JP5439696B2 - Integrator - Google Patents

Description

  The present invention relates to an integrator for integrating discrete numerical series data.

  Conventionally, as a method of integrating time-discrete numerical series data (hereinafter referred to as “discrete numerical series data”) using a computer, a broken line approximation in which discrete numerical series data is continuous with a broken line by linear interpolation A method of integrating using a trapezoidal formula as a signal is known (Non-Patent Document 1).

  As a method for programming a mathematical model of a continuous dynamic system by a computer, a method using an extended signal flow graph is known (Non-Patent Documents 2 and 3). This extended signal flow graph extends the signal flow graph not only to linear elements but also to non-linear elements, and uses a visual (graphical) programming language to show how signals are calculated and transmitted over time. Is composed of an operation node that performs an algebraic operation between transmitted data and a transmission arc that transmits the data of the operation node to other operation nodes.

: Toto Hayato, et al .: Numeric calculations that are well understood-Actual algorithms and error analysis, Nikkan Kogyo Shimbun, p.154, (2001.11) : Koji Takahashi, Kensuke Hasegawa: Realization of system integration model with Mark Flow Graph and Extended Signal Flow Graph, Society of Instrument and Control Engineers, Systems and Information Division, Discrete Event Systems Subcommittee, Proc. 67/72, (2008,6) : Kensuke Hasegawa, Koji Takahashi: Proposal of Control and Computing System Builder (CSB) for system integration-Programming simulation and case model, IEEJ System and Control Study Group Material, SC-08-12, pp. 59/64 (2008,3)

  However, in the integration method disclosed in Patent Document 1 described above, there is a problem that when the numerical series data includes discontinuous points such as jump points, an error occurs and sufficient accuracy cannot be ensured.

  The present invention has been made in view of these points, and an object of the present invention is to provide an integrator capable of realizing sufficient accuracy when a mathematical model of a continuous dynamic system by a computer is programmed.

  Another object of the present invention is to realize an integrator that can achieve the above object and can be easily introduced into the formation of a feedback loop by a simple algorithm, and to facilitate easy programming in simulation and improvement of calculation accuracy. To do.

  The integrator according to the present invention inputs discrete numerical series data, regards the discrete numerical series data as a polygonal line approximation signal continuous by a polygonal line by linear interpolation, and integrates it using a trapezoidal formula, thereby integrating fundamental terms. A basic arithmetic unit that calculates a correction point, which samples the jump points of the discrete numerical series data, calculates and outputs a correction term for correcting the basic term calculated by the basic arithmetic unit, and the basic And a subtractor that generates and outputs a corrected integral value by subtracting the correction term obtained by the correction computing unit from the basic term obtained by the computing unit.

  The basic arithmetic unit is characterized in that there is no direct signal transmission path from the input discrete numerical sequence data to the basic term.

  In another embodiment of the present invention, the correction calculation unit monitors whether or not a jump point has occurred in the discrete numerical series data, and if a jump point has occurred, the jump of the discrete numerical series data is performed. Point, sampling two preceding data preceding it, and calculating a correction term based on the difference between the extrapolated point and the jumping point at the time of the jumping point obtained from the two preceding data To do.

  In still another embodiment of the present invention, the basic operation unit, the correction operation unit, and the subtractor are programmed using an extended signal flow graph and executed by a computer.

  ADVANTAGE OF THE INVENTION According to this invention, when programming the mathematical model of the continuous dynamic system by a computer, the integrator which can implement | achieve sufficient precision can be provided.

It is a block diagram which shows the structure of the integrator which concerns on 1st Embodiment of this invention. It is a figure which shows an example of the discrete numerical series data used as the source data in the integrator. It is an extended signal flow graph which shows the structure of the integrator. It is a graph which shows the discrete numerical series data of each part of the integrator. It is a graph which shows the discrete numerical series data of each part of the integrator which concerns on the 2nd Embodiment of this invention. It is an extended signal flow graph which shows the structure of the integrator. It is an extended signal flow graph which shows the production | generation process of the high order polynomial data which applied the integrator. It is an extended signal flow graph which shows the first order lag system to which the integrator is applied. It is an extended signal flow graph which shows the precision of the data of the first order lag system to which the integrator is applied. It is a graph which shows the relationship between the integral gain and response in the first order lag system to which the integrator is applied. It is an extended signal flow graph which shows the continuous vibration secondary system which applied the integrator. It is a graph which shows the cycle test result of the continuous vibration secondary system which applied the integrator. It is a graph which shows the discrete numerical series data which have a numerical jump point in the middle of being input into the integrator which concerns on the 3rd Embodiment of this invention. It is an extended signal flow graph which shows the structure of the integrator. It is a figure which shows the calculation cell of the extended signal flow graph for demonstrating the integrator which concerns on the 4th Embodiment of this invention. It is the extended signal flow graph which applied the integrator to the NW integrator. It is a figure which shows the example which expressed the process from the event generation in the jump origin arc of the same integrator to correction | amendment term incorporation with an intermediate language. It is a 1st figure for demonstrating the programming of the integrator. It is a 2nd figure for demonstrating the programming of the integrator.

