WO1999046647A1 - Control method and apparatus therefor - Google Patents

Abstract

In order to output a value calculated by using a controlled variable, a manipulated variable and a usable disturbance value and used to bring a predicted value of the controlled variable into agreement with or close to a desired value S to an operation means having a small number of preset levels (to convert preset values to a series of integer values), the ripple of the controlled variable are evaluated at a pole having the smallest memory effect, and the control period is determined; a correction value expressed by a linear equation of an integrated value of fractions which are rounded to integers and a sign of the change in the manipulated variable added to convert the value into an integer and to output the integer as a manipulated variable; and thus it is possible for the manipulated variable to vary between the preset values (between n and n+1 in the diagramed example) which are acquired values on both sides of a desired value S. When the difference between the acquired value of the manipulated variance and the desired value is great, the correcting value need not be added. The ripple of the controlled variance is small and deviation between the controlled variance and the desired value is small.

Description

 Description Control method and device Technical field

 The present invention provides a control cycle in which a pulsation (ripple) of a control value is equal to or less than a desired value, and corrects an operation value obtained as a value that matches a control value predicted using a response function to a target value, thereby improving resolution. The present invention relates to a control method having a characteristic that a constant bias does not occur even when an operation means (including ON / OFF control) with insufficient is used, and a control device using the method. Background art

 The control device inputs the target value S, control value R, and disturbance value (A, B: sometimes not used), and uses these values and the operation value C to calculate S and R in an arithmetic unit having a storage device. Find C that matches, and output C as a result.

 In actual control, input values obtained from observations and settings are pre-processed, then control calculations are performed, and the obtained values are post-processed and output.

Examples of preprocessing include converting the thermocouple electromotive force to temperature, converting voltage and current values to power values, and performing statistical processing to increase the signal Z noise ratio.

Examples of post-processing include converting the calculated power value to an AC phase value, and rounding a real value to an integer value.

Except for the post-processing related to the present invention, this pre-processing and post-processing is expressed as inputting and outputting values used in control calculations in accordance with customary practices, and also means inputting and outputting converted values.

Recently, in order to realize more precise and faster control, the conventional PID system Modern control is used instead of classical control represented by control.

In modern control, a response function is determined, and an operation value is calculated so that the control value predicted by the response function matches the target value.

 The calculation of these predictions and calculations has dealt with the number of discrete (digital) numbers with the development of computing devices (computers).

The number of operation values (levels) that can be set by digitization is also limited.

The operation value has only 0 and 1 0 NZOFF control is an operation method with two levels of set values. In a control system with a control cycle of 10 seconds, ON operation is performed in integer units of seconds. If the operating value is fixed to one of these levels, the control value will also reach the value determined by this level (attained value). The number of reached values and the number of set levels are equal. The attained value corresponding to the minimum setpoint is one limit value, and the attained value corresponding to the maximum setpoint is the other limit value. The range between these two limits is the controllable range. The value obtained by dividing the controllable range by the number of set levels is the control value resolution.

For convenience, this operation level and the reached value are represented by a series of integer values.

If the resolution is 23.4, it is expressed as an integer with 23.4 as the unit. Because the operation target is high temperature, unstable, foams, and there are restrictions on the materials that can be handled, it is almost impossible to use operation means with a sufficient number of setting levels (operation means with high resolution), or it is often expensive and cannot be used There is none.

In modern control theory, discussion is made from the viewpoint of observability (observable) or control (controllable).

And control over the resolution by means of low-resolution operation was not considered controllable, and there was no prescription.

Next, we will explain how to make the control value predicted by the transfer equation match the target value, and approach the target value.However, if it is limited to the conventional technology, it is essentially a prescription when the resolution of the measured value and the set value is high . Control has a starting point, and it is not necessary to mention an infinite past within a reasonable approximation.

Therefore, as the two infinite sequences that pass from the past to the present and continue into the future, only the following (left regular sequence: hereinafter simply referred to as a sequence) is considered.

A) A sequence (a left regular sequence) with a term that is not 0 itself but has a term that is all 0 on the past side of that term (called the first term, and its term number is called the first place) B) All terms are 0 Is a sequence (represented by 0)

A sequence that has a term that is not 0, but whose futures are all 0 after that term (called the terminating term, and the term number is terminating) is called a finite sequence. The number of terms from the first term to the last term is called the term number (= final one-first-place + 1).

