JP5450121B2 - Model predictive control device and program - Google Patents

Description

  The present invention relates to a technique for predicting a change in a controlled amount based on a process model and changing an operation amount.

  Conventionally, process control that has been performed in industries such as steel, petrochemical, cement, etc., the controlled variable (Process Variable) such as temperature and pressure indicating the state of the process is a predetermined target value (Set point Variable) This is done by automatically adjusting the manipulated variable of the valve or the like. In such an automatic control system, a control method generally referred to as PID control is used. However, when it is necessary to control multivariate simultaneously or when it is necessary to predict the state of a process with a long dead time. The advanced control method called Model Predictive Control is widely applied.

  For example, Patent Document 1 discloses a multivariable model predictive control system. In this multivariable model predictive control system, a control value target value SV for controlling the output of the plant from the outside, the current control value PV, and “SV-PV” calculated by the calculator are input, and the plant is sent from the inside to the plant. The past manipulated variable MV and disturbance DV are input, and data for each control time step is output to the neuro model unit. Based on this output value, the neuro model unit outputs a predicted value of each control amount change to the sensitivity calculation unit. Based on this output value, the sensitivity calculator calculates the sensitivity of the predicted value for each manipulated variable and outputs it to the optimization calculator. Based on this output value, the optimization calculation unit outputs the operation amount MV obtained by performing the optimization calculation of the control amount and the operation amount to the plant and the data processing unit.

JP 2002-157003 A

Jan M. Maciejowski, Shuichi Adachi, Translated by Masaaki Kanno, “Optimum control under model predictive control constraints”, Tokyo Denki University Press Iori Hashimoto, Shinji Hasebe, Manabu Kano, “Process Control Engineering”, pp.131-149, Asakura Shoten

  However, in the above-mentioned conventional technology, it corresponds to the control target “I want to make the control amount close to the target value”, and “I want to make the control amount equal to or less than the target value” or “I want to make the control amount as small as possible”. The goal could not be handled easily. Examples of such types of targets include those related to quality standards and costs.

  Here, when it is going to respond to the goal of “I want to make the controlled variable below the target value” using the conventional model predictive control, it seems that it should be incorporated as a constraint condition instead of treating it as a target. However, in this case, if the control amount exceeds the target value due to some disturbance, there is a disadvantage that the constraint condition is not satisfied and the calculation is impossible. In addition, considering the variation, a value less than the target value may be used as the target value of the conventional model predictive control. In this case, when the control amount is less than the target value, an operation for directing the target value is performed. Not only is unnecessary, but also causes a disturbance to the process and causes a decrease in operating efficiency.

  On the other hand, it is conceivable that the target value is set to a level that cannot be realized when the conventional model predictive control is applied to the target of “reducing the control amount as much as possible”. However, there is a problem that it is not clear to what level the target value should be adjusted including the tuning of the control parameter with respect to the control amount that varies depending on the situation.

  The present invention has been made in view of the circumstances as described above. In addition to the goal of setting the control amount as the target value, the control amount is set to be equal to or less than the target value, or the control amount is made as small as possible. An object of the present invention is to provide a model predictive control apparatus and program capable of simultaneously realizing the goal of performing.

  (1) In order to achieve the above object, the present invention takes the following measures. That is, the model predictive control device of the present invention is a model predictive control device that predicts a change in the controlled amount based on the process model and changes the manipulated variable, and uses the prediction formula for the controlled amount, A prediction unit that calculates a predicted value of the change in the controlled amount; a variable indicating an excess of the controlled amount from the calculated predicted value and the target value; or a shortage of the controlled amount from the target value Using the evaluation function including at least one of the variables indicating the control amount, the manipulated variable is determined such that the controlled variable is equal to or less than the target value, and the controlled variable is equal to or greater than the target value. The operation amount is determined, the operation amount is determined so that the controlled amount becomes the target value, and the operation amount is determined so that the controlled amount is minimized, or the controlled amount Determine the amount of operation so that the And the operation amount determination unit, characterized in that it comprises a.

