JP2024044583A - PLANT RESPONSE ESTIMATION APPARATUS, PLANT RESPONSE ESTIMATION METHOD, AND PROGRAM - Google Patents

Abstract

[Problem] To provide a technology capable of stably estimating parameters of a response model from operational data of a plant in operation. [Solution] A plant response estimation device according to one aspect of the present disclosure includes an estimation calculation unit configured to sequentially calculate, based on operational data of a controlled plant, estimates of model parameters, which are parameters of a function representing a plant response model of the controlled plant, a stabilization calculation unit configured to calculate stabilized model parameters obtained by stabilizing the estimates of the model parameters, and a response calculation unit configured to calculate a response of the controlled plant by the function representing the plant response model based on the estimates of the model parameters, and the estimation calculation unit is configured to calculate the estimates of the model parameters based on the operational data and the stabilized model parameters obtained by stabilizing the estimates of the model parameters calculated previously by the stabilization calculation unit. [Selected Figure] Figure 2

Description

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

Controllers such as temperature control devices, programmable logic controllers (PLCs), distributed control systems (DCSs), and controllers implemented on personal computers and embedded control devices are widely used in industry.

In addition, various control methods are known that aim to make the control amount of the controlled object follow a target value, such as PID (Proportional-Integral-Differential) control, model predictive control, internal model control, LQG (Linear-Quadratic-Gaussian) control, H2 control, and H∞ control.

Model predictive control is a method to obtain a desired response by sequentially performing optimization calculations using a state space model of the controlled object and a future time response model, and is widely used in industry (for example, patented Literature 1, Non-Patent Literature 1). Recursive least squares method (RLS method), Kalman filter method, etc. are known as methods for estimating (identifying) model parameters for linear predictive models used in such model predictive control, etc. (for example, , Non-Patent Document 2, Non-Patent Document 3).

In addition, there is also a known technique for estimating model parameters that include an offset term that represents the steady state of the controlled plant (for example, Patent Document 3).

JP 2020-21411 A Patent No. 7047966

Yang M. Maciejowski, “Model Predictive Control: Optimal Control under Constraints”, Tokyo Denki University Press, 2005. Shuichi Adachi, "System Identification for Control Using MATLAB", Tokyo Denki University Press, 1996 Shuichi Adachi, "Advanced System Identification for Control Using MATLAB", Tokyo Denki University Press, 2004

The iterative least squares method and the Kalman filter method are very useful in that they allow model parameters to be estimated sequentially from data of an operating (operating) plant, but since the estimated values of the model parameters are updated sequentially, the following There are two issues.

The first problem is that the reliability of estimated values of model parameters is not guaranteed during the intermediate stage until convergence to the true value. The second problem is that since the degree of the true model parameter is unknown in advance, multicollinearity may occur if the model parameter to be estimated has an excessive degree.

Due to the above two issues, for example, model parameters that have unstable poles for a plant that is supposed to be stable may be calculated midway through, model parameters may fluctuate greatly due to the influence of observation noise, or multiple There is a risk that instability may occur due to linearity, such as multiple locally optimal solutions.

When updating model parameters and controlling the controlled object online, it is important to ensure the stability of the model parameters during convergence, since instability of the model parameters can have a significant impact on the control.

The present disclosure has been made in view of the above points, and provides a technique that can stably estimate parameters of a response model from operating data of a plant in operation.

A plant response estimation device according to one aspect of the present disclosure includes an estimation calculation unit configured to sequentially calculate, based on operation data of a controlled plant, estimates of model parameters, which are parameters of a function representing a plant response model of the controlled plant; a stabilization calculation unit configured to calculate stabilized model parameters obtained by stabilizing the estimates of the model parameters; and a response calculation unit configured to calculate a response of the controlled plant using a function representing the plant response model based on the estimates of the model parameters, and the estimation calculation unit is configured to calculate an estimate of the model parameters based on the operation data and the stabilized model parameters obtained by stabilizing the estimates of the previously calculated model parameters by the stabilization calculation unit.

A technology is provided that can stably estimate response model parameters from operational data of an operating plant.

