JP2023053573A - Plant response estimation device, plant response estimation method and program - Google Patents

Abstract

To estimate a response model from operational data of a plant under operation.SOLUTION: A plant response estimation device according to one embodiment comprises: a model parameter estimating unit that calculates an estimated value of a model parameter of a plant response function which is a function for representing a plant response model of a plant to be controlled and having the model parameter including an offset term for representing a steady state of the plant to be controlled based on operational data of a plant to be controlled; and a step response calculating unit that calculates a step response of the plant to be controlled using the plant response function based on the estimated value of the model parameter.SELECTED DRAWING: Figure 1

Description

The present invention relates to a plant response estimation device, a plant response estimation method, and a program.

Control devices such as temperature control devices, PLCs (Programmable Logic Controllers), DCSs (Distributed Control Systems), and control devices mounted on personal computers and built-in control devices are widely used in industry.

In addition, PID (Proportional-Integral-Differential) control, model predictive control, internal model control, LQG (Linear-Quadratic-Gaussian) control, Various control methods such as H2 control and H∞ control are known.

Model predictive control is a method of obtaining a desired response by sequentially performing optimization calculations using a state space model of the controlled object and a future time response model. Document 1, Non-Patent Document 1). As a method for estimating the parameters of a linear prediction model used in such model predictive control, a recursive least squares method (RLS method: Recursive Least Squares method), a Kalman filter method, and the like are known (for example, non-patent literature 2, Non-Patent Document 3).

Here, when controlling a plant by model predictive control or the like, it is common to perform a model identification test in advance in order to estimate the parameters of the response model of the plant. In such a model identification test, a signal of a certain shape such as a step signal, a ramp signal, an M-sequence signal, etc. is applied to the plant response model as a manipulated variable, and parameter estimation (identification) is performed from the response and the target value at that time. done.

Japanese Patent Application Laid-Open No. 2020-21411

Yang M. Matiejovsky, "Model Predictive Control: Optimal Control Under Constraints", Tokyo Denki University Press, 2005 Shuichi Adachi, "System Identification for Control by MATLAB", Tokyo Denki University Press, 1996 Shuichi Adachi, "Advanced System Identification for Control by MATLAB", Tokyo Denki University Press, 2004

The model identification test requires a great deal of time and effort, and there is a problem that the operational cost and burden are large. Therefore, it is desirable to be able to estimate the parameters of the plant response model using operational data during normal plant operation. However, in general, since plants in operation are often operated within a narrow controlled range, the possible values of the operating data are also often within a narrow range. In addition, since the plant in operation is often in a steady state where the controlled variable and the manipulated variable are constant, the so-called PE (Persistently Exciting) property is not satisfied and is often inappropriate as a signal for model identification.

One embodiment of the present invention has been made in view of the above points, and aims at estimating a response model from operational data of a plant in operation.

In order to achieve the above object, a plant response estimation device according to one embodiment provides a function representing a plant response model of the controlled plant based on operation data of the controlled plant, and a model parameter estimator that calculates estimated values of the model parameters of a plant response function that is a function having model parameters that include an offset term that represents a steady state; and a step response calculator for calculating a step response of the plant to be controlled.

A response model can be deduced from operational data of the plant in operation.

It is a figure which shows an example of the hardware constitutions of the plant response estimation apparatus which concerns on this embodiment. It is a figure showing an example of functional composition of a plant response estimating device concerning this embodiment. FIG. 4 is a diagram for explaining an example of the operation of a buffer unit; FIG. 9 is a flowchart for explaining an example of enlarged model parameter estimation processing; FIG. 4 is a diagram for explaining an example of the operation of a parameter conversion unit; FIG. It is a figure for demonstrating an example of operation|movement of a step response calculation part. 4 is a flowchart for explaining an example of step response calculation processing; FIG. 4 is a diagram for explaining an example of state vector update; FIG. 3 is a diagram for explaining an example of data targeted in an embodiment; FIG. FIG. 10 is a diagram for explaining an example of results of estimating model parameters and step responses by a normal RLS method; FIG. 4 is a diagram for explaining an example of results of estimating model parameters, offset terms, and step responses by the plant response estimation device according to the present embodiment;

An embodiment of the present invention will be described below. In this embodiment, a plant response estimation device 10 capable of estimating a response model from operation data of a plant in operation will be described. Note that "in operation" refers to a state in which the plant is operating normally and performing normal operation, and may be called, for example, online, in operation, or in operation. A plant is an industrial facility composed of one or more machines, devices, devices, etc., and is a controlled object controlled by model predictive control using a plant response model. Specific examples of plants include, for example, petrochemical plants, food plants, steel plants, power generation plants, etc., but these are just examples and are not limited to these.

