JP2000105760A - Device for analyzing vector variable block diagram - Google Patents

Abstract

PROBLEM TO BE SOLVED: To make stably and quickly performable the time response calculation of a vector variable block diagram. SOLUTION: The device for analyzing a vector variable block diagram is provided with a terminal means 2 having an input part and a display part and a calculating means 1 for performing input and output processing between it and the terminal means 2. The calculating means 1 is provided with a time response calculating part 8 for performing calculation by virtually inserting a sample holder between a scalar variable part and a vector variable part. Moreover, the calculating means 1 is provided with a block diagram data inputting part 3, pre-processing part 4 before time response calculation, calculation model for vector variable model generating part 5, input variable calculating part 6, calculation model for scalar variable model generating part 7, and output processing part 9.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a time response analyzer for a vector variable block diagram in which vector variables and scalar variables coexist.

[0002]

2. Description of the Related Art In a multivariable control system which optimally controls a plurality of control variables which influence each other in consideration of the relation, a relationship between a control variable Y to be controlled and an operation variable for executing the control is described. That is, the control method is generally described using a vector variable as follows.

[0003]

(Equation 1)

FIG. 8 is an example of a vector variable block diagram of a boiler. The implementation of the control system, estimator of X _A is also necessary, useful to designers Including it representation in block diagram using vector variable as indicated by the multivariable control system of FIG. 8 It is. The present invention calls this a vector variable model. In a vector variable model, a control system is expressed using so-called linear operation elements such as addition and subtraction of a vector variable, and a product of a vector variable, a constant matrix, and a vector variable.

On the other hand, the dynamic behavior of the boiler to be controlled in FIG. 8 includes an energy balance equation, a continuous equation, a momentum conservation equation,
It is expressed by a vapor state formula. In an actual analysis, components such as a furnace and a superheater are divided in a steam flow direction, and four equations are simultaneously established for each section. In such a model, the number of variables is large, but directly related are variables in adjacent sections. However, since the relationship is complicated and a non-linear equation is used for the analysis, it is more convenient to represent each signal line with a scalar variable block diagram corresponding to one scalar variable as shown in the lower right diagram of FIG. It is. Here, this is referred to as a scalar variable model, and an example of the scalar variable model is represented as “ SVM ” (the same as that shown in FIG. 5).

A scalar variable model and a vector variable model are connected using a (vector → scalar) conversion element and a (scalar → vector) conversion element.

The present invention is directed to a time response analyzer for a vector variable block diagram which is a composite of such a vector variable model and a scalar variable model.

FIG. 9 is an explanatory diagram for explaining a vector variable block diagram analyzer according to the prior art. In the vector variable model, a linear state variable model as shown in FIG. 9 can be derived by performing partial derivative calculation in the upstream direction of the signal starting from the integral element and the (vector → scalar) conversion element. A state transition equation can be derived by applying a numerical solution of a differential equation, for example, a trapezoidal method to the linear state equation.

On the other hand, examples of scalar variable model of scalar variable model (Fig. 9 be the same as that shown in FIG. 5, "SV
M ”), starting from a dynamic element such as an integral element or a first-order lag element, tracing the signal in the upstream direction, using a partial derivative, and applying a numerical calculation method of a differential equation to obtain 1
A state transition equation is obtained for each dynamic element.

In the vector variable block diagram, since the vector variable model and the scalar variable model by the (vector → scalar) conversion element and the (scalar → vector) conversion element are connected, the two types of state transition shown in FIG. The equations need to be solved simultaneously, and as shown in FIG.
Into one calculation model. The simultaneous equations, which are the calculation models, are solved for each time and time step, and the time response is obtained.

With such a calculation method, the time response of the vector variable block diagram can be calculated stably, but the order of the calculation model becomes large, and the coefficient matrix T (k)
Is a dense matrix, so that a high-speed simultaneous equation calculation method cannot be applied, and the calculation time is long. For example, a simulation of a multivariable control system of a boiler requires 500 seconds to execute a simulation.
It takes 0 seconds, more than five times the real time, and it is difficult to study many cases.

[0012]

The problem of the time response calculation of the vector variable block diagram is that the vector variable model is composed of linear elements, and the state transition equation is a system of constant coefficients. When incorporated into the entire state transition equation, the coefficients at each time step change, so that simultaneous equations need to be solved at each time step, and the amount of calculation increases. On the other hand, if the vector variable model and the scalar variable model can be calculated separately,
The calculation speed can be greatly improved for the following reasons.