[First Embodiment]
Next, the tr integrator based on the number formula according to the first embodiment of the present invention will be described in detail.

  FIG. 1 is a diagram illustrating a configuration of an integrator according to the present embodiment.

  The integrator includes an arithmetic system construction unit 1 (hereinafter referred to as “CBS”) that forms the center of processing, and a source data storage unit that stores source data to be processed supplied to the CBS 1. 2, an input unit 3 for performing an operation necessary for processing, a display unit 4 for displaying a GUI (Graphic User Interface) for an operation necessary for processing, and an output unit 5 for outputting a processing result. Configured.

  The CBS 1 constructs a graph program based on the extended signal flow graph and executes it on the provided source data. The program data library 11 that stores data necessary for constructing the graph program and the program data library 11 A graph program creating / editing unit 12 for creating / editing a graph program using stored program data, a GUI creating unit 13 for creating a GUI for creating / editing a graph program on the display unit 4, and a graph And a program execution unit 14 for converting the program into an executable program and executing the program.

  The specific function of this integrator will be described later. Here, the principle of the software integrator will be described first.

[Principle explanation]
Now, as shown in FIG. 2, it is assumed that the continuous function u (t) is sampled at equal intervals ΔT. When the continuous function u (t) is integrated using a formula (trapezoidal formula) relating to trapezoidal approximate integration as a linear approximation function between sample values, it is obtained as follows.

That is, using the symbol ΔS _n as the value of the trapezoidal area from the points u _n-1 to u _n in FIG.

[Equation 1]

Is required. However, the initial triangle ΔS ₀ is not considered here, and ΔS ₀ = 0. Further, the value of u (t) on the abscissa point n.DELTA.T, and _{u n.} Therefore, the total area _{S N} in the range of 0 ≦ t ≦ NΔT is

[Equation 2]

Or

[Equation 3]

It is represented by

  Hereinafter, a calculation algorithm for executing the approximate integration by the trapezoidal approximation described above is derived.

  For the sake of convenience of explanation, the sampled value signal obtained by modulating the input numerical sequence shown in FIG.

[Equation 4]

And then z-transform and U (z)

[Equation 5]

It becomes. In the above equation coefficients z ^-n is represented as the n-th numerical u _n.

Next, when u ^* (t) is right-shifted by ΔT and z-transformed, the following equation is obtained.

[Equation 6]

When formulas (5) and (6) are added and organized,

[Equation 7]

It becomes. Furthermore, if both sides of the above equation are multiplied by ΔT / 2,

[Equation 8]

It becomes. The coefficient of z ⁻ⁿ on the right side of the above equation corresponds to the area ΔS _n of the _nth trapezoid as can be understood from the equation (1). That is,

[Equation 9]

It becomes. In _order to sequentially add and integrate the trapezoidal area ΔS _n , the discrete value transfer function 1 / (1-z ⁻¹ ) representing the accumulation may be multiplied on both sides of the equation (8) or (9). As a result, the integral value can be obtained as in the following equation (10).

[Equation 10]

The arc on the right side of the above equation represents the integrated value from the sampling time point ΔT to the sampling time point NΔT, and this is expressed as S _N.

[Equation 11]

Then, equation (10) becomes

[Equation 12]

It becomes. The entire left side of the above formula is represented by TR (z),

[Equation 13]

Then, TR (z) represents an approximate integration value calculation system at the sampling time point NΔT when performing integration by linearly interpolating a numeric string input represented by U (z) based on the right side of the above equation.

If the first term of TR (z) is defined as a basic term, the second term is defined as a correction term, and A _tr (z) and B _tr (z), respectively,

[Formula 14]

[Equation 15]

It becomes. Note that the character symbol “tr” or “TR” used in the above-described mathematical expression means a trapezoid. Further, in FIG. 2, the correction term represents that the area of the triangle ΔS ₀ (the area of the triangle ΔS ₀ whose base is ΔT and height u ₀ ) in the period from −ΔT to ₀ is subtracted from the basic term.

