JP3352701B2 - Control method and device - Google Patents

Description

The present invention relates to a digital predictive control that directly calculates an operation value using a response function from a set value and a measured value of a target value, an operation value, a control value, and an intellectual disturbance, and the operation value can be set. When operating means with insufficient resolution due to a small number of levels are used, the pulsation (ripple) of the control value is suppressed, and the operating value obtained as a value that matches the control value to the target value is constantly corrected. Provides a way to eliminate bias.

2. Description of the Related Art A control device inputs a target value S, a control value R, and a disturbance value (A, B: sometimes not used), and uses these and an operation value C in an arithmetic unit having a storage device to generate S and R. Find C that matches and outputs C as a result.

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

As an example of preprocessing, convert the thermocouple electromotive force to temperature,
It converts voltage and current values into power values, and performs statistical processing to increase the signal / 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, the pre-processing and post-processing are expressions of inputting and outputting values used in control calculation according to a custom, and also mean input and output of converted values.

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

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

The calculation of this prediction and calculation is performed by an arithmetic
With the development of, it has come to handle discrete (digital) numbers.

The number of operation values (levels) that can be set by digitalization becomes finite.

ON / OFF control with only 0 and 1 operation values is an operation method with two levels of set values. In a control system with a control cycle of 10 seconds, the operation method of turning on for an integer number of seconds is an 11-level operation method.
If the manipulated value is fixed at one of these levels, the control value will also reach the value (attained value) determined by this level. The number of reached values and the number of set levels are equal. The reached value corresponding to the minimum set value is one limit value, and the reached value corresponding to the maximum set value 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. Due to the high temperature, instability, foaming, and limitations on the materials that can be operated, it is often impossible or impossible to use operation means with a sufficient number of settings (high-resolution operation means) due to their high cost. . Observation is possible in modern control theory that uses not only control values and target values but also intellectual disturbances to calculate operation values in the past.
And control is possible (controllable).
And control over the resolution by operating means with low resolution was not considered controllable, and there was no prescription.

Next, the control value predicted by the transfer equation matches the target value /
I will explain how to make it closer, but if you limit it to conventional technology, it is essentially a prescription when the resolution of measured values and set values is high.

Control has a starting point, and it is not necessary to mention an infinite past within a reasonable approximation. So, as an infinite sequence of numbers that goes from the past to the present and continues into the future,
Consider only the following A) and B) (left regular sequence: hereinafter simply referred to as a sequence).

A) A sequence (left regular sequence) having a term that is not 0 but has a term that is all 0 on the past side of the term (called the first term, and the term number is referred to as the first place) B) All terms are 0 Is a finite number sequence that has a term that is not 0 itself, but whose future side is all 0 than that term (terminating term, term number of which is terminating). .

The number of terms from the first term to the last term is called the number of terms (= final term-first term + 1).

Define addition (+), subtraction (-), multiplication (•), and division (/).

a + b = b + a≡ { a n + b n} a-b≡ {a n -b n} ( Hatsukurai represents a final position denoted S, the E) a · b = b · a = {c n} ≡ ｛…, 0, c _{cS = aS + bS} = a _aS b _bS ,…, c _n = a _{aSb n-aS} + a _{aS + 1} b _n-aS-1 +… + a _n-bS b _bS ,…｝ a / b = {C _n } ..., 0, c _{cS = aS−bS} = a _aS / b _bS , c _{aS−bS + 1} = (a _{aS + 1} −b _{bS + 1} c _aS−bS ) / b _bS , …, C _{aS-bS + m} = (a _{aS + m} −b _{bS + 1} c _{aS-bS + m−1} −… −b _{bS + m} c _aS-bS ) / b _bS ,…｝ Multiplication is defined by convolution The division is a solution to this from the first term side. A sequence k = 0 except for the 0th term.
｛…, 0,0,0, k ₀ = k, 0,0,0,…｝ is identified with the numerical value (scalar) of the 0th term, and the numerical value k represents a sequence. Sequence 0
Is also an example, where 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 = a a · 1 = a This identification defines the scalar product by multiplication.