(A) The inverse matrix of the coefficient matrix of the constant coefficient state transition equation of the vector variable model can be calculated in advance, and the state at each time step can be obtained only by the matrix product operation, which greatly reduces the calculation time. Shorten.

(B) Since the coefficients of the scalar variable model change at each time step, it is necessary to solve the simultaneous equations at each time step, but the order is reduced. In addition, since the coefficient matrix is also a sparse matrix in which most of the coefficient matrix is zero, a high-speed calculation method of simultaneous equations can be applied.

An object of the present invention is to be able to stably and quickly perform a time response calculation of a vector variable block diagram.

[0016]

According to the present invention, there is provided an apparatus for analyzing a vector variable block diagram in which a vector variable and a scalar variable are mixed, comprising: a terminal having an input section and a display section; Calculating means for performing input / output processing with the means, the calculating means having a time response calculating unit for calculating by inserting a sample holder virtually between the scalar variable part and the vector variable part. It is to become.

Further, in the above-described apparatus for analyzing a vector variable block diagram, the calculating means includes a block diagram data input unit for inputting data of the block diagram, a preprocessing unit for generating a calculation model, A vector variable model calculation model generation unit, an input variable calculation unit for calculating an output value of an external input, a scalar variable model calculation model generation unit, and a time series change of a designated variable is displayed on the terminal means. And an output processing unit.

Further, the present invention includes an operation for virtually inserting a sample holder between a scalar variable portion and a vector variable portion and performing a time response calculation.

Further, according to the present invention, as a pre-process of the time response calculation, a state variable model is derived for a vector variable portion, and a state transition between one hour steps can be calculated by a matrix-sum operation based on the model. An operation to generate an expression, an operation to derive a calculation model capable of stably calculating a time response using an automatic calculation of partial derivatives and an implicit solution of a differential equation for a scalar variable part at each time step, and an operation from a sample holder. The method includes a state transition equation for a vector variable part and an operation for independently calculating a calculation model for a scalar variable part based on the output.

FIG. 7 is an explanatory diagram for explaining a vector variable block diagram analyzing apparatus according to the prior art and the present invention. The present invention is constituted by two processes.

Generation of calculation model: between the vector variable model and the scalar variable model, the output value of the (vector → scalar) conversion element calculated by the vector variable model and the (scalar → vector) conversion element calculated by the scalar variable model Is virtually inserted between the vector variable model and the scalar variable model.

Time response calculation: During the one-hour calculation step, the output of the sample holder holds a constant value,
The vector variable model and the scalar variable model can be calculated independently. In the vector variable model, the inverse matrix T _Vの¹ of the coefficient matrix T _V of the state transition equation is obtained in preprocessing,
In the time response calculation, the independent term Z _V (k + 1) calculated from the output value of the dynamic element and the (scalar → vector) conversion element in the previous time step (k) is multiplied by T _V ⁻¹ from the left. The state variable value X (k + 1), that is, the output vector value of the integral element is obtained. On the other hand, for a scalar variable, a dynamic variable in k steps, (k + 1)
T _S (k + 1) and Z _S (k obtained from the external input variable of the step and the output value of the (vector → scalar) conversion element
+1) from the simultaneous equations T _S (k + 1) X _S (k + 1) = Z
Solve the _S (k + 1), determine the X _S (k + 1). By these two processes, the effects (a) and (b) described above can be obtained, and the time response calculation can be speeded up.

[0023]

DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. 1 is a diagram for explaining an embodiment of a vector variable block diagram analyzing apparatus according to the present invention. The analysis device for the vector variable block diagram is a workstation or personal computer (PC)
(Calculation means) 1 and a terminal (terminal means) 2 for inputting data and displaying a trend graph of calculation results. The computer 1 includes a block diagram data input unit 3, a pre-processing unit 4, a vector variable model calculation model generation unit 5, an input variable calculation unit 6, a scalar variable model calculation model generation unit 7, and a time response calculation unit 8. And an output processing unit 9. The processing contents of each processing unit will be described below.

Block Diagram Data Input Unit 3 The operation elements of the vector variable block diagram are expressed in the following format.

Variable name = function name (input variable 1,..., Input variable n ＄ coefficient 1,..., Coefficient m) In a scalar variable model, for example, addition of two variables is described as follows.

V _S = ADD (vi _S1 , vi _S2 ＄) (1) where v _S : scalar element output variable, vi _S1 : input 1, vi _S2 : input 2 Even in a vector variable model, addition of two vector variables Can be similarly expressed.

