nonlinear dynamical system. According to Toshiaki Kawagoshi and Takashi Hikihara, “An Experimental Study on Stabilization of Periodic Motion in Magneto-Elastic Chaos,” Technical Report of IEICE, NLP94-80 (1994) (hereinafter, referred to as Non-PTL 2)); Higashino, Kawagoshi, Hikihara, “Stabilization of unstable periodic orbits in magnetic elastic chaos using time-delayed feedback,” Shingaku Giho, NLP95-11 (1995) (hereinafter, referred to as Non-PTL 3); and Takashi Hikihara and Toshiaki Kawagoshi, “An experimental study on stabilization of unstable periodic motion in magneto-elastic chaos,” Physics Letters A, Vol.211, pp. 29-36 (1996) (hereinafter, referred to as Non-PTL 4), in the magnetoelastic system, the chaotic oscillation of the pendulum is stabilized by feeding back the measured value of the displacement of the pendulum with a time delay (delayed feedback).
Further, Takashi Hikihara and Yoshisuke Ueda, “An expansion of system with time delayed feedback control to spatio-temporal state space,” Chaos, Vol.9, No.4, pp. 887-892 (1999) (hereinafter, this is referred to as Non-PTL 5) explains that a nonlinear dynamical system including a delay can be mapped to an infinite-dimensional topological space including a continuous state and its discrete time evolution in a time duration having a time width equal to the delay (hereinafter, referred to as a finite delay duration), and the solution behavior of a nonlinear dynamical system with a delay can be replaced by the problem of the convergence of the time evolution (wave propagation) of a function in a finite delay duration. That is, stabilization by controlling the nonlinear dynamical system with delayed feedback is equivalent to ensuring the stability of the wave propagation solution indicated by the function in the finite delay duration. This equivalence corresponds to the preservation of dynamical properties such as stability and the like before and after the transformation of the process model 6, and suggests the theoretical validity of the transformation. (The contents of the known documents described in this paragraph are based on the guidance provided by Professor Takashi Hikihara of the Graduate School of Engineering, Kyoto University.)
Furthermore, in recent years, the application of delay coordinate systems is progressing in the analysis and control of nonlinear dynamical systems based on data. For example, Yoshihiko Susuki, Kyoichi Sako, and Takashi Hikihara, “On the Spectral Equivalence of Koopman Operators through Delay Embedding,” arXiv preprint, arXiv:1706.01006, 2017 (hereinafter, this is referred to as Non-PTL 6) explains that the spectrum of the nonlinear autonomous dynamical system is conserved before and after the conversion by the delay coordinate system. This suggests the theoretical validity of the conversion of the process model 6 (however, note that the process model 6 is a linear non-self-excited system and is different from the nonlinear self-excited system targeted in Non-PTL 6, so this does not suggest the general validity). As an application of the above idea, Yoshihiko Susuki and Kyoichi Sako, “Data-Based Voltage Analysis of Power Systems via Delay Embedding and Extended Dynamic Mode Decomposition,” IFAC-PapersOnLine, Vol. 51, No. 28, pp. 221-226, 2018 (hereinafter, this is referred to as Non-PTL 7) explains that the spectrum of the state space equation model described above can be calculated by using the delay coordinate system even when only the voltage at a single point can be observed in the nonlinear state space equation model of the power system.
Meanwhile, the model update unit 23 aims to absorb changes in the structure of the process model 6 by using the delay coordinate system as described above. That is, with respect to the problem of updating the process model so as to reflect the secular change of the process, the difference between the researches described in Non-PTLs 1 to 7 described above and the model update unit 23 is that a unique delay coordinate system application technique is devised.