KA = ・ k｝ _n ｝ Defines positive and negative powers in the same way as real numbers by repeating multiplication and division.

a ⁰ ≡1 a ^{k + 1} ≡a · a ^{k ak-1} ≡a ^k / a However, in the a ≠ 0 sequence operation, division by 0 cannot be performed, and the exchange law of the distribution law, the coupling law, and the multiplication method is Satisfy and calculate in the same way as ordinary algebraic calculations.

If a · b = 0, a = 0 or b = 0 holds.

As in ordinary algebraic expressions, multiplicative symbols and may be omitted.

A sequence where the first term is 1 and all other terms are 0 is represented by Λ.

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

The reciprocal of Λ, 1 / Λ = Λ ^-1, has the same effect as the Z operator in the Z transform.

The product of the sequence Δ≡1-Λ, Σ = Δ ^-1 whose first term is 1 and any sequence a is the difference and sum of a.

Δ = {..., 0,0, Δ 0 = 1, -1,0,0, ...} Σ = {..., 0,0, Σ 0 = 1,1,1 ...} Δ · a = {a n - a _n-1 ｝ Σ · a = ｛a _aS + a _{aS + 1} + ... + a _{n a} (aS is the first place of a) 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 0 that there is no change, the cause and effect shall represent the difference (change amount) at each time point.

a = ｛…, a ₋₁ , a ₀ , a ₁ ,…｝, b = ｛…, b ₋₁ , b ₀ , b ₁ ,…｝, c = ｛…, c ₋₁ , c ₀ , c ₁ ,…｝, R = ｛…, r ₋₁ , r ₀ , r ₁ ,…｝, (The number of disturbances is not limited to two, but it is described as two for convenience. (It will be explained one by one for simplicity.) We assume the linearity of the transfer equation and the principle of superposition.

If the changes a _n , b _n , b _n caused by the causes a, b, c at the n time point cause the effects of h _i · a _n , g _i · b _n , f _i · c _n , after the i time point , change r _m that occur in the m-th point in _{time, r m = h 1 · a} m-1 + h 2 · a m-2 + ...
+ G ₁ · b _m-1 + g ₂ · b _m-2 +… + f ₁ · c _m-1 + f ₂ · c _m-2 +… In this formula, the second item is a that occurred two times before.
The effect (h ₂ ) of the change (a _m-2 ) after two time points changes from the _m- th time point to r _m
It means that it is realized by.

The sequence connecting the cause and the result expressed in the amount of change like h, g, f is called (pulse) response function.

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

f = ｛…, 0, f ₁ , f ₂ , f ₃ ,…｝ g = ｛…, 0, g ₁ , g ₂ , g ₃ ,…｝ h = ｛…, 0, h ₁ , h ₂ , h ₃ ,…｝ This transfer equation can be expressed as a sequence as follows.

r = fc * g * b + ha * (first expression) This first expression has an intuitive and easy-to-understand form. However, since the response function is not a finite sequence, the calculation goes back and forth as control progresses. will become necessary. (A,
aS, bS, cS are the first ranks of b and c) r _m = f ₁ · c _m-1 + f ₂ · c _m-2 + ... + f _m-CS · c _CS + g ₁ · b _m−1 + g ₂・ B _m-2 + ... + g _m-bS・ b _bS + h ₁・ a _m-1 + h ₂・ a _m-2 + ... + h _m-aS・ a _aS Then, the energy theorem "For finite energy, finite work You can only do it, that is, the effect of the cause will attenuate and stop changing over time. " For example, even if there is a difference in the temperature between 1 second and 2 seconds before the input of the 100W electric heater, it is not possible to measure the difference between 1 hour and 10 hours ago.

Using this theorem, the finite sequence d ', f', g ',
Approximate the response function f, g, h with h '(end is dE, fE, gE, hE) by the following formula.

f = f '/ (1-d'), g = g '/ (1-d'), h = h '/ (1-d') (Conversion formula) The response function becomes exponential after a certain time has passed. Since it decreases and approaches 0, if fE, gE, hE are sufficiently large, the end dE of d '
Can be 1.

Using these finite sequences, the transfer equation is

r = f ′ · c + g ′ · b + h ′ · a + d ′ · r (2) Since d ′, f ′, g ′, h ′ satisfies the condition as a response function (first or more than 1), The equation can be interpreted as changing the external causes c, b, a into a cause (internal cause) r that is also the result.