  Next, the above-described system will be described using an extended signal flow graph (hereinafter referred to as “SFG.e”) shown in Non-Patent Document 2. SFG.e extends the signal flow graph to not only linear elements but also non-linear elements, and uses a visual (graphical) programming language to show how signals are calculated and transmitted over time. An arithmetic node that performs an algebraic operation (excluding subtraction and division) between data and a transmission arc that transmits the data of the arithmetic node to other arithmetic nodes.

FIG. 3A shows the structure of the software integrator by SFG.e, and the arc is composed of a constant coefficient arc and a unit delay arc. Hereinafter, this is referred to as a TR integrator. As shown in the figure, the TR integrator includes an A _tr calculation unit (basic calculation unit) 21 that calculates a basic term A _tr (z), and a B _tr calculation unit (correction calculation unit) that calculates a correction term B _tr (z). ) 22 and a subtracter 23 that subtracts the correction term calculated by the B _tr calculation unit 22 from the basic term calculated by the A _tr calculation unit 21.

A _tr calculating section 21 (5) of the input signal U (z), i.e. the initial numerical _{u 0} step progression from 1,2,3 calculation step 0, ..., number with the n _{u 0, u} 1, _{u 2,} u _3, ..., enter the u n _..., and outputs the integrated value indicated by the equation of the upper below the number 16 for each step as the fundamental term _{a tr.}

On the other hand, as shown in FIG. 3A, the B _tr calculation unit 22 samples u ₀ with a sampler when t = 0, and the correction term B _tr (u ₀ + u ₀ z ⁻¹ ) integrated for each step. + U ₀ z ⁻² +...) ^Is output. The multiplication node of the B _tr calculation unit 22 has a function as a sampler, and samples u ₀ by multiplying the input data string by a unit impulse δ (t) generated at t = 0.

An adder 23 for correcting the integral value adds the sign conversion values of the basic term A _tx and the correction term B _tr . As a result, an integrated output as shown in the lower part of Expression 16 is obtained.

[Equation 16]

FIG. 3B shows the TR integrator as an integral arc having a transmissivity of 1 / s _tr by combining the input node to the output node in FIG. 3A with one arc. Here, s _tr is given symbolically as corresponding to the Laplace variable s.

  Note that the multiplication node in FIG. 3A has a sampler role, and is easily realized by coding the algorithm including the timing at the start of calculation.

[Second Embodiment]
In the first embodiment, as shown in FIG. 3A, the _Atr calculation unit 21 has a direct transmission path through which time-series data input to the input unit is directly transmitted to the output unit. However, the second embodiment provides an integrator capable of integration without direct signal transmission path (hereinafter referred to as “nw integration”).

  Since approximate integration by the trapezoidal formula is based on a method of linear interpolation between numerical values, integration for a constant numerical input is executed accurately. Here, a new algorithm is derived on the precondition that the integration with respect to a constant numerical value input can be accurately executed as in the tr integration method described above, and that the approximate integration without a direct signal transmission path can be executed.

  First, the behavior for a constant value input signal by the tr integration method described above will be described in detail.

In the basic term A _tr (z) of FIG. 3A, the input signal U (z) is a numerical sequence of a constant value u ₀ (in this example, u ₀ = 1) as shown in FIG. 4A.

[Equation 17]

Then the fundamental term A _tr (z) is

[Equation 18]

(See FIG. 4B). When this is expanded, the value at each sample time is obtained as in the following equation.

[Equation 19]

On the other hand, the correction term B _tr (z) is developed from the equation (15) and expressed as follows (see FIG. 4C).

[Equation 20]

Therefore, the integral output TR (z) in this case is the difference between the above-mentioned A _tr (z) and B _tr (z).

[Equation 21]

(See FIG. 4D). This indicates that the numerical value starts from 0 at the sampling time point 0 on the horizontal axis, and the numerical value as the integration result is accurately increased by ΔTu ₀ every time interval ΔT. When these numerical values are linearly interpolated, the slope starting from the origin becomes a straight line of ΔTu ₀ , and the response of the integration result is virtually virtually indicated by a continuous signal.

  By the way, as can be seen from the response of this basic term, 0.5ΔT is transmitted as an initial value through the direct signal transmission path described above. Due to this existence, the TR integrator described above is a dynamic that uses many closed loops. It will not be suitable for the mathematical model of the system.