V _V = VADD (Vi _V1 , Vi _V2 ＄) (2) where V _V : vector element output variable, Vi _V1 : input 1, Vi _V2 : input 2 In the block diagram data input unit 3, Reads data and develops it internally into a table consisting of variables, operation elements, input variables, and coefficients.

Preprocessing Unit 4 The preprocessing unit 4 performs the following processing in order to efficiently create a calculation model.

(A) Conversion of variable names (character strings) to variable numbers using the hash method for high-speed identification of variables (b) Calculation order of downstream and upstream directions of scalar variable model Step input Input such as input and lamp input, integration and 1
The order of calculation is determined in the downstream direction of the signal, starting from the dynamic element such as the next delay element and the (vector → scalar) transformation element. The obtained calculation order is used for calculation of algebraic elements such as addition, subtraction, multiplication and division, that is, element partial differential values related to output values of intermediate variables and inputs of outputs.

Dynamic elements such as integral and primary delay factors,
(Scalar → vector) The calculation order is determined in the direction opposite to the signal flow with the conversion element as a starting point. The obtained calculation order is used for calculating the partial derivative of the dynamic variable of the input variable of the dynamic element, the external input variable, and the (vector → scalar) conversion element.

(C) Calculation order in the upstream direction of the vector variable model The calculation order is performed in the direction opposite to the signal flow, starting from the (vector → scalar) conversion element and the vector integration element.
This is used for deriving the state equation of the vector variable model.

FIG. 2 is a diagram showing a processing flow of the vector variable model calculation model generation unit of FIG. FIG. 3 is a diagram illustrating an example of a vector variable model. The processing is performed in the following steps.

(A) Step 1 (reference numeral 510): (vector → scalar) One unprocessed element is selected from a conversion element or an integration element. Let 5001 in FIG. 3 be the selected one element.

(B) Step 2 (reference numeral 520): The signal is traced in the reverse direction, and the partial derivative is calculated. At this time, the gain matrix of the element to be calculated is multiplied from the left. FIG. 3 shows a part of the calculation.

(C) Step 3 (reference numeral 530): When all the paths arrive at the integral element or the (scalar → vector) conversion element, a state variable expression (partial state variable expression) of the selected integral element is created. Referring to FIG. 3, the following state variable equation is obtained.

[0036]

(Equation 2)

(Vector → Scalar) When all the conversion elements or vector dynamic elements have been processed (reference numeral 540),
Proceed to the next step 4.

(D) Step 4 (reference numeral 550): A state transition formula for calculating the state of the dynamic variable after one hour step is obtained by applying a numerical calculation method of a differential equation. In the example of FIG. 3, when the trapezoidal method is applied to the state variable equation obtained in step 3, the following equation can be derived.

[0039]

(Equation 3)

[0040] _{However, X V1 (k + 1)} :( k + 1) step of X _V1, α: weight, h: represents the time step size.

Since T _{V in the} above equation is a constant matrix, an inverse matrix is obtained, and X _V1 (k), U _V1 (k) and (k
If Z _V (k + 1) is obtained from U _V (k + 1) at the point of time +1), X _V (k
+1) is determined.

[0042]

(Equation 4)

Input Variable Calculation Unit 6 The following processing units 6, 7, 8, and 9 are repeated (calculation period) / (time increments) times. The external input variable calculator 6 performs the following processing.

(A) Step 1: The output value of an external input that depends only on time, such as a step input of a scalar variable model and a sine wave input, is calculated.

(B) Step 2: As shown in FIG. 7, in this embodiment, a sample holder is virtually provided between the vector variable model and the scalar variable model. In other words, in terms of calculation, the (scalar → vector) conversion element and the (vector →
(Scalar) The output values of the transform elements are stored for one hour steps, and their values are treated as unchanged.

Generation Method 7 for Calculation Model for Scalar Variable Model A method for generating a calculation model for a scalar variable model is described below.

The dynamic variables of the scalar variable model can be generally expressed in the following format.

[0048]

(Equation 5)

Where x _{si is} a state variable of a dynamic element,
u _si : external input to the scalar variable model ((vector →
Scalar) Transformation element is included), F _si : An unknown equation is an unknown non-linear function. A calculation model such as

[0050]

(Equation 6)

X _si : a state variable of a dynamic element, F _si : a non-linear function (unknown) x _si (k + 1) is obtained by solving the above equation for all x _si and solving them simultaneously. F _si is unknown, but if the partial derivative with respect to x _si is obtained, equation (8) can be generated.

