JP7047966B1 - Plant response estimator, plant response estimation method, and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To estimate a response model from operation data of a plant in operation. A plant response estimation device according to an embodiment is a function representing a plant response model of the controlled plant based on operation data of the controlled plant, and has a steady state of the controlled plant. The control target by the plant response function based on the model parameter estimation unit that calculates the estimated value of the model parameter of the plant response function, which is a function having the model parameter including the offset term to be represented, and the estimated value of the model parameter. It has a step response calculation unit for calculating the step response of the plant. [Selection diagram] Fig. 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) and DCSs (Distributed Control Systems), and control devices mounted on personal computers and embedded control devices are widely used in industry.

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

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

Here, when controlling a plant by model prediction 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 lamp signal, an M-sequence signal, etc. is applied to the plant response model as an operation amount, and parameters are estimated (identified) from the response and the target value at that time. Will be done.

Japanese Unexamined Patent Publication No. 2020-21411

Yang M. Matieyovsky, "Optimal Control under Model Predictive Control Constraints", Tokyo Denki University Press, 2005 Shuichi Adachi, "System Identification for Control by MATLAB", Tokyo Denki University Press, 1996 Shuichi Adachi, "Identification of Advanced Systems for Control by MATLAB", Tokyo Denki University Press, 2004

The model identification test requires a great deal of labor and time, and has a problem that the operational cost and burden are large. Therefore, it is desired to be able to estimate the parameters of the plant response model using the operation data during normal plant operation. However, in general, since a plant in operation is often operated within a controlled narrow range, the values that can be obtained from the operation data are often within the narrow range. Further, in an operating plant, the controlled amount and the manipulated amount are often in a constant steady state, so that the so-called PE (Persistently Exciting) property is not satisfied and it 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 an object thereof is to estimate a response model from the operation data of an operating plant.

In order to achieve the above object, the plant response estimation device according to the embodiment is a function representing the plant response model of the controlled plant based on the operation data of the controlled plant, and is a function of the controlled plant. Based on the model parameter estimation unit that calculates the estimated value of the model parameter of the plant response function, which is a function having the model parameter including the offset term representing the steady state, and the plant response function based on the estimated value of the model parameter. It has a step response calculation unit for calculating the step response of the controlled plant.

The response model can be estimated from the operating data of the plant in operation.

It is a figure which shows an example of the hardware composition of the plant response estimation apparatus which concerns on this embodiment. It is a figure which shows an example of the functional structure of the plant response estimation apparatus which concerns on this embodiment. It is a figure for demonstrating an example of the operation of a buffer part. It is a flowchart for demonstrating an example of extended model parameter estimation processing. It is a figure for demonstrating an example of the operation of a parameter conversion part. It is a figure for demonstrating an example of the operation of a step response calculation unit. It is a flowchart for demonstrating an example of a step response calculation process. It is a figure for demonstrating an example of a state vector update. It is a figure for demonstrating an example of the target data in an Example. It is a figure for demonstrating an example of the result of estimating a model parameter and a step response by a usual RLS method. It is a figure for demonstrating an example of the result of estimating the model parameter, the offset term and the step response by the plant response estimation apparatus which concerns on this embodiment.

Hereinafter, an embodiment of the present invention will be described. In this embodiment, the plant response estimation device 10 capable of estimating the response model from the operation data of the operating plant will be described. It should be noted that the term “in operation” means that the plant is operating normally and is in normal operation, and may be referred to as, for example, online, in operation, in operation, or the like. A plant is an industrial facility composed of one or more machines, equipment, devices, etc., and is a control target controlled by model prediction control using a plant response model. Specific examples of the plant include, for example, petrochemical plants, food plants, steel plants, power plants, etc., but these are examples and are not limited thereto.

<Hardware configuration of plant response estimation device 10>
FIG. 1 shows a hardware configuration example of the plant response estimation device 10 according to the present embodiment. As shown in FIG. 1, the plant response estimation device 10 according to the present 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 hardware is communicably connected via the bus 17.

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

The external I / F 13 is an interface with an external device such as a 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.

The communication I / F 14 is an interface for connecting the plant response estimation device 10 to the 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.