  With this configuration, desired control can be performed not only when the controlled amount is set to the target value, but also when the controlled amount is equal to or less than the target value. In addition, the controlled amount can be minimized or maximized regardless of the target value. As a result, it is possible to achieve at least five kinds of various goals, and these can be used in combination according to the situation.

  (2) A program according to the present invention is a program executed by a model predictive control device that predicts a change in a controlled variable based on a process model and changes a manipulated variable, and predicts the controlled variable. A process for calculating a predicted value of a change in the controlled amount using an equation, a variable indicating an excess of the controlled amount from the calculated predicted value and the target value, or the controlled value from the target value A process for determining the manipulated variable such that the controlled variable is equal to or less than the target value using an evaluation function including at least one of variables indicating a shortage of the quantity, and the controlled variable is equal to or greater than the target value. The operation amount is determined so that the operation amount is determined, the operation amount is determined so that the controlled amount becomes the target value, and the operation amount is determined so that the controlled amount is minimized. Processing or the controlled quantity To maximize, wherein the operation amount and the processing of one of the processing for determining the were a series of processes can read on a computer and can execute commands of.

  With this configuration, desired control can be performed not only when the controlled amount is set to the target value, but also when the controlled amount is equal to or less than the target value. In addition, the controlled amount can be minimized or maximized regardless of the target value. As a result, it is possible to achieve at least five kinds of various goals, and these can be used in combination according to the situation.

  According to the present invention, the manipulated variable is determined using the evaluation function including at least one of the variable indicating the excess of the controlled amount from the target value or the variable indicating the insufficient controlled amount from the target value. Thus, it is possible to realize a target that could not be achieved by the conventional model predictive control, that is, a control amount equal to or less than the target value.

It is a figure which shows a step response coefficient. It is a figure which shows a step response coefficient. It is a block diagram which shows schematic structure of the model prediction control apparatus which concerns on this embodiment.

Next, embodiments according to the present invention will be described with reference to the drawings. In this specification, the typeface of the symbol in the text and the typeface of the symbol in the mathematical formula may be different, but this is merely the typeface and is substantially the same. First, an output prediction method when a step response model is used as a model to be controlled will be described. Consider the output y _m (k + j) at the j-th future sample time point k + j from the current sample time point k. The input Δu (k + i) that entered the control target at time k + i appears as an output a _ji Δu (k + i) at time k + j (j> i). Depending on the input from Δu (−∞) to Δu (k + j−1), the output is expressed as in equation (1).

Here, Δu (k + i) = u (k + i) −u (k + i−1), and a _i (i = 1,..., N,...) Is the step response of the determined sample interval. Coefficient (see FIGS. 1A and 1B).

1A and 1B are diagrams showing step response coefficients. In FIG. 1A and FIG. 1B, the step response is represented as a first-order lag, but depending on the control target, there may be a dead time or an inverse response system. It is only necessary to know the sequence from a ₁ to a _N.

Here, when the time of equation (1) is rewritten separately for the future and past inputs, it is expressed as equation (2).

Also, the current time output is represented by past inputs only as shown in equation (3), and the predicted value of time k + j is expressed as a finite number of inputs as expressed in equation (4) from equations (2) and (3) It can be calculated by value.

It is assumed that a step response model a _i with respect to the operation amount u of the target process has been obtained. Here, the disturbance term d (k + j) that cannot be measured is also added, and the future value of the output is expressed as in equation (5).

Further, if the disturbance in the future is constant as in equation (6) and the value is the difference between the actual measurement value and the predicted value, equation (5) is expressed as equation (7).

When the present time is k and the future to be predicted is from k + 1 to k + P (P ≦ N), the predicted output value is expressed by equation (8).

とステップ応答係数行列に拡張する。これを用いて(8)式を拡張すると多入力多出力系のモデル(9)式が得られる。

Next, consider multiple inputs (q) and multiple outputs (r). Step response coefficient a _i

And the step response coefficient matrix. Using this, the equation (8) is expanded to obtain the model (9) of a multi-input / multi-output system.