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 apparatus according to a first embodiment. FIG. 3 is a diagram for explaining an example of the operation of a buffer section. 11 is a flowchart illustrating an example of a model parameter estimation process. 11 is a flowchart illustrating an example of a stabilization model parameter calculation process. 11 is a diagram for explaining an example of an operation of a step response calculation unit. FIG. 11 is a flowchart illustrating an example of a step response calculation process. FIG. 11 is a diagram illustrating an example of a functional configuration of a plant response estimation apparatus according to a second embodiment. 11 is a diagram for explaining an example of an operation of a parameter conversion unit. FIG. It is a figure for explaining the step response of a plant in one example. FIG. 2 is a diagram for explaining an example of data 1 targeted in one embodiment. FIG. 3 is a diagram (part 1) for explaining an example of a model parameter estimation result (without a stabilizing model parameter calculation unit) in one embodiment. FIG. 3 is a diagram (part 1) for explaining an example of a control result of model predictive control (without a stabilizing model parameter calculation unit) in one embodiment. FIG. 11 is a diagram (part 1) for explaining an example of a model parameter estimation result (with a stabilization model parameter calculation unit) in one embodiment. FIG. 11 is a diagram (part 1) for explaining an example of a control result of the model predictive control (with a stabilization model parameter calculation unit) in one embodiment. FIG. 2 is a diagram for explaining an example of data 2 that is a target in an embodiment. FIG. 13 is a diagram (part 2) for explaining an example of a model parameter estimation result (without a stabilization model parameter calculation unit) in one embodiment. FIG. 13 is a diagram (part 2) for explaining an example of a control result of the model predictive control (without a stabilization model parameter calculation unit) in one embodiment. FIG. 13 is a diagram (part 2) for explaining an example of a model parameter estimation result (with a stabilization model parameter calculation unit) in one embodiment. FIG. 13 is a diagram (part 2) for explaining an example of a control result of the model predictive control (with a stabilization model parameter calculation unit) in one embodiment.

An embodiment of the present invention will be described below. In each of the following embodiments, a plant response estimation device 10 that can stably estimate parameters of a response model (model parameters) from operating data of an operating plant and estimate a plant response using the parameters 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.

[First embodiment]
The first embodiment will be described below.

<Hardware configuration example of the plant response estimation device 10>
An example of a hardware configuration of a plant response estimation device 10 according to this embodiment is shown in Fig. 1. As shown in Fig. 1, the plant response estimation device 10 according to this embodiment has 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. Each of these pieces of hardware are connected to each other via a bus 17 so as to be able to communicate with each other.

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 HDD (Hard Disk Drive), 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 is not limited to this, and may have other hardware configurations. For example, the plant response estimation device 10 may have multiple processors 15 and multiple memory devices 16, may not have some of the hardware shown in the figure, or may have various hardware other than the hardware shown in the figure.

<Example of functional configuration of plant response estimation device 10>
An example of a functional configuration of the plant response estimation device 10 according to this embodiment is shown in Fig. 2. As shown in Fig. 2, the plant response estimation device 10 according to this embodiment has a model parameter estimation unit 101 and a step response calculation unit 102. These units are realized, for example, by processing 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 observed values of operation data (control variable y, operation variable u, and disturbance v) from the plant to be controlled (or an instrument such as a sensor that measures the operating state of the plant) for each sampling period Δ, and estimates model parameters of the plant response model according to the sampling period Δ. Note that the operation data may be called, for example, measurement data or observation data.

Here, if time is t, the controlled variable y, manipulated variable u, and disturbance v are represented as y(t), u(t), and v(t), respectively, and t _k+1 - _{t k} = Δ holds for each sampling time t _k (k is an index representing the sampling time), where k is an integer equal to or greater than 0. In the following, unless otherwise specified, each sampling time t _k will be regarded as the same as its index k, and will also be represented as y(k), u(k), and v(k).

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. As the plant response model, various models represented by a plant response function S _θ can be adopted, but in the following, a polynomial model such as an ARMA model (Autoregressive Moving Average Model) is mainly assumed. When the plant response model is a polynomial model such as an ARMA model, the model parameter θ is a vector having coefficients of the polynomial as elements. It goes without saying that various models other than the ARMA model can be adopted as the plant response model.

The step response calculation unit 102 calculates an estimate of the step response of the plant at a given time t (hereinafter also referred to as a step response estimate) S _θ (t) by using the model parameter (hereinafter also referred to as a model parameter estimate) θ estimated by the model parameter estimation unit 101. Note that the step response is a controlled variable when a step signal is applied to the plant as a manipulated variable.