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 a plurality of processors 15 and a plurality of memory devices 16, or may have various hardware other than the hardware shown in the figure.

<Functional configuration of plant response estimation device 10>
FIG. 2 shows an example of the functional configuration of the plant response estimation device 10 according to the present embodiment. As shown in FIG. 2, the plant response estimation device 10 according to the present embodiment has a model parameter estimation unit 101 and a step response calculation unit 102. Each of these parts is realized, for example, by a process in which one or more programs installed in the plant response estimation device 10 are executed by a processor 15 or the like.

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

Here, if the time is t, the control amount y, the operation amount u, and the disturbance v are expressed as y (t), u (t), and v (t), respectively, and each sampling time tk ( _k is the sampling time). For the index to be represented), tk _{+ 1} −t _k = Δ holds. In addition, k is an integer of 0 or more. In the following, unless otherwise specified, each sampling time t _k is equated with its index k and is also expressed as y (k), u (k) and v (k).

Further, in the following, the plant response model is represented by the plant response function S _θ (t) having the parameter θ, and the parameter θ is referred to as a model parameter. As the plant response model, it is possible to adopt a model expressed by various plant response functions S _θ , but in the following, a polynomial model such as an ARMAX model is mainly assumed. When the plant response model is an ARMAX model, the model parameter θ is a coefficient of the ARMAX model. Needless to say, various models other than the ARMAX model can be adopted as the plant response model.

Further, in the following, a model in which an offset term (constant term) representing the steady state of the controlled plant is added to the plant response model represented by the ARMAX model will be referred to as an expanded plant response model.

The step response calculation unit 102 uses the model parameter (hereinafter, also referred to as model parameter estimation value) θ estimated by the model parameter estimation unit 101 to estimate the step response of the plant at a given time t (hereinafter, also referred to as model parameter estimation value) θ. It is also called a step response estimated value.) S _θ (t) is calculated. The step response is a control amount when a step signal is applied to the plant as an operation amount.

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 stores (buffers) the control amount y (k), the operation amount u (k), and the disturbance v (k) in the memory device 16 in a predetermined period. The state vector conversion unit 112 resamples the control amount y (k), the operation amount u (k), and the disturbance v (k) buffered in the memory device 16 to create a vector called an enlarged state vector. .. The sequential estimation calculation unit 113 estimates the expansion model parameter, which is the model parameter of the expansion plant response model, by the RLS method using the expansion state vector. The parameter conversion unit 114 converts the estimated value of the enlarged model parameter into the model parameter estimated value θ.

<Operation of buffer unit 111>
It is assumed that the control amount buffer at the sampling time tk is Y ( _k ), the operation amount buffer is U (k), and the disturbance buffer is V (k), and each of these buffers is represented by the following vector.

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) is the control amount y from kB ₁ to k, the operation amount buffer U (k) is the operation amount u from kB ₂ to k, and the disturbance buffer V (k). It is assumed that the disturbance v from k-B ₃ to k is stored in each. Here, B ₁ , B ₂ and B ₃ are integers of 0 or more, respectively, and are parameters that determine the sizes of the control amount buffer, the operation amount buffer, and the disturbance buffer. The values of 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 control amount y (k), the operation amount u (k), and the disturbance v (k), the control amount y (k) and the control amount buffer Y (as shown in FIG. 3). From k-1) control amount buffer Y (k), operation amount u (k) and operation amount buffer U (k-1) to operation amount buffer U (k), disturbance v (k) and disturbance buffer V (k-). Update from 1) to the disturbance buffer V (k).