  A method for solving this problem will be described with reference to FIG.

Now, as shown in FIG. 5A, it is assumed that the input signal is a numeric string of a constant value u ₀ (in this example, u ₀ = 1) as in the previous example. The response A _tr (z) (FIG. 5 (b)) of the basic term to this is transformed by the signal of FIG. 5 (c) into the following equation to directly transmit the signal path 0.5ΔTu ₀ · z ^0. Erase.

[Equation 22]

_Assuming that this is the basic term A _nw (z), the basic term A _nw (z) can be expressed as shown in _Equation 23.

[Equation 23]

  The result is shown in FIG.

On the other hand, the correction term B _tr (z) is transformed to B _nw (z) as follows in the same manner as the transformation from A _tr (z) to A _nw (z) (see FIG. 5E). .

[Equation 24]

[Equation 25]

  As a result, the following relationship is established.

[Equation 26]

  This expression indicates that a new approximate integration algorithm equivalent to TR (z) based on the trapezoidal formula on the right side is obtained. Therefore, a new approximate integration algorithm is represented by NW (z) and is defined as follows.

[Equation 27]

Here, A _nw (z) is formulated as follows. From the equations (15) and (23), A _nw (z) = A _tr (z) −ΔTu ₀ (0.5z ⁰ −0.5z ⁻¹ ).

[Equation 28]

Is guided. The input (1 / (1-z ⁻¹ )) u ₀ of the constant value u ₀ on the right side of the above equation is replaced with a general input signal U (z),

[Equation 29]

And

On the other hand, B _nw (z) is obtained as follows from equations (16) and (24).

[Equation 30]

The character symbol “nw” or “NW” used in the above-described mathematical expression means “new ( n e w ) approximate integration”.

[Effects of Second Embodiment]
[Equivalence of NW integration with analog integration]
The above algorithm is represented by SFG.e as one software integrator as shown in FIG. Hereinafter, this is referred to as an NW integrator. The NW integrator includes an A _nw calculation unit (basic calculation unit) 31 that calculates a basic term A _nw (z) and a B _nw calculation unit (correction calculation) that calculates a correction term B _nw (z) as shown in FIG. Part) 32 and a subtractor 33 that subtracts the correction term calculated by the B _nw calculation unit 32 from the basic term calculated by the A _nw calculation unit 31. FIG. 6B shows the above function expressed by an integral arc of _{transmissivity} 1 / s _nw from the input node to the output node as in the case of the TR integrator. Note that s _nw is given symbolically as corresponding to the Laplace variable s. In this way, the NW integrator can execute exactly the same integration as the TR integrator for a constant value input sequence, and is based on a trapezoidal approximation algorithm. The same accuracy as the TR integrator can be expected. In addition, it has a structure that does not hold a direct signal transmission path, and its output can be fed back directly to the input side in the same calculation step. Therefore, unlike the TR integrator, the NW integrator is qualitative in terms of programming. It can be regarded as having a continuous value transfer function equivalent to that of an analog integrator without restriction.

The multiplication node in FIG. 6A has a sampler role. In this case, u ₀ is sampled by multiplying at a time point ΔT by a unit impulse (δ (t−ΔT) as a time function, z ⁻¹ in the z-transform type, but the time function is used in the following description). Represents that.
[Examination of errors in TR / NW integrator]
As described above, the NW integrator is extended from the TR integrator and is based on linear interpolation approximation, but there is a difference in the integration calculation process at each calculation step. In the TR integrator, the calculation is a direct calculation based on a trapezoidal formula including the current input as shown in the equation (15), whereas in the NW integrator, as shown by the presence of z ⁻¹ outside the molecular brackets on the right side of the equation (29). Extrapolation without input. Therefore, it is conceivable that the degree of approximation with respect to the numerical input of the general form is somewhat deteriorated as compared with the TR integrator. For the NW integrator, it is necessary to consider the degree of approximation with respect to analog integration in the configuration of the feedback system. Each of its usage limitations, solutions, and cautions are described through comparisons using representative examples.

Example 1. Calculation of a high- order polynomial A high-order polynomial is a mathematical expression constituted by x ⁿ (n: positive integer). Therefore, for application to higher-order polynomial calculations, the calculation of ^xn is performed by NW integration and the accuracy is examined. When x is selected as the integration variable and ^xn is represented in the signal flow graph, it is as shown in FIG.