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

The buffer unit 111 accumulates (buffers) the controlled variable y(k), the manipulated variable u(k), and the disturbance v(k) in a certain predetermined period in the memory device 16. The state vector conversion unit 112 resamples the controlled variable y(k), the manipulated variable u(k), and the disturbance v(k) buffered in the memory device 16 to create a vector called a state vector. The sequential estimation calculation unit 113 estimates model parameters of the plant response model by the RLS method using the state vector. The stabilization model parameter calculation unit 114 calculates the stabilization model parameters from the model parameters. The stabilization model parameters are vectors in which the model parameters are stabilized by certain statistics (for example, the average value of the autoregressive coefficients, the average value of the moving average coefficients, etc.). Hereinafter, the stabilization model parameters are represented as θ _S , and the stabilization model parameters at the sampling time t _k are represented as θ _S (k).

<Example of 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) stores the control amount y from k- _B1 to k, the manipulated variable buffer U(k) stores the manipulated variable u from k- _B2 to k, and the disturbance buffer V(k) stores the disturbance v from k- _B3 to k. Here, _B1 , _B2 , and _B3 are each integers equal to or greater than 0, and are parameters that determine the sizes of the control amount buffer, the manipulated variable buffer, and the disturbance buffer. The values of _B1 , _B2 , and _B3 are determined appropriately depending on the size of the memory device 16, etc.

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).

<Example of 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ＡＲＭＡ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＋１、Ｌは外乱ｖに関する項の係数の数＋１）である。また、再サンプリング制御量ベクトルＹ_Ｄ（ｋ）ではＡＲＭＡ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 ARMA model, and M is the number of coefficients of the term related to the manipulated variable u). number + 1, L is the number of coefficients of the term related to the disturbance v + 1). 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), following the ARMA model.

In general, larger values of N, M, and L allow for more diverse expressions and are expected to enable more accurate prediction of plant response, but they require more computational resources and memory to estimate the model parameter θ.

Then, the state vector conversion unit 112 creates a state vector ξ(k) from the resampled control amount vector Y _D (k), the resampled manipulated variable vector U _D (k), and the resampled disturbance vector V _D (k) as follows.

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）の要素を持つベクトルのことである。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。

That is, the state vector ξ(k) is a vector having elements Y _D (k), U _D (k), and V _D (k). 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).

<Example of Operation of Sequential Estimation Calculation Unit 113>
When the state vector ξ(k) is generated, the recursive estimation calculation unit 113 uses the state vector ξ(k) to estimate the value of the model parameter θ. That is, the recursive estimation calculation unit 113 recursively estimates the value of the model parameter θ for each sampling time t _k .

The process of estimating the value of the model parameter θ with respect to a certain k will be explained with reference to FIG. Note that, hereinafter, the model parameter θ or its estimated value at the sampling time _tk will also be expressed as θ(k).

Step S101: First, the sequential estimation calculation unit 113 determines whether to initialize the model parameter θ 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=0), and when an initialization instruction is given by a user or the like.

If it is determined that the model parameters θ and the covariance matrix P are to be initialized (YES in step S101), the sequential estimation calculation unit 113 proceeds to step S102. On the other hand, if it is determined that the model parameters θ and the covariance matrix P are not to be initialized (NO in step S101), the sequential estimation calculation unit 113 proceeds to step S103.

Step S102: The recursive estimation calculation unit 113 initializes an index k of a sampling time _tk to k=0, and also initializes θ(0)= _θ0 and P(0)=I, where _θ0 is a preset initial value of a model parameter, and I is a preset arbitrary matrix (e.g., a unit matrix, etc.).

Step S103: The sequential estimation calculation unit 113 calls the stabilization model parameter calculation unit 114 to calculate the stabilization model parameter θ _S (k−1). Note that a method for calculating the stabilizing model parameter θ _S (k−1) will be described later.

Step S104: The sequential estimation calculation unit 113 sets the stabilized model parameter θ _S (k−1) to the model parameter estimated value θ(k−1). That is, the sequential estimation calculation unit 113 sets θ(k-1)←θ _S (k-1). This can also be said to be converting the model parameter estimate θ(k-1) into a stabilized model parameter θ _S (k-1).

Step S105: The sequential estimation calculation unit 113 calculates the prediction error ε(k) using the model parameter estimate θ(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) ^T θ(k−1), where T represents the transpose.

Step S106: 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 satisfying 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 more rapidly the influence of past data decreases, and the closer it is to 1, the more the influence of past data is retained.