<Hardware Configuration of Plant Response Estimating Device 10>
FIG. 1 shows a hardware configuration example of a plant response estimation device 10 according to this embodiment. As shown in FIG. 1, the plant response estimation device 10 according to this embodiment includes an input device 11, a display device 12, an external I/F 13, a communication I/F 14, a processor 15, and a memory device 16. have. Each of these pieces of hardware is communicably connected via a bus 17 .

The input device 11 is, for example, a keyboard, mouse, touch panel, various physical buttons, and the like. The display device 12 is, for example, a display, a display panel, or the like. Note that the plant response estimation device 10 may not have at least one of the input device 11 and the display device 12, for example.

The external I/F 13 is an interface with an external device such as the recording medium 13a. Examples of the recording medium 13a include a CD (Compact Disc), a DVD (Digital Versatile Disk), an SD memory card (Secure Digital memory card), a USB (Universal Serial Bus) memory card, and the like.

Communication I/F 14 is an interface for connecting plant response estimation device 10 to a communication network. The processor 15 is, for example, various arithmetic units such as a CPU (Central Processing Unit). The memory device 16 is, for example, various storage devices such as SSD (Solid State Drive), RAM (Random Access Memory), ROM (Read Only Memory), and flash memory.

Note that the hardware configuration shown in FIG. 1 is an example, and the plant response estimation device 10 may have another hardware configuration. For example, the plant response estimation device 10 may have multiple processors 15 and multiple memory devices 16, or may have various hardware other than the illustrated hardware.

<Functional Configuration of Plant Response Estimation Device 10>
FIG. 2 shows a functional configuration example of the plant response estimation device 10 according to this embodiment. As shown in FIG. 2 , the plant response estimation device 10 according to this embodiment has a model parameter estimation section 101 and a step response calculation section 102 . These units are implemented by, for example, processing that one or more programs installed in the plant response estimation device 10 cause the processor 15 or the like to execute.

The model parameter estimating unit 101 receives observation values of operation data (control amount y, operation amount u, and disturbance v) from the plant to be controlled (or a device such as a sensor that measures the operating state of the plant) at each sampling period Δ. Then, the model parameters of the plant response model are estimated according to the sampling period Δ. Operation data may be called measurement data, observation data, or the like, for example.

Here, if time is t, the controlled variable y, the manipulated variable u, and the disturbance v are represented by y(t), u(t), and v(t), respectively, and each sampling time t _k (k is the sampling time t _k+1 −t _k =Δ with respect to Note that k is an integer of 0 or more. In the following, unless otherwise specified, each sampling time t _k is identified with its index k and also denoted as y(k), u(k) and v(k).

Also, hereinafter, the plant response model is represented by a plant response function S _θ (t) having a parameter θ, and the parameter θ is called a model parameter. As the plant response model, it is possible to employ various models represented by the plant response function _Sθ , but below, a polynomial model such as the ARMAX model is mainly assumed. If the plant response model is an ARMAX model, the model parameter θ is the coefficient of the ARMAX model. Needless to say, various models other than the ARMAX model can be adopted as the plant response model.

Furthermore, hereinafter, a model obtained by adding an offset term (constant term) representing the steady state of the plant to be controlled to the plant response model represented by the ARMAX model will be referred to as an extended plant response model.

The step response calculator 102 uses the model parameter (hereinafter also referred to as model parameter estimated value) θ estimated by the model parameter estimator 101 to estimate the step response of the plant at given time t (hereinafter referred to as Also called step response estimate.) Compute S _θ (t). Note that the step response is a controlled variable when a step signal is applied to the plant as a manipulated variable.

Here, the model parameter estimation unit 101 includes a buffer unit 111 , a state vector conversion unit 112 , a sequential estimation calculation unit 113 and a parameter conversion unit 114 .

