JP7428288B1 - Plant response estimation device, plant response estimation method, and program - Google Patents

Abstract

[Problem] To provide a technology for accurately estimating a response model from operational data of an operating plant. A plant response estimation device according to an aspect of the present disclosure includes a state vector creation unit that creates a state vector representing a state of a controlled plant based on operation data of the controlled plant; a learning data selection unit that determines whether or not the state vector is to be used as learning data; and a parameter updating unit that updates parameters of a function representing a response model. [Selection diagram] Figure 2

Description

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

Model predictive control is known as a control method that aims to make the controlled variable of a controlled object follow a target value. Furthermore, as a method for estimating parameters of a linear prediction model used in model predictive control, the Recursive Least Squares method (RLS method) and the like are known. For example, Patent Document 1 describes a technique for estimating the parameters of a plant response model using the RLS method using operational data of a plant in operation.

JP 2023-53573 Publication

However, in the conventional technology, for example, operating data that includes only constant values in a steady state is used as learning data used to update parameters of a plant response model, and inappropriate model parameters may be estimated. Operation data that includes only a constant value or one frequency component lacks information on plant dynamics and is inappropriate as learning data, but it can easily occur during operation. In learning using such inappropriate operational data, the estimated values of the parameters of the plant response model may deviate from the true values.

The present disclosure has been made in view of the above points, and provides a technique for accurately estimating a response model from operational data of an operating plant.

A plant response estimation device according to an aspect of the present disclosure includes a state vector creation unit that creates a state vector representing a state of the controlled plant based on operation data of the controlled plant; a learning data selection unit that determines whether the vector is to be used as learning data; and when it is determined that the state vector is to be used as learning data, the state vector is used as learning data to represent a response model of the controlled plant; and a parameter update unit that updates parameters of the function.

A technique is provided for estimating a response model with high accuracy from operating data of a plant in operation.

1 is a diagram illustrating an example of a hardware configuration of a plant response estimation device according to a first embodiment; FIG. 1 is a diagram illustrating an example of a functional configuration of a plant response estimation device according to a first embodiment. FIG. FIG. 3 is a diagram for explaining an example of the operation of a buffer section. It is a flowchart for explaining an example of learning data selection processing concerning a first embodiment. 7 is a flowchart for explaining an example of expanded model parameter estimation processing according to the first embodiment. FIG. 3 is a diagram for explaining an example of the operation of a parameter conversion section. FIG. 3 is a diagram for explaining an example of the operation of a step response calculation section. 7 is a flowchart for explaining an example of step response calculation processing according to the first embodiment. FIG. 3 is a diagram for explaining an example of state vector updating. It is a flowchart for explaining an example of learning data selection processing concerning a second embodiment. It is a flowchart for explaining an example of learning data selection processing concerning a third embodiment. 13 is a flowchart for explaining an example of learning data selection processing according to the fourth embodiment. It is a figure which shows the step response of the target plant in an Example. FIG. 3 is a diagram (part 1) showing model parameter estimation results and control results when a learning data selection unit is not used. FIG. 7 is a diagram (part 2) showing model parameter estimation results and control results when the learning data selection unit is not used. FIG. 3 is a diagram (part 1) showing model parameter estimation results and control results when a learning data selection unit is used. FIG. 7 is a diagram (part 2) showing model parameter estimation results and control results when the learning data selection unit is used.

Embodiments of the present invention will be described below. In each of the following embodiments, a plant response estimation device 10 that can accurately estimate a plant 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 is performing normal operation, and may also be called, for example, on-line, in operation, or in operation. Furthermore, a plant is an industrial facility composed of one or more machines, devices, devices, etc., and is a control target that is 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. Further, in general, in these plant control systems, input/output data such as plant control amounts, operation amounts, and disturbance amounts are treated as operational data.

Here, depending on the operating conditions of the plant, for example, a steady state may continue, or the value of the operating data may be biased towards the upper limit value or the lower limit value. Therefore, if the parameters of the plant response model are updated using steady-state operating data or operating data that is biased toward the upper and lower limits as learning data, the parameters will converge based on those operating data, and as a result, the parameters will The estimated value may deviate from the true value. In this way, it can be said that operating data in a steady state, operating data biased towards upper and lower limit values, etc. are not suitable as learning data for a plant response model. Note that the learning data is data used to update parameters of the plant response model.

Therefore, in each of the following embodiments, unsuitable operation data such as operation data in a steady state or operation data biased toward upper and lower limit values is not used as learning data, and other operation data is used as learning data. The case where the parameters of the plant response model are updated will be explained. Thereby, the plant response estimating device 10 according to each embodiment below can estimate a highly accurate plant response model.

[First embodiment]
First, a first embodiment will be described.

<Example of hardware configuration of plant response estimation device 10>
FIG. 1 shows an example of the hardware configuration of a plant response estimation device 10 according to the first embodiment. As shown in FIG. 1, the plant response estimation device 10 according to the first 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. and has. Each of these pieces of hardware is communicably connected via a bus 17 .

The input device 11 is, for example, a keyboard, a mouse, a touch panel, various physical buttons, or 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 include 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 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), and a USB (Universal Serial Bus) memory card.