Step S107: Then, the sequential estimation calculation unit 113 updates the model parameter estimate θ(k-1) as follows to obtain the model parameter estimate θ(k).

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

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

<Example of Operation of Stabilization Model Parameter Calculation Unit 114>
The stabilization model parameter calculation unit 114 calculates the stabilization model parameter θ _S (k-1) when called by the sequential estimation calculation unit 113. That is, every time the stabilization model parameter calculation unit 114 is called by the sequential estimation calculation unit 113 at sampling time t _k , it calculates the stabilization model parameter θ _S (k-1) from the model parameter estimate value θ(k-1).

The process by which the stabilized model parameter calculation unit 114 calculates the stabilized model parameters when called by the sequential estimation calculation unit 113 at a certain sampling time _tk will be described with reference to FIG. However, below, as an example, the following ARMA model is assumed as the plant response model.

y(k)=a ₁ y(k-1)+...+a _N y(k-N)+b ₀ u(k)+...+b _M u(k-M)
Further, at this time, the model parameter estimated value θ(k-1) is expressed as follows.

θ(k−1)=[a ₁ , . . . , a _N , b ₀ , . . . , b _M ] ^T
Here, N is the order of the controlled variable y, and M is the order of the manipulated variable u. That is, the above plant response model is an (N, M)-th order ARMA model. Note that a ₁ , ..., a _N are also called autoregressive coefficients, and N is also called the order of the autoregressive coefficients. Also, b ₀ , ..., b _M are also called moving average coefficients, and M is also called the order of the moving average coefficients.

Step S201: First, the stabilization model parameter calculation unit 114 calculates the centroid parameter θ _c . The stabilization model parameter calculation unit 114 calculates the centroid a _c of the autoregressive coefficients a ₁ , ..., a _N and the centroid b c of the moving average coefficients b ₀ , ..., b _M , and then replaces each autoregressive _coefficient of the model parameter estimate θ(k-1) with the centroid a _c and each moving average coefficient with the centroid b _c to obtain the centroid parameter θ _c . That is, the centroid parameter θ _c is expressed as follows.

θ _c = [ _ac , ..., a _c , b _c , ..., b _c ] ^T
Here, a _c =(a ₁ +...+a _N )/N, and b _c =(b ₀ ,..., b _M )/(M+1).

Step S202: Next, the stabilized model parameter calculation unit 114 calculates parameters that are candidates for stabilized model parameters (hereinafter also referred to as candidate parameters). The stabilized model parameter calculation unit 114 calculates the candidate parameter θ _r as follows.

_θr = (1-β) × θ(k-1) + β × _θc
Here, β is a blending coefficient that satisfies 0<β≦1 and is a preset value. As the blending coefficient β approaches 1, the candidate parameter _θr approaches the centroid parameter _θc , and as the blending coefficient β approaches 0, the candidate parameter _θr approaches the model parameter estimate θ(k−1).

Step S203: Next, the stabilized model parameter calculation unit 114 calculates two types of prediction errors. That is, the stabilized model parameter calculation unit 114 calculates the prediction error e ₀ when using the model parameter estimate θ(k-1) and the prediction error e _r when using the candidate parameter θ _r , respectively, as follows. calculate.

e ₀ =y ₀ -ξ(k) ^Τ θ(k-1)
e _r =y ₀ -ξ(k) ^Τ θ _r
Here, y ₀ is the current value of the controlled variable, ie, y ₀ =y(k). Moreover, ξ(k) is a state vector. That is, e ₀ represents the error between the predicted value of the controlled variable when using the model parameter estimated value θ(k-1) and the current controlled variable value. Similarly, e _r represents the error between the predicted value of the control amount when using the candidate parameter θ _r and the current value of the control amount.

Step S204: Next, the stabilization model parameter calculation unit 114 compares the absolute value of the prediction error e ₀ with the absolute value of the prediction error e _r . For example, the stabilization model parameter calculation unit 114 compares the absolute value of the prediction error e ₀ with the absolute value of the prediction error e _r , and determines whether the following is satisfied:

｜e _r ｜＜α｜e ₀ ｜
Here, α is a comparison coefficient satisfying 0<α≦1, and is a preset value. The comparison coefficient α controls how strictly the prediction error e _r is evaluated when using the candidate parameter θ _r , and the closer it is to 0, the better the prediction error e _r is improved relative to the prediction error e _0. It is required to be conspicuous.