Internal causes are actions that store external causes.
It is known as a cause of phenomena such as inertia, resonance, and tailing.

The effects of internal causes are called memory effects.

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

The root of the following equation for X is called the memory effect d 'and the pole.

X ^dE −d ′ ₁・ X ^dE-1 −d ′ ₂・ X ^dE-2 −… −d ′ _dE = 0 The pole of the memory effect indicates the damping 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 the second equation is a finite sequence, it can always be calculated using a certain number of past values. N-th
The terms are as follows:

r _n = f ' ₁ · c _n-1 + ... + f' _fE · c _n-fE + g ' ₁ · b _n-1 +… + g' _gE · b _n-gE + h ' ₁ · a _n-1 +… + h ' _hE · a _n-hE + d' ₁ · r _n-1 + ... + d ' _dE · r _{n-dE The} response function d', f ', g', h 'is based on this equation, Determined by the identification method, sequential identification method, etc.

Yasuhito Takahashi System and control Upper and lower Iwanami Shoten 19
Year 78 The response functions f, g, h are calculated using d ', f', g ', h' and a conversion formula.

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 change in cause and effect (difference) becomes the actual value (the raw value of the measurement or setting).

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

(Example) R≡Σ · rr = Δ · R = R−Λ · R R = Λ · R + r F≡Σ · f = Σ · f ′ / (1-d ′)） · R is 1 more than R Means the sequence before the point.

Since it is easier to express the target value and the control value with the actual value (sum of the difference) than with the difference, the first expression and the second expression
Rewrite the expression.

R = F · c + G · b + H · a (Equation 3) R = (Λ + d ′ · Δ) · R + f ′ · c + g ′ · b + h ′ · a (Equation 4) Usually, a parameter m representing the present time for each control cycle. Increase by one or fix the local point to the 0th term and shift the sequence of cause and effect by one term.

The m-th term may be used, but the present time will be expressed in the 0th term.

c is an operation value when the previous time is not changed last time (no operation) (current and future are 0), R is a measured value up to the present and a control value representing a prediction at the time of no operation, and c ′ is a current value after the present. Set the operation value (0 in the past) and the control value when c 'is performed after R' after c (measured value in the past and present, predicted value in the future).

Then, the predicted value R at the time of no operation can be calculated sequentially from the first time to the required time by the formula (4).

Past and present values can be used as disturbance values if they are measurable disturbances, and past values, present values, and future values (planned values) can be used if disturbances are caused intentionally. 4th
The expression can eliminate this intellectual disturbance effect.

With PID control, it is difficult to remove such intellectual disturbances (feedforward), and it requires a lot of trial and error.

The required time point is fE in finite settling and program settling.
Up to the point of + dE, the optimal control method depends on the selection 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 settling time n, the predicted value R ′ at the time of operation is the target. It is equal to the value S.

F _n · c ′ ₀ +... + F _n−CE · c ′ _CE = S _n −R _n (F · c ′) _n = (SR) _n (n = settling time) (Equation 6) Finite settling method Is a method that makes the target value S invariable from the current time. The program settling method is a method that recognizes a change. (These two methods are referred to as a multipoint settling method.) To obtain the control value c ′, the multipoint settling method regards the sixth equation as a simultaneous linear equation of unknown c ′, and the optimal control method uses the sixth equation. It is regarded as the observation equation of the least squares method (selecting the weight considered as the optimal condition and the settling time).

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

It is said that setting / approaching the control value to / to the target value is settled, and that the control value is settled.

Variations on these methods are of course conceivable.

In equation (6), the time after the time fE + dE on the left side of F · c ′ is linearly dependent on the left side from the time fE to the time fE + dE.

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

Therefore, usually, the point of settling is set from the point fE to the point
Select at the time of fE + dE, and set the final term of the operation value c 'to dE to match the number of equations and unknowns.

When the operation value c ′ is obtained based on the sixth equation, the latest operation value C ₀ =
Output as C _-1 + c _'0, go to the next control cycle.

DISCLOSURE OF THE INVENTION When selecting an operation means having a low resolution (a small number of levels), pulsation (ripple) of a control value caused by reciprocating between levels (two-sided levels) sandwiching a target value is inevitable to some extent. In addition, it must be avoided that the time average of the control values causes a constant difference (bias).