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 devices such as a CPU (Central Processing Unit). The memory device 16 is, for example, various storage devices such as an SSD (Solid State Drive), a RAM (Random Access Memory), a ROM (Read Only Memory), and a 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 include a plurality of processors 15 and a plurality of memory devices 16, or may include various hardware other than the illustrated hardware.

<Example of 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 first embodiment. As shown in FIG. 2, the plant response estimation device 10 according to the first embodiment includes a model parameter estimation section 101 and a step response calculation section 102. Each of these units is realized, for example, by one or more programs installed in the plant response estimating device 10 causing the processor 15 or the like to execute the process.

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

Here, if time is t, the controlled variable y, the manipulated variable u, and the disturbance v are expressed as 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 holds true for t k+1 −t _k =Δ. It is assumed that k can take an integer greater than or equal to 0, and that the sampling time _tk starts from _t1 . In the following, unless otherwise specified, each sampling time t _k will be equated with its index k, and will also be expressed as y(k), u(k), and v(k).

Further, in the following, the plant response model is represented by a plant response function S _θ (t) having a parameter θ, and the parameter θ is referred to as a model parameter. Although it is possible to employ various models expressed by a plant response function S _θ as the plant response model, a polynomial model such as an ARMAX model is mainly assumed below. When the plant response model is an ARMAX model, the model parameter θ becomes a coefficient of the ARMAX model. It goes without saying that various models other than the ARMAX model can be employed as the plant response model.

Further, hereinafter, a model obtained by adding an offset term (constant term) representing the steady state of the controlled plant 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 parameters (hereinafter also referred to as model parameter estimated values) θ estimated by the model parameter estimation unit 101 to calculate an estimated value of the step response of the plant at a given time t (hereinafter referred to as (Also referred to as step response estimate.) Calculate 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.

However, the step response calculation unit 102 is one of the methods of using the model parameter estimated value θ, and the plant response estimation device 10 according to this embodiment may have a configuration including only the model parameter estimation unit 101. Moreover, the plant response estimating device 10 according to the present embodiment may be configured to include a functional unit that calculates a plant response other than a step response. For example, the configuration may include an "impulse response calculation unit" that calculates an impulse response, or a configuration that includes a "lamp response calculation unit" that calculates a lamp response. In addition to these, the present invention can be applied to various other usage methods without departing from the spirit of the present embodiment.

Here, the model parameter estimation section 101 includes a buffer section 111 , a state vector conversion section 112 , a learning data selection section 113 , a sequential estimation calculation section 114 , and a parameter conversion section 115 .

The buffer unit 111 stores (buffers) the control amount y(k), the manipulated variable u(k), and the disturbance v(k) in the memory device 16 during a certain predetermined period. The state vector conversion unit 112 resamples the controlled variable y(k), the manipulated variable u(k), and the disturbance v(k) buffered in the memory device 16, and converts the resampled controlled variable y( k), a state vector ξ(k) including the manipulated variable u(k) and the disturbance v(k) is created. The learning data selection unit 113 uses the state vector ξ(k) to determine whether or not to use the resampled control amount y(k), operation amount u(k), and disturbance v(k) as learning data. However, when the data is used as learning data, the update flag is set to ON, and when the data is not used as learning data, the update flag is set to OFF. When the update flag is ON, the sequential estimation calculation unit 114 estimates expanded model parameters that are model parameters of the expanded plant response model using the state vector ξ(k). The parameter conversion unit 115 converts the estimated value of the expanded model parameter into the model parameter estimated value θ. Note that a state vector is a term used in the field of control, and is a vector that represents the state of a controlled object or a system that includes it.

<Operation of buffer unit 111>
Assume that the control amount buffer at sampling time t _k 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) contains the control amount y from k-B ₁ to k, the operation amount buffer U(k) contains the operation amount u from k-B ₂ to k, and the disturbance buffer V(k). It is assumed that disturbances v from k-B ₃ to k are stored respectively. Here, B ₁ , B ₂ , and B ₃ are each integers greater than or equal to 0, and are parameters that determine the sizes of the control amount buffer, the operation amount buffer, and the disturbance buffer. The values of these B ₁ , B ₂ , and B ₃ are determined as appropriate depending on the size of the memory device 16 and the like.

At this time, when the buffer section 111 receives the controlled variable y(k), the manipulated variable u(k), and the disturbance v(k), the buffer section 111 receives the controlled variable y(k) and the controlled variable buffer Y( k-1) to the control amount buffer Y(k), the manipulated variable u(k) and the manipulated variable buffer U(k-1) to the manipulated variable buffer U(k), the disturbance v(k) and the disturbance buffer V(k- 1) to the disturbance buffer V(k).

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). By storing , the control amount buffer Y(k) is updated to store the control amounts from y(k-B ₁ ) to y(k). 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). is updated to the manipulated variable buffer U(k) in which the 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). As a result, the disturbance buffer V(k) is updated to store the disturbances from v(k-B ₃ ) to v(k).

It is assumed that the control amount buffer Y(0), the operation amount buffer U(0), and the disturbance buffer V(0) have been appropriately initialized (for example, all are initialized to 0, etc.). Furthermore, although the above explanation assumes that there is a disturbance v, the disturbance buffer V(k) may not be provided if there is no disturbance v.