The buffer unit 111 accumulates (buffers) the controlled variable y(k), the manipulated variable u(k), and the disturbance v(k) in a certain predetermined period in the memory device 16 . The state vector conversion unit 112 resamples the control amount y(k), the manipulated variable u(k) and the disturbance v(k) buffered in the memory device 16 to create a vector called an expanded state vector. . The sequential estimation calculation unit 113 uses the expanded state vector to estimate the expanded model parameters, which are the model parameters of the expanded plant response model, by the RLS method. A parameter conversion unit 114 converts the estimated values of the enlarged model parameters into model parameter estimated values θ.

<Operation of Buffer Unit 111>
Let Y(k) be the control amount buffer, U(k) be the manipulated variable buffer, and V(k) be the disturbance buffer at the sampling time _tk , and each of these buffers is represented by the following vectors.

すなわち、制御量バッファＹ（ｋ）にはｋ－Ｂ_１からｋまでの制御量ｙ、操作量バッファＵ（ｋ）にはｋ－Ｂ_２からｋまでの操作量ｕ、外乱バッファＶ（ｋ）にはｋ－Ｂ_３からｋまでの外乱ｖがそれぞれ格納されているものとする。ここで、Ｂ_１、Ｂ_２及びＢ_３はそれぞれ０以上の整数であり、制御量バッファ、操作量バッファ及び外乱バッファの大きさを決めるパラメータである。これらのＢ_１、Ｂ_２及びＢ_３はメモリ装置１６のサイズ等に応じて、適宜、その値が決定される。

That is, the control amount buffer Y(k) stores the control amount y from kB ₁ to k, the operation amount buffer U(k) stores the operation amount u from kB ₂ to k, and the disturbance buffer V(k) kB stores disturbances v from ₃ to k. Here, B ₁ , B ₂ and B ₃ are each integers equal to or greater than 0, and are parameters that determine the sizes of the control amount buffer, manipulated amount buffer and disturbance buffer. The values of these B ₁ , B ₂ and B ₃ are appropriately determined according to the size of the memory device 16 and the like.

At this time, when the buffer unit 111 receives the controlled variable y(k), the manipulated variable u(k), and the disturbance v(k), as shown in FIG. k−1) to control amount buffer Y(k), manipulated variable u(k) and manipulated variable buffer U(k−1) to manipulated variable buffer U(k), disturbance v(k) and disturbance buffer V(k− 1) to the disturbance buffer V(k) respectively.

Specifically, the buffer unit 111 deletes y(k−B ₁ −1) stored in the control amount buffer Y(k−1), and then deletes the newly observed control amount y(k). is stored, the control amount buffer Y(k) storing the control amounts from y(k−B ₁ ) to y(k) is updated. Similarly, the buffer unit 111 deletes the manipulated variable u(k−B ₂ −1) stored in the manipulated variable buffer U(k−1), and then deletes the newly observed manipulated variable u(k). to update the manipulated variable buffer U(k) in which manipulated variables from u(k−B ₂ ) to u(k) are stored. Similarly, the buffer unit 111 deletes the disturbance v(k−B ₃ −1) stored in the disturbance buffer V(k−1), and then stores the newly observed disturbance v(k). Thus, the disturbance buffer V(k) storing disturbances from v(k−B ₃ ) to v(k) is updated.

<Operation of State Vector Conversion Unit 112>
Let D be the resampling period. At this time, when the control amount buffer Y(k), the manipulated variable buffer U(k), and the disturbance buffer V(k) are updated, the state vector conversion unit 112 updates these buffers Y(k), U(k). ) and V(k) at a resampling period D to obtain the following resampling control amount vector Y _D (k), resampling operation amount vector U _D (k), and resampling disturbance vector V _D (k ) respectively.

ここで、Ｎ、Ｍ及びＬはプラント応答モデルに応じて決定されるパラメータ（具体的には、ＮはＡＲＭＡＸモデルの制御量ｙに関する項の係数の数、Ｍは操作量ｕに関する項の係数の数、Ｌは外乱ｖに関する項の係数の数）である。また、再サンプリング制御量ベクトルＹ_Ｄ（ｋ）ではＡＲＭＡＸモデルにならい、現在のサンプリング時刻を表す要素ｙ（ｋ）がスキップされる（つまり、ｙ（ｋ）は再サンプリングされない。）。

Here, N, M and L are parameters determined according to the plant response model (specifically, N is the number of coefficients of the term related to the controlled variable y in the ARMAX model, M is the number of coefficients of the term related to the manipulated variable u number, L is the number of coefficients of the term for the disturbance v). Also, in the resampling control amount vector Y _D (k), following the ARMAX model, the element y(k) representing the current sampling time is skipped (that is, y(k) is not resampled).