Specifically, the buffer unit 111 deletes y (kB 1-1) stored in the control amount buffer Y (k- ₁ ), and then newly observes the control amount y (k). Is stored in the control amount buffer Y (k) in which the control amounts from y (k-B ₁ ) to y (k) are stored. 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 newly observes the manipulated variable u (k). Is stored in the operation amount buffer U (k) in which the operation amounts from u (k-B ₂ ) to u (k) are stored. Similarly, the buffer unit 111 stores the newly observed disturbance v (k) after deleting the disturbance v (kB 3-1) stored in the disturbance buffer V (k- ₁ ). As a result, the disturbance buffer V (k) in which the disturbances from v (k-B ₃ ) to v (k) are stored 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 operation amount buffer U (k), and the disturbance buffer V (k) are updated, the state vector conversion unit 112 determines each of these buffers Y (k) and U (k). ) And V (k) with the resampling period D, the following resampling control amount vector Y _D (k), resampling operation amount vector _{UD (k), and resampling disturbance vector V D (} k). ) Are created 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 control amount y of the ARMAX model, and M is the coefficient of the term related to the manipulated variable u. The number, L is the number of coefficients of the term relating to the disturbance v). Further, in the resampling control amount vector Y _D (k), the element y (k) representing the current sampling time is skipped (that is, y (k) is not resampled) according to the ARMAX model.

In general, the larger the values of N, M, and L are, the more various expressions are possible, and highly accurate prediction of the plant response can be expected. However, a large amount of computational resources and memory are required for estimating the model parameter θ. You will need it.

Then, the state vector conversion unit 112 expands the state vector ξ (k) from the resampling control amount vector Y _D (k), the resampling operation amount vector _{UD (k), and the resampling disturbance vector V D (} k) by the following. 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 expanded by adding “1” as an element representing an offset term to the elements of Y _D (k), _{UD (k), and V D (} k). It is a state vector. Here, the offset term is a constant term that appears as a term representing a steady state in the ARMAX model, as described above. As a result, the resampling control amount vector Y _D (k), the resampling operation amount vector _UD (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>
In the following, the expanded model parameters are referred to as θ _e . When the expanded state vector ξ (k) is created, the sequential estimation calculation unit 113 estimates the value of the expanded model parameter θ _e using the expanded state vector ξ (k). That is, the sequential estimation calculation unit 113 sequentially estimates the value of the expanded model parameter θ _e at every sampling time _tk .

The process of estimating the value of the expanded model parameter _θe with respect to a certain k will be described with reference to FIG. In the following, the estimated value of the expanded model parameter θ _e at the sampling time tk is referred to as θ _e ( _k ).

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

When it is determined that the expanded model parameter θ _e and the covariance matrix P are initialized (YES in step S101), the sequential estimation calculation unit 113 proceeds to step S102. On the other hand, if it is not determined 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 at the sampling time t _k to k = 0, and initializes θ _e (0) = θ ₀ and P (0) = I. Here, θ ₀ is an initial value of a preset enlarged model parameter, and I is an arbitrary matrix (for example, an identity matrix) set in advance.

Step S103: The sequential estimation calculation unit 113 calculates a 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, for example, by ε (k) = y (k) −ξ (k) ^Τ θ _e (k-1). In addition, Τ represents transpose.

Step S104: The sequential 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 coefficient that takes 0 <λ ≦ 1, and is a preset value. The forgetting coefficient λ is a coefficient for forgetting past data, and the closer it is to 0, the sharper the influence of the past data decreases, and the closer it is to 1, the more the influence of the past data is retained.

Step S105: Then, the sequential estimation calculation unit 113 updates the expanded model parameter estimated value θ _e (k-1) as follows to obtain the expanded 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 expanded model parameter estimated value θ _e ( _k ) at the sampling time tk can be obtained.

<Operation of parameter conversion unit 114>
The expanded model parameter estimated value θ _e (k) is shown 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 element is the coefficient of the term related to the control amount y of the ARMAX model at the sampling time tk, and θ _U ( _k ) is M whose element is the coefficient of the term related to the manipulated variable u. The dimensional vector, θ _V (k) is an L-dimensional vector whose element is the coefficient of the term related to the 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 the enlarged model parameter estimated value θ e (k) into a vector excluding θ _C (k) as shown in FIG. 5, thereby converting the model parameter estimated value. Obtain θ (k). As a result, the following model parameter estimates

が得られる。

Is obtained.

As described above, when estimating the step response of the controlled plant, the model parameter estimated value θ (k) can be obtained by removing θ _C (k) from the expanded model parameter estimated value θ _e (k). The reason for this will be described below.