<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 converts each of these buffers Y(k) and U(k ) and V(k) at a resampling period D to obtain the following resampling control amount vector Y _D (k), resampling manipulated variable 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 of the ARMAX model, and M is the number of coefficients of the term related to the manipulated variable u). (L is the number of coefficients of the term related to the disturbance v). Furthermore, 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), following the ARMAX model.

In general, the larger the values of N, M, and L, the more diverse expressions can be made, and more accurate predictions of plant responses can be expected. It becomes necessary.

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

すなわち、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」を追加したベクトルである。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）が状態ベクトルξ（ｋ）に変換されたことになる。この状態ベクトルξ（ｋ）は「拡大状態ベクトル」等と呼ばれてもよい。

That is, the state vector ξ(k) is a vector in which "1" is added as an element representing an offset term to the elements of Y _D (k), U _D (k), and V _D (k). 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 manipulated variable vector U _D (k), and the resampling disturbance vector V _D (k) are converted into the state vector ξ(k). This state vector ξ(k) may be called an "expanded state vector" or the like.

It is assumed that the state vector ξ(0) has been initialized to an appropriate value (for example, initialized to a zero vector, etc.). Furthermore, although the above description assumes that there is a disturbance v, the resampling disturbance vector V _D (k) may not be provided if there is no disturbance v.

<Operation of learning data selection unit 113>
When the state vector ξ(k) is created, the learning data selection unit 113 uses this state vector ξ(k) to determine the resampling control amount vector Y _D (k) and the resampling operation amount vector U _D (k ) and the resampled disturbance vector V _D (k) are determined whether to be used as learning data, and then the update flag is turned ON or OFF according to the determination result. As a result, driving data (observed values thereof) to be used as learning data are selected.

Hereinafter, a process for selecting driving data to be used as learning data for a certain k (learning data selecting process according to the first embodiment) will be described with reference to FIG. 4. However, if k=0, the update flag is set to ON and the process ends.

Step S101: First, the learning data selection unit 113 calculates the norm d(k) of the difference between the state vector ξ(k) and the state vector ξ(k-1) one time ago. That is, the learning data selection unit 113 calculates d(k)=||ξ(k)−ξ(k−1)|| _p . Here, p is either p=1, p=2 or p=∞, ||・|| ₁ is L1 norm, ||・|| ₂ is L2 norm, ||・|| _∞ is Each represents the L∞ norm. Hereinafter, d(k) is also referred to as vector difference norm.

Step S102: Next, the learning data selection unit 113 determines whether the vector difference norm d(k) is greater than or equal to a preset threshold value γ.

If it is determined that d(k)≧γ (YES in step S102), the learning data selection unit 113 proceeds to step S103. On the other hand, if it is not determined that d(k)≧γ (NO in step S102), the learning data selection unit 113 proceeds to step S104.

Step S103: The learning data selection unit 113 turns on the update flag. Here, the update flag is a flag indicating whether or not the resampling operation amount vector U _D (k) and the resampling disturbance vector V _D (k) are used as learning data. When the update flag is ON, the resampling operation amount vector U _D (k) and the resampling disturbance vector V _D (k) are used as learning data to update the enlarged model parameters. On the other hand, when the update flag is OFF, the resampling operation amount vector U _D (k) and the resampling disturbance vector V _D (k) are not used as learning data, and the enlarged model parameters are not updated.

Step S104: The learning data selection unit 113 turns off the update flag.

<Operation of sequential estimation calculation unit 114>
In the following, the expanded model parameters are expressed as θ _e . When the update flag is set to ON or OFF by the learning data selection unit 113, the sequential estimation calculation unit 114 estimates the value of the expanded model parameter θ _e using the state vector ξ(k). That is, the sequential estimation calculation unit 114 sequentially estimates the value of the expanded model parameter θ _e at every sampling time t _k .

Hereinafter, the process of estimating the value of the expanded model parameter θ _e for a certain k (extended model parameter estimation process according to the first embodiment) will be described with reference to FIG. 5. Note that hereinafter, the estimated value of the expanded model parameter θ _e at the sampling time t _k is expressed as θ _e (k).

Step S201: First, the sequential estimation calculation unit 114 determines whether the update flag is ON.

If it is determined that the update flag is ON (YES in step S201), the sequential estimation calculation unit 114 proceeds to step S202. On the other hand, if it is not determined that the update flag is ON (NO in step S201), the sequential estimation calculation unit 114 ends the expanded model parameter estimation process. That is, when the update flag is OFF, the sequential estimation calculation unit 114 ends the process without estimating or updating the value of the expanded model parameter θ _e .

Step S202: The sequential estimation calculation unit 114 determines whether to initialize the expanded model parameter θ _e and the covariance matrix P. Here, cases in which it is determined that initialization is to be performed include, for example, at the time of first calculation (that is, when k=1), and when an initialization instruction is given by a user or the like.

If it is determined that the expanded model parameter θ _e and the covariance matrix P are to be initialized (YES in step S202), the sequential estimation calculation unit 114 proceeds to step S203. On the other hand, if it is not determined that the expanded model parameter θ _e and the covariance matrix P are to be initialized (NO in step S202), the sequential estimation calculation unit 114 proceeds to step S204.