In general, the larger the values of N, M, and L, the more diverse expressions are possible, and highly accurate prediction of plant response can be expected. necessary.

Then, the state vector conversion unit 112 converts the resampling control amount vector Y _D (k), the resampling operation amount vector U _D (k), and the resampling disturbance vector V _D (k) into the expanded state vector ξ(k) as follows: to create

すなわち、拡大状態ベクトルξ（ｋ）とは、Ｙ_Ｄ（ｋ）、Ｕ_Ｄ（ｋ）及びＶ_Ｄ（ｋ）の要素に対して、オフセット項を表す要素として「１」を追加し、拡大した状態ベクトルである。ここで、オフセット項とは、上述したように、ＡＲＭＡＸモデルで定常状態を表す項として出現する定数項のことである。これにより、再サンプリング制御量ベクトルＹ_Ｄ（ｋ）、再サンプリング操作量ベクトルＵ_Ｄ（ｋ）及び再サンプリング外乱ベクトルＶ_Ｄ（ｋ）が拡大状態ベクトルξ（ｋ）に変換されたことになる。

That is, the expanded state vector ξ(k) is obtained by adding “1” as an element representing an offset term to the elements of Y _D (k), U _D (k) and V _D (k) and expanding is a state vector. Here, the offset term is a constant term that appears as a term representing the steady state in the ARMAX model, as described above. As a result, the resampling control vector Y _D (k), the resampling manipulation vector U _D (k), and the resampling disturbance vector V _D (k) are converted into the expanded state vector ξ(k).

<Operation of Sequential Estimation Calculation Unit 113>
Below, the enlarged model parameter is represented as θ _e . When the expanded state vector ξ(k) is created, the sequential estimation calculation unit 113 uses this expanded state vector ξ(k) to estimate the value of the expanded model parameter θ _e . That is, the sequential estimation calculation unit 113 sequentially estimates the value of the enlarged model parameter _θe at each sampling time _tk .

The process of estimating the value of the augmented model parameter θ _e for some k will now be described with reference to FIG. In addition, below, the estimated value of the enlarged model parameter θ _e at the sampling time t _k is expressed as θ _e (k).

Step S101: First, the iterative estimation calculation unit 113 determines whether or not to initialize the expanded model parameter θ _e and the covariance matrix P. Here, cases where it is determined to be initialized include, for example, when the initial calculation is performed (that is, when k=0), and when an initialization instruction is given by the user or the like.

When determining to initialize the expanded model parameter θ _e and the covariance matrix P (YES in step S101), the sequential estimation calculation unit 113 proceeds to step S102. On the other hand, if it is determined not to initialize the expanded model parameter θ _e and the covariance matrix P (NO in step S101), the sequential estimation calculation unit 113 proceeds to step S103.

Step S102: The sequential estimation calculation unit 113 initializes the index k of the sampling time t _k to k=0, and also initializes θ _e (0)=θ ₀ and P(0)=I. Here, θ ₀ is a preset initial value of an enlarged model parameter, and I is an arbitrary preset matrix (for example, a unit matrix, etc.).

Step S103: The iterative estimation calculation unit 113 calculates the prediction error ε(k) using the expanded model parameter estimated value θ _e (k−1), the expanded state vector ξ(k), and the control amount y(k). do. The prediction error ε(k) is calculated by, for example, ε(k)=y(k)−ξ(k) ^Τ θ _e (k−1). Note that T represents transposition.

Step S104: The iterative estimation calculation unit 113 updates the covariance matrix P(k-1) as follows to obtain the covariance matrix P(k).

ここで、λは０＜λ≦１を取る忘却係数であり、予め設定された値である。忘却係数λは過去データを忘却するための係数であり、０に近いほど急激に過去データの影響が減少し、１に近いほど過去データの影響が保持される。

Here, λ is a forgetting factor that takes 0<λ≦1 and is a preset value. The forgetting coefficient λ is a coefficient for forgetting past data.

Step S105: Then, the iterative estimation calculation unit 113 updates the extended model parameter estimated value θ _e (k−1) as follows to obtain the extended model parameter estimated value θ _e (k).

これにより、サンプリング時刻ｔ_ｋにおける拡大モデルパラメータ推定値θ_ｅ（ｋ）が得られる。

As a result, the augmented model parameter estimate θ _e (k) at sampling time t _k is obtained.