The idea of identifying a model in a delay coordinate system itself is also widely known, and Milan Korda and Igor Mezic, in “Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control,” Automatica, Vol.93, pp. 149-160, 2018 (hereinafter, referred to as Non-PTL 8), and by Lennart Ljung, in “System Identification,” in A. Prochazka, J. Uhlir, P. W. J. Rayner, N. G. Kingsbury (eds), Signal Analysis and Prediction: Applied and Numerical Harmonic Analysis, Birkhauser, Boston, Mass., pp. 163-173, 1998” (hereinafter, referred to as Non-PTL 9) propose an identification method similar to Equation (2). In the context of this embodiment, the idea described above corresponds to identifying A0+ΔA and B0+ΔB using the operation data 24 when the process input PIN is test signals such as an M sequence and the like. However, as described above, since the process input PIN includes only a limited time scale change component as compared to the test signals such as an M sequence and the like, it is difficult to directly identify A0+ΔA and B0+ΔB by the methods described in Non-PTLs 8 and 9, and the processing of steps S32 and S33 is required.
The regularization used in steps S32 and S33 is a technique often used in system identification problems with small amounts of data. For example, Alexandre Mauroy and Jorge Goncalves, in “Koopman-based lifting techniques for nonlinear systems identification,” IEEE Transaction on Automatic Control, 2019 (Published Online) (hereinafter, referred to as Non-PTL 10) explains that L1 regularization is effective in identifying a nonlinear dynamical system when the number of data samples is small. However, there is no particular description regarding the method for determining the regularization parameter corresponding to λ in Equation (5).
Meanwhile, the model update unit 23 automatically calculates the regularization parameter by cross validation from the delay coordinate system format data converted in step S31 as described above for Equation (2). That is, the difference between the Non-PTL 10 and the model update unit 23 is that a regularization parameter determination method unique to the problem of model update of the MIMO process under the control of MPC is devised.
Subsequently, the model update unit 23 transmits the operation data 24 (time series data of process input PIN and process output POUT) used for generating the update model and the data of the update model to the second input and output device 8 (
Further, the model update unit 23 determines whether or not the user performs an operation of approving the update of the process model 6 on the model update data and update model display screen 30 (S36). When confirming that the user performs an operation of refusing to update the process model 6 on the model update data and update model display screen 40, the model update unit 23 ends this model update processing.
On the contrary, when confirming that the user performs the operation of approving the update of the process model 6 on the model update data and update model display screen 40, the model update unit 23 converts the update model generated in step S34 into a format suitable for the process model 6 in the control device 3 (S37), and replaces the process model 6 held by the control device 3 at that time with the converted update model to update the process model 6 of the control device 3 (S38). Then, after that, the model update unit 23 ends this model update processing.
Then, in the model update data display area 41, each waveform representing a temporal change of the process input PIN and the process output POUT is respectively displayed based on the time series data of the individual process input PIN and individual process output POUT used to generate the update model described above that is transmitted from the model update unit 23.
Note that
Further, as the respective feature amounts of the model update data, the current process model 6 and the update model, two-dimensional coordinates 42A representing the analysis results of the spectral analysis for the model update data, two-dimensional coordinates 42B representing the analysis results of the spectral analysis for the current process model 6, and two-dimensional coordinates 42C representing the analysis results of the spectral analysis for the update model are displayed in the spectral display area 42.
Then, in the model update data and update model display screen 40, by clicking the YES button 43, the user can approve the process model 6 held by the control device 3 (
The user can also click the NO button 44 to refuse to update the process model 6 to the update model. In this case, a notification refusing the update is given from the second input and output device 8 to the model update unit 23 of the model update device 4, and based on this notification, the model update unit 23, which obtains a negative result in step S35 of
Further, the user can also click the update cancel button 45 to cancel the update of the process model 6 immediately after the update. In this case, a notification canceling the update is given from the second input and output device 8 to the model update unit 23 of the model update device 4, and based on this notification, the model update unit 23 executes a process of returning the process model 6 immediately after the update to the process model 6 before the update.
As described above, in the process control system 1 of the present embodiment, since the process model 6 can be updated without using the test signal, the process model 6 can be updated in a state that reflects the temporal change of the MIMO process 2 without causing a loss of operating profit or violating the operating regulations of the plant due to the use of the test signal.