As a result of the above comparison, if |e _r |<α|e ₀ | is satisfied, the stabilization model parameter calculation unit 114 proceeds to step S205. On the other hand, if |e _r |<α|e ₀ | is not satisfied (i.e., if |e _r |≧α|e ₀ | is satisfied), the stabilization model parameter calculation unit 114 proceeds to step S206.

Step S205: If |e _r |<α|e ₀ | is satisfied, the stabilized model parameter calculation unit 114 sets the candidate parameter θ _r to the stabilized model parameter θ _S (k−1). That is, the stabilized model parameter calculation unit 114 sets θ _S (k−1)←θ _r .

Step S206: If |e _r |<α|e ₀ | is not satisfied, the stabilization model parameter calculation unit 114 sets the model parameter estimate value θ(k-1) as the stabilization model parameter θ _S (k-1). That is, the stabilization model parameter calculation unit 114 sets θ _S (k-1)←θ(k-1).

Note that although the above description does not take into account disturbances as an example, it goes without saying that the same application is possible even when disturbances exist. When considering disturbance, for example, a moving average model regarding the disturbance is added to the ARMA model, and as a result, an autoregressive coefficient regarding the disturbance is added to the model parameters.

In the above, as an example, the average value of the autoregressive coefficients a ₁ , ..., a _N is a _c , and the average value of the moving average coefficients b ₀ , ..., b _M is b _c , but this is not limited to the above. Any statistic that can be calculated from the autoregressive coefficients a ₁ , ..., a _N can be used as a _c . Similarly, any statistic that can be calculated from the moving average coefficients b ₀ , ..., b _M can be used as b _c . More generally, any statistic that can be calculated from the coefficients in the dimensional direction can be used for each dimension. Examples of such statistics include the average, as well as the weighted average, the median, the mode, and the like.

<Example of Operation of Step Response Calculation Unit 102>
Hereinafter, the model parameter estimate value θ=θ(k) used for estimating the step response (i.e., the model parameter estimate value set in the plant response function _Sθ ) is also referred to as the “model parameter set value θ.” In addition, in the following, for simplicity, a unit step signal is assumed as the step signal.

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

A process for calculating a 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 following ARMA model is assumed as a plant response model as an example.

y(k') = a ₁ y(k'-1) + ... + a _N y(k'-N) + b ₀ u(k') + ... + b _M u(k'-M)
In addition, in this case, the state vector φ(k′) at index k′ is expressed as follows.

φ(k') = [y(k'-1), y(k'-2), ..., y(k'-N), u(k'), u(k'-1), . ..., u(k'-M)] ^T
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 .

φ(0)=[0,0,...,0,1,0,...,0] ^Τ
That is, the state vector φ(0) is initialized so that only u(0) is 1 and the other elements are 0. This represents the initial value when simulating a unit step response.

Step S302: Next, the step response calculation unit 102 calculates a controlled variable prediction value y(k') by y(k')=φ(k') ^T θ.

Step S303: Next, the step response calculation unit 102 converts the state vector φ(k') into the state vector φ(k'+1) at the next index k'+1 using the predicted control amount value y(k'). Update to. At this time, 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 sets y(k' -N+1) to y(k'-1) are set to the same values as the state vector φ(k'). 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.

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

Step S305: Next, 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 process. As a result, the finally calculated controlled variable prediction value y(k′) is obtained as the unit step response S _θ (t) (i.e., S _θ (t)=y(k) is obtained as the unit step response of the plant response model).

[Second embodiment]
The second embodiment will be described below. In the second embodiment, model parameters including an offset term representing the steady state of a plant to be controlled are targeted. Note that for model parameters including an offset term representing the steady state of the plant and related techniques, please refer to, for example, the above-mentioned Patent Document 3.

Specifically, in the second embodiment, an ARMAX model (Autoregressive Moving Average Model with Exogenous Variables) including the following offset terms is assumed as a plant response model.

y(k) = a ₁ y(k-1) + ... + a _N y(k-N) + b ₀ u(k) + ... + b _M u(k-M) + c ₀
where c ₀ is the offset term.

At this time, the model parameter (and its estimated value) θ can be expanded to the model parameter expressed below.

θ _e = [a ₁ , ..., a _N , b ₀ , ..., b _M , c ₀ ] ^T
This model parameter (and its estimated value) θ _e is also called the “augmented model parameter”.