Step S203: The sequential estimation calculation unit 114 initializes the index k of the sampling time _tk to k=1, and also initializes θ _e (0)=θ ₀ and P(0)=I. Here, θ ₀ is a preset initial value of the enlarged model parameter, and I is a preset arbitrary matrix (for example, a unit matrix, etc.).

Step S204: The sequential estimation calculation unit 114 calculates the prediction error ε(k) using the expanded model parameter estimate θ _e (k−1), the state vector ξ(k), and the control amount y(k). . The prediction error ε(k) is calculated, for example, by ε(k)=y(k)−ξ(k) ^Τ θ _e (k−1). Note that T represents transposition.

Step S205: The sequential estimation calculation unit 114 updates the covariance matrix P(k-1) as follows to obtain the covariance matrix P(k).

ここで、λ＞０は調整係数であり、予め設定された値である。調整係数λはその値に応じて以下の２つの使い方をすることができる。

Here, λ>0 is an adjustment coefficient and is a preset value. The adjustment coefficient λ can be used in the following two ways depending on its value.

First, by setting 0<λ≦1, it can be used as a forgetting coefficient for forgetting past driving data. The closer λ is to 0, the more rapidly the influence of past driving data is reduced, and the closer λ is to 1, the more the influence of past driving data is retained.

Second, by setting λ>1, it can be used as a coefficient for accelerating parameter updating. The larger the value of λ, the faster the parameter convergence can be accelerated.

Step S206: Then, the sequential estimation calculation unit 114 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 estimate θ _e (k) at the sampling time t _k is obtained.

<Operation of parameter conversion unit 115>
The expanded model parameter estimate θ _e (k) is expressed 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 term related to the controlled variable y of the ARMAX model at sampling time t _k , and θ _U (k) is an M vector whose elements are the coefficients of the term related to the manipulated variable u. The dimensional vector θ _V (k) is an L-dimensional vector whose elements are coefficients of terms related to the disturbance v, and θ _C (k) is a scalar value representing the offset term.

At this time, when the expanded model parameter estimated value θ _e (k) is obtained, the parameter conversion unit 115 converts it into a vector excluding θ _C (k), as shown in FIG. Obtain θ(k). This yields the following model parameter estimates.

このように、制御対象プラントのステップ応答を推定する際には、拡大モデルパラメータ推定値θ_ｅ（ｋ）からθ_Ｃ（ｋ）を除くことで、モデルパラメータ推定値θ（ｋ）が得られる。この理由については、例えば、特許文献１等を参照されたい。

In this way, when estimating the step response of the controlled plant, the model parameter estimate θ(k) is obtained by removing θ _C (k) from the expanded model parameter estimate θ _e (k). For the reason for this, please refer to, for example, Patent Document 1.

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

As shown in FIG. 7, 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. Note that the unit step response is the response when a unit step signal is applied as the manipulated variable u (that is, the output of the plant response model of the plant to be controlled).

See FIG. 8 for 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 (step response calculation process according to the first embodiment). I will explain while doing so. In addition, below, the state vector φ(k') at index k' shall be expressed as follows.

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

Step S301: The step response calculation unit 102 initializes τ=0, k'=0, with τ as an index representing a time used only in this process, 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, the state vector φ(0) is initialized so that only u(0) is 1 and the other elements are 0.

Step S302: The step response calculation unit 102 calculates the predicted control amount value y(k') using y(k')=φ(k') ^T θ.

Step S303: 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 control amount predicted value y(k'). . At this time, as shown in FIG. 9, the step response calculation unit 102 sets the control amount predicted value y(k') calculated in step S302 above to y(k') of the state vector φ(k'+1). and set the same value as the state vector φ(k') for y(k'-N+1) to y(k'-1). In addition, u(k'+1) of state vector φ(k'+1) is set to 1, and u(k'-M+1) to u(k') are set to the same value as state vector φ(k'). Set. Furthermore, v(k'+1) of state vector φ(k'+1) is set to 0, and v(k'-L+1) to v(k') are set to the same values as state vector φ(k'). Set.

Step S304: The step response calculation unit 102 updates the time τ to τ+Δ and updates the index k' to k'+1.

Step S305: The step response calculation unit 102 determines whether τ≧t. If it is not determined that τ≧t (NO in step S305), the step response calculation unit 102 returns to step S302. As a result, steps S302 to S304 are repeatedly executed until τ≧t.

On the other hand, if it is determined that τ≧t (YES in step S305), the step response calculation unit 102 ends the step response calculation 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).

[Second embodiment]
Next, a second embodiment will be described. In the second embodiment, the learning data selection process is different from the first embodiment. Note that matters not specifically mentioned in the second embodiment may be the same as those in the first embodiment.

Hereinafter, a process for selecting driving data to be used as learning data for a certain k (learning data selecting process according to the second embodiment) will be described with reference to FIG. 10. However, if k=0, the update flag is set to ON and the process ends.

Step S401: First, similarly to step S101 in FIG. 4, the learning data selection unit 113 determines the norm d(k) of the difference between the state vector ξ(k) and the state vector ξ(k-1) one time before. ||ξ(k)−ξ(k−1)|| Calculate _p as the vector difference norm.