とすれば、予測値との偏差ベクトルが計算できる。この偏差を用いて(10)式のような評価関数Ｆを定義する。 The output target value vector is

Then, a deviation vector from the predicted value can be calculated. Using this deviation, an evaluation function F such as equation (10) is defined.

ここで、

Γ^tΓＢ^tＢは、偏差および操作量に係る重み係数であり、この評価関数Ｆを最小にする、

を決定する。また、制約条件を考慮する必要がある場合には、以下のような２次計画問題に変換すればよい。

here,

Γ ^t ΓB ^t B is a weighting factor related to the deviation and the manipulated variable, and minimizes this evaluation function F.

To decide. In addition, when it is necessary to consider the constraint condition, it may be converted into the following quadratic programming problem.

The constraint equation is as follows when considering the upper and lower limits of all manipulated variables.

目標値の上下限を

とする。 Here, I _q is a unit matrix of (q × q), the current target value,

The upper and lower limits of the target value

And

  Here, in such model predictive control, it is not possible to handle the goal of making the controlled variable below the target value. Therefore, a variable representing the difference from the target value is newly introduced and defined as follows.

ここで、

は、目標値からの超過分を表し、

は、目標値からの不足分を表すものである。

を、

以下にしたい場合には、目標からの超過分を最小化するように(10)式の評価関数Ｆを次のようにすれば良い。

here,

Represents the excess from the target value,

Represents the shortage from the target value.

The

When the following is desired, the evaluation function F in the equation (10) may be set as follows so as to minimize the excess from the target.

Similarly, when the control amount is desired to be greater than or equal to the target value, the shortage from the target is minimized.

  In addition, when aiming at a target value as in the past, minimizing both excess and deficiency variables yields the same result as equation (10).

さらに、目標値とは関係なく最小化したい場合には、

Furthermore, if you want to minimize regardless of the target value,

とすればよい。つまり、本発明による定式化によれば、従来と同じタイプの制御目標を含めて５種類の多様な目標に対応でき、これを状況によって任意に組み合わせて使用することが可能になる。 Similarly, if you want to maximize regardless of the target value,

And it is sufficient. That is, according to the formulation according to the present invention, it is possible to deal with five kinds of various targets including control targets of the same type as the conventional one, and it is possible to use them in any combination depending on the situation.

  FIG. 2 is a block diagram showing a schematic configuration of the model predictive control apparatus according to the present embodiment. The model predictive control device 10 predicts a change in the controlled amount based on the process model, and changes the manipulated variable so that the controlled amount matches the target value. The prediction unit 11 calculates the predicted value of the change in the controlled amount using the prediction formula for the controlled amount in the controlled object 13. The operation amount determination unit 12 determines the operation amount using the predicted value and the evaluation function calculated by the prediction unit 11. The manipulated variable determiner 12 determines the manipulated variable by applying the variable indicating the difference between the controlled variable and the target value to the evaluation function as described above. Further, as described above, the operation amount determination unit 12 changes the evaluation function so that the difference is minimized.

[Example]
The raw material blending process in cement production is automatically controlled by manipulating the blending ratio of limestone (general, high grade), clay, shale, iron raw material, and silica so as to become a predetermined blending target. The raw materials used here vary from factory to factory, but in factories where unavoidable raw materials are used, they must be managed manually so as to limit their use within the range that satisfies the restrictions on formulation. There may be.

  Therefore, this embodiment shows a raw material blending control program having a real-time optimization function that always minimizes the cost regardless of the raw material circumstances. Based on the model predictive control (Model Predictive Control) described above, the control method adopts a method of adding not only the conventional blending target but also minimizing the raw material cost to the control target. It is also possible to consider constraints such as alkali and mineral composition (C3A) at the same time.

(1) Formulation target LSF = 95.7 A = 5.0 F = 4.0 R ₂ O ≦ 0.65
(2) Raw material components and unit costs

The following table shows the data used for the calculation.