<Operation of Parameter Conversion Unit 114>
The augmented model parameter estimates θ _e (k) are represented below.

ここで、θ_Ｙ（ｋ）はサンプリング時刻ｔ_ｋにおけるＡＲＭＡＸモデルの制御量ｙに関する項の係数を要素とするＮ次元ベクトル、θ_Ｕ（ｋ）は操作量ｕに関する項の係数を要素とするＭ次元ベクトル、θ_Ｖ（ｋ）は外乱ｖに関する項の係数を要素とするＬ次元ベクトル、θ_Ｃ（ｋ）はオフセット項を表すスカラー値である。

Here, θ _Y (k) is an N-dimensional vector whose elements are the coefficients of the terms related to the control amount y of the ARMAX model at the sampling time t _k , and θ _U (k) is an M A dimensional vector, θ _V (k), is an L-dimensional vector whose elements are the coefficients of terms related to disturbance v, and θ _C (k) is a scalar value representing an offset term.

At this time, when the enlarged model parameter estimated value θ _e (k) is obtained, the parameter conversion unit 114 converts it into a vector excluding θ _C (k) as shown in FIG. Obtain θ(k). This gives the following model parameter estimates

が得られる。

is obtained.

Thus, when estimating the step response of the plant to be controlled, the model parameter estimate θ(k) is obtained by removing θ _C (k) from the expanded model parameter estimate θ _e (k). The reason for this will be explained below.

Let the expanded plant response model be y(k) _{=θY(k)TYD(k)+θU(k)TUD ( k} ⁾ ₊ ^θV ₍ k) ^TVD ( _k )+ _θC (k) .

Moreover, θ _Y (k), θ _U (k), θ _V (k) and θ _C (k) are respectively

とする。以下、表記の簡単のため、θ_Ｙ＝θ_Ｙ（ｋ）、θ_Ｕ＝θ_Ｕ（ｋ）、θ_Ｖ＝θ_Ｖ（ｋ）、θ_Ｃ＝θ_Ｃ（ｋ）とする。なお、ｄ_０がオフセット項である。

and Hereinafter, for simplicity of notation, _θY = _θY (k), _θU = _θU (k), _θV = _θV (k), and _θC = _θC (k). Note that _d0 is the offset term.

At this time, Z-transforming the extended plant response model y ₍ k ⁾ = _θYTYD ( ^k )+ _θUTUD (k)+ _θVTVD ( ^k )+ _θC is equivalent to the following _{equation :} .

y=(a ₁ z ⁻¹ y+a ₂ z ⁻² y+ …+a _N z ^−N y)+(b ₀ u+b ₁ z ⁻¹ u+b ₂ z ⁻² u+ …+b _M z ^−M u)+ (c ₀ v+c ₁ z ⁻¹ v+c ₂ z ⁻² v+ . . . +c _L z ^−L v)+d ₀
(1-a ₁ z ^-1 -a ₂ z ^-2 -...-a _N z ^-N )y=(b ₀ u+b ₁ z ^-1 u+b ₂ z ^-2 u+...+b _M z ^−M u ₎ +(c ₀ v+c _{1 z} ⁻¹ _v +c ^{2 z} _{−2 v} ⁺ . z) and _Fd (z) are respectively defined below, the above equation can be expressed as y= _Fu (z)u+ _Fv (z)v+ _Fd (z) _d0 .

F _u (z)=(b ₀ u+b ₁ z ^-1 u+b ₂ z ^-2 u+...+b _M z ^-M u)/(1-a ₁ z ^-1 -a ₂ z ^-2 -...- aNz ^- _N )
F _v (z)=(c ₀ v+c ₁ z ^-1 v+c ₂ z ^-2 v+...+c _L z ^-L v)/(1-a ₁ z ^-1 -a ₂ z ^{-2 -...-} aNz ^- _N )
_Fd (z)=1/(1-a1z ^-1 _{- a2z} - ² -...-aNz ^- _N )
Here, let Δy be the amount of change in the controlled variable y when only the manipulated variable u is changed by Δu. At this time, if only the manipulated variable u changes by Δu, y= _Fu (z)u+ _Fv (z)v+ _Fd (z)d ₀ is
y+Δy= _Fu (z)(u+Δu)+ _Fv (z)v+ _Fd (z) _d0
becomes. Therefore, Δy is expressed as Δy=F _u (z)Δu. That is, it can be seen that the offset term does not affect the amount of change Δy of the control amount y.