Defines addition (+), subtraction (1), multiplication (·), and division (Z).

a + b = b + a≡ { a m + bm} a- b ≡ {am- bm}

 a · b = b · a = {} ≡ {· · ·, 0, c s + s, s + s + 1, · · ·, C k, · ■ ■}

= {· · ', 0, aA s be s, · ·', aAsbk-A s + aA s + ibk-A s- i + * · - + ak- B s bB s, · · ·} a / b = {Cm} ≡ {· ·-, 0, CA S-BS, CA S-BS + 1,--", CAS-B S + k," *-}

 , 0, aA s / be s, (aAs + i-+ i CA s) / bB s,

 , (& + K-ID + k-1-· + k CAS-, The multiplication is defined by the convolution convolution, and the division is solved from the first term side.

A sequence n = {····, 0,0,0, n where all the items other than the 0th term are O = n, 0,0,0, ···} is identified with the numerical value (scalar) of the 0th term, and the numerical value n represents a sequence. The sequence 0 is another example of this, but a 1 represents a sequence where the 0th term is 1 and all other terms are 0. 0 and 1 are the units of addition and multiplication, respectively.

 a + 0 = aa1 = a

 This identification defines the scalar product by multiplication.

n · a = ί n-am} Defines positive and negative powers as if they were real numbers by repeating multiplication and division. a ° ≡ 1 a ^{k + 1} a a 'a ^k a ^{k _ 1} ≡ a ^k / a However, a ≠ 0 can not be divided by 0, and the distribution law, the associative law, and the addition law And can be calculated in the same way as ordinary algebraic calculations.

If a * b = 0, then a = 0 or b = 0.

As in ordinary algebraic expressions, the multiplication symbol · may be omitted.

数 represents a sequence in which the first term is 1 and all other terms are 0.

The m-th power of 乗 is 1 for only the m-th term and 0 for the other terms.

The reciprocal of 1 1 ΖΛ = Λ— ¹ has the same effect as the Ζ operator of the Ζ transformation.

The product of a sequence whose first place is 1 Δ ョ 1 — Λ, ∑ = Δ ¹ and an arbitrary sequence a is the difference or sum of a.

Room = {· '·, 0, 0, Δ. = 1, -1, 0, 0, ···} ∑ = {· · ·, 0, 0, ∑. = 1, 1,1

_{Σ - a = {a A s} + aAs + i + ■ · · + a »} (AS Hatsukurai of a is)

 Next, the transfer equation is expressed using a sequence.

The transfer equation is an equation that relates the cause (operation value c, disturbance a, b, etc.) to the result (control value r). In order to express zero that there is no change, the cause and effect shall represent the difference (change amount) at each time point.

 a = {· · ·, a- 1, ao, ai, ■ · ·}, b = {· · ·, b- 1, bo, bi, · · ·}, c = {..., c- 1 , Co, ci, ...}, r = {…, r-1, r. , R l, ...},

 (The number of disturbances is not limited to two, but it will be described as two for convenience. There may be multiple operation values and control values, but for simplicity we will explain each one separately.) Linearity and superposition of transfer equations Assume the principle of

Cause a, b, c changes a _n that caused to the n time point, b ", b" hi · a n is after i point, gi 'bfi -c, if Hikiokose the effect of changes that occur in the m time Fm = 111am-1 + 1ΐ2am-2 + ■. + Gl, bm-l + g2.bm-2 +. '+ F1' Cm-l + f2-Cm-2 + ¹ . It becomes. In this equation, the second item, the change of a that took place in two time points before. - Indicates that the (a _"2) of two time points after the effect (h ₂₎ is realized by the m-th time → r _m this A sequence connecting the cause and the result expressed in the amount of change, such as h, g, and f, is called a (pulse) response function.