Note that in the second embodiment, the differences from the first embodiment will be mainly described, and descriptions of the parts that may be the same as in the first embodiment will be omitted.

<Example of functional configuration of plant response estimation device 10>
FIG. 8 shows an example of the functional configuration of the plant response estimation device 10 according to this embodiment. As shown in FIG. 8, the plant response estimation device 10 according to the present embodiment differs from the first embodiment in that a parameter conversion section 115 is included in the model parameter estimation section 101.

The parameter conversion unit 115 converts the expanded model parameter θ _e into a model parameter θ.

<Example of operation of state vector conversion unit 112>
The state vector conversion unit 112 differs from the first embodiment in that it creates a vector called an expanded state vector, which is an expanded state vector. Other points may be the same as the first embodiment.

The expanded state vector is obtained by expanding the state vector ξ(k) by adding an element corresponding to the offset term, and is expressed as follows.

最後の要素「１」がオフセット項に対応する要素である。

The last element "1" is the element corresponding to the offset term.

<Example of Operation of Sequential Estimation Calculation Unit 113>
The recursive estimation calculation unit 113 differs from the first embodiment in that it uses an expanded model parameter _θe instead of the model parameter θ, and uses an expanded state vector _ξe (k) instead of the state vector ξ(k).

<Example of operation of stabilization model parameter calculation unit 114>
The stabilized model parameter calculation unit 114 uses the expanded model parameter θ _e instead of the model parameter θ, and uses the expanded state vector ξ _e (k) instead of the state vector ξ (k) in the first embodiment. different from. Other points may be the same as the first embodiment.

It should be noted that the offset term is not subject to replacement when calculating the centroidization parameter θ _c in step S201 above. That is, when the model parameter estimate θ(k-1) is θ _e (k-1)=[a ₁ ,..., a _N , b ₀ ,..., b _M , c ₀ ] ^T , The centroiding parameter θ _c becomes θ _c =[ _ac , . . . , _ac , b _c , . . . , b _c , c ₀ ] ^T.

<Example of Operation of Parameter Conversion Unit 115>
Hereinafter, as an example, the augmented model parameter estimate θ _e (k) is expressed as follows:

_θe (k)=[ _θY (k), _θU (k), _θV (k), _θC (k)] ^T
Here, _θY (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 _tk , _θU (k) is an M-dimensional vector whose elements are the coefficients of the term related to the manipulated variable u, _θV (k) is an L-dimensional vector whose elements are the coefficients of the term related to the disturbance v, and _θC (k) is a scalar value representing the offset term.

In this case, when the parameter conversion unit 115 obtains the augmented model parameter estimate θ _e (k), it converts it into a vector excluding θ _C (k) as shown in Fig. 9 to obtain the model parameter estimate θ(k). As a result, the following model parameter estimate is obtained.

θ(k)=[θ _Y (k), θ _U (k), θ _V (k)] ^Τ
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). The reason for this is that, as described in Patent Document 1, the offset term does not affect the amount of change in the control amount y.

[Example]
An example will be described below. In this example, model parameters and a step response are estimated by the plant response estimation device 10 according to the second embodiment.

The following ARMAX model was adopted as the plant response model for the plant to be controlled.

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, an ARMAX model having a two-dimensional element related to the controlled amount y, a three-dimensional element related to the manipulated variable u, and an offset term was adopted.

In this case, the extended state vector ξ _e (k) is expressed as follows.

ξ _e (k) = [y (k-1), y (k-2), u (k), u (k-1), u (k-2), 1] ^T
Moreover, the enlarged model parameter θ _e is expressed as follows.

θ _e (k) = [a ₁ (k), a ₂ (k), b ₀ (k), b ₁ (k), b ₂ (k), c ₀ (k)] ^Τ
The predicted value of the control amount (hereinafter also referred to as y _est ) is expressed as follows.

y _est (k)=ξ _e (k) ^Τ θ _e (k-1)
Here, it is assumed that the step response of the plant to be controlled in this embodiment is as shown in FIG. Note that r represents the target value, y represents the controlled amount, u represents the manipulated amount, and v represents the disturbance. Further, in this embodiment, the resampling period D=2, the forgetting coefficient λ=0.999, and the comparison coefficient α=0.9.

In this embodiment, two pieces of data (data 1 and data 2 described below) were used to estimate the model parameters and step response.