Therefore, using _{the plant response model y(k)=θY(k)TYD(k)+θU(k)TUD(k)+θV(k)TVD ( k )} ^without _the ^offset _term ^, It can be seen that the step response of the controlled plant can be estimated.

<Operation of Step Response Calculator 102>
Hereinafter, the model parameter estimated value (that is, the model parameter estimated value set in the plant response function S _θ ) θ=θ(k) used for estimating the step response is also referred to as "model parameter set value θ". Also, in the following, for simplicity, a unit step signal is assumed as the step signal.

As shown in FIG. 6, the step response calculation unit 102 calculates a unit step response S _θ (t) at time t after time t has elapsed from initial time 0 when model parameter setting value θ and time t are given. do. The unit step response is the response (that is, the output of the plant response model of the plant to be controlled) when a unit step signal is applied as the manipulated variable u.

A process of calculating the step response S _θ (t) given a certain time t and a certain model parameter set value θ will be described with reference to FIG. Note that the state vector φ(k') at the index k' is represented below.

なお、インデックスｋ'は、サンプリング時刻ｔ_ｋのインデックスｋと同じ値を取り得る変数であるが、本処理の中でのみ利用され、インデックスｋとは独立に値が更新されることに留意されたい。

Note that the index k' is a variable that can take the same value as the index k at the sampling time _tk , but it is used only in this process and the value is updated independently of the index k. .

Step S201: The step response calculation unit 102 initializes τ=0 and k′=0, where τ is an index representing the time used only in this process, and the state vector φ(0) is set as follows. initialized to

すなわち、ｕ（０）のみ１、それ以外の要素は０と状態ベクトルφ（０）を初期化する。

That is, only u(0) is set to 1, the other elements are set to 0, and the state vector φ(0) is initialized.

Step S202: The step response calculator 102 calculates the control amount predicted value y(k') by y(k')=φ(k') ^Τθ .

Step S203: The step response calculator 102 updates the state vector φ(k') to the state vector φ(k'+1) at the next index k'+1 using the control amount prediction value y(k'). . At this time, as shown in FIG. 8, the step response calculation unit 102 assigns the control amount prediction value y(k') calculated in step S202 to y(k') of the state vector φ(k'+1). y(k'-N+1) to y(k'-1) are set to the same values as the state vector φ(k'). Also, u(k'+1) of the state vector φ(k'+1) is set to 1, and u(k'-M+1) to u(k') are set to the same values as the state vector φ(k'). set. Furthermore, v(k'+1) of the state vector φ(k'+1) is set to 0, and v(k'-L+1) to v(k') are set to the same values as the state vector φ(k'). set.

Step S204: The step response calculator 102 updates the time τ to τ+Δ and updates the index k′ to k′+1.

Step S205: The step response calculator 102 determines whether or not τ≧t. Then, if it is not determined that τ≧t (NO in step S205), the step response calculator 102 returns to step S202. As a result, steps S202 to S204 are repeatedly executed until τ≧t.

On the other hand, if it is determined that τ≧t (YES in step S205), the step response calculator 102 terminates the process. As a result, the finally calculated controlled variable prediction value y(k′) is obtained as the unit step response S _θ (t) (that is, S _θ (t)=y(k) is the unit of the plant response model obtained as a step response).

<Example>
An example will be described below. In this example, model parameters and step responses were estimated by the plant response estimation device 10 according to the embodiment described above.

In this embodiment, the extended plant response model of the plant to be controlled is represented by the following equation.

y(k)=θ ₁ y(k−1)+θ ₂ y(k−2)+θ ₃ u(k)+θ ₄ u(k−1)+θ ₅ u(k−2)+θ ₆
That is, it is assumed that the control amount y has two-dimensional elements, and the manipulated variable u has three-dimensional elements.

At this time, the expanded state vector ξ(k) and the expanded model parameters θ _e (k) are expressed as follows.

このとき、本実施例では、再サンプリング周期Ｄ＝４、忘却係数λ＝０．９８として、図９に示す２種類のデータをそれぞれ用いて、モデルパラメータとステップ応答を推定した。

At this time, in this embodiment, the resampling period D=4 and the forgetting factor λ=0.98, and the two types of data shown in FIG. 9 were used to estimate the model parameters and the step response.