In the figure, the transmissivity 1 / s represents the integral, but in the programming by the extended signal flow graph shown in FIG. 7B, this is replaced with 1 / s.nw which is the NW integral.
By the way, as described above, the NW integration, like the TR integration, can be accurately integrated at n = 1. Theoretically, the above integration can therefore be performed accurately. Further, with respect to the x ² n = 2, the since n = 1 for x corresponding to this derivative is that the actual function and linear interpolation match, the calculation can be performed accurately. Therefore, when n is 3 or more, a calculation error occurs due to the mismatch between the linear interpolation and the actual function. In order to confirm this level, the following simulation was performed using a personal computer.

[conditions]
(i) Variable: Double-precision floating-point number type
(ii) n = 3 and n = 4
(iii) Integration interval: 0 to 1
(iv) Number of steps in integration interval = 4, 10, 25, 50, 100
(v) Definition of error: (| NW integral value−theoretical value | / theoretical value) × 100 (%)

[result]
(i) The maximum error is 0.33% (n = 4, number of steps = 4). This condition is an extreme case in practice.
(ii) For n = 4,
Number of steps 10, 25, 50, 100
Each error in
1.3 × 10 ^-2 %, 9.8 × 10 ^-4 %, 5.2 × 10 ^-4 %, 1.6 × 10 ^-4 %
It became.
(iii) For n = 3, all are less than the corresponding error at n = 4, so there is no practical problem.
(iv) As a result of the above, it is recommended that the number of steps be 10 or more in the calculation of higher order polynomials.

Example 2. Accuracy verification by definite integration

[Equation 31]

Table 1 shows the calculation of the pi ratio by the definite integration shown in Fig. 1 by TR integration and NW integration, and the difference from the analysis value π is compared for each number of steps in the integration interval (0 to 1). Although the accuracy of the NW integration is slightly lower than that of the TR integration, it can be seen that when the number of steps is 200 or more, no difference is found and sufficient accuracy is obtained.

Example 3 Error verification of NW integrator in first-order lag system A first-order lag system is constructed using an NW integrator and the difference from the theoretical value is examined. FIG. 8 is a first-order lag system expressed by an extended signal flow graph.
The transfer function between the input and output of this system is obtained as follows.

[Formula 32]

  FIG. 9 shows a graphic program for obtaining an initial response of this system. In this case, the integral gain K of the NW integrator is set to 1, and therefore the time constant T is 1 sec. In the figure, the step response value y (T) after 1 second (time constant T) after adding the unit step signal is shown.

FIG. 9 also shows a program for calculating the theoretical value 1-e ⁻¹ of y (T) for comparison. In this calculation, the time required for one calculation step is 10 msec. Therefore, the number of calculation steps is 100. In FIG. 9, as a result, the response value y (T) is 0.6321234107, whereas the theoretical value is 0.6321205497, which matches up to 5 digits after the decimal point.

  In the simulation, when such a first-order lag system is constituted by an NW integrator, the value of K is theoretically limited, but 25 (time constant) is understood from the relationship between the integral gain and the response shown in FIG. 0.04 sec) or less is appropriate. The response value y (T) at this limit is 0.625. The minimum time constant that matches up to 4 digits after the decimal point is 0.08 sec (K value is 12.5).

  Table 2 shows the relationship between the integral gain and the initial response value after the elapse of time T.

Example 4 Verification of integration performance by cycle test of continuous vibration secondary system When two integrators with gain constant 1 are connected in cascade and their outputs are fed back to the input unit as a unit, theoretically, the stability limit is reached, and continuous vibration is generated. To what extent this state can be maintained is called a cycle test. FIG. 11 shows a program based on the extended signal flow graph for this purpose. This system is a program of the differential equations in the figure, and corresponds to the equation of motion related to the vibration of the pendulum in vacuum. In this case, y is the pendulum string angle, and x ′ is the angular velocity. Here, one of the two integrators is NW integration and the other is TR integration. That is, it is necessary to use at least one NW integrator in the closed loop of the graph in the figure.

  FIG. 12 shows the x '(dashed line) and y (solid line) responses of this system. From this cycle test result, it can be seen that the performance as an integrator is sufficiently fulfilled. In this case, the integral gain is 1 (1 / sec), the vibration angular frequency is 1 rad / sec, the period is 2π, and the calculation step size is sufficiently small. Since the accuracy of approximate integration is affected by the step size, there is a restriction on the magnitude of the closed-loop integration gain. FIG. 4C shows the case where the integral gain is 10 (1 / sec), and although it cannot be confirmed in the figure, a slight amplitude attenuation was observed. Conversely, no increased vibration occurs.