Let the expanded plant response model be y (k) = θ _Y (k) ^Τ Y _D (k) + θ _U (k) ^{Τ UD} ₍ k) + θ _V (k) ^Τ V _D (k) + θ _C (k). ..

In addition, θ _Y (k), θ _U (k), θ _V (k), and θ _C (k), 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 the sake of simplicity of notation, θ _Y = θ _Y (k), θ _U = θ _U (k), θ _V = θ _V (k), and θ _C = θ _C (k). Note that d ₀ is an offset term.

At this time, if the expanded plant response model y (k) = θ _Y ^Τ Y _D (k) + θ _U ^Τ U _D (k) + θ _V ^Τ V _D (k) + θ _C is Z-transformed, it becomes 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
The above formula is (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 Since the formula can be transformed as _M z ^- Mu) + (c ₀ v + c ₁ z ^-1 v + c ₂ z ^-2 v + ... + c _L z ^-L v) + d ₀ , the transfer functions _Fu (z), F _v ( If z) and F _d (z) are defined below, the above equation can be expressed as y = Fu (z) _u + F _v (z) v + F _d (z) d ₀ .

_Fu (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 -...- a _N z ^-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 -...- a _N z ^-N )
F _d (z) = 1 / (1-a ₁ z ^-1 -a ₂ z ^-2 -...- a _N z- ^N )
Here, let Δy be the amount of change in the controlled variable y when only the manipulated variable u changes by Δu. At this time, assuming that only the manipulated variable u changes by Δu, y = Fu (z) _u + F _v (z) v + F _d (z) d ₀ is
y + Δy = Fu (z) ( _u + Δu) + F _v (z) v + F _d (z) d ₀
Will be. Therefore, Δy is represented by Δy = Fu (z) _Δu . That is, it can be seen that the offset term does not affect the change amount Δy of the control amount y.

Therefore, using the plant response model y (k) without offset term = θ _Y (k) ^Τ Y _D (k) + θ _U (k) ^{Τ UD} ₍ k) + θ _V (k) ^Τ V _D (k) It can be seen that the step response of the controlled plant can be estimated.

<Operation of step response calculation unit 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”. Further, in the following, for the sake of simplicity, a unit step signal is assumed as a step signal.

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

The process of calculating the step response S _θ (t) when a certain time t and a certain model parameter setting value θ are given will be described with reference to FIG. 7. In the following, the state vector φ (k') at the index k'will be represented by the following.

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 t _k , 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 with the index representing the time used only in this process as τ, and sets the state vector φ (0) as follows. Initialize 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 1, the other elements are 0, and the state vector φ (0) is initialized.

Step S202: The step response calculation unit 102 calculates the controlled variable amount y (k') by y (k') = φ (k') ^Τθ .

Step S203: The step response calculation unit 102 updates the state vector φ (k') to the state vector φ (k'+ 1) at the next index k'+ 1 using the controlled variable predicted value y (k'). .. At this time, as shown in FIG. 8, the step response calculation unit 102 inputs the controlled variable predicted value y (k') calculated in step S202 to y (k') of the state vector φ (k'+ 1). It is set, and the same value as the state vector φ (k') is set in y (k'-N + 1) to y (k'-1). Further, 1 is set for u (k'+ 1) of the state vector φ (k'+ 1), and the same value as the state vector φ (k') is set for u (k'-M + 1) to u (k'). Set. Further, 0 is set for v (k'+ 1) of the state vector φ (k'+ 1), and the same value as the state vector φ (k') is set for v (k'-L + 1) to v (k'). Set.

Step S204: The step response calculation unit 102 updates the time τ to τ + Δ and the index k'to k'+ 1.

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

On the other hand, when it is determined that τ ≧ t (YES in step S205), the step response calculation unit 102 ends the process. As a result, the finally calculated controlled variable predicted 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>
Hereinafter, one embodiment will be described. In this embodiment, the model parameters and the step response are estimated by the plant response estimation device 10 according to the embodiment described above.

In this embodiment, the expanded plant response model of the controlled plant is expressed 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 a two-dimensional element and the operation amount u has a three-dimensional element.

At this time, the expanded state vector ξ (k) and the expanded model parameter θ _e (k) are represented by the following.