When controlling the temperature of A, when controlling indirectly, such as controlling the outlet temperature of the cooling medium supplied to A, bias is a big problem, but pulsation is only a small problem. Is normal. In this case, the pulsation tolerance increases.

Figures 1 and 2 show how the settling (control value coincides with the target value) by the finite settling method, where a = 0, b = 0; dE = 1, fE = 1. FIG.1 is the case where output value C _O is just rounded.

It shows how the target value changes by control from points a to g between levels n-1 to n + 1 when the target value is set between levels n and n + 1. Thus, simply converting the operation value to an integer will result in a constant bias し て も regardless of the starting point.

In this example, if there is a target value between each achievement level ± 0.5 (1-d ' ₁ ), there will be a constant bias. If d' ₁ = 0.5, it will be 50% of the entire setting range.

Normally, the step response function F = Σ · f of the manipulated value is a simple increasing function, and | S−R ^* | <0.5 · F _fE is the dead zone (the range of the target value _causing bias).

In this case, the decimal point has no meaning as a target value.

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

 Resolve this problem as follows:

First, as is the usual method of modern control method, the response value d ', f' is obtained by appropriately changing the operation value by predictive measurement at the control period t. In order to know the response function g ', h' of the intellectual disturbance, it must be changed. As for the manipulated value, a pulse-like or step-like change with the full range of the manipulated value is attempted. Observe this situation and find the response function using the least squares method, for example. Using this response function,
Use the following measures to reduce the pulsation below the desired value. When the pole of the memory effect having the minimum absolute value is d ″, the allowable ripple size is ε, and Y = log (1−ε) / log (| d ″ |), the new control cycle is Y · t or less. Value of (X
Select to t).

If d ″ is 0.8 to 0.98, one of the options is to endure the ripple without shortening the control cycle too much.

The response function in the control cycle selected in this way is expressed as an extended Z
Calculate by applying the transformation method, or measure the response function again and set it to the initial value of the response function.

Control is started using the initial value of this response function.

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

When the poles of the memory effect are d _a , d _b ,..., D _z , d ′ in the changed cycle is d ′ = 1− (1−d _aX ^X ) · (1−d _b ^{X X} ) … (1-d _z ^X Λ).

For f ', g', h ', draw a graph of Σ · f', Σ · g ', Σ · h' (FIG. 3), approximate it with a smooth curve, and add a new control cycle (1X, 2X 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 is sure to be re-measured.

By selecting such a control cycle, the pulsation (ripple) of the control value will be less than the desired value. However, all figures show cases where the control cycle is slightly inappropriate in order to make it easier to see the pulsation.

Next, the response function is modified using the preferred identification method (finite identification method, least square 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 occur and the control can be started in a better state next time.

In addition, the control method of preference (finite settling a conventional method, program integer conventional method, optimal control method, ‥‥), we asked for the last operation value C _0.

Before _converting this operation value C ₀ = C ₋₁ + c ′ ₀ into an integer and outputting it,
The integrated value obtained by integrating (accumulating) the fraction δ δ = k · δ + C -2 + c '-1 -C -1 0 <k ≦ 1 the left side of [delta] when the operation value up to the previous time and integer C _-1 The current value, δ on the right side is the value at the previous time.

And the sign of the most recent operation value sgn (c ' ₀ ) sgn (x) is a function that takes a value of -1,0,1 with x being positive, 0, negative. The value of sgn (0) is +1 or -1 You can also.

Η = p · δ + q · sgn (c ′ ₀ ) 0 ≦ p, q p + 2 · q ≦ 1 The correction value η is expressed by a linear expression of a non-negative coefficient p, q The function is equivalent if it is a simple increasing function of.

The value C ₀ + η = C _-1 + c ' ₀ + η obtained by adding is converted to an integer and output.

C ₀ = Int (C ₋₁ + c ′ ₀ + η) Int (x) is a function that converts x to an integer, and uses rounding.

If p ≠ 0, any function such as rounding, rounding down, rounding up, etc. will be almost equivalent as an integer conversion function.