Since the result is later than the cause, the first order of the response function is 1 or more.

 f = {· · ·, 0, f i. fa. fs, · · ·}

g = {· · ·, 0, gl, g2, g3, · · ·}

h = {· · ·, 0, hi, h ₂ , h ₃ , ·;

This transfer equation can be expressed using a sequence as follows.

 r = f-c + g-b + h-a (Formula 1) Although this formula 1 has an intuitive and easy-to-understand form, the response function is not a finite sequence, so as the control progresses, it increases more and more. You need to go back to the past. (The first place of a, b, c is AS, BS, CS)

 = f 1Cm-1 + ί2Cm-2 +

 + g l 'bm- l + g2't) m-2+'-'+ gm-B S' bB S

+ hi-a _m- : i + h2- am-2 + · · · + hm- A s ■ aA S

Therefore, we use the energy theorem "Limited energy can only do finite work. That is, the cause effect attenuates and stops changing." For example, even if there is a difference in temperature between the input of a 100 W electric heater one second and two seconds before, it is not possible to measure the difference between one hour and ten hours ago. From this theorem, the response function f, g, h is approximated by the following equation using a finite sequence d ', f', g ', h' whose first rank is 1 or more (ends are DE, FE, GE, HE) I can do it.

f = f V (l-d '), g = g' / (l-d '), h = h' / (l-d ') (Conversion formula) Response function decreases exponentially after a certain period of time Then, if FE, GE, and HE are large enough, the final DE of d 'can be set to 1.

Using these finite sequences, the transfer equation is r = f-c + g '-b + h'-a + d '-r (Formula 2)

Since d ', i', _g ', and h' satisfy the condition as a response function (at least one of the first ranks), this equation can be expressed as a cause (external cause c, b, a)

) can be interpreted as changing to r.

An internal cause is an accumulation of external causes and is known as a cause of phenomena such as memory, accumulation, inertia, resonance, and tailing.

The effects of internal causes are called memory effects.

Then, d 'can be thought of as a response function of the memory effect, and f', g ', and h' can be thought of as response functions considering the memory effect.

The root of the following equation for X is called the memory effect (the pole of Γ

_{... χ π Β _ (} } ι χ 0 Ε-ι _ (1, 2 χ ΟΕ - 2 d 'DE = 0 pole of memory effect, represents the attenuation state of the control system.

In a control system that does not oscillate, the pole of the memory effect is positive and less than 1.

d ', f g', h '; f, g, h are pulse response functions.

Since the response function of this second equation is a finite sequence, it can always be calculated using a certain number of past values. The second expression is as follows.

 = f 1 · "-1 + · · + f F E · Cm- F E

 + g 1-bm-l +-', + g G E * bm-G E

 + ll '1' am- 1 +-'* + h' H Eam-H E

 + (1 ·-1 +… + CT D E · -DE

The response functions d ', f g', and h 'are determined by the least squares method, finite identification method, sequential identification method, etc. based on this equation.

Author: Yasuhito Takahashi System and control: Lower Iwanami Shoten 19778 Response functions f, g, h are calculated using d ', f, g', h 'and conversion formulas. The method for determining the operation value that matches or approaches the predicted control value to the target value s using the transfer function (response function) is as follows. The sum of the pulse response function becomes the step response function, and the sum of the cause and the change in the result (difference) becomes the actual value (the raw value of the measurement or setting).

The pulse response function and the cause and effect changes are expressed in lowercase letters, and the step response function and the actual values of the cause and effect are expressed in uppercase letters.

 (Example) R≡∑ 'r r = A' R = R— A 'R R = Λ · R + r

 F≡∑f = ∑f '/ (1 -d')

Λ · R means a sequence one point before R.

Expressions 1 and 2 are rewritten because it is easier to express target values and control values as real values (sum of differences) than as differences.

R = F-c + G-b + H-a (Equation 3)

R = (A + d, 'm)' R + f '-c + g'-b + h '-a (Formula 4) Normally, the parameter m representing the current time is increased by one for each control cycle. Or fix the current time to the 0th term and shift the sequence of causes and effects by one term. The m-th term can be used, but the current time will be expressed as the 0th term.

 c is the last time point, the operation value when no change is made in the future (no operation) (current and future is 0), R is the measured value up to the present and the control value representing the prediction of no operation, c 'is the current The subsequent operation value (0 in the past) and R 'are the control values when c' is executed after c (the measured value in the past and present, and the predicted value in the future).

Then, the predicted value R at the time of no operation can be calculated sequentially from the 1st time to the required time by the 4th formula.

Past and present values can be used as the disturbance values if they are measurable disturbances, and past values, present values, and future values (planned values) can be used if the disturbances are caused intentionally. . Equation 4 removes the effect of this intellectual disturbance. With PID control, the removal of such intellectual disturbances (feedforward) was difficult and required a lot of trial and error.