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 model parameters and the step response were estimated using the two types of data shown in FIG. 9 with the resampling period D = 4 and the forgetting coefficient λ = 0.98, respectively.

The data 1 shown in FIG. 9 is artificial data. In the data 1, the operation amount u and the control amount y are constant values until the time 400, and the operation amount u changes stepwise at the time 400, and the control amount y also changes accordingly.

On the other hand, FIG. 2 shown in FIG. 9 is operation data obtained by measuring the controlled plant. In the 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 rises in steps, and the controlled variable y also rises accordingly. Further, after that, the manipulated variable u descends in a stepwise manner, and the controlled variable y also decreases accordingly.

As a feature of these data, in the data 1, the step-like change of the operation amount u and the change of the control amount y are synchronized, but in the data 2, the control amount y is gradual even when the operation amount u does not change. There is a point of change (that is, there is a drift).

In order to compare with the plant response estimation device 10 according to the present embodiment, the model parameters and the step response were also estimated by the usual RLS method. The results are shown in FIG. FIG. 10 (a) shows the results 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 the data 1. b) is the result of _estimating the step response using the data 1. On the other hand, FIG. 10 (c) shows the results 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 the data 2. FIG. 10 (d) is the result of _estimating the step response using the data 2.

FIG. 11 shows the results of estimating the model parameters, the offset term, and the step response by the plant response estimation device 10 according to the present embodiment. FIG. 11 (a) shows the results 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 the data 1. b) is the result of estimating the offset term θ ₆ = d ₀ using the data 1, and FIG. 11 (c) is the result of _estimating the step response using the data 1. On the other hand, FIG. 11 (d) shows the results 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 the data 2. FIG. 11 (e) is the result of estimating the offset term θ ₆ = d ₀ using the data 2, and FIG. 11 (f) is the result of _estimating the step response using the data 2.

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

In the data 1, when the operation amount u changes from 20 to 30, the control amount y changes from 20 to 30. Therefore, the steady-state gain is 1.

Comparing FIGS. 10 (b) and 11 (c), they are almost the same, and both have a steady gain of 1 and a time required for convergence of about 200. Therefore, regarding the data 1, it can be seen that the plant response estimation device 10 according to the present embodiment has obtained a plant response model with the same accuracy as the ordinary RLS method.

On the other hand, in the data 2, when the operation amount u changes from 10 to 20 around time 620, the control amount y changes from about 62 to about 82, and the operation amount u changes from 20 to 10 around time 1250. When it changes, the control amount y changes from about 82 to about 64. Therefore, the steady-state gain is about 1.8 to 2. Further, at this time, it takes about 700 to 800 for the control amount y to converge.

Comparing FIGS. 10 (d) and 11 (f), they are quite different. In the normal RLS method, the steady-state gain is 5 or more, and the time required for convergence is 2000 or more. On the other hand, in the plant response estimation device 10 according to the present embodiment, the steady-state gain is about 2, and the time required for convergence is about 750. Therefore, regarding the data 2, it can be seen that the plant response estimation device 10 according to the present embodiment has obtained a plant response model closer to the actual response than the normal RLS method.

<Summary>
As described above, the plant response estimation device 10 according to the present embodiment has a steady value (that is, a controlled amount or an operation amount in which the controlled plant is in a steady state and takes a constant value) or a value close to it (that is, a narrow range). It is possible to obtain a plant response model that is effective even for operation data that includes a large amount of control amount or operation amount that takes the value within. Further, the plant response estimation device 10 according to the present embodiment can obtain a highly accurate plant response model as compared with the existing RLS method for the drifting operation data 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 operation data to be taken.

Further, in the plant response estimation device 10 according to the present embodiment, since the operation data is buffered and resampled, for example, when the time constant is longer than the sampling cycle (observation cycle) or the order of the model parameters is relatively high. Even if the number is small, it can be expected that model parameters can be estimated with higher accuracy than in the prior art.

In the present 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, and for example, the plant response estimation device 10 according to the present embodiment has a plant response in which the parameters are set. It may function as a control device that actually controls the controlled plant by the model. At this time, the plant response estimation device 10 according to the present embodiment may control the controlled plant by the plant response model in which the parameter is set by using a known control method such as model prediction control.