(3) Optimization function The following table shows an example of optimal formulation. As is apparent from this table, the raw material cost varies depending on the blending even with the same control target. In other words, it can be seen that there is an optimum formulation according to the raw material circumstances. Therefore, if an optimization function is incorporated in the raw material mixing control, even if there is a fluctuation in the components of each raw material, it is possible to always act in the optimum direction, and cost reductions that have been overlooked so far can be expected.

  Note that the present invention can also be implemented by causing a computer to execute a program. That is, the program according to the present invention is a program that is executed by a model predictive control device that predicts a change in the controlled variable based on the process model and changes the manipulated variable. And a process for calculating a predicted value of the change in the controlled amount, a variable indicating an excess of the controlled amount from the calculated predicted value and the target value, or the controlled amount from the target value. Processing for determining the manipulated variable so that the controlled variable is equal to or less than the target value using an evaluation function including at least one of variables indicating a deficit, and the controlled variable is equal to or greater than the target value A process for determining the manipulated variable, a process for determining the manipulated variable so that the controlled variable becomes the target value, a process for determining the manipulated variable so that the controlled variable is minimized, Or the controlled So you maximize, wherein the operation amount and the processing of one of the processing for determining the were a series of processes can read on a computer and can execute commands of.

  With this configuration, desired control can be performed not only when the controlled amount is set to the target value, but also when the controlled amount is equal to or less than the target value. In addition, the controlled amount can be minimized or maximized regardless of the target value. As a result, it is possible to achieve at least five kinds of various goals, and these can be used in combination according to the situation.

  As described above, according to the present embodiment, in addition to the conventional target of “I want to set the control amount as the target value”, “I want to make the control amount to be less than or equal to” or “I want to make the control amount as small as possible”. Goals can be considered simultaneously. For example, the present invention is particularly effective when quality specifications and raw material costs must be considered at the same time.

DESCRIPTION OF SYMBOLS 10 Model prediction control apparatus 11 Prediction part 12 Operation amount determination part 13 Control object

Claims (2)

A model predictive control device that predicts a change in a controlled amount based on a process model and changes an operation amount,
A prediction unit that calculates a predicted value of the change in the controlled amount using the prediction formula for the controlled amount;
Using the evaluation function including a variable indicating an excess of the controlled amount from the calculated predicted value and a target value , determining the manipulated variable so that the controlled amount is equal to or less than the target value;
Using the evaluation function including a variable indicating a shortage of the controlled amount from the calculated predicted value and the target value, determining the manipulated variable to make the controlled amount equal to or greater than the target value;
Using the evaluation function including the calculated predicted value, a variable indicating an excess of the controlled amount from the target value, and a variable indicating an insufficient amount of the controlled amount from the target value, the controlled amount is calculated. Determination of the manipulated variable to be minimized, or
Using the evaluation function including the calculated predicted value, a variable indicating an excess of the controlled amount from the target value, and a variable indicating an insufficient amount of the controlled amount from the target value, the controlled amount is calculated. An operation amount determination unit that performs any one of the determination of the operation amount to be maximized . A program that is executed by a model predictive control device that predicts a change in controlled amount based on a process model and changes an operation amount,
A process of calculating a predicted value of the change in the controlled amount using the control amount prediction formula;
Using the evaluation function including a variable indicating an excess of the controlled amount from the calculated predicted value and a target value , determining the manipulated variable so that the controlled amount is equal to or less than the target value;
Using the evaluation function including a variable indicating a shortage of the controlled amount from the calculated predicted value and the target value, determining the manipulated variable to make the controlled amount equal to or greater than the target value;
Using the evaluation function including the calculated predicted value, a variable indicating an excess of the controlled amount from the target value, and a variable indicating an insufficient amount of the controlled amount from the target value, the controlled amount is calculated. Determination of the manipulated variable to be minimized, or
Using the evaluation function including the calculated predicted value, a variable indicating an excess of the controlled amount from the target value, and a variable indicating an insufficient amount of the controlled amount from the target value, the controlled amount is calculated. A program for causing a computer to execute a series of processes of determining any one of the manipulated variables to be maximized .

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