The required time is up to the FE + DE point in the finite settling method and the program settling method. Optimal control depends on the choice of optimal conditions.

When there is an operation, the fifth equation is obtained as R → R ', c → c + c' in the third equation.

R '= F-(c + c') + G-b + H-a

R '= R + F' c '

F-c '= R'-R (Equation 5) At a specific point in time n, the predicted value R 'during operation is equal to the target value S.

Fn 'C'. Tens h Fn- C E-C 'c E = S „-Rn

(F-c ') n = (S-R) _π ( _n = specific time point) (Equation 6) The finite settling method is a method in which the target value S is invariable from the present time, and the program stabilization method allows for change. How. (These methods are called multipoint settling method.) To find the control value c ', in the multipoint settling method, Equation 6 is regarded as a simultaneous linear equation of unknown c', and in the optimal control method, Equation 6 is It is regarded as an observation equation of the least square method (selecting a weight and a specific point in time considered as an optimal condition).

In other words, the control value and the target value are matched in the multipoint settling method, and close in the optimal control method.

The control value coincides with the target value. It is said that setting closer to Z is settled.

Variations on these methods are of course conceivable.

In equation (6), the time after FE + DE on the left side of F · C 'is linearly dependent on the left side from time FE to time FE + DE.

As a result, in the method of obtaining the manipulated value as a system of linear equations, data before the FE + DE time point is used.

Therefore, usually, using the multipoint settling method, a specific point in time is selected from the FEth point to the FE + DE point, and the last term of the operation value c 'is set to DE to match the number of equations with the unknown. After obtaining the operation value c 'based on Equation 6, output the most recent operation value Co = C-i + c' o, and move on to the next control cycle. Disclosure of the invention

 When selecting the operation means with low resolution (small number of levels), the pulsation (ripple) of the control value caused by reciprocating between the levels (two-sided levels) sandwiching the target value is unavoidable to some extent, It must be avoided that the time average of the control values will cause a constant difference (bias).

 When controlling the temperature of A, such as when controlling the outlet temperature of the cooling medium supplied to A, indirect control is a big problem, but pulsation is a small problem. Usually there is no. In this case, the permissible value of pulsation increases.

Settling by the finite settling method (control value matches target value) is a = 0, b = 0; DE = 1, FN = 1 It is shown in. F I G. 1 is when the output value Co is simply rounded.

It shows how the target value changes with control from each point a to g between level n — 1 to n + 1 when set between level n and level n + 1. You. Thus, simply converting the manipulated value to an integer will result in a constant bias し て も, no matter where it starts.

In this example, if the target value is between ± 0.5 (1-d '), there will be a constant deviation. (If 1 = 0.5, it will be 50% of the whole setting range. The step response function F = ∑ · f of the manipulated value is a simple increase function, and IS-R * I <0.5'F _FB is the dead band (the range of the target value causing bias). The part after the decimal point has no meaning.

 In this way, simply converting the low-resolution operation means to integers and outputting them cannot provide high accuracy.

 Resolve this problem as follows:

First, as is usual in modern control methods, the response values d 'and f' are determined by appropriately changing the operation values in preliminary measurements. To know the response function g ', h' of the intelligent disturbance Must make that change happen. As for the operating value, a pulse-like or step-like change with a safe operating value range is attempted. Observe this situation and find the response function using the least squares method, for example. Using this response function, the pulsation is reduced below the desired value by the following means.

The pole of the memory effect with the smallest absolute value is d ", the allowable ripple size is s, and Y = log (1-ε) / log (ld" l)

Then, select a new control cycle with a value less than Y · t (X · t). If d "is 0.8 to 0.98, one of the options is to endure the ripple without shortening the control cycle.

Either calculate the response function in the control cycle selected in this way by applying the extended Z-transform method, or measure the response function again to set the initial value of the response function. Control starts using the initial value of this response function.

The following methods can be used as an application of the extended Z transform method.

The poles of the memory effect _{d a, d b, · ·} ·, when d, and, 'a d' d in period after change = 1 over ^{(1- (Κ Χ Λ) ·} (1- d b x A) · · ■ (1— dU ^x A)

will do.

For f g ', h', draw a graph (Fig. 3) of ∑ · ί ', ∑' g ', ∑' h, and approximate it with a smooth curve. Then, create a new control cycle (1Χ, 2Χ, · Read the value at the time corresponding to '·).