The present invention is not limited to the above-described embodiment disclosed specifically, and various modifications and modifications, combinations with known techniques, and the like are possible without departing from the description of the scope of 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 estimation unit 102 Step response calculation unit 111 Buffer unit 112 State vector conversion unit 113 Sequential estimation calculation unit 114 Parameter conversion unit

Claims (8)

Based on the operation data of the controlled plant, it is a function representing the plant response model of the controlled plant and having a model parameter including an offset term representing the steady state of the controlled plant. A model parameter estimation unit that calculates the estimated value of the model parameter of the function, and
A step response calculation unit that calculates the step response of the controlled plant by the plant response function based on the parameter obtained by excluding the estimated value of the offset term from the estimated value of the model parameter.
Have,
The model parameter estimation unit includes
A buffer unit that buffers the operation data in a predetermined period in a memory,
A state in which the operation data buffered in the memory is resampled at a predetermined resampling cycle, and the resampled operation data is converted into an expanded state vector which is a state vector including an element corresponding to the offset term. Vector converter and
A plant response estimation device including a sequential estimation calculation unit that calculates an estimated value of the model parameter by a sequential least squares method based on the expanded state vector and a covariance matrix . The model parameter estimation unit is
The plant response estimation device according to claim 1, wherein the estimated value of the model parameter is sequentially calculated for each sampling cycle based on the operation data for each sampling cycle. The operation data includes a controlled amount of the controlled plant and an operation amount with respect to the controlled plant.
The buffer unit is
The plant response estimation device according to claim 1 or 2 , wherein the control amount in a predetermined first period is buffered in the memory, and the operation amount in the predetermined second period is buffered in the memory. The operation data further includes disturbances to the controlled plant.
The buffer unit is
The plant response estimation device according to claim 3 , wherein the disturbance in a predetermined third period is further buffered in the memory. The plant response estimation device according to any one of claims 1 to 4 , wherein the resampling cycle is a multiple of the sampling cycle of the operation data. The plant response estimation device according to any one of claims 1 to 5 , wherein the plant response function is an ARMAX model including the offset term, and the model parameter is a coefficient of the ARMAX model. Based on the operation data of the controlled plant, it is a function representing the plant response model of the controlled plant and having a model parameter including an offset term representing the steady state of the controlled plant. The model parameter estimation procedure for calculating the estimated value of the model parameter of the function, and the model parameter estimation procedure.
A step response calculation procedure for calculating the step response of the controlled plant by the plant response function based on the parameter obtained by excluding the estimated value of the offset term from the estimated value of the model parameter.
The computer runs ,
The model parameter estimation procedure includes
A buffer procedure for buffering the operation data in a memory for a predetermined period, and a buffer procedure.
A state in which the operation data buffered in the memory is resampled at a predetermined resampling cycle, and the resampled operation data is converted into an expanded state vector which is a state vector including an element corresponding to the offset term. Vector conversion procedure and
A plant response estimation method comprising a sequential estimation calculation procedure for calculating an estimated value of the model parameter by a sequential least squares method based on the expanded state vector and a covariance matrix . Based on the operation data of the controlled plant, it is a function representing the plant response model of the controlled plant and having a model parameter including an offset term representing the steady state of the controlled plant. The model parameter estimation procedure for calculating the estimated value of the model parameter of the function, and the model parameter estimation procedure.
A step response calculation procedure for calculating the step response of the controlled plant by the plant response function based on the parameter obtained by excluding the estimated value of the offset term from the estimated value of the model parameter.
Let the computer run
The model parameter estimation procedure includes
A buffer procedure for buffering the operation data in a memory for a predetermined period, and a buffer procedure.
A state in which the operation data buffered in the memory is resampled at a predetermined resampling cycle, and the resampled operation data is converted into an expanded state vector which is a state vector including an element corresponding to the offset term. Vector conversion procedure and
A program including a sequential estimation calculation procedure for calculating an estimated value of the model parameter by a sequential least squares method based on the expanded state vector and the covariance matrix .

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