Integral fraction integral δ and sign of the last manipulated value sgn (c ' ₀ )
Promotes a 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 both 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 the case of this transition under the condition of FIG.1. Since the integral term rotates the phase in one-cycle transmission and the proportional term increases the gain by increasing the gain, the non-negative numbers p and q in the range of p + 2 · q ≦ 1 are selected.

By setting the positive number k less than 1 to less than 1, the phase rotation can be reduced.

If the oscillation is very small or no oscillation occurs, k may be set to 1.

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

If you do not want the correction is the _{C 0 = Int (C -1 +} c '0).

If the absolute value of the operation value change C ₀ -C _-1 becomes 2 or more, it is a transition 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 due to this noise alone
The fluctuation of the average value (Juragi) in a slightly longer time period becomes larger.

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

By outputting the most recent operation value C ₀ , this control cycle is ended, a procedure for updating the control cycle is performed, and the next control cycle (time)
Move on to

In addition, when observing the operation value, a numerical value different from the set operation value may be observed.

In this case, use the measured value.

In this case, the operation value C _-1 in the previous cycle (previous point) is not always an integer value.

In this case, correct the error integral with the measured C- ₁ .

δ = k · δ + C _-2 + c ' _-1 -C _-1 0 <k ≦ 1 Brief Description of the Drawing FIG. 1 is a graph in which an operation value is output to a low-resolution operation means only by converting the operation value into an integer. is.

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

n-1, n, n + 1 indicate the control level, and 0-7 indicate the control time. FIG. 2 is a graph showing the operation state according to the present invention.

The change from any of a to g repeats the pulsation across the target value S.

n−1, n, n + 1 indicate 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.

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

Best mode for carrying out the invention The actual state of control varies, and there is no always the best mode. Therefore, the case where dE = 1 and there is one predictable disturbance will be described. In advance, the approximate form of the transfer equations d ', f', g 'is determined at the control cycle t.

In the case of dE = 1, will be _{d "= d '1 = d} a is the only pole.

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

Normally, it is a positive number less than 1.

If this is not the case, 1 <dE must be set.

When the allowable ripple is ε, set the actual control cycle T to T ≦ t · log (1-ε) / log (d ″).

As in Fig.3, f ', g' is approximated by a smooth curve, the value at period T is read, and the term number that may be regarded as f ' _n = 0, g' _m = 0
Find n, m and make n, m the end of f ', g'.

If it is less than 1/5 of the peak value, there is almost no practical problem even at the end.

Therefore, in the example shown in FIG.

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

Measure the response function again at the new control cycle, and set it to the actual initial value.

Favorite identification methods (finite identification method, least squares method, sequential identification method,
Correct the response function in step ‥‥) and record it in nonvolatile memory as appropriate, so that it can be used as the initial value at the next control start.

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

In addition, the control method of preference (finite settling a conventional method, program integer conventional method, optimal control method, ‥‥), we asked for the last operation value C _0.

If the selected finite integer conventional _{method, r 0 = R 0 -R 1} R 1 = R 0 + d '1 · r 0 + f' 2 · c -1 + f '3 · c -2 + g' 1 · b 0 + g ' ₂ · b _-1 + g' ₃ · b _-2 R ₂ = R ₁ + d ' ₁ · (R ₁ -R ₀ ) + f' ₃ · c _-1 + g ' ₁ · b ₁ + g' ₂ · b ₀ + g ' ₃ · b _-1 R ₃ = R ₂ + d ' ₁ · (R _2- R ₁ ) + g' ₁ · b ₂ + g ' ₂ · b ₁ + g' ₃ · b ₀ , R _{1 to} R ₄ at the time of no operation And solving the simultaneous equations F ₂ · c ' ₀ + F ₁ · c' ₁ = S _2- R ₂ F ₃ · c ' ₀ + F ₂ · c' ₁ = S _3- R ₃ , and c ' ₀ = _{{F 2 (S 2 -R 2} ) -F 1 (S 3 -R 3)} / {F
₂ ² −F ₁ F ₃ ｝

As a correction method, we will use only integration. That is, CC = C ₋₁ + c ′ ₀ C ₀ = Int (CC) If C ₀ <C ₋₁ −1 or C ₋₁ +1 <C ₀ , if η = 0, then C ₀ = Int ( CC + η) η = k · η + CC-C
₀ Fixed, Update, outputs C _0, the next cycle operation value C _-1 ← C
_Set to ₀ .