Step S402: Next, the learning data selection unit 113 calculates the threshold value γ(k) using the state vector ξ(k). That is, the learning data selection unit 113 calculates the threshold value γ(k) as follows.

ここで、Ｅ_ξ（ｋ）は状態ベクトルξ（１），・・・，ξ（ｋ）の平均値、Ｖ_ξ（ｋ）は状態ベクトルξ（１），・・・，ξ（ｋ）の分散、γ（ｋ）は状態ベクトルξ（１），・・・，ξ（ｋ）の標準偏差のα倍を表す。また、αは調整係数であり、予め設定された値である。

Here, E _ξ (k) is the average value of state vectors ξ (1), ..., ξ (k), and V _ξ (k) is the average value of state vectors ξ (1), ..., ξ (k). The variance γ(k) represents α times the standard deviation of the state vector ξ(1), . . . , ξ(k). Further, α is an adjustment coefficient and is a preset value.

Step S403: Next, the learning data selection unit 113 determines whether the vector difference norm d(k) is greater than or equal to the threshold value γ(k).

If it is determined that d(k)≧γ(k) (YES in step S403), the learning data selection unit 113 proceeds to step S404. On the other hand, if it is not determined that d(k)≧γ(k) (NO in step S403), the learning data selection unit 113 proceeds to step S405.

Step S404: The learning data selection unit 113 turns on the update flag, similar to step S103 in FIG.

Step S405: The learning data selection unit 113 turns off the update flag, similar to step S104 in FIG.

[Third embodiment]
Next, a third embodiment will be described. In the third embodiment, the learning data selection process is different from the first embodiment. Furthermore, the method of calculating the threshold value γ(k) is different from the second embodiment. Note that matters not specifically mentioned in the third embodiment may be the same as those in the first embodiment.

Hereinafter, a process for selecting driving data to be used as learning data for a certain k (learning data selecting process according to the third embodiment) will be described with reference to FIG. 11. However, if k=0, the update flag is set to ON and the process ends.

Step S501: First, the learning data selection unit 113 determines whether k=1.

If it is determined that k=1 (YES in step S501), the learning data selection unit 113 proceeds to step S502. On the other hand, if it is not determined that k=1 (NO in step S501), the learning data selection unit 113 proceeds to step S503.

Step S502: The learning data selection unit 113 initializes E _ξ (0)=0 and S _ξ (0)=0. Here, E _ξ (0) is the initial value of the average value of the norm of the state vector, and S _ξ (0) is the initial value of the average value of the square of the norm of the state vector.

Step S503: Similarly to step S101 in FIG. 4, the learning data selection unit 113 determines the norm of the difference between the state vector ξ(k) and the state vector ξ(k-1), d(k)=||ξ(k). −ξ(k−1)|| Calculate _p as the vector difference norm.

Step S504: Next, the learning data selection unit 113 calculates the threshold value γ(k) using the state vector ξ(k). That is, the learning data selection unit 113 calculates the threshold value γ(k) as follows.

ここで、Ｅ_ξ（ｋ）は状態ベクトルξ（１），・・・，ξ（ｋ）のノルムの平均値、Ｓ_ξ（ｋ）は状態ベクトルξ（１），・・・，ξ（ｋ）のノルムの２乗の平均値、Ｖ_ξ（ｋ）は状態ベクトルξ（１），・・・，ξ（ｋ）のノルムの分散、γ（ｋ）は状態ベクトルξ（１），・・・，ξ（ｋ）のノルムの標準偏差のα倍を表す。また、αは調整係数であり、予め設定された値である。

Here, E _ξ (k) is the average value of the norm of the state vector ξ (1), ..., ξ (k), and S _ξ (k) is the state vector ξ (1), ..., ξ (k ), V _ξ (k) is the variance of the norm of the state vector ξ(1),..., ξ(k), and γ(k) is the average value of the square of the norm of the state vector ξ(1),...・, represents α times the standard deviation of the norm of ξ(k). Further, α is an adjustment coefficient and is a preset value.

Step S505: Next, the learning data selection unit 113 determines whether the vector difference norm d(k) is greater than or equal to the threshold value γ(k).

If it is determined that d(k)≧γ(k) (YES in step S505), the learning data selection unit 113 proceeds to step S506. On the other hand, if it is not determined that d(k)≧γ(k) (NO in step S505), the learning data selection unit 113 proceeds to step S507.

Step S506: The learning data selection unit 113 turns on the update flag similarly to step S103 in FIG.

Step S507: The learning data selection unit 113 turns off the update flag, similar to step S104 in FIG.

[Fourth embodiment]
Next, a fourth embodiment will be described. In the fourth embodiment, the learning data selection process is different from the first to third embodiments. Note that matters not specifically mentioned in the fourth embodiment may be the same as those in the first embodiment.

Hereinafter, a process for selecting driving data to be used as learning data for a certain k (learning data selecting process according to the fourth embodiment) will be described with reference to FIG. 12. However, if k=0, the update flag is set to ON and the process ends.

Step S601: First, the learning data selection unit 113 determines whether k=1.

If it is determined that k=1 (YES in step S601), the learning data selection unit 113 proceeds to step S602. On the other hand, if it is not determined that k=1 (NO in step S601), the learning data selection unit 113 proceeds to step S603.