Data 1 shown in FIG. 9 is artificial data. In data 1, the manipulated variable u and the controlled variable y are constant values until time 400. At time 400, the manipulated variable u changes stepwise, and the controlled variable y also changes accordingly.

On the other hand, 2 shown in FIG. 9 is operation data obtained by measuring the plant to be controlled. In data 2, the manipulated variable u is constant until around time 620, but the controlled variable y gradually increases. After that, the manipulated variable u increases stepwise, and the controlled variable y also increases accordingly. Further, after that, the manipulated variable u decreases stepwise, and the controlled variable y also decreases accordingly.

A feature of these data is that, in Data 1, the stepwise change in the manipulated variable u and the change in the controlled variable y are synchronized, but in Data 2, the controlled variable y changes gradually even when the manipulated variable u does not change. A point that is changing (that is, there is a drift) can be mentioned.

For comparison with the plant response estimation device 10 according to this embodiment, model parameters and step responses were also estimated by the normal RLS method. The results are shown in FIG. FIG. 10(a) shows the result of estimating model parameters θ ₁ =a ₁ , θ ₂ =a ₂ , θ ₃ =b ₀ , θ ₄ =b ₁ , θ ₅ =b ₂ using data 1. b) _is the result of estimating the step response using the data 1; On the other hand, FIG. 10C shows the result of estimating model parameters θ ₁ =a ₁ , θ ₂ =a ₂ , θ ₃ =b ₀ , θ ₄ =b ₁ , θ ₅ =b ₂ using data 2. FIG. 10(d) is the result of estimating the step response using data 2, _yes .

FIG. 11 shows the result of estimating the model parameters, the offset term, and the step response by the plant response estimation device 10 according to this embodiment. FIG. 11A shows the result of estimating the model parameters θ ₁ =a ₁ , θ ₂ =a ₂ , θ ₃ =b ₀ , θ ₄ =b ₁ , θ ₅ =b ₂ using data 1. b) is the result of estimating the offset term θ ₆ =d ₀ using data 1, and FIG. 11C _is the result yes of estimating the step response using data 1. On the other hand, FIG. 11D shows the result of estimating model parameters θ ₁ =a ₁ , θ ₂ =a ₂ , θ ₃ =b ₀ , θ ₄ =b ₁ , θ ₅ =b ₂ using data 2. 11(e) shows the result of estimating the offset term θ ₆ =d ₀ using data 2, and FIG. 11(f) shows the result of estimating the step response using data 2, _yes .

As shown in FIGS. 11(b) and 11(e), the offset term θ ₆ =d ₀ changes greatly at times when the manipulated variable u changes stepwise, and gradually converges to a constant value. .

In data 1, the controlled variable y changes from 20 to 30 when the manipulated variable u changes from 20 to 30. Therefore, the steady-state gain is one.

Comparing FIG. 10(b) and FIG. 11(c), they are almost the same. Therefore, regarding data 1, it can be seen that the plant response estimation apparatus 10 according to the present embodiment obtained a plant response model with an accuracy equivalent to that of the normal RLS method.

On the other hand, in data 2, when the manipulated variable u changed from 10 to 20 around time 620, the controlled variable y changed from about 62 to about 82, and around time 1250, the manipulated variable u changed from 20 to 10. When changed, the controlled variable y changes from about 82 to about 64. Therefore, the steady-state gain is about 1.8 to 2 or so. At this time, it takes about 700 to 800 hours for convergence of the controlled variable y.

Comparing FIG. 10(d) and FIG. 11(f), they are quite different, and in the normal RLS method, the steady-state gain is 5 or more, and the required time to convergence is 2000 or more. On the other hand, in the plant response estimation device 10 according to this embodiment, the steady-state gain is about 2 and the required time until convergence is about 750. Therefore, with respect to data 2, the plant response estimation apparatus 10 according to the present embodiment obtained a plant response model closer to the actual response than the normal RLS method.

<Summary>
As described above, the plant response estimator 10 according to the present embodiment provides steady-state values (that is, controlled variables and manipulated variables that take constant values when the plant to be controlled is in a steady state) or values close thereto (that is, narrow range It is possible to obtain an effective plant response model even for operation data containing many controlled variables and manipulated variables that take values within the range. In addition, the plant response estimation device 10 according to the present embodiment can obtain a highly accurate plant response model compared to the existing RLS method for operation data with drift that is often seen during normal plant operation. . In the plant response estimation device 10 according to the present embodiment, in addition to the relationship between the manipulated variable and the controlled variable, the offset term representing the steady state is also estimated at the same time. This is because the model parameters can be estimated with high accuracy even with the operating data that is taken.