As for k, k = 1, 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, highly accurate control can be performed by using an operation means with a small number of set levels, which is inexpensive by the simple method of selecting the control cycle and correcting the operation value, and in some cases, is a reliable means that is unlikely to fail. Is possible.

Applying to temperature control using refrigerant, just controlling the open 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.

──────────────────────────────────────────────────続 き Continuation of the front page (56) References JP-A-63-128401 (JP, A) JP-A-2-249001 (JP, A) JP-A-4-64107 (JP, A) Automatic control handbook (basic bias) ", Ohmsha, Japan, October 30, 1983, p. 73-75 (58) Field surveyed (Int. Cl. ⁷ , DB name) G05B 13/02-13/04 G05B 21/02

Claims (2)

(57) [Claims] 1. R, S, C, A, and B are each a control value; a target value; an operation value; and a sequence representing two types of intellectual disturbances.
When the sequence representing the difference of B is r; s; c; a, b, r is a finite sequence f ', g', h ', d' whose first rank is 1 or more (ends are fE, gE, respectively) , hE, dE) using the following equation: r = {r _n } = d ′ · r + f ′ · c + g ′ · b + h ′ · a = ・ d ′ ₁ · r _n−1 + ... + d ′ _dE · r _n-dE + F ' ₁ · c _n-1 + ... + f' _fE · c _n-fE + g ' ₁ · b _n-1 +… + g' _gE · b _n-gE + h ' ₁ · a _n-1 +… + h' _hE · In the control system represented by a _n−hE ｝, the operation value c is fixed to the output value at the previous time (when the current time is represented by the 0th term, c _{n ≧ 0} =
0), and using past, present, and future available data for the intellectual disturbances a and b, R = {R _n } = (Λ + d '· Δ) · R + f' · c + g '· b + h' · a = ｛R _n-1 + d ' ₁ · r _n-1 + ... + d' _dE · r _n-dE + f ' ₁ · c _n-1 + ... + f' _fE · c _n-fE + g ' ₁ · b _{n- 1} + ... + g ' _gE · b _n-gE + h' ₁ · a _n-1 + ... + h ' _hE · a _n-hE ｝ _predicts a future control value (R _{n> 0} ), and f = f ′ / (1−d ′) = ｛f _n = f ′ _n −d ′ ₁ f _n−1 −d ′ ₂ f _{n−2 −...−} d ′ _dE f _n−dE ｝ F = Σf = ｛F _n = f ₁ + f ₂ + ... using the step response function F is calculated by + f _n}, condition setting time point _n (c 'n ₌ simultaneous linear equations _{0~dE) (F · c')} n = F n-dE c ′ _dE + F _{n + 1−dE} c ′ _dE−1 +... + F _n c ′ ₀ = S _n −R _n n = fE to fE + dE, c ′ _{n> dE} = 0 is obtained, and an operation value C is obtained. ₀ = at C _-1 + c _'0 in the set can be values (referred to as integer) output controlling method, capable of setting a manipulation value value In case the resolution of the value to be reached if the equity is greater than desired, in order to suppress the ripple, d was previously identified in the control cycle t '= {d' _n} equation X made from sections of ^dE -d ' ₁ · X ^dE-1 −d ′ ₂ · X ^dE-2 −… −d ′ _dE = 0 when the absolute value of the solution (pole) is minimum d ″, and the allowable ripple size is ε, Calculate Y = log (1−ε) / (log (| d ″ |), set the control cycle T to a value of Y · t or less, and identify f ′, g ′, h ′, d ′ in the control cycle T. Before recalculating f and F, and correcting the bias of the control value, before converting the operation value C ₀ = C _-1 + c ' ₀ into an integer for each control cycle and outputting it, integer operations value up to C _-1 was cumulatively adding the fractional time value [delta] and _{δ = k · δ + C -2} + c '-1 -C -1 0 <k ≦ 1 left-hand side of [delta] are at the moment, Δ on the right side is the sg with the sign sgn (c ' ₀ ) of the operation value nearest the value at the previous time. n (x) is a function that takes a value of -1,0,1 with x being positive, 0, or negative, and the value of sgn (0) can be set to +1 or -1. Let η be η = p · δ + q · sng (c ′ ₀ ) 0 ≦ p, q p + 2 · q ≦
