JPH07191709A - Parameter setting method for model estimating control - Google Patents

Abstract

PURPOSE:To prevent the control calculation from being numerically unstable by setting the parameter of a model so as to set the weighing sum of the square sum of the deviation between an estimated value and the target value at a future time and the square sum of the changing part of a manipulated variable to be minimum based on the model of a process. CONSTITUTION:When the parameter inputted to a parameter changing part 1 is confirmed, an estimating expression deciding part 2 decides the estimating expression of the model from the parameter. An estimating arithmetic part 3 executes arithmetic based on the estimating expression of the model decided by the estimating expression deciding part 2. The estimating arithmetic part 3 is composed of a conditional number arithmetic part 4 calculating the conditional number of <tau>GG+lambdaI which needs to obtain a retrograde train from the estimating expression, a judgement part 5 judging whether the conditional number is within an allowable range or not, and a correction part 6 correcting a weighing coefficient lambda when it is not within the allowable range. When the conditional number is within the allowable range, the changed amount DELTAU of the manipulated variable setting an evaluation function J to be minimum is obtained by using the present lambda as it is, and outputted.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a model predictive control parameter setting method used for process control of a chemical plant or the like.

[0002]

2. Description of the Related Art In model predictive control, generally, a model of a process is created, a predicted value of a process control amount at a future time is calculated based on the model, and a deviation between the predicted value and a target value at the future time is calculated. This is a control method in which the sum of squares of and the sum of squares of the variation of the manipulated variable is used as an evaluation function, and the manipulated variable is determined so that this evaluation function is minimized.

[0003]

In the model predictive control as described above, the parameters to be set have many process models, various weights of evaluation functions and their types, and their intuitive meanings are not always clear. For example, if the weights of the evaluation function have different absolute values, the same operation amount is calculated if the ratio between the weights is the same. In some cases, if an unrelated control amount-manipulation amount pair is incorporated into the evaluation function, the control algorithm itself may become unstable.

An object of the present invention is to automatically correct a certain type of parameter (weighting coefficient for change in manipulated variable) so that the system does not become unstable when changed to another parameter. The object of the present invention is to provide a parameter setting method for model predictive control that can reduce the load on the model.

[0005]

In order to achieve the above object, the present invention obtains a predicted value of a process control amount at a future time based on a model of a process, and the predicted value and a target value at the future time. In the parameter setting method of the model predictive control, the sum of squares of the deviation of and the sum of squares of changes in the manipulated variables is used as an evaluation function, and the manipulated variables are determined so that this evaluation function is minimized. , When the predicted value of the controlled variable when the manipulated variable by the model is changed at the time of changing the parameter is calculated by the evaluation function, the condition number of the matrix for which it is necessary to calculate the inverse matrix to be used for the control calculation is checked, and this value is determined The weight applied to the squared portion of the operation amount is corrected so as to fall within the range of.

[0006]

The above-described model predictive control parameter setting method can have the following effects.

In order to simplify the description, a case where the control amount is 1 and the operation amount is 1 will be described as an example. First, in the model predictive control, the control amount at the next time is determined so that the evaluation function J according to the equation (1) becomes the minimum.

[0008]

[Equation 1] Here, y is a control amount, γ is a target value, u is an operation amount, and Δu is a change amount of the operation amount. Also, ya is a predicted value of y. λ is a weighting coefficient, which is one of tuning parameters.

[0009]

[Equation 2] When expressed in the form of a vector and the like, using a linear model and a prediction method, the prediction is generally given in the form of Ya = GΔU + Y ₀ (2).

However, G is a matrix, ΔU is a future operation amount, and Y
₀ is a predicted value obtained from past observation values. Where G
Assuming that is the model used for prediction, it does not change over time unless the model is changed. Y ₀ is determined by the model used for prediction, the prediction method, and the value of the control amount from the past to the present time. Substituting the equation (2) into the equation (1), J = ^t (GΔu + Y ₀ −γ) (GΔU + Y ₀ −γ) + λ
^t ΔU · Δu, and ΔU that minimizes J is obtained by ΔU = ( ^t GG + λI) ^−1t G (γ−Y ₀ ). Alternatively, it can be obtained by solving a linear simultaneous equation of ( ^t GG + λI) ΔU = ^t G (γ−Y ₀ ).

On the other hand, in general, the numerical ease of solving the linear simultaneous equation Y = AX is the condition number of A (= σmax / σmin, where σmax is the maximum singular value of A and σmin is the minimum singular value of A).
It is known that the equation is ill condition as the number of conditions increases.

Therefore, the condition number of ^t GG + λI-which is λ
It is possible to avoid numerical instability of the control operation when the model etc. is changed by examining the function of and the correction of λ so that it is below a certain level.

[0013]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the present invention will be described below with reference to the drawings.