You can convert the response function using other methods.

 However, such a conversion is only a guide and it is safe to re-measure. By selecting such a control cycle, the pulsation of the control value will be less than the desired value. However, all figures show cases where the control cycle is slightly inappropriate to make it easier to see the pulsation.

Next, the response function is modified using the preferred identification method (finite identification method, least squares method, sequential identification method, · ■ ·) in the actual production. If it is recorded in the non-volatile memory in a timely manner so that it can be used as the initial value at the start of the next control, a learning effect will be generated and the control can be started in a better state next time.

Also, find the latest operating value Co using your favorite control method (finite settling method, program setting method, optimal control method, ...).

 This operation value = +. Before converting the output value into an integer, the integral value δ is obtained by integrating (accumulating) the fraction obtained when the operation value up to the previous point is converted into an integer C.

 δ δ + C c C 0 <k≤ 1

 5 on the left is the current value, and <5 on the right is the previous value.

And the sign of the last operation value sgn (c 'o)

 sgn (x) is a function that takes positive, 0, and negative values of X and takes values of -1, 0, and 1.

 The value of sgn (0) can be +1 or 11 as well.

Correction value n expressed by the linear expression

 Τ) = ρ · <5 + q-sgn (co) 0≤, q p + 2 · q≤ 1 If the correction value 7] is a simple increasing function of The functions will be equivalent.

Plus C. +? 7 = C- + + "is converted to an integer and output.

 Co = Int (C- + c Ό + η)

 Int (x) is a function that converts χ to an integer and uses rounding.

 If p ÷ 0, any function such as rounding, rounding down, rounding up, etc., is a nearly equivalent means of converting to an integer.

The integral of the fractional integral δ and the sign of the last manipulated value, sgn (c'Q), promote the transition between the two levels in a manner similar to the integral and proportional terms in PID control.

As a result, the manipulated value transitions between the two levels, the control value pulsates above and below the target value, and the average value over time of the control value matches the target value.

Fig. 2 shows a case where this transition is made under the condition of Fig. 1. The non-negative numbers p and q in the range of p + 2'q≤l are selected because the integral term rotates the phase in the loop transfer and the proportional term creates an oscillation cause by increasing the gain.

 A positive number k less than or equal to 1 can be reduced to less than 1 to reduce phase rotation. If the oscillation is very small or no oscillation occurs, k can be set to 1.

If there is a transition to a level other than the two-sided level, no correction is required.

If you do not make corrections,

 Co = Int (C-1 + c Ό)

It becomes.

Change in operating value C. — C— If the absolute value of i is 2 or more, the transition is to a level other than the two-sided level.

You can use this as a criterion.

In the presence of noise, a transition to a two-sided level occurs without correction. However, the transition caused by this noise alone causes large fluctuations (average) in the average value over a slightly longer time span.

By using smaller values of p and q, we can make this Juragi smaller.

By outputting the most recent operation value Co, this control cycle is completed, the control cycle is updated, and the procedure moves to the next control cycle (time).

Note that when operating values are observed, values different from the set operating values may be observed.

In this case, use the measured value.

 In this case, the manipulated value C-i in the previous cycle (previous point) is not always an integer value.

 In this case, the error integral is corrected with the measured C-i.

δ =-3 + C- 2 + c'-iCi 0 <k≤ 1 BRIEF DESCRIPTION OF THE FIGURES

 Fig. 1 is a graph when the operation value is converted to an operation method with low resolution by simply converting the operation value to an integer.

From any of a to g, there is a constant difference 目標 from the target value S.

η-1, η, η + 1 indicates the control level, and 0 to 7 indicate the control time

 FIG. 2 is a graph showing the operation state according to the present invention.

Changes from any of a to _g repeat the pulsation across the target value S. n-1, η, _η + 1 indicates the control level, and 0 to 7 indicate the control time

 Fig. 3 shows how to modify the response function using a graph when changing the control cycle.

FI G. 4 shows a graph that determines the end of the response function.

BEST MODE FOR CARRYING OUT THE INVENTION

 The realities of control vary and there is no always the best form. Therefore, let us explain the case where DE = 1 and there is one predictable disturbance. In advance, the approximate form of the transfer equations d 'and f g' is obtained at the control cycle t.