Step S602: The learning data selection unit 113 initializes E _y (0)=0 and S _y (0)=0. Here, E _y (0) is the initial value of the average value of the control amount, and S _y (0) is the initial value of the average value of the square of the control amount.

Step S603: The learning data selection unit 113 calculates (the absolute value of) the prediction error d(k) using the state vector ξ(k). The prediction error d(k) is calculated by d(k)=|y(k)−ξ(k) ^Τ θ _e (k−1)|, similarly to step S204 in FIG.

Step S604: Next, the learning data selection unit 113 calculates the threshold value γ(k) using the control amount y(k). That is, the learning data selection unit 113 calculates the threshold value γ(k) as follows.

ここで、Ｅ_ｙ（ｋ）は制御量ｙ（１），・・・，ｙ（ｋ）の平均値、Ｓ_ｙ（ｋ）は制御量ｙ（１），・・・，ｙ（ｋ）の２乗の平均値、Ｖ_ｙ（ｋ）は制御量ｙ（１），・・・，ｙ（ｋ）の分散、γ（ｋ）は制御量ｙ（１），・・・，ｙ（ｋ）の標準偏差のα倍を表す。また、αは調整係数であり、予め設定された値である。

Here, E _y (k) is the average value of the controlled quantities y(1),..., y(k), and S _y (k) is the average value of the controlled quantities y(1),..., y(k). The average value of the squares, V _y (k) is the variance of the control amount y(1),..., y(k), and γ(k) is the control amount y(1),..., y(k). represents α times the standard deviation of Further, α is an adjustment coefficient and is a preset value.

Step S605: Next, the learning data selection unit 113 determines whether the prediction error d(k) is greater than or equal to the threshold value γ(k).

If it is determined that d(k)≧γ(k) (YES in step S605), the learning data selection unit 113 proceeds to step S606. On the other hand, if it is not determined that d(k)≧γ(k) (NO in step S605), the learning data selection unit 113 proceeds to step S607.

Step S606: The learning data selection unit 113 turns on the update flag similarly to step S103 in FIG.

Step S607: The learning data selection unit 113 turns off the update flag, similar to step S104 in FIG.

[Example]
Hereinafter, an example of the plant response estimation device 10 according to the first embodiment will be described.

In this embodiment, it is assumed that the expanded plant response model of the plant to be controlled is expressed by the following equation.

y(k)=a ₁ y(k-1)+a ₂ y(k-2)+b ₀ u(k)+b ₁ u(k-1)+b ₂ u(k-2)+c ₀
That is, it is assumed that the control amount y has a two-dimensional element, and the manipulated variable u has a three-dimensional element. In this example, it is assumed that there is no disturbance v.

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

また、制御量ｙの推定値はｙ_ｅｓｔ（ｋ）＝ξ（ｋ）^Τθ_ｅ（ｋ－１）で表される。

Further, the estimated value of the control amount y is expressed as y _est (k)=ξ(k) ^T θ _e (k−1).

Furthermore, in this embodiment, the learning data selection unit 113 uses the L1 norm as the norm when calculating the vector difference norm d(k), and the threshold value is set to γ=0.1. Further, as the step response of the plant to be controlled in this embodiment, the step response shown in FIG. 13 is assumed.

Under the above settings, a case where the learning data sorting section 113 is not used and a case where the learning data sorting section 113 is used were compared.

FIG. 14 shows model parameter estimation results and control results when the learning data selection unit 113 is not used and the adjustment coefficient is λ=0.999. Further, FIG. 15 shows model parameter estimation results and control results when the learning data selection unit 113 is not used and the adjustment coefficient is set to λ=1.1.

In both FIGS. 14 and 15, the controlled variable y and the manipulated variable u are constant from time 0 to 1000, so the model parameters also fluctuate from their initial values near time 0 and then remain constant until time 1000.

As for after time 1000, in FIG. 14, the model parameters change, and changes can be seen up to around time 4000. On the other hand, in FIG. 15, the model parameters have not changed. This is because when the adjustment coefficient λ is large, the covariance matrix is updated quickly and becomes close to zero.

Regarding the control response, in FIG. 14, the control amount is able to follow the target value due to the change in the model parameters. On the other hand, in FIG. 15, the model parameters have not changed from the initially estimated values, so the model is not estimated correctly, the control amount cannot follow the target value, and the response is unstable.

FIG. 16 shows model parameter estimation results and control results when the learning data selection unit 113 is used and the adjustment coefficient is λ=0.999. Further, FIG. 17 shows model parameter estimation results and control results when the learning data selection unit 113 is used and the adjustment coefficient is set to λ=1.1.

In both FIGS. 16 and 17, the controlled variable y and the manipulated variable u are constant from time 0 to 1000, so the model parameters also fluctuate from their initial values near time 0 and then remain constant until time 1000.

As for after time 1000, in FIG. 16, the model parameters change and converge around time 1500. On the other hand, in FIG. 17, unlike FIG. 15, the model parameters change and converge around time 1200. This is because the operation data in the steady state from time 0 to 1000 is not used for updating due to the operation of the learning data selection unit 113, so the covariance matrix does not converge to zero even in the steady state, and the control amount y This is because the operation data in which the manipulated variable u has changed is used for updating, so the parameter updating is accelerated and becomes closer to the true value, resulting in faster convergence.