Furthermore, in the plant response estimation apparatus 10 according to the present embodiment, since the operation data is buffered and re-sampled, for example, when the time constant is longer than the sampling period (observation period) or when the order of the model parameter is relatively Even if the number is small, estimation of model parameters with higher accuracy than the conventional technique can be expected.

In this embodiment, the case of estimating the parameters of the plant response model has been mainly described, but the present invention is not limited to this. The model may function as a controller that actually controls the plant to be controlled. At this time, the plant response estimation apparatus 10 according to the present embodiment may control the plant to be controlled using a known control method such as model predictive control, using a plant response model in which the parameters are set.

The present invention is not limited to the specifically disclosed embodiments described above, and various variations, modifications, combinations with known techniques, etc. are possible without departing from the scope of the claims. be.

10 plant response estimation device 11 input device 12 display device 13 external I/F
13a recording medium 14 communication I/F
15 Processor 16 Memory Device 17 Bus 101 Model Parameter Estimator 102 Step Response Calculator 111 Buffer 112 State Vector Transformer 113 Sequential Estimation Calculator 114 Parameter Transformer

Claims (12)

A plant response that is a function representing a plant response model of the plant to be controlled based on operating data of the plant to be controlled and having model parameters that include an offset term representing a steady state of the plant to be controlled. a model parameter estimator that calculates estimates of the model parameters of a function;
a step response calculation unit that calculates a step response of the plant to be controlled using the plant response function based on the estimated values of the model parameters;
A plant response estimator having The model parameter estimator,
2. The plant response estimation device according to claim 1, wherein an estimated value of said model parameter is sequentially calculated for each sampling period based on said operating data for each sampling period. The model parameter estimation unit includes:
a buffer unit that buffers the operating data for a predetermined period in a memory;
a state vector conversion unit that converts the operating data buffered in the memory into an expanded state vector that is a state vector including an element corresponding to the offset term;
3. The plant response estimator according to claim 1, further comprising a sequential estimation calculation unit that calculates the estimated values of the model parameters based on the expanded state vector. The operating data includes a controlled variable of the controlled plant and a manipulated variable of the controlled plant,
The buffer section
4. The plant response estimating apparatus according to claim 3, wherein said controlled variable in a predetermined first period is buffered in said memory, and said manipulated variable in a predetermined second period is buffered in said memory. The operating data further includes disturbances to the plant to be controlled,
The buffer section
5. The plant response estimator of claim 4, further buffering said disturbance in said memory for a predetermined third time period. The sequential estimation calculation unit
6. The plant response estimation device according to any one of claims 3 to 5, wherein the estimated values of the model parameters are successively calculated by a successive least squares method based on the expanded state vector and the covariance matrix. The state vector conversion unit
re-sampling the operating data buffered in the memory at a predetermined re-sampling cycle;
The plant response estimation device according to any one of claims 3 to 6, wherein said operation data after resampling is converted into said expanded state vector. 8. The plant response estimation device according to claim 7, wherein said re-sampling period is a multiple of the sampling period of said operation data. 9. The plant response estimation device according to any one of claims 1 to 8, wherein said plant response function is an ARMAX model including said offset term, and said model parameters are coefficients of said ARMAX model. The step response calculator,
The plant response estimation device according to any one of claims 1 to 9, wherein the step response is calculated by the plant response function based on parameters obtained by excluding the estimated value of the offset term from the estimated value of the model parameter. . A plant response that is a function representing a plant response model of the plant to be controlled based on operating data of the plant to be controlled and having model parameters that include an offset term representing a steady state of the plant to be controlled. a model parameter estimation procedure for calculating estimates of said model parameters of a function;
a step response calculation procedure for calculating a step response of the plant to be controlled by the plant response function based on the estimated values of the model parameters;
A computer-implemented plant response estimation method. A plant response that is a function representing a plant response model of the plant to be controlled based on operating data of the plant to be controlled and having model parameters that include an offset term representing a steady state of the plant to be controlled. a model parameter estimation procedure for calculating estimates of said model parameters of a function;
a step response calculation procedure for calculating a step response of the plant to be controlled by the plant response function based on the estimated values of the model parameters;
A program that makes a computer run

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