If DE = 1, then d "= d 'i-cU is the only pole.

Except for special cases, when d "is 1 or more, the control cycle is too short, and when it is negative, the measurement time is too short.

Normally, it is a positive number less than 1.

If this doesn't happen, we have to make one DE. When the allowable ripple is £, the actual control cycle T is

T≤ t · log (1-ε) / log (d ").

 As shown in FI G.3, Γ, g 'are approximated by a smooth curve, the values at period T are read, and the term numbers n, m that can be regarded as f ヽ = 0, g = 0 are obtained. Set n and m to the end of f 'and g'.

If the peak value is less than 1 Z5, there is little practical hindrance to the final position.

Therefore, in an example like FIG.4, the final position is 4.

Here, the end of f 'and g' is assumed to be 2 and 3 for convenience of explanation.

Measure the response function again at the new control cycle and set it to the actual initial value. Modify the response function using the preferred identification method (finite identification method, least square method, sequential identification method, etc.), record it in nonvolatile memory as appropriate, and use it as the initial value at the next control start. I will do so.

Convert d ', f g' to obtain f, g, F.

In addition, using the control method you prefer (finite settling method, program settling method, optimal control method, ...), the most recent operation value C is used. Ask for.

If you choose the finite settling method, Rl = Ro + d 'l To + f' 2-C- l + f '3-C-2 + g'l'bo + g '2-b- l + g' 3-b-2

R ₂ = Ri + d ':-(Ri-Ro) + f' 3-c- i + g 'i -bi + g' ₂ -bo + g ' ₃ -b- i

_{R 3 = R2 + d 'l} - (R 2 -Ri) + g' l · ba + g '2 · bi + g' 3 · bo

Guess ~ 1 ~ ₄ at the time of no operation by

To find c ' ₀ = {F ₂ (S ₂ -R ₂ ) —F ^ Ss-R ₃ )} / {F ₂ ² —FF ₃ }. As a correction method, we will use only integration. That is,

CC = C-i + c'o

Co = Int (CC)

 If Co <C- i-1 or C-i + 1, then? ? = 0

Otherwise, C. = Int (CC +) n = k- 7} + CC- Correct and update with C0, output Co, and manipulated value of the next cycle C— i— (:. Where k is k = l, k = 0.9, ...

If no improvement is found, set k = 1, and if an improvement is found, set the value to the optimal value.

 In this way, using a simple method of selecting the control cycle and correcting the operation value, it is possible to use a simple and inexpensive operating method with a small number of setting levels, which is a reliable means that is less likely to break down. High control is possible.

 Applying to temperature control using a refrigerant, just controlling the opening time of the refrigerant supply has made it possible to achieve higher accuracy than with conventional inverters and pulse valves. The control valve for refrigerant foams in the part that controls the flow rate, and hysteresis appears in the flow rate, and the reproducibility is usually poor. Achieving control equal to or better than a coarse time-controlled on-off valve is of great value along with the economics of parts.

Claims

The scope of the claims 1. Using the past and present control values, past operation values and available past, present, and future disturbance values, estimate future control values, and determine the operation value that causes the control value to match or approach the target value. In the required control method, the pulsation evaluated at the minimum memory effect pole is acceptable by using an operating means that is larger than the desired control resolution by dividing the control range by the number of set levels (represented by a series of integers). The control cycle is determined so as to obtain the value that is calculated, and the correction value expressed by the linear expression of the integrated value of the fraction and the sign of the change of the latest operation value when the operation value is converted to an integer with the change of the latest operation value (However, in the case of a transition to a level other than the two-sided level, the correction value does not need to be added). 2. Estimate future control values using past and present control values, past operation values, and available past, present, and future disturbance values, and determine the operation values that cause the control values to match or approach the target values. In a device that uses the control method that is sought, use the operating means that divides the control range by the number of set levels (represented by a series of integers) larger than the desired control resolution, and evaluates at the extreme of the minimum memory effect. The control cycle is determined so that the magnitude of the pulsation becomes the allowable value, and the integral value of the fraction when the operation value is converted to an integer in the change of the latest operation value and the sign of the change of the latest operation value are determined. A control device characterized by adding a correction value represented by a linear expression (however, if a transition to a level other than the two-sided level occurs, it is not necessary to add the correction value) and outputting the result as an integer.