When data 1 is used Data 1 obtained by controlling the controlled plant by PID control is shown in FIG. 11. In this case, the result of estimating the model parameters without using the stabilization model parameter calculation unit 114 and the control result of the model predictive control are shown in FIG. 12 and FIG. 13, respectively. Also, the result of estimating the model parameters by the plant response estimation device 10 according to the second embodiment and the control result of the model predictive control are shown in FIG. 14 and FIG. 15, respectively. In FIG. 12 and FIG. 14, the model parameters a ₁ , a ₂ , b ₀ , b ₁ , and b ₂ are shown in time series. Comparing FIG. 12 (without the stabilization model parameter calculation unit 114) with FIG. 14 (with the stabilization model parameter calculation unit 114), it can be seen that the autoregressive coefficients a ₁ and a ₂ are closer to the center of gravity in the case with the stabilization model parameter calculation unit 114, and the moving average coefficients b ₀ , b ₁ , and b ₂ are closer to the center of gravity in the case with the stabilization model parameter calculation unit 114. On the other hand, when comparing FIG. 13 (without the stabilization model parameter calculation unit 114) with FIG. 15 (with the stabilization model parameter calculation unit 114), it is found that there is no significant difference, and that the stabilization model parameter calculation unit 114 does not cause any degradation in control performance.

- When using data 2 Data 2 obtained by controlling the plant to be controlled using PID control is shown in FIG. 16. In data 2, observation noise is added to the controlled variable y, and as a result, noise is also added to the manipulated variable u. Note that the conditions for data 1 and data 2 are the same except for the influence of noise. At this time, the results of estimating the model parameters without using the stabilizing model parameter calculation unit 114 and the control results of the model predictive control are shown in FIGS. 17 and 18, respectively. Further, the results of estimating model parameters by the plant response estimating device 10 according to the second embodiment and the control results of model predictive control are shown in FIGS. 19 and 20, respectively. In FIGS. 17 and 19, model parameters a ₁ , a ₂ , b ₀ , b ₁ , and b ₂ are shown in time series. Comparing FIG. 17 (without the stabilizing model parameter calculating section 114) and FIG. 19 (with the stabilizing model parameter calculating section 114), the autoregressive coefficients a ₁ and a ₂ are better with the stabilizing model parameter calculating section 114. It can be seen that the moving average coefficients b ₀ , b ₁ , and b ₂ are closer to the center of gravity when the stabilizing model parameter calculation unit 114 is present. Furthermore, in the case without the stabilizing model parameter calculation unit 114 (FIG. 17), the autoregressive coefficients a ₁ and a ₂ gradually become values that are far apart from each other, but in the case with the stabilization model parameter calculation unit 114 ( In Fig. 19), it can be seen that the movement can be suppressed. That is, in the noisy data 2, the autoregressive coefficient and the moving average coefficient are estimated to be values far from the center of gravity due to the noise, but the stabilization model parameter calculation unit 114 can suppress the movement away from the center of gravity.

On the other hand, comparing FIG. 18 (without the stabilization model parameter calculation unit 114) with FIG. 20 (with the stabilization model parameter calculation unit 114), the manipulated variable u changes relatively sharply in FIG. 18. In contrast, in FIG. 20, there are fewer sharp changes like those described above, and the result is relatively similar to the response waveform of the control result for noise-free data 1 (FIG. 15). Therefore, it can be said that the stabilization model parameter calculation unit 114 suppresses the effects of noise and contributes to the stabilization of model predictive control.

[summary]
As described above, the plant response estimation device 10 according to the first and second embodiments can stably estimate the model parameters of the plant response model from the operation data of the plant during operation. That is, since the centering parameter exerts a force on the estimation of the model parameters in the center of gravity direction, it is possible to suppress, for example, a movement in which _a1 and _a2 gradually become values farther apart from each other (i.e., a movement in which the model parameters diverge) as shown in FIG. 17, and as a result, it is possible to stably estimate the model parameters. This ensures the reliability of the model parameter estimates even in the middle stage until the convergence to the true value, and the first problem described above is solved. Therefore, according to the plant response estimation device 10 according to the first and second embodiments, it is possible to easily use the estimated model parameters for control (e.g., model predictive control).

In addition, in the plant response estimation device 10 according to the first and second embodiments, even if the order of the model parameters is unknown and an order higher than necessary is set, a force acts to estimate the model parameters in the direction of the center of gravity, making it easier to estimate model parameters close to the center of gravity, and making it possible to avoid problems resulting from high orders such as multicollinearity. This solves the second problem mentioned above.