[Third Embodiment]
Next, a third embodiment of the present invention in which the correction term is generalized will be described.

In the numerical sequence as the integration variable, there may be a case where the numerical value jumps in the middle, as in the case where the initial numerical value u ₀ is not zero. This jump is accompanied by an event occurring inside or outside the system. Now, as shown in FIG. 13, it is assumed that a numerical jump occurs at the time point jΔT. If this is approximately linearly interpolated from u _j−2 to u _j−1 and further extended to time jΔT as u _j ′, it is regarded as jumping from here to u _j . If this is not regarded as a jump and linear interpolation is performed from u _j−1 to u _j , the area of the triangle connecting u _j , u _j−1 , u _j ′ is an error in TR integration and NW integration. Therefore, it is necessary to correct this.

If this area is c _j ,

[Equation 33]

  However,

[Formula 34]

It is represented by Based on this, the correction term for the TR integrator is based on the TR integration correction term (16) for the initial value.

[Equation 35]

It becomes. This is a general expression of the correction term, and the expression (16) corresponds to j = 0 in the above expression. In this case, while u _j = u ₀ , u _j−1 = u _j−2 = 0, and equation (34) matches equation (16).

  Also, the correction term for the NW integrator is the same with reference to equation (30).

[Equation 36]

Is obtained.

These are represented by an extended signal glow graph as shown in FIG. The only difference from the extended signal glow graph of FIGS. 3 and 6 is the signal transmission paths 41 and 42 from the A _tr calculation unit 21 and the _Anw calculation unit 31. The accumulating units 24 and 34 of the B _tr calculating unit 22 and the B _nw calculating unit 32 in FIG. 14 function to accumulate correction values generated at the jump points.

[Method of transmitting the cause of jump to the integrator correction unit]
The jump in the input signal is caused by the occurrence of an event in an element other than the integrator. In the extended signal glow graph, discontinuous non-linear arcs are prepared as transfer arcs. Among them, the following are typical causes of jumping.

  (1) On-off arc with dead zone: It has an on-off state and has a dead zone in the transition between them.

  (2) Hysteresis arc: has an on / off state, and has a certain width of hysteresis in the transition between them.

  (3) Sample holder arc: A continuous signal is sampled and held at a constant period.

  (4) Dead time arc: Signal transmission is performed with a fixed dead time (an integral multiple of the minimum sample time).

  (5) Switching arc: A logical variable is an external variable, and the transmission coefficient is 1 or 0 when the logical variable is true or false.

  These are defined as “jumping arc”. In the jump-induced arc, the output signal value jumps and changes under certain conditions (logical conditions such as threshold and time). The jumping arc group has a common step register for temporarily storing the calculation step number at which this occurs, and when an event occurs in the arc during a certain calculation step, the step number at that time is immediately used as the jump generation number for the TR integrator. For the NW integrator, 1 is added to the NW integrator and a number including a unit delay is stored in the step register as a jump occurrence number.

On the other hand, the integrator side receives the calculation counter data for each calculation step, and at the same time, always determines whether or not this coincides with the jump occurrence number. As shown by the sampling signal and the sampler in the B _tr calculation section 22 of FIG. 14 or the B _nw calculation section 32 of FIG. 14B, the correction signal is calculated and the correction is executed.

All integrators in the simulation program are expressed by a single arc as shown in FIG. 3B or 6B, and in this case, the integrator has the above-mentioned function and directly or indirectly on the input side. When a signal jump is received, the above-described operation corresponding to this is performed. Therefore, an integrator that is not affected by the jump phenomenon also performs the operation. In this case, a sufficiently small sampling interval (generally, a computer's interval) can be estimated from FIGS. 14 and (32). in equivalent) to the minimum calculation step interval, since the u _{j 'which} extends outwardly to almost matches the value of u _j from u _{j-2, u j-1,} since Delta] u _j can be regarded as zero, substantially Therefore, only the integrator that receives the jump of the input signal is selected. Even if jumps occur in a plurality of jump-causing arcs in the same calculation step, each integrator will comprehensively correct the input signal value as a result.

  Note that j described above corresponds to an event generation step. Details of the above will be described later in the code expression of the method of the integrator.

[Fourth Embodiment]
Next, a description will be given of a fourth embodiment relating to a software structure and execution form relating to an algorithm of graph expression.