FIG. 4 is a diagram showing the processing flow of the scalar variable model calculation model generation unit of FIG. FIG.
FIG. 4 is a diagram showing an example of a scalar variable model (this is represented as “ SVM ”). The partial derivative and the calculation model are derived from the block diagram according to the procedure shown in FIG.

(A) Step 1 (symbol 710): Calculation is advanced in the downstream direction of the signal based on the stored values of the dynamic variables, external input variables and the output of the (vector → scalar) conversion element,
The value of the algebraic element, that is, the intermediate element and the element partial differential value for each element are obtained.

(B) Step 2 (reference numeral 720): One unprocessed element is selected from the dynamic elements. For example, the integration element 22 in FIG. 5 is selected.

(C) Step 3 (reference numeral 730): Starting from the selected element as a starting point, trace the signal in the upstream direction and proceed with the partial derivative calculation. The order is as follows: element 22 → 21 → 20 → 19 → 18 → 22 (d) Step 4 (reference numeral 740): When all paths reach a dynamic element, an external input, or a (vector → scalar) transformation element, Complete the derivative calculation. For example, when a route starting from the element 22 arrives at the element 22, ∂E _S22 / ∂x _{S 22} is determined. Substituting those partial derivatives into equation (8) generates a calculation model.

Time Response Calculation Unit 8 FIG. 6 is a diagram showing a processing flow of the time response calculation unit in FIG. The time response calculation proceeds in the following steps according to the procedure of FIG.

(A) Step 1 (reference numeral 810): An independent term Z _V (k + 1) in equation (6) is obtained by using the stored value of the (scalar → vector) conversion element. Next, using _TV - ¹
The state variable X _V (k + 1) of the (k + 1) step of the vector variable model is obtained from the equation (6). Further, with the integration element and the (scalar → vector) conversion element as starting points, the calculation proceeds in the downstream direction of the signal to obtain the value of the (vector → scalar) conversion element.

(B) Step 2 (reference numeral 820): The calculation model of the scalar variable block diagram is simultaneously established for all dynamic elements, and the simultaneous equations are solved to obtain a new state variable value x _si (k + 1).

(C) Step 3 (reference numeral 830): For a scalar variable model, calculate an algebraic element in the downstream direction of the signal.

Output processing unit 9 The time series change of the designated variable is displayed on the terminal means 2 in a trend graph.

[0061]

According to the vector variable block diagram analyzer of the present invention, the time required to calculate the time response of a large-scale vector variable block diagram whose order of a state variable is about 400 is 1 /.
10, the time response calculation of the vector variable block diagram can be performed stably and at high speed.

[Brief description of the drawings]

FIG. 1 is a diagram illustrating an embodiment of an apparatus for analyzing a vector variable block diagram according to the present invention.

FIG. 2 is a diagram showing a processing flow of a vector variable model calculation model generation unit of FIG. 1;

FIG. 3 is a diagram illustrating an example of a vector variable model.

FIG. 4 is a diagram showing a processing flow of a generation unit of a calculation model for a scalar variable model in FIG. 1;

FIG. 5 is a diagram illustrating an example of a scalar variable model.

FIG. 6 is a diagram showing a processing flow of a time response calculation unit in FIG. 1;

FIG. 7 is an explanatory diagram illustrating an analysis device for a vector variable block diagram according to the related art and the present invention.

FIG. 8 is an example of a vector variable block diagram for a boiler.

FIG. 9 is an explanatory diagram illustrating an apparatus for analyzing a vector variable block diagram according to the related art.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Computer (calculation means) 2 Terminal (terminal means) 3 Block diagram input part 4 Preprocessing part 5 Vector variable model calculation model generation part 6 Input variable calculation part 7 Scalar variable model calculation model generation part 8 hours Response calculation unit 9 Output processing unit

Claims (2)

[Claims] 1. An apparatus for analyzing a vector variable block diagram in which vector variables and scalar variables coexist, comprising: a terminal unit having an input unit and a display unit; and a calculation unit for performing input / output processing between the terminal unit and the terminal unit. An apparatus for analyzing a vector variable block diagram, comprising: a time response calculator for virtually inserting a sample holder between a scalar variable part and a vector variable part for calculation. 2. A calculation system according to claim 1, wherein said calculation means includes a block diagram data input unit for inputting data of a block diagram, a preprocessing unit for generating a calculation model, and a calculation model for a vector variable model. A generation unit, an input variable calculation unit that calculates an output value of an external input, a generation unit of a calculation model for a scalar variable model, and an output processing unit that displays a time-series change of a specified variable on the terminal unit. An apparatus for analyzing a vector variable block diagram.