1 Added numerical value C ₀ + η = C ₋₁ + c ′ ₀ + η C ₀ = Int (C ₋₁ + c ′ ₀ + η) Int (x) is a function that converts x to an integer, and outputs the result. Control method. 2. R; S; C; A, B are each a sequence representing a control value; a target value; an operation value; and two types of intellectual disturbances.
When the sequence representing the difference of B is r; s; c; a, b, r is a finite sequence f ', g', h ', d' whose first rank is 1 or more (ends are fE, gE, respectively) , hE, dE, and dE = 1), and r = {r _n } = d ′ · r + f ′ · c + g ′ · b + h ′ · a = ｛d ′ ₁ · r _n−1 + f ′ ₁ · C _n-1 + ... + f ' _fE · c _n-fE + g' ₁ · b _n-1 + ... + g ' _gE · b _ng E + h' ₁ · a _n-1 + ... + h ' _hE · a _n-hE ｝ In the control system represented by the following expression, the operation value c is fixed to the output value at the previous time (when the current time is represented by the 0th term, c _{n ≧ 0} =
0), and using past, present, and future available data for the intellectual disturbances a and b, R = {R _n } = (Λ + d '· Δ) · R + f' · c + g '· b + h' · a = ｛R _n-1 + d ' ₁ · r _n-1 + f' ₁ · c _n-1 + ... + f ' _fE · c _n-fE + g' ₁ · b _n-1 + ... + g ' _gE · b _{n- gE} + h ′ ₁ · a _n−1 +... + h ′ _hE · a _n−hE ｝ _predict a future control value (R _{n> 0} ), and f = f ′ / (1−d ′) = ｛f _n = f _'n -d' using _{1 f n-1} F =} Σf = {F n = f 1 + f step response function F is calculated by ₂ + ... + f _n}, condition setting time point n (c ' ( _Equivalent linear equation of _{n = 0,1} ) (F · c ′) _fE = F _fE−1 c ′ ₁ + F _fE c ′ ₀ = S _fE− R _fE (F · c ′) _{fE + 1} = F _fE c ′ ₁ + F _{fE + 1} c ' ₀ = S _{fE + 1} -R _{fE + 1} is satisfied c' ₀ = ｛F _fE (S _fE -R _fE ) -F _fE-1 (S _{fE + 1} -R _{fE + 1} ) ^{_{} / (F fE 2 -F fE}} -1 F fE + 1) is calculated, and (referred to as integer) operating value _{C 0 = C -1 + c '} 0 in the set capable values control the output By law, in the case the resolution of the value to be reached when holding the operation value to a configurable value is greater than desired, in order to suppress the ripple control period d which was previously identified by t '= {d n _<1 = 0, d ₁ , d
_{From n> 1} = 0 ° and the allowable ripple magnitude ε, Y = log (1−ε) / log (| d ₁ |) is calculated, and the control cycle T is set to a value equal to or less than Y · t. f in the control period T ', g', h ' , d' again identified, f, recalculates F, in order to correct the deviation of the control value, the operation value C ₀ = C for each control cycle _{- 1} + c _'0 and prior to outputting the integer value obtained by accumulating the fraction [delta] and _{δ = k · δ + C -2} + c when the operation value up to the previous time and integer C _{-1' -1} -C _{- 1} 0 <k ≦ 1 δ on the left side is the value at the current time, δ on the right side is the value at the previous time point The sign of the most recent operation value sgn (c ′ ₀ ) and sgn (x) are positive, 0, and negative of x A function that takes a value of −1,0,1 with sgn (0) can be set to +1 or −1. The correction value η expressed by a linear expression is expressed as η = p · δ + q · sgn (c ′ ₀ ) 0 ≦ p, q p + 2 · q ≦
1 Added numerical value C ₀ + η = C ₋₁ + c ′ ₀ + η C ₀ = Int (C ₋₁ + c ′ ₀ + η) Int (x) is a function that converts x to an integer, and outputs the result. Control method.