  Here, the visual program based on the extended signal flow graph is described, edited, and executed by a CSB (Computing System Builder) 1 (FIG. 1), which is a virtual visual programming tool (Non-patent Document 3). Since the software integrator is also described and executed as a transfer arc in the visual program, an outline of the software structure and execution form related to CSB 1 for this purpose will be described. As described above, the extended signal flow graph includes an operation node that performs an algebraic operation (excluding subtraction and division), and a transmission arc that converts the data of the operation node into data used by other operation nodes and transmits the data. Composed.

[Graph program]
In a program drawn in an extended signal flow graph (hereinafter referred to as a “graph program”), it is requested by repeatedly performing a single calculation step that is performed by going through all operation nodes in a certain order. Calculation is performed. In that case, a single calculation step includes an execution sequence of one algebraic calculation step for each calculation node. The period of this execution sequence is called a calculation step period, and the time required for this execution is called a calculation step time. The calculation order is determined for each calculation node in one calculation step cycle. An index indicating this is called an execution index of the operation node. The execution index starts from 1 according to the natural ordinal number and increases by 2, 3, 4 ... Each operation node has already been assigned a unique index in a natural ordinal order in the order of arrangement in graph programming. Since this does not necessarily match the execution index, it is necessary to convert the unique index to the execution index before executing the calculation.

[Calculation cell]
A specific calculation is executed based on the calculation cell. As shown in FIG. 15, the computation cell includes a computation node (hereinafter referred to as a node) and a transmission arc (hereinafter referred to as an arc). That is, the arithmetic cell is configured to include one nucleus node, one or more child nodes, and an arc connecting them. All nodes except the source constitute one arithmetic cell as a nucleus node. The source does not become a nuclear node but serves as a signal source as a child node. The addition node as a source is given zero as an initial value at the time of placement on the GUI, but can be changed as needed. The multiplication node has an initial value of 1 on the GUI and cannot be changed. In addition, time drive functions such as a step function, an impulse function, a sine wave function, a cosine wave function, a random function, and a user-defined time function are given as special source nodes.

  The calculation cell performs an operation at the core node as soon as the data of all the child nodes belonging to the calculation cell is updated every calculation step cycle. That is, the data of each child node is converted and transmitted to the nucleus node by an arc method (subroutine) starting from the node, and new data is generated by an algebraic operation specific to the nucleus node.

  A nucleus node of a computation cell can be a child node of another computation cell. As a result, a plurality of calculation cells are combined to create a mathematical formula, which becomes an equation and a graph program. A nucleus node that does not become a child node of another operation cell becomes a sink and indicates data of a calculation result.

[Transmission arc type]
There are two types of arcs, A-type arcs and D-type arcs, with respect to the execution order between operation nodes connected thereby.

  An A-type arc has an arrival node execution index larger than the execution index of the departure node of the arc, whereas a D-type arc has an arrival node execution index smaller than the execution index of the departure node of the arc. Refers to the arc. ("A" means that the execution index rises (Ascent) along the arc direction, and "D" means that the execution index falls (Descent) along the arc direction).

From the above, in the calculation in one calculation cell, the child node connected by the A type arc uses the data updated earlier than the core node in the same calculation step, and is connected by the D type arc. For the child node, the data already updated in the previous calculation step is used. Therefore, the A type arc is an arc having a direct numerical transmission path, and the D type arc is an arc having no direct numerical transmission path. For example, in the TR integrator represented by the graph program of FIG. 14A described above, the path through the fundamental term and the correction term from U (z) to R (z) has a direct numerical transmission path. This is an A-type arc. On the other hand, in the NW integrator represented by the graph program in FIG. 14 (b), all the paths passing through the basic term and the correction term from U (z) to W (z) contain z ^-1 . Since it does not have a direct numerical transmission path, it is a D-type arc. In the case of a D-type arc, if the z ⁻¹ in the path is collectively multiplied by the input U (z) and regarded as the input z ⁻¹ U (z), the remaining graph program is effectively regarded as a D-type arc. Represents the algorithm. FIG. 16 applies this to an NW integrator.

[Execution Index Determination Process]
The procedure for determining the execution index of the operation node in the graph program is as follows. A node to which an execution index has already been assigned is called a decision node.

  (1) First, execution indexes are assigned to source nodes in order from 1. This is a decision node. The allocation order is in the order of the unique indexes of the source nodes.

  (2) Select nodes other than the decision node in the order of unique indexes. When this selection reaches the maximum unique index, the selection is repeated from the smallest unique index.