In addition, in this process control system 1, since the user can update the model by himself or herself, the number of times of the support by the MPC vendor can be reduced, and the labor, time, and financial cost required for system maintenance can be significantly reduced accordingly.
Further, the method of updating the process model 6 of the present embodiment does not require a special device integrally formed with a test signal generator (tester) and MPC, and further, as described above for step S36 in
Therefore, according to the present embodiment, it is possible to implement the process control system 1 which significantly reduces the labor, time, and monetary cost required for updating the model, and is also easily applicable to a plant in which an existing model predictive control is introduced, without causing a loss of operating profit.
Further, as described above with respect to
The model update device 51 reflects the temporal change of the MIMO process 2 in the process model 6 by using the initial process dynamical property data 52 instead of extracting the process model 6. As a result, even when the maintenance service of the vendor of the control device 3 is required for the extraction of the process model 6 and the extraction of the predictive control algorithm, it is possible to decrease the number of maintenance services required for model update and reduce the cost of model update.
The system identification processing unit 53 is a functional unit implemented by the CPU 10 (
As described above, in the present embodiment, the model update device 51 generates the initial process model 6 by using the initial process dynamical property data 52 instead of extracting the process model 6 from a control device 4, and generates an update model reflecting the temporal change of the MIMO process 2 by using the generated process model 6. Therefore, as in the first embodiment, according to the model update device 51 of the present embodiment, the process model 6 held by the control device 4 can be updated to a state reflecting the temporal change of the MIMO model 2, such that it is possible to obtain the same effect as that of the first embodiment.
In the first and second embodiments described above, a case where the process model 6 and the update model have different formats is described, but the present invention is not limited to this, and the control device 3 may be constructed such that the update model in the form of an evolutional equation can be used as it is as the process model 6. By doing so, the load on the model update unit 23 can be reduced.
Further, in the first and second embodiments described above, a case where the process model extraction processing unit 20, the prediction error calculation processing unit 21, the model update data duration selection unit 22, the model update unit 23, and the system identification processing unit 53 are configured by software is described, but the present invention is not limited to this, and some or all of the above may be configured by dedicated hardware.
Further, in the first and second embodiments described above, although a case is described in which the conversion unit that converts the data format of the operation data 24 of the MIMO process 2, which is the target process, into the delay coordinate format, the update model generation unit that generates an update model reflecting the secular change information of the MIMO process 2 by solving a regression problem including a regularization term for the operation data 24 converted to the delay coordinate format, and the model update unit that updates the process model 6 of the control device 3 by replacing the model with the update model generated by the update model generation unit are constructed by one model update unit 23, the present invention is not limited to this, and the update unit, the update model generation unit, and the model update unit may be provided separately.
The present inventors received valuable advice from Professor Takashi Hikihara of the Graduate School of Engineering, Kyoto University, and Associate Professor Yoshihiko Susuki, Professor of the Graduate School of Engineering, Osaka Prefectural University about the contents of the prior literature on the delay coordinate system and regularization from [0092] to [0096]. The present inventors would like to express our gratitude here.
The present invention can be widely applied to various model update devices that update a model of a target process in a model predictive control.
1, 50: process control system
2: MIMO process
3: control device
4, 51: model update device
5: predictive control processing unit
6: process model
7, 8: input and output device
9: reference value
10: CPU
17: operation data management table
18: model update data management table
20: process model extraction processing unit
21: prediction error calculation processing unit
22: model update data duration selection unit
23: model update unit
30: prediction error monitoring screen
40: model update data and update model display screen
52: initial process dynamical property data
53: system identification processing unit
PIN: process input
POUT: process output
| Number | Date | Country | Kind |
|---|---|---|---|
| 2020-014324 | Jan 2020 | JP | national |
| Filing Document | Filing Date | Country | Kind |
|---|---|---|---|
| PCT/JP2021/001242 | 1/15/2021 | WO |