Regarding the control response, since the model parameters in both FIGS. 16 and 17 are estimated relatively correctly, the control amount is able to follow the target value.

Therefore, when the adjustment coefficient λ is made larger than 1 to speed up the convergence of the model parameters, it can be said that the operation of the learning data selection unit 113 avoids the situation where the parameters converge with the operating data in the steady state. .

As described above, the learning data selection unit 113 stops parameter updating when the operating data does not include sufficient information, such as when a steady state continues, for example, and the control amount y and operation amount u change. If so, the parameters are updated. This allows, for example, to avoid situations where parameters inadvertently converge to local values that are far from the true value in a steady state, while converging to values closer to the true value more quickly than when the training data is not selected. , there are advantages.

In each of the above embodiments, the case where the parameters of the plant response model are estimated has been mainly described, but the present invention is not limited to this. For example, the plant response estimation device 10 according to each of the above embodiments may estimate the parameters. It may also function as a control device that actually controls the plant to be controlled using the set plant response model. At this time, the plant response estimation device 10 according to each of the embodiments described above may control the plant to be controlled using a plant response model in which the parameters are set using a known control method such as model predictive control. In this way, the plant response estimation device 10 according to each of the above embodiments can contribute to control followability and response stabilization by combining with known control methods such as model predictive control, for example. .

The present invention is not limited to the above-described specifically disclosed embodiments, and various modifications and changes, combinations with known techniques, etc. can be made 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 estimation section 102 Step response calculation section 111 Buffer section 112 State vector conversion section 113 Learning data selection section 114 Sequential estimation calculation section 115 Parameter conversion section

Claims (6)