  (3) The selected node is a nuclear node, all nodes connected to it by A-type arcs are already determined nodes, and all nodes connected from the core node by D-type arcs are already determined nodes. Only when it is, the core node is determined as a decision node, and the process returns to (2).

  (4) When all the nodes become decision nodes, the execution index assignment ends.

  From the definition of D-type arc, the source cannot be the starting node of D-type arc. This is because there is no core node having an execution index that has priority over the execution index of the source. If so connected, the D-type arc is considered as an A-type arc.

  A virtual application (CSB1) when executing simulation through a graph program will be conceptually described.

  The CSB 1 can perform graph programming and editing through a graphical user interface. At that time, the program can be edited through a trial experiment while converting from the unique index of each node to the execution index.

  Arithmetic nodes and transfer arcs are given unique attributes, relations, and methods through programming, and are grouped into a set of node object types and arc object types.

  The algebraic operation function of the operation node and the transfer arc conversion function belong to the method.

  An arithmetic cell is a structure composed of arithmetic nodes and transfer arcs, which are objectified by a hierarchical structure of indexes through the “association” of arcs and nodes.

  The method of the transfer arc prepared as a menu (for example, TR integral arc, NW integral arc, jump-causing arc among the arcs already explained) is a command word on the software (eg Visual Basic or C language). It is described by. The integration arc (software integrator) has been described in the form of an extended signal flow graph (FIG. 14 or FIG. 16), but it can also be programmed directly as a graph program. In practice it is verbalized. This will be described below.

[Jump-induced arc]
The processing from the event occurrence in the jumping arc to the correction term incorporation is performed as follows. A jump point generation step register exj is commonly provided for all TR integrators, and a jump point generation step register exjj is commonly provided for all NW integrators.

  Now, when a jump occurs when a jump-induced arc is activated and signal is transmitted, the value j of the calculation step counter exnn at that time is substituted into the register exj, and j + 1 is substituted into the register exjj. As shown in (a) and (b), the correction term can be incorporated by operating the sampler.

  FIG. 17 shows a procedure for transferring values from the step counter exnn to the registers exj and exjj in an intermediate language by taking an on-off arc with a dead zone as an example. However, the on / off characteristics are point-symmetric from 0 to ± 1 for the output and from 0 to ± h for the dead band.

[TR integrator]
FIG. 14 (a) can be described as shown in FIG. 18 (b) by assigning a variable character / symbol again as shown in FIG.

[NW integrator]
As in the case of the TR integrator, the variable character symbols in FIG. 19A are assigned based on FIG. 16, and an intermediate language expression is obtained as shown in FIG.

  Note that T in FIGS. 18A and 19A is a sampling period, but in practice it is fixed at, for example, 10 ms or the like in the calculation step period in the simulation tool used.

DESCRIPTION OF SYMBOLS 1 ... Arithmetic system construction part, 2 ... Source data storage part, 3 ... Input part, 4 ... Display part, 5 ... Output part, 11 ... Program data library, 12 ... Graph program creation / editing part, 13 ... GUI generation part, DESCRIPTION OF SYMBOLS 14 ... Program execution part, 21 ... A _tr calculating part, 22 ... B _tr calculating part, 23, 33 ... Adder for integral value correction, 31 ... A _nw calculating part, 32 ... B _nw calculating part, 24, 34 ... Accumulation Part, 41, 42... Signal transmission path.

Claims (4)

Basic arithmetic unit that inputs time-discrete numerical series data and calculates the basic terms by integrating these time-discrete numerical series data as a polygonal line approximation signal that is continuous with a polygonal line by linear interpolation and using a trapezoidal formula When,
Sampling a jump point of the time-discrete numerical series data, calculating and outputting a correction term for correcting the basic term calculated by the basic calculation unit;
An integrator comprising: a subtractor that generates and outputs a corrected integral value by subtracting the correction term obtained by the correction operation unit from the basic term obtained by the basic operation unit.   2. The integrator according to claim 1, wherein the basic arithmetic unit does not have a direct signal transmission path from input time-discrete numerical sequence data to the basic term.   The correction calculation unit monitors whether or not a jump point has occurred in the time-discrete numerical value series data, and when a jump point has occurred, the jump point of the time-discrete numerical value series data and two preceding points 2. The integral according to claim 1, wherein preceding data is sampled, and a correction term is calculated based on a difference between the extrapolated point and the jumping point when the jumping point is obtained from the two preceding data. vessel. The integrator according to claim 1, wherein the basic operation unit, the correction operation unit, and the subtractor are programmed using an extended signal flow graph and executed by a computer.

Images