Furthermore, in the plant response estimation device 10 according to the first and second embodiments, the stabilization model parameter calculation unit 114 compares the prediction error when the current model parameters are used with the prediction error when the candidate parameters are used, and adopts the candidate parameters as stabilization model parameters only if the prediction accuracy improves. Therefore, an improvement in prediction accuracy can also be expected.

In addition, in the plant response estimation device 10 according to the first and second embodiments, the model parameter estimates are stable even in the presence of noise in the observed values, making it possible to perform estimation with the effects of noise suppressed.

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 Sequential estimation calculation section 114 Stabilized model parameter calculation section 115 Parameter conversion section

Claims (8)

an estimation calculation unit configured to sequentially calculate, based on operation data of a controlled plant, estimates of model parameters, which are parameters of a function representing a plant response model of the controlled plant;
a stabilization calculation unit configured to calculate stabilized model parameters by stabilizing the estimates of the model parameters;
a response calculation unit configured to calculate a response of the controlled plant using a function representing the plant response model based on the estimated values of the model parameters;
having
The estimation calculation unit is
a plant response estimation device configured to calculate an estimate of the model parameter based on the operation data and a stabilized model parameter obtained by stabilizing a previously calculated estimate of the model parameter by the stabilization calculation unit. The stabilization calculation unit
2. The plant response estimation device according to claim 1, configured to calculate a predetermined statistic from each element of a vector representing the estimated value of the model parameter, and to calculate a stabilized model parameter by stabilizing the estimated value of the model parameter using the statistic. the plant response model is a polynomial model;
The stabilization calculation unit
calculating the statistics from elements in the dimension direction among the elements of a vector representing the estimated values of the model parameters for each dimension of the polynomial model;
calculating a first parameter by replacing an element in the dimension direction with the statistic for each dimension;
Calculating second parameters by mixing the first parameters and the model parameters in a predetermined ratio;
3. The plant response estimation device according to claim 2, configured to: when a first prediction error when predicting a response of the controlled plant using the second parameter is improved by a predetermined amount or more than a second prediction error when predicting a response of the controlled plant using the model parameter, the second parameter is set as the stabilization model parameter; and when the first prediction error is not improved by the predetermined amount or more than the second prediction error, the model parameter is set as the stabilization model parameter. the polynomial model is an ARMA model or an ARMAX model;
4. The plant response estimation device according to claim 3, wherein the model parameters are expressed as vectors having coefficients of the ARMA model or the ARMAX model as elements. The stabilization calculation section includes:
Calculating a first centroid representing the average value of the autoregressive coefficient of the ARMA model or ARMAX model and a second centroid representing the average value of the moving average coefficient of the ARMA model or ARMAX model as the statistic,
5. The second parameter is calculated by replacing the autoregressive coefficient with the first center of gravity and the moving average coefficient with the second center of gravity, respectively. Plant response estimation device. The plant response estimation device according to claim 4 or 5, wherein the ARMA model or the ARMAX model includes an offset term that represents a steady state of the controlled plant. an estimation calculation procedure for sequentially calculating estimated values of model parameters, which are parameters of a function representing a plant response model of a controlled plant, based on operation data of the controlled plant;
a stabilization calculation step for calculating stabilized model parameters by stabilizing the estimated values of the model parameters;
a response calculation step of calculating a response of the controlled plant using a function representing the plant response model based on the estimated values of the model parameters;
The computer executes
The estimation calculation procedure includes:
the plant response estimation method further comprising: calculating an estimated value of the model parameter based on the operating data and a stabilized model parameter obtained by stabilizing an estimated value of a previously calculated model parameter through the stabilization calculation procedure; an estimation calculation procedure for sequentially calculating estimated values of model parameters, which are parameters of a function representing a plant response model of a controlled plant, based on operation data of the controlled plant;
a stabilization calculation step for calculating stabilized model parameters by stabilizing the estimated values of the model parameters;
a response calculation step of calculating a response of the controlled plant using a function representing the plant response model based on the estimated values of the model parameters;
Run the following on your computer:
The estimation calculation procedure includes:
a program for calculating an estimated value of the model parameter based on the operating data and a stabilized model parameter obtained by stabilizing an estimated value of a previously calculated model parameter through the stabilization calculation procedure;

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