a state vector creation unit that creates a state vector representing the state of the controlled plant based on operation data of the controlled plant;
a learning data selection unit that uses the state vector to determine whether or not the state vector is to be used as learning data;
a parameter updating unit that uses the state vector as learning data to update parameters of a function representing a response model of the controlled plant when it is determined that the state vector is to be used as learning data;
has
The learning data selection unit is
Calculate the norm of the difference between the current value and the previous value of the state vector,
Calculating the product of the standard deviation of all the state vectors created so far by the state vector creation unit and a predetermined coefficient having a value greater than 0 as a threshold;
If the norm is greater than or equal to the threshold, the operating data is neither a steady state nor an upper limit value nor a lower limit value, and the state vector is determined to be learning data;
If the norm is less than the threshold, it is determined that the state vector is not to be used as learning data because the driving data is in a steady state, an upper limit value, or a lower limit value;
The parameter update unit includes:
Using the state vector determined to be the learning data, sequentially update the covariance matrix and the estimated value of the parameter by an iterative least squares method each time it is determined to be the learning data,
Creation of the state vector by the state vector creation unit, calculation of the threshold by the learning data selection unit and determination of whether or not to use the learning data, and updating of the parameters by the parameter update unit are based on the operation. A plant response estimation device that is executed sequentially at each data sampling period . a state vector creation unit that creates a state vector representing the state of the controlled plant based on operation data of the controlled plant;
a learning data selection unit that uses the state vector to determine whether or not the state vector is to be used as learning data;
a parameter updating unit that uses the state vector as learning data to update parameters of a function representing a response model of the controlled plant when it is determined that the state vector is to be used as learning data;
has
The learning data selection unit is
Using the current value of the state vector and the parameter, calculate an estimated value of the controlled variable of the controlled plant,
calculating a prediction error representing an error between the estimated value of the controlled variable and the current value of the controlled variable;
The product of the standard deviation of all the state vectors created up to now by the state vector creation unit and a predetermined coefficient that takes a value greater than 0 , or the product of the standard deviation of all the control variables up to now and more than 0. Calculate the product with a predetermined coefficient that takes a large value as a threshold ,
If the prediction error is greater than or equal to the threshold, determining that the state vector is to be learning data because the driving data is neither a steady state nor an upper limit value nor a lower limit value ;
If the prediction error is less than the threshold, it is determined that the state vector is not to be used as learning data because the driving data is in a steady state, an upper limit value, or a lower limit value;
The parameter update unit includes:
Using the state vector determined to be the learning data, sequentially update the covariance matrix and the estimated value of the parameter by an iterative least squares method each time it is determined to be the learning data,
Creation of the state vector by the state vector creation unit, calculation of the threshold by the learning data selection unit and determination of whether or not to use the learning data, and updating of the parameters by the parameter update unit are based on the operation. A plant response estimation device that is executed sequentially at each data sampling period . a state vector creation procedure for creating a state vector representing the state of the controlled plant based on operational data of the controlled plant;
a learning data selection procedure that uses the state vector to determine whether or not the state vector is to be used as learning data;
If it is determined that the state vector is to be used as learning data, a parameter updating procedure of updating parameters of a function representing a response model of the controlled plant using the state vector as learning data;
The computer executes
The learning data selection procedure is as follows :
Calculate the norm of the difference between the current value and the previous value of the state vector,
Calculating the product of the standard deviation of all the state vectors created so far by the state vector creation procedure and a predetermined coefficient having a value greater than 0 as a threshold;
If the norm is greater than or equal to the threshold, the operating data is neither a steady state nor an upper limit value nor a lower limit value, and the state vector is determined to be learning data;
If the norm is less than the threshold, it is determined that the state vector is not to be used as learning data because the driving data is in a steady state, an upper limit value, or a lower limit value;
The parameter update procedure is as follows:
Using the state vector determined to be the learning data, sequentially update the covariance matrix and the estimated value of the parameter by an iterative least squares method each time it is determined to be the learning data,
Creation of the state vector by the state vector creation procedure, calculation of the threshold value and determination of whether or not to use the learning data by the learning data selection procedure, and updating of the parameters by the parameter update procedure are the same as those for the operation. A plant response estimation method that is executed sequentially at each data sampling period . a state vector creation procedure for creating a state vector representing the state of the controlled plant based on operational data of the controlled plant;
a learning data selection procedure that uses the state vector to determine whether or not the state vector is to be used as learning data;
If it is determined that the state vector is to be used as learning data, a parameter updating procedure of updating parameters of a function representing a response model of the controlled plant using the state vector as learning data;
The computer executes
The learning data selection procedure is as follows :
Using the current value of the state vector and the parameter, calculate an estimated value of the controlled variable of the controlled plant,
calculating a prediction error representing an error between the estimated value of the controlled variable and the current value of the controlled variable;
The product of the standard deviation of all the state vectors created up to now by the state vector creation procedure and a predetermined coefficient that takes a value greater than 0 , or the product of the standard deviation of all the control variables up to now and more than 0. Calculate the product with a predetermined coefficient that takes a large value as a threshold ,
If the prediction error is greater than or equal to the threshold, determining that the state vector is to be learning data because the driving data is neither a steady state nor an upper limit value nor a lower limit value ;
If the prediction error is less than the threshold, it is determined that the state vector is not to be used as learning data because the driving data is in a steady state, an upper limit value, or a lower limit value;
The parameter update procedure is as follows:
Using the state vector determined to be the learning data, sequentially update the covariance matrix and the estimated value of the parameter by an iterative least squares method each time it is determined to be the learning data,
Creation of the state vector by the state vector creation procedure, calculation of the threshold value and determination of whether or not to use the learning data by the learning data selection procedure, and updating of the parameters by the parameter update procedure are the same as those for the operation. A plant response estimation method that is executed sequentially at each data sampling period . a state vector creation procedure for creating a state vector representing the state of the controlled plant based on operational data of the controlled plant;
a learning data selection procedure that uses the state vector to determine whether or not the state vector is to be used as learning data;
If it is determined that the state vector is to be used as learning data, a parameter updating procedure of updating parameters of a function representing a response model of the controlled plant using the state vector as learning data;
make the computer run
The learning data selection procedure is as follows :
Calculate the norm of the difference between the current value and the previous value of the state vector,
Calculating the product of the standard deviation of all the state vectors created so far by the state vector creation procedure and a predetermined coefficient having a value greater than 0 as a threshold;
If the norm is greater than or equal to the threshold, the operating data is neither a steady state nor an upper limit value nor a lower limit value, and the state vector is determined to be learning data;
If the norm is less than the threshold, it is determined that the state vector is not to be used as learning data because the driving data is in a steady state, an upper limit value, or a lower limit value;
The parameter update procedure is as follows:
Using the state vector determined to be the learning data, sequentially update the covariance matrix and the estimated value of the parameter by an iterative least squares method each time it is determined to be the learning data,
Creation of the state vector by the state vector creation procedure, calculation of the threshold value and determination of whether or not to use the learning data by the learning data selection procedure, and updating of the parameters by the parameter update procedure are the same as those for the operation. A program that is executed sequentially at each data sampling period . a state vector creation procedure for creating a state vector representing the state of the controlled plant based on operational data of the controlled plant;
a learning data selection procedure that uses the state vector to determine whether or not the state vector is to be used as learning data;
If it is determined that the state vector is to be used as learning data, a parameter updating procedure of updating parameters of a function representing a response model of the controlled plant using the state vector as learning data;
make the computer run
The learning data selection procedure is as follows :
Using the current value of the state vector and the parameter, calculate an estimated value of the controlled variable of the controlled plant,
calculating a prediction error representing an error between the estimated value of the controlled variable and the current value of the controlled variable;
The product of the standard deviation of all the state vectors created up to now by the state vector creation procedure and a predetermined coefficient that takes a value greater than 0 , or the product of the standard deviation of all the control variables up to now and more than 0. Calculate the product with a predetermined coefficient that takes a large value as a threshold ,
If the prediction error is greater than or equal to the threshold, determining that the state vector is to be learning data because the driving data is neither a steady state nor an upper limit value nor a lower limit value ;
If the prediction error is less than the threshold, it is determined that the state vector is not to be used as learning data because the driving data is in a steady state, an upper limit value, or a lower limit value;
The parameter update procedure is as follows:
Using the state vector determined to be the learning data, sequentially update the covariance matrix and the estimated value of the parameter by an iterative least squares method each time it is determined to be the learning data,
Creation of the state vector by the state vector creation procedure, calculation of the threshold value and determination of whether or not to use the learning data by the learning data selection procedure, and updating of the parameters by the parameter update procedure are the same as those for the operation. A program that is executed sequentially at each data sampling period .

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