FIG. 1 is a block diagram for explaining a parameter setting method for model predictive control according to the present invention. In FIG. 1, reference numeral 1 denotes a parameter changing unit for inputting a weighting coefficient λ, constants a ₁ , a ₂ , ... For changing a parameter of a model, and 2 denotes a parameter inputted to the parameter changing unit 1. Prediction formula determining unit 3 that determines the prediction formula of the model from the parameter and its parameter are prediction calculation units that execute calculations based on the prediction formula of the model determined by the prediction formula determining unit 2.

The prediction calculation unit 3 needs to obtain an inverse matrix from the prediction formula determined by the prediction formula determination unit 2 ^t GG + λ.
The condition number calculation unit 4 that calculates the condition number of I, the determination unit 5 that determines whether or not the condition number obtained by the condition number calculation unit 4 is within an allowable range, and the condition number is allowed by the determination unit 5. If it is determined that the weight does not fall within the range, the weighting coefficient λ
Is modified and input to the parameter changing unit 1.

In this case, when the judging unit 5 judges that the condition number is within the allowable range, the current λ is used as it is and the evaluation amount J is calculated by the operation amount calculating unit (not shown).
The change amount ΔU of the operation amount that minimizes is calculated and output.

Next, the operation based on the above configuration will be described with reference to FIGS.

Now, for example, as shown in FIG.
Consider a system of two operation outputs and one control variable that feeds back a controlled variable y of 0 to the controller 10 to supply two manipulated variables u ₁ and u ₂ to the plant 20.

In this case, the following equation is given as an evaluation equation.

J = (ya (t + 1) -γ) ² + λ {Δu
₁ (t + 1) ² + Δu ₂ (t + 1) ² } (a) where ya is a predicted control amount, γ is a target value, λ is a tuning parameter, and Δu ₁ and Δu ₂ are changes in the predicted manipulated variable. .

If a variable unrelated to the plant 20 is selected as the manipulated variable u ₂ , its prediction is

[0022]

[Equation 3] It becomes the form. At this time, if λ is further set to 0, Δu ₁ (t + 1), Δu which minimizes the equation (a).
₂ (t + 1) can be obtained by solving the following equation.

[0023]

[Equation 4] However, this solution becomes indefinite, and the condition number at this time becomes ∞.

Therefore, if this λ is set to a value other than 0, (a)
The solution that minimizes the equation is

[0025]

[Equation 5] Then, the condition number is (a ₁ ² + λ) / λ << ∞, and at this time, the equation (c) can be easily solved, and Δu ₁ (t + 1) = a ₁ (γ-y ₀ ) / (a ₁ ² + λ) Δu ₂ (t + 1) = 0, which gives a very reasonable result of not moving irrelevant variables.

FIG. 3 is a flow chart showing the parameter setting procedure of the model predictive control described above.
When the weighting factor λ and the constants a ₁ , a ₂ ... Are input as parameters, the parameters are displayed in step S1 and the prediction formula for predictive control is obtained using the parameters in step S2. Next, in step S3, a part of the equation is obtained by performing optimization calculation from the prediction equation, and in step S4, ^t GG + λI for which an inverse matrix needs to be obtained is obtained,
The condition number is calculated at 5. Then, the magnitude of the condition number is determined in step S6, and if the condition number is small, the equation is used as it is, and the change amount of the manipulated variable is obtained and output in step S8.

If it is determined in step S6 that the condition number is large, the weighting coefficient λ is slightly increased in step S7 and the same process as described above is repeated until the condition number becomes small.

By adopting such a parameter setting method, when the parameter change by the operator does not cause the instability of the control calculation, the value is used as it is, and if the operator mistakenly sets it to an irrelevant value. In such a case, the system is automatically corrected so as not to become unstable, so that it is possible to avoid the situation where the control calculation becomes unstable and a value that is unexpectedly calculated is calculated.

[0029]

As described above, according to the present invention, it is possible to avoid numerical instability of the control calculation when the parameters of the model etc. are changed. It is possible to provide a parameter setting method for model predictive control that can reduce the load on the system to some extent.

[Brief description of drawings]

FIG. 1 is a block circuit diagram for explaining an embodiment of a parameter setting method for model prediction control according to the present invention.

FIG. 2 is a diagram showing a control system for explaining the operation of the embodiment.

FIG. 3 is a flowchart showing a parameter setting procedure of the embodiment.

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 1 ... Parameter change part, 2 ... Prediction formula determination part, 3 ... Prediction calculation part, 4 ... Condition number calculation part, 5 ... Condition number determination part, 6 ... lambda
Correction department.

Claims (1)

[Claims] 1. A predicted value of a process control variable at a future time is obtained based on a process model, and a sum of squares of deviations between the predicted value and a target value at a future time and a change amount of the manipulated variable are calculated. In the parameter setting method of model predictive control in which the sum of weights and the sum of weights is used as the evaluation function, and the operation amount is determined so that this evaluation function is minimized, the control amount when the operation amount by the model is changed when the parameter is changed. When the predicted value of is calculated by the evaluation function, the condition number of the matrix for which it is necessary to calculate the inverse matrix to be used for the control calculation is examined, and the weight applied to the square part of the manipulated variable so that this value falls within a predetermined range. A method of setting parameters for model predictive control, characterized by: