WO1999057617A1 - Push-pull predictive control - Google Patents

Abstract

A control method using a response function, in which using a pair of operating means (operating pair: the set values are nonnegative) for operation in the mutually opposite directions, such as cooling and heating, and a pair of full-close means (full-close pair: the set values are open and close) for closing the operating pair, the controlled variables when the controlled pair are both closed and the full close pair are both opened are predicted. An operating pair having static characteristics having predicted values of desired values and similar signs to the estrangement are selected. The manipulated variable of the selected operating means is found. If the found manipulated variable is negative, the manipulated variable is set at zero. If another control means is not selected yet, the control means is selected so as to start over. If the controlled variables of both control means are negative, the controlled variables are set at zero. If the controlled variables are nonnegative, the controlled variables are stored, and controlled variables of when the companion full-close means is closed are found. If the controlled variables are nonnegative, the controlled variables are used; if the controlled variables are negative, the companion full-close means is opened and the stored manipulated variables are used. When there is any full-close means which cannot be used, the means is kept open. The manipulated variable of at least one of the operating pair can be set at zero, enabling power saving.

Description

Push-pull predictive control

Technical field

This invention is a digital control that predicts a control value and obtains an operation value.

When there is a means (fully closed pair) that sets the output of each operating pair to 0 (fully closed) with the set value of the operating pair using a pair of operating means (operation pair) acting in the opposite direction like cooling. Relates to a method of using the fully closed pair to minimize the set value of at least one of the operation pairs, and a device using the method.

Background art

 Defined by ≡, consequent by →, equivalent by, element by 6, non-element by, existence by 、, negation by, negation by V, all by V, and by V or by Min (), minimum value by Max ( ) Indicates the maximum value, II indicates the absolute value, 'indicates the transposed matrix, ∑ indicates the continuous sum, and Π indicates the continuous product.

 In control, along a time series, a value (called an operation value, called an operation value) that matches a certain value (called a control value, denoted by R) with a target value (also called a set value, denoted by S) (Represented by C). Therefore, the control device includes at least input means for R and S, output means for C, means for performing periodic processing, and means for determining C according to the difference between R and S. (Represented by U). U requires storage device M. M contains programs and initial value data required for control. If necessary, a display device, an alarm device, a safety device, an available disturbance (referred to as an intellectual disturbance, represented by D) or an abnormal control state (for example, when the control system is disconnected or the safety device is activated) It comes with input devices, such as the output value is not output normally), various sensors, communication means, etc. These programs, data or timer signals can also be obtained externally using communication means. In recent years, the performance of computers has been improved, and most of the equipment originally attached to the control device has become part of the parent device that has the control device as a part, and the control device replaces S, R, C, D with There are many cases where only functions that return C based are available. In other words, in digital control devices, the calculation between input and output values is a device that exchanges numerical values that serve as machine gears and gears. The object to be controlled (control system) has a causal relationship that causes C output from the control device and D observed, and R as a result. The equation describing the causal relationship is called the transfer equation, and the coefficient when the transfer equation is described by a linear equation is called the response function.

In actual control, input values obtained from observations and settings are preprocessed. Control calculation, post-process the obtained numerical value and output. Examples of preprocessing include converting voltage and current values to power values, converting thermocouple electromotive force to temperature, performing freezing point correction, and statistical processing to increase signal-to-noise ratio. Examples of post-processing include converting the calculated power value to an AC phase value and converting a real value to an integer value. The expression of input and output of values used in control calculations also means performing such general and necessary pre-processing and post-processing.

In control theory, it is necessary to express the past. Usually, a time series is represented by a sequence starting from the 0th term and continuing to the first term, the second term, ··· and infinity (called the right infinite sequence), but the number of the term in the sequence Use a sequence that can be expressed in the past (called both infinite sequences) with (-1), (-2) and negative terms (where the terms are called). When all terms that are smaller than a non-zero term are all zero, that term is called the first term. The first term is called the first term and is indicated by a prefix before the sequence. For example, the first place in the sequence a, the expression b10c is aa, hi (b + c). A sequence with the first term is called a left regular sequence. A sequence in which all terms are 0 is called a zero sequence, and is represented by 0. A left regular sequence is combined with a left regular sequence and 0. The term in which all terms that are larger in terms than non-zero terms are 0 is called the final term. The last term is called the last term, and it is expressed by adding ω before the sequence. A left regular sequence with a final term is called a finite sequence, and the number of non-zero terms is a finite number of 1 or more. The number of terms from the first term to the last term in a finite sequence is called the number of terms in the finite sequence, and is indicated by adding r before the symbol that represents the sequence. When calculating a assuming that the terms in the sequence a are less than X and more than Y are 0, X, Y, Y—X + 1 are called the first, last, and number of terms for convenience, and aa, oa, ra It is represented by In actual calculations, we mainly use left regular sequences and finite sequences. Using a left regular sequence instead of a right infinite sequence has the following conveniences. (1) Arbitrary time points can be included in paragraph 0. (2) The conventional control theory holds as it is. (3) The Z operator becomes a sequence. ) Easy use of historical data in a sequence (It is not necessary to convert the information indicating the past into a state vector, etc.). (5) The recurrence formula is a multiplication of a sequence, and the transfer equation is a recurrence formula. (6) The operation of a left-regular sequence, like the operation of a matrix, does not have the irritability such as the failure of the exchange law (AB Φ BA) and the failure of the reduction rule (ョ Φ Φ Ο, Β 0 → AB = 0). And can be calculated in the same way as real algebra.

In mathematics, real open intervals; half-open intervals; closed intervals are sometimes expressed as (Χ, Υ); [Χ, Υ), (Χ, Υ); [Υ, Υ]. The non-zero section of the sequence and the range of the term to be noted are represented by [(,)]. The term that is less than the term X is 0 is represented by "(X" and "(one οο" is replaced by "( "," [X] indicates that X is the first place, "[" indicates that the first place is present, and "Υ)" indicates that the term with more than zero is 0. Where ")" is represented by ")", that 終 is a terminal is represented by "ΥΓ", and that a terminal is present is represented by "]", and "," is inserted between X and Υ. Using these symbols, the finite sequence of first X and the last 初 is [Χ, Υ], the left nonsingular sequence of first 1 is [1,), and the terms of terms greater than 3 are 0. A sequence is represented by (, 3), a left regular sequence is represented by [), a left regular sequence is represented by [) +0, and a finite sequence is represented by []. For example, if A = B holds between the Xth and Yth terms in the sequence, then A = B [X, Y], and if A = B holds between the 1st and 2nd terms, Α = Β (, Υ], and the condition between the X and ∞ terms is expressed as ∞ = Β [Χ,).

A special sequence is a digit or Greek letter, a general sequence is a letter or a symbol that starts with a letter, and a subscript is placed to the right of the symbol that represents the sequence, and the term of that position is placed. , The general term is the η term, and the limit is the ∞ term a _∞ .

a = { _a „} =---, a-2, ai, ao, ai .a ^,---}, Λ1) a∞≡ 1 ima _n (A2) Addition and subtraction of a sequence by term And subtraction (A3).

{a „} Sat {b„} ≡ {a „± b„} (A3) The multiplication of the number IJ is represented by the Cauchy product (also called convolution). {a „} ■ {b„} ≡ {(a-b = ∑_ai b _n -i} 0 · {a „} ≡ 0 (A4) The multiplication symbol (') may be omitted. Since the product of left regular sequences has first terms in both directions, any term becomes a finite number of product sums, the product also becomes a left regular sequence, and the first term of ab is a, so it is never 0 .

ab ≡ {(ab) _n ku _{α a} + „ _b = 0, (ab)„ _{a + α b} = a „ _a b„ _b ,

Expressing this in reverse, it becomes the reduction rule (A5).

ab = 0 Λ ae [) +0 Λ b [) +0 → a = 0 V b = 0 (A5) Given the left regular sequence b and c, replace the left regular sequence a that satisfies ab = c with (A ^The division can be defined by finding ⁴ ') one by one from the first term.

 {{C / b) n = an} ≡ {an <a c-a b = 0, a «c-r, b = C a c / bab,

a „>„ c-„b = (∑ a, b„-i) / b „ _b } (A6) Any left regular sequence can be divided freely, and the quotient becomes a left regular sequence. Defines a power No non-regular power other than a left regular sequence is not defined a ¹ ≡ a, a ≡ a · a, a G ノ a ¹ ≡ a "/ a (A7) Definition of the four arithmetic operations The coupling law (A8), the exchange law (A9), and the distribution law (A00) are established. However, division is limited to left regular sequences.

(a soil b) soil c = a ± (b soil c) (ab) c = a (bc) (A8) a + b = b + a, ab = ba (A9) a (b soil c) = ab ac (b sat c) Za = b Za sat c / a (A10) Also, according to the usual algebraic rules, when addition and subtraction and multiplication and division are mixed, the multiplication, division, and addition and subtraction are performed in order from the left. I will do it.

ab — c + wq / fg = ((a 'b) — _C ) + ((oq) Z (f-g)) (All) A sequence where the 0th term is ri and other terms are 0 And ri are arbitrary sequences {a. } Is multiplied by each term. In other words, you can equate Les with scalar. D

v ≡ {■ ■ ■, 0, vo = v, 0, ■ · ■}, u {a „} = {ya„},-{ _a „} ≡ {-a„} (A12) When v = 0 The sequence 0 of is an additive element and a multiplicative zero element, and the sequence 1 when = 1 is a multiplicative element.

 0,3 {0} = {· · ·, 0,0,0, · · ·}, 1≡ {· ·., 0,0,1. = 1, 0,0, · · ·} (A13) a ± 0 = a '0a = 0, la = a (A14) A sequence in which the first term is 1 and the other terms are 0 is defined as Λ You.

Λ ≡ {· · ·, 0,0, Λ! = 1, 0,0, ···} (A15) Then, A ^k is a sequence in which the k-th term is 1 and the other terms are 0.

{a. } Change the n-th to k-th terms of Also, any sequence {a _n }

Laurent series can be expanded. Λ — ¹ is a sequence representation of the Z operator.

Λ ⁿ ≡ {· · ·, 0, 0, Λ ^k _k = 1, 0, 0 '' · ·} Λ ^k {a „} = {a„} (A16)

{a „} = ∑ a„ Λ "(A17) —

1 The product of the sequence Δ to be 一 and the arbitrary sequence {a „} is the difference of {a„}. Δ ≡ 1—mm {a. } = {a „— a„ _-1 } (A18) When the sequence a is the difference of the sequence A, the sequence a to be the difference is represented by lowercase letters, and the original sequence A is represented by uppercase letters. If 数 is a sequence in which the first order is 0 and all terms in the 0th and positive terms are 1, then the product of ∑ and any sequence {a „} is the sum of {a„} You. ∑ is the reciprocal sequence of Δ.

 ∑ ≡ {· · ·, 0,0, ∑. = 1, 1, 1, · · '' ∑ {a „} = {∑ aK} (A19)

∑ Δ = Δ ∑ = 1 Σ = Δ — ¹ (Α20) Next, we explain the theorem that is frequently used in the calculation of a sequence.

The starting and ending relations of multiplication are as shown in (A21).

a (ab) = aa + b, ω (ab) = ω a + ω b (The relationship between the division and the first place is (A22), but the relation with the last place is the quotient a (A23) holds only when (a / b) = aa-bv A22) becomes a finite sequence. a / be [] → ai (a / h) = ω a-ω b (A23) The k-th formula of n is represented by n ^<k> . When all terms in and after the in term of the sequence {b „} are _n ^<k> q ⁿ , q is called a pole, and (1-1 qA) {b„} after the m + 1 term is n ^<k — ¹ > q ⁿ , and (1- qA) ^{k + 1} {b „} is a finite sequence.

b „> _m = n ^k> q ⁿ → ((1-qA) {b„}) „> _{m + 1} = _n ^k ""^1>q" (A24) b „ _{> m} = n ^<k> q ⁿ → ((1- qA) ^{k + 1} {b „})„> _{ra + k + 1} = 0 (A25) .. (1-qA) {n ^k q "} = {n ^k q ^n- (n-l ) ^k qq "}

^{= {Kn k _ 1 - k-} (kl) n k '2/2 + (- l)} k q "}

(1-qA) {n ° q ⁿ } = {q ⁿ — qq ⁿ - ¹ } = 0

Therefore, if the m-th and subsequent terms of {b „} are the sum of such sequences with different q and k, multiplying (1-1 qA) ^{k + 1} for all q will result in a finite sequence.

b „> _m = ∑ a, n ^<k " ¹ ^ ( _,, "→ ((1-q) {b„}) „> _{m + ∑k} (i, _{+ L} = 0 (A25) i =

q ≡ 1-Π (1- q ₍ i) ^k ) ^{k π 1 + 1} e [l, ∑ k _(i ) + L] (A26) i = i =

When a finite sequence a is factored as in (A27), a> is called the zero. a ≡ a „ _a Λ ^aa Π (1- a <i, Λ) ^{k π 1} (A27)

 i =

The reciprocal of a is the coefficient of Ai,, (1-a _(i , the linear combination of Λ 广¹ ) and the formula (A29) using the binomial coefficient „Ck (1- au> A) A = ¹表 "" ^a ∑ ∑ A,, j (la _(i , Λ (A28)

 i =

(1-x) " ^m = ∑ _{m + n} χ ^π (A29) a — ¹ = a" _a — ¹ ∑ Λ ⁿ — " ^{a L} ∑ a") ^π ∑ „10 'Ai,' (A30) i = j =

You can do it. If there are zeros with absolute values of 1 or more, a- ¹ does not converge, and if the absolute values of all zeros are less than 1, it converges to a-0.

 If the number of terms in a is 1, it is (A31), and the zero of a is regarded as 0.

(a _x A ^x wide ^ ax- 'Λ-(A31) The system is in an equilibrium state before the control starts, and the control value r, the operation value c, and the disturbance d are expressed in units where the equilibrium state is set to 0. The control calculates the operating value c and the disturbance d. As a cause, a causal relationship is established with the control value r as the result. Therefore, if the control system can be represented by a linear difference equation, it should be represented by a general form of causality. A causal relationship is that the consequences have to occur after the cause has occurred. Unless the measurement sequence is such that the consequences of a cause that occurred at a certain point in the time series occur at the same point in time, the n- _th term in the result _r is only the causes c and d before the n- _th term And is represented as (I).

Γη = ∑ fi C „-i + ∑ gi CU-, = fl C _n -l + f ₂ Cn-+ '-' + gl d _n — i + g ₂ d _n —

 —

r = fc + gdfe (l,), _g e (l,) (I) Let's consider the meaning of f and g. In this state, c is 1 only during the 0th time, and 0 otherwise, so we consider a state without disturbance. The value of r at this time is called the pulse response. r = f · 1 + g · 0 = f, where f is the pulse response function. g is the pulse response function for d. Next, consider the case where d = 0, c is 0 until the first time point, and 1 after the 0th time point. Since r = ∑ f, F ∑ ∑ f is the step response function. Similarly, G = ∑g is the disturbance step response function. The characteristics of the operating means are expressed as static values, for example, for a control valve, the flow rate per change in opening can be changed by A kg ec at a given pressure difference. Static means ignoring temporal changes after changing the operating means, assuming that the state before the change is in an equilibrium state, and returning to an equilibrium state after a sufficient time has elapsed after the change. It is expressed as the difference between the two equilibrium values when it is assumed that the Expressing this static characteristic as a response function is the extreme value of the step response function. If the result does not disappear immediately, such as resonance or reverberation, you can think of the result as a memory effect that caused you. As is known, the solution of a constant coefficient differential equation has an exponential function in its components. At this time, if f and g are represented by a sequence, it satisfies the premise of (A25), so there are q _f and q _s that make f and g finite sequences. 1 q ≡ (1— q _f ) (1— q _g ) and Then, it becomes a representation (Π) using finite sequence q, a, b.

r „= q ₁ r„ -i + _{) q} r „ _-wq + ai c„ -i + _--- + a ₍ „ _a c + bid„ -i +---+ b „- _(U br = qr + ac + bdqe (1,], _a e (1,], _c e (1,] (fl) a ≡ (1 q) f, b ≡ (1— q) g

f „

_{f "- ως g" = b} "+ qi g" - i + - - • + q (uq g "- wq f = a + qf, g = b + qg (I)

 In the conventional control theory, the response function of (II) was often described only as an arithmetic parameter. Here, we try to interpret it.

Each of q, a, and b has a response function condition called a transfer function coefficient in the first rank or higher. That is, q is the response function due to the resulting r. This is the response function of the elements that affect the future stored in the result. You want to ring a bell. Even if the bell is momentarily impacted, the bell will ring for a while. The instantaneous impact (c, d) gives the bell a deformation (r = ac + bd). This deformation (r) is the strain energy and kinetic energy that causes a new deformation (r = qr), and the deformation is this total effect (r = ac + bd + qr). Deformation continues to vibrate the surrounding air, producing sound. For the same variant, the subsequent effect depends on the bell and not on the means of impact. However, in many cases, different means c and d give different transformations ac and bd. In this way, q indicates the effect accumulated inside the result! ·, And is a response function that describes phenomena such as memory effect and resonance effect. Let a and b be net functions, f, and g that consider the memory effect, and consider them as gross functions. In (Π), since q, a, and b are finite sequences, it can be calculated by the least squares method based on the observed data, and 、 and g can be determined from (で) from _q , a, and b.

It is a little complicated to explain that a control system can be represented by a difference equation using coefficients (response functions) as a finite sequence of fields represented by constant coefficient differential equations. However, the difference is essentially different from the differentiation and cannot be completely shifted. Hmm. Other than the method described here, (A) Z-transformation is used to derive from differential equations. (B) Use an approximation that simply replaces the derivative with the difference. (C) Derivation methods are known, such as replacing the derivative with a difference by expanding the function to an appropriate order following the Runw b-Kutta method, which is known from the numerical analysis of differential equations. . However, these methods use a mixture of cause and effect. In other words, it is expressed as _c '≡ A c, d' 3 Λ d that advances the terms of c and d in (Ι) (Π) in the future. Using these c 'and d, the response function is f'≡ Λ f E (0,), g'≡ A— ige J' a 'e J' b 'E io,]. r = qr + Λ ^_1 a A c + Λ ^_1 b A d = qr ten a 'c' + b'd '

r = Λ— 'f A c + Λ g A d = f' c '+ g'd'

The causal relationship is expressed by a differential equation with the maximum order of the time derivative of r and the coefficients u „, v„, and w 実 as real numbers. The origin of time is taken before control starts, and the units of c, d, and r are d. "

(t) = ∑ v „¾-" „c (t) + ∑ w:„ d (t) 1 (B1) _n = o at 0 a

ω v; u, ω w ≤ ω u (B2) 7n r (t) = ^ _n c (t) = ^ ird (t)-0 η = 0, 1, 2, · ·, ιι t ≤ 0 ( B3) at at at

 Select as (B3) holds. The functions before and after conversion use the same symbols. Laplacian transformation and dividing both sides by u (s) gives (B7).

u (s) r (s) = v (s) c (s) + w (s) d (s) (B4) u (s) ≡ ∑ u „s" v (s) ≡ s "w (s) ≡ ∑ w „s ⁿ (B5)

 0 0 0

f ( _s ) ≡ v (s) / u (s) g (s) ≡ w (s) / u (s) (B6) r (s) = f (s) c (s) + g (s) d the (s) (B7) u ( s) and factorization, f (s), g a (s) (s +,) - rewrite the coefficient of ^k X, a linear combination formula was Yi _k.

Yi _k (s + ii) " ^k (B8)

= l

The inverse Laplace transform of (B7) and (B8) gives (B9) and (B10). (t> 0) = ∑ ∑ Xj — ¹ e— ^; -1) 0) = 0

 j = 1 k = 1

g (t> 0)-∑ ∑ Y) _k t ^k — ¹ e / (k-1)! g (t≤ 0) = 0 (B9)

 j = 1 k = 1

r (t) = S f (x) c (tx) dx + S g (x) d (tx) dx (BIO) The control is executed at period T, and _{r is changed} to time nT (n: integer) by r „ and to measure the "information that has become known the until time nT to the measurement, etc. (r" operation value _{c Γη - Γη - 2 .. ·} ;! c "- 2, · · ·). calculated on the basis of the And output. The time required for output from this measurement is εε. The manipulated value c changes from stepwise to c „only at the time (η + ε) Τ (0 <ε≤1) .The disturbance d originally occurs at the time of incompatibility, but for convenience, the time (η + d „-to d stepwise only at ε ') Τ (0 <ε'≤1). Suppose that changes to By using these conditions (B12) and (B13) for (B10), (I) can be obtained. In contrast to the result r „on the left side of (I), the causes c„ —, d „-, on the right side have small terms, that is, are expressed only in past data. Clearly show the causal relationship between

 + g d (I)

≡ ir „1, c, d ≡ (d, (Bll) f„ ≡ $ f (t) dt _gn ≡ (g (t) dt

 One

= S ∑ Xi _k t ^k e '/ k! Dt = $ ∑ Yj, t ^k e "/ k! Dt

 (0. {0. (u. Υ j)

= ∑ Xi _k L, _k (n ') q "Λ" = ∑ Y Lj k (nq Λ ⁿ (B12) k) = (2.0.0.0.0.0.0

 F0≡ S f (t) dt gi ≡ S g (t) dt (B13)

0 0

„So = 0 i, 0 = 0 (B14) q (i) ^≡ e ^{1 T} (B15) nn— ε n ≡ n— ε (B16) L, _k () ≡ q ((q ¹ h ^m- (hl ) ^m } / m!

))---Q ^h (q 1) ∑ l) ^m- ] h] / j! (Ffl + lj)! (B17)

 __ „-^ i

q (i) = e is called a pole. n ^m q _(i ) ⁿ A Then, it becomes (B18) (B19). Furthermore, the dead time that is difficult to express in differential equations

(B20) and (B21) when partial dead time is accepted.

f and g satisfy the condition of (A25), and the expression q ≡l- (l- q. A) ^{kl + 1} ---(l- q Λ) ^{k L} using the finite sequence q, a, b ^{+ 1} e [l, _ω q] (B22) a ≡ (1-q) fe (l, _{ω a} ) (B23) b ≡ (1-q) g ^ (1, _ω b) (B24)

(1-q) r = ac + bd (B25) r _n = qi r „-1 + · ·-+ q _wq rn + ai c„-1 + · • + a «, a C„-„ _a + bl d „-l +---+ b, ad„ r = qr + ac + bd (Π)

(II) is obtained. In contrast to the result on the left-hand side of (D), the cause c „-i, (!„ —, On the right-hand side has a small term, that is, is represented only by past data. The result occurs later than the cause Clearly show the causal relationship between

r, c, d is I is 1 or more Hatsukurai Ri good (B3), for any n, the (I) is multiplied by ^lambda-n to both sides of ^{(D) (B 2 6)} (B27) Become.

Λ ^"n r = f Λ one ^{n c + g Λ - n d} (Β26) Λ one ^{n r = q A- n r +} a A- n c tens b A d (B27) Λ" n r, Λ- n The first place of c, d— ⁿ d is l— n, and the 0th term is the original nth term. If A- ⁿ r, Λ c, Λ ~ "d is written again as r, c, d, it returns to (I) (Π). That is, (I) (Π) sets any point to the 0th term I can do it.

 This equivalent equation (I) (Π) gives the recurrence form (DI).

 In (H), f and g can be calculated sequentially from the first term using q, a, and b.

r = { _a / (1-q)} c + {b / (l-q)} d (B28) f = a / (l-q), g = b Z (1— q) (B29)

f = qf + a, g = qg + b (I use c, c (), · · ·, c; r (), r (r instead of cd; r (B30) to (B33).

r = Q r + A cr = F c (B30) r ≡ ^I (r), r) ₎ ---, r („)), c ≡ ^l (c (B31)

Q ≡ (q.)), A A (a _(i .)), F F (f), Ε ≡ (δ _; )) (B32)

F = (E - Q) - If ¹ A (B33) diagonalization in regular sequence U and Q (B3 ⁴⁾ good is, you will (B35) (B36). r "= U r, Q" = UQU ^{_ 1} , A "= UA r" = Q "r" + A "c (B34) rqr) + a (· + a" (

 r "q" () r ') + a "(+ · · + a" (

 q) e) e (l], a "(i) e (1,] (B35) Q" r '(„) + a (+ · + + a",

 q r + a "c q": diagonal matrix (B35 ') r "= f c (

r () ⁼ f (+ f '

 f "f" a e (1,) (B36)

 + f '

r "= f" c (B36 ') (B30) is the most general expression system for describing causal relations using a finite sequence in a linear difference equation. This condition is called a finite sequence. Instead of removing, we avoided the cause of the result as it is (B31). The elements of the matrix are sequences, but since the law of formation of the four arithmetic operations is the same as that of real and complex numbers, It can be calculated in the same way as a matrix with elements. In a complex system, the response function is not a constant but a function of r ₍ i), c _(i >. In the present invention, it is assumed that the system is linear and the complexity is avoided and explained in (I) and (II). Some systems, such as an inverted pendulum, may run away if left alone, but many controlled systems will eventually settle into an equilibrium state if left unattended. Stopping the change of D results in the equilibrium state of the result R. "The energy theorem holds. Measured values and set values are usually values that do not become 0 in the equilibrium state. Therefore, if the temperature is 25 ° C before the control starts, it is not possible to form a left regular sequence unless the numerical value is obtained by subtracting 25 ° C. Expressed as R, C, D.

 R = fC + gD (CI) R = qR + aC + bD (C2) Now, let's consider the difference instead of the raw measured value and set value. The difference is 0 when the original r ≡ A R, c ≡ A C, d ≡ A D (C3) values are constant. At equilibrium, the difference is zero. The theorem of energy is as follows: "If the causes c and d become 0, the r of the result eventually becomes 0." Therefore, if the raw value is not a left-regular sequence, and if it can be assumed that the raw value is always in equilibrium in the past from an appropriate time before the start of control, the difference values r, c, and d will be a left-regular sequence. . (CI) If both sides of (C2) are multiplied by the sequence Δ, and replaced by (C3), it returns to (I) (H). Conversely, if both sides of (の) and (() are multiplied by 置 き 換 え る and replaced by (C4), it becomes (ci) (c2). That is, (I) (n) is an invariant equation as long as it uses variables that are left regular sequences. And natural variables

R = ∑r, C = ∑c, D = ∑d (C4) are r, c, and d. From (B20) and (B21), for the energy theorem to hold, the absolute value of all poles q (i> is less than 1).

Condition (B2) is a condition in which the constant coefficient linear differential equation has a straightforward solution. This is a condition expressed in the form, and is a condition that is often used in control theory. With (B2), f and g can be expressed as a linear combination of (s +) — ⁿ (n≥1) as in (B8). In Laplace transform table (s + λ) over "is ^{t n 1 e", / (} η- 1)! (Including = 0). If is a complex number, it contains sinw t.cosw t, but it is nothing but a complex representation of the exponential function. In the case of n = 1 where (B8) does not hold, looking at the Laplace conversion table, the function does not correspond to a continuous function when it approaches t = 0 from the side of 0 to t.

 Describes the control method and stability. In the control, the operation value C is changed in a direction to eliminate the difference E (deviation) between the control value R and the target value S.

E ≡ S-I R (D1) A method of considering a model in a control system and actively considering the model is called modern control theory. In PID control, etc., C is calculated by PID and other calculations for E, regardless of the control system, but this calculation method is also a model Ψ. To determine the stability of the control, find the E of the platform with this C as the input to the model Φ- ¹ of the control system. This operation Φ— is called loop transmission. With "", Ψ means that Ε is an input value and C is an output value, while Φ means that C is an input value and Ε is an output value. By repeating Φ—, when the absolute value of Ε approaches 0, it is determined that the control state is stable. Although described in literature Α), a method of calculating C that satisfies specific settling conditions using a control system model is called MRAS (Model Reference Adaptive System). In other words, MRAS uses Φ- ¹ . Therefore, E is the C calculation condition using Φ, so stability was not much of an issue. If you actually try MRAS, you will surely achieve fast and accurate control. However, a stable and good control situation can suddenly break down. This is due to the model being destroyed and to the fact that E is stable but C is stable. However, it was pointed out in literature ii) that it may not always be the case, and a countermeasure was proposed. Model destruction is described next. With MRAS, an accurate and stable state is reached at high speed. Due to its high accuracy, in a stable state, if the noise is large, it will be buried in the noise, and if the noise is small, R and C will only change by about 1 to 2 digits. The noise has no response function information. On the other hand, if the number of digits is small, the calculation accuracy of the response function will be insufficient. If we continue to identify the response function based on these data, the response function will be significantly different from the true control system, and control will be impossible (failure). This can be avoided if the response function is identified only with reliable information. The identification method and settling method of MRAS (New Adaptive Control System: NACS) using left regular sequence as a model of (I) (() will be explained considering stability.

Taking the current time as item 0, and writing down item 0 in (Π) gives (D2). ro = qi r- 1 + q2 r-2 + ... + q _{ω Q} r- _{ω q} + ai c-i + a∑ c-2 + ... + a _wa c- _wa

_{+ Bi d + b 2 d-} 2 + · · · + bd (D2) that is, the primary independent ω q + ω a + ω b sets or more of (r, c, d) = (r 0, r-!, R- ₂ , ·

, Γ- _ως ; C, C-2, _··· , C; d, d-2, _··· , d), the least squares method or the sequential identification method can be used to obtain (q, a, b ) = (qi, q2, - - -, q M; ai, a2, - - -, a «a; bi, b 2, you can · · ·, _b, b) the determination (identification). As the control progresses, the data of r, c, and d are accumulated. However, certain information (such as a large signal-to-noise ratio, a data group with a large number of digits, and the output value of a safety circuit, etc.) If the data is not abnormal, such as when the data is corrected or operation is disabled, select) and identify q, a, and b. The determination of ω q, ω a, and ω b is determined by analyzing the control system if it is expressed by a constant coefficient differential equation. If q, a, and b can be determined by analysis, there is no need to calculate based on r, c, and d. If analysis is not possible, assume a sufficiently large ぃ 3, 3, 0; 1 for identification. Identification As a result, terms that can be considered almost zero can be deleted or left as they are. If none of the terms are considered to be 0 and the control state is not good, increase oq,> a, ob, and try again. If q, a, and b cannot be estimated at all, perform a response test such as a step response to identify q, a, and b.

In this way, after q, a, and b have been identified with a certain degree of accuracy, the required number of terms f and g are calculated in (H), and the actual control starts.

f = qf + a, g = qg + b (Π) Actually output values up to the first term, and appropriate assumptions from the 0th term onwards (eg, invariant c 'e (, 1 1) Let C 'be the difference between the manipulated values consisting of the value of, and c' the correction value from c 'in the 0th term onwards for stabilization. If d is available (called intellectual disturbance), it will be used regardless of the past, present, or future (planned). Then, let r 'be the r at the base where c = c', and r 'if c = c' + c '. In (IV), calculate the required number of points, and at point [、, Υ], find the value of c 'that matches the control value r' with the target value s using (D5) or (D6).

r '= qr ° + ac + bda E [h a, o »a' I h a (IV) r" = fc ° + gd (D3) r '= f (c' + c ') + gdc' e ( 0,) (D4) f _c '= r'-r * e (i,) (V) ac '= (1-q) (r'-r ') () fc' = e (D5) ac '= (1 q) e (D6) e ≡ s-r 's Δ ΔS [X, Y] (D7)

By using (D6) as [X, Y] = [1,), (D8) is obtained.

 c '= (1-q) a ― e (D8) then j (i)

a — ¹ = a _aa — ¹ ∑ Λ ⁿ — ^aa ∑ a) ⁿ ∑ „ _{+ i} C„ Ai, (D9) a (,, is a zero of a and A,, i is a — ¹ is a fraction of a This is the factor when disassembled. a - ¹ of since first place is one a, in order to first place of c 'is greater than or equal to zero, you will need is greater than or equal to aa first position of the e Ri good (D9). In other words, it cannot be set until time a. In this case, e must be changed to (D10).

e _a = ei + e ₂ +. .. + _a -i + e _wa , ei = e ₂ =... = e _wa- = 0 (D10) Also, if the absolute values of all zeros are less than 1, We can expect that c 'will eventually approach zero. However, if there is a zero with an absolute value greater than 1, the absolute value of c 'will continue to increase as the order increases. The method of determining c in (D8) is called the reciprocal method. Therefore, the reciprocal sequence method gives a stable solution only for the case where the absolute values of all zeros are less than 1. The method of finding c 'by the least squares method using the structural equation of (D5) is called the optimal control method. However, as in the reciprocal sequence method, c is not stable if there is a zero whose absolute value is 1 or more. If there is a zero with an absolute value of 1 or more, another method is required. Consider a solution in which c 'is a finite sequence of terms ω c'. Suppose you are in Tokyo and want to come within 10 minutes of New York. However, it may take time to arrange a ticket, time to get to the airport, flight time, time from New York airport to the site. Ten minutes later is certainly the future, but at least not possible with current traffic conditions. Trying to go in a short time can be overkill. Therefore, after the X point, settle at the same number of points as the number of operation values (number of unknowns). Settling is not required before the X-th point, but since the number of terms in c 'is ω c' + 1, settling is performed from the X-th point to the χ + _ω c '-th point.

(∑ _e ) x = Ex = Sx-R "; e = s — r '[X + 1, X + ω c'] (Dll)

E = S-R '[X, X + ωc,] (Dll') When c 'is determined by a certain method Φ, r can be described by c and d by the transfer equation. It is a function of d and s. Since c 'is assumed to be a finite sequence, condition c' is (D12). (D1 ⁴⁾ using the c 'C. And ω c 'ku ω c' (D12) c '= (D (cd; s) e (0, ω c) (D13)

Move on to the next control cycle. In the next control cycle, when the 0th term is the current time and Φ by φ is calculated, (D15) is obtained. That is, 'corrected before time to ^{c "= Φ (Λ- 1 (} c tens c.' Operating value ^{c), Λ- 1 d; Λ} s one Si) (D15) value c 'is applied, the predetermined value joins the modification by the moment of realization value r this c "'c just was shifted to just past the section = Λ one ¹ (c is obtained c in the previous control period"' -!. c '.) (D16) It is said that it is immovable if it is.If Φ gives a finite sequence, if it is immovable, the manipulated value will be kept constant after a finite number of time points. However, if there is a disturbance or the target value keeps changing, it cannot be expected to be stationary, so the target value is fixed and there is no disturbance (D17) , (D18 D19) hold.

d = 0, S e (0, X), c 'e (0, ω c') (D17) r _n = qi r „-i + q2 r„-2 + •• + q _Mq r „ _{-IU [1} ... a ≡ (l, ω a)

r = qrac = 0, d = 0 [ω a + ω c '+ 1,) (D18) r = Γ 0 = · = = _{ω ω 3} 1 = 0

 1 = 2 =

 r = 0 ίω a + ω ο'— ω q + I, ω a + ω ο ']

→ r = 0 [ωa + ωc '+ 1,) (D19) The assumption (D20) of (D19) satisfies (D21). This means that the next control cycle r = 0 [ω a + ω c — ω q + 1, ω a + ω c ”(D20) r = 0 ίω Ά + ω c'— ω q + 2, ω a + ω ο ' + 1] means that the solution in (D21) shifts c one time past, resulting in a solution called c 0. That is, it is immovable. (D20) only needs to be satisfied when d or S becomes D17), so if it is expressed by the target value at normal time, it will be (D22). s — r 匸 ω a + ω c '— ω q + 1, ω a + ω c'] (D22) Compared with (Dll), if (D23) and (D2 ⁴ ) hold, the control method is immobile. Χ≤ ω a + OJ C '— di q, ω a + ω ο'≤ Χ + ω c

o »a¾ ≤ ω a + ω c'— ω q (D23) From ω q ≤ ω c '(D24) (D23), the fastest settling time is ω a, so apply to (V) to get (D25) . r)

•

 ∑ f c '= F c' = E (o a, o) a + ω ο 'c' E (0 ω q) (D25)

'

This solution is called the multipoint settling method, and the field stand limited to (D27) is usually called the finite settling method.

ω c '= ω q, d = 0 i .e. Ε _ωβ = S-° _wa , E „> _ω3 =-R' _n (D27) Causality is expressed in the form of a recurrence formula. Recognizing the transfer equations (I) and (Π) and using the multipoint settling method as the standard method, the expression becomes extremely simple. The real pleasure of using a left-regular sequence instead.

When there is an oscillating element, the poles are represented by more than one pair of complex numbers, and it is considered that energy exchange occurs between these poles. Examples are sound pressure and kinetic energy, pendulum position energy and kinetic energy, and electromagnetic and magnetic fields. Therefore, considering a complex conjugate pair as a set It is thought that the total energy decreases monotonically. In other words, the vibrating element is a positive real number with a pole less than 1 because the energy can be considered as a set (sum) to eliminate the effects of vibration. Considering temperature control as a model, the area around the temperature control point is wrapped in multiple layers with small heat transfer partitions such as air and heat insulation. Even if it is exposed, it is still a multi-environment around the laboratory bench, the laboratory, and the research building. The thermal equilibrium within these multiple-environment bulkheads increases in time constant from inside to outside. In other words, the array of poles represents multiple spaces. The immediate control is enough harm in the smallest space, but once it is in a stable state, the effect of the outside space will be observed one after another. There are many platforms where only the pole with the smallest absolute value can be considered without considering the other poles. You can increase the number of poles as needed to account for negative and complex poles.

Methods other than those introduced here are described in A) B). D) has a detailed description of the left regular sequence. MRAS is described in A) B) C). The lower volume of A) details the classic theory.

 A) Yasuhito Takahashi System and control Upper and lower Iwanami Shoten 19a8

B) two tree Takehiko et al, PCT International Patent Application PCT / JP99 / 0083 ^{7 February} 1999 24 filed

C) Mathematical Seminar vol.21, no.07,1982 PP.38-44

_D ) Hayahara Shiro. Shigeru Haruki New operator method and discrete analysis function theory Bookstore

E) Iwanami Mathematics Dictionary Edited by The Mathematical Society of Japan Iwanami Shoten

In control, pre-processing of input values and post-processing of output values are performed to improve linearity and signal-to-noise ratio. For example, statistical processing such as weighted average, potential difference of thermistor and electromotive force of thermocouple. Conversion to C, conversion of voltage value or current value to power value, conversion of power value to firing angle of thyristor, opening of control valve to valve position or valve shaft rotation angle, etc. . This is shown in FIG.1. As for the output, the setting value X of the operating means and the effect value Y The relationship includes a rising area A, a linearly proportional area B, a saturation area C, and a non-setting range D. A and C usually have extremely poor linearity. In such a case, after calculating the effect value as the operation value, the set value corresponding to the effect value is calculated and output. As for the input, a value that improves the linearity of the transfer equation is used as the input value. This alleviates nonlinearities due to input and output values, and widens the range in which the response function can be considered an invariant function. However, besides the range of stable firing angles, there are unstable firing angles and misfiring angles. The firing angle at 0 W for single-phase AC is 180 ', but the maximum value of the stable firing angle and the maximum value of the unstable firing angle are also smaller than 180'. Many control valves prohibit full closing and do not guarantee operation below a certain opening to prevent bite and deformation of the valve. In order to fully close (effect value = 0), in the case of a thyristor, a firing pulse is not generated, and with other means, an open / close valve and an on-off valve are connected in series. Fig. 2 shows the linearized state by post-processing, and the settable values are indicated by small circles.

The existence of a non-configurable area is a serious problem in control using operation pairs. The reason for using an operation pair is to control the non-settable area D of both means. From an energy-saving point of view, push-pull control to open only one side (ON) is desirable, but it was virtually impossible with MRAS, whose theory is difficult. Therefore, a method is used in which only one of the pair is controlled, the other set value is kept almost constant, and the average value of long-term control is used to make small changes. In this way, there has been a demand for a method of performing push-like control with predictive control using operation pairs and measures against unsettable areas. Using N ACS with a left-regular sequence gives a better view of the theory. Also, even if the number of causes and effects increases, the transfer equation of NACS only becomes (B35) (B36).

The important thing is that the calculation conditions to make the number of means to be operated the same as the number of results are set with excellent control accuracy, speed, and ease of programming. Can be determined. Controls, fully closed means, etc., do not increase the number of results, but increase the causes. The target value s is often programmed and given in a time series, and is often changed without notice. In this case, it is assumed that S = S x A ^χ毎 in each control cycle. There is a technical problem in using any of the response function identification methods, such as the sequential identification method, the finite identification method, and the least squares method (there are various modification methods such as the sequential update type least squares method), depending on technical issues. However, mid-choice is a hobby. Even if a sequence is used, if the sequence expression is written down in terms of the relevant part according to the operation rules, it is exactly the same as the conventional matrix expression. This is as illustrated in the matrix representation. The difference lies in the technical formalization of the state vector, etc., and the handling of initial values. Both of these make it difficult to understand control theory. The initial value is folded in the left-regular matrix as a sequence representing the cause, and the expression does not depend on the initial value. Change of the control period is made to correspond to Z inverse operator Z ¹ in sequence lambda, extended Z conversion is available.

Disclosure of the invention

 Start-up processing at the start of control (including calculation of operation values and suppression of output until system, data and equipment are stabilized), identification method of response function, determination method of control cycle, selection method of settling time Well-known techniques are used for the basic techniques in predictive control methods such as the weighting method of the least squares method, the solution method, and the inconvenience avoidance method when the response function is identified at the same time as the control.

 Figures 3 and 4 show flow charts of the present invention expressed in numerical sequence. The basic control procedure is described in FIG. 3 and 4 as follows.

 (A) Initialize necessary for control,

(B) Read the basic response function identified in advance or in the previous control, and 2A

(c) For each control cycle,

 (D) Read target values, measured values and the latest information,

 (E) Perform pre-processing necessary for calculation,

 (F) Identify the basic response function and

 (G) Calculate the derived response function,

 (H-R) Predict and calculate operation values,

 (S) Outputs the latest operation value,

 Update at (T)

 (C) Wait for the next cycle timing.

(U) When control is over,

 (V) Save the basic response function in non-volatile memory,

(W) Performs processing necessary for termination.

 Consider one side of the operation pair.

The setting value of the operation means is the operation value C, and the effect value is the control value R. The static characteristics of the operating means are causal relationships depending on the operating means of interest, but they are characteristics that do not take into account the time delay, and are the limit value F _応答 of the response function F.

Linearization by post-processing involves changing the scale of the set value so that this Fee is constant over the widest possible range of C. Therefore, even if the static characteristic Fo can be matched by linearization, the dynamic characteristic F / F _∞ cannot always be matched. Furthermore, there is no evidence that the dynamic characteristics of fully closed means match those in the linear region. This is what made push-pull difficult in predictive control. Taking this fact back, we reconsider the operation pair as follows. Except for the effect of the fully closed means, the completely closed means is considered as a kind of intelligent disturbance D, except for the operation means which was conventionally considered as one control means. In other words, the part of the fully closed pair is separated from the normal operation value, and R = Foe-C + Η∞D You. The status of the fully closed means is D, the set value of the control means is C, and the effect value is R.

D is 0 (closed) or 1 (open), and C is the minimum setting for reliable operation.

It is assumed to be a non-negative value that is 0 so that the operation versus the body can be regarded as linear and there is no unsettable area. At this time, operations that satisfy the following conditions are required.

 If D = 0 then C = 0 0 <C then D = 1

 As long as C = 0, there are cases where D = 0 and where D = l.

Consider this as an operation pair. Since the operation pair has the opposite combination of the static characteristics F0 _∞ and F, the sign is known even if the absolute value is not known. Therefore, determine the operation pair 0, 1 so that FOco <0 <Floo.

Since the action all閉対and operation pair are the same direction, you will G0 _∞ rather than 0 <G. According to the principle of superposition, the transfer equation is

r = f0-c0 + f 1cl + g0- d0 + gl-dl + g d

 = a0-c0 + al-cl + b0-d0 + bl-dl + b d + q r

f0 = a0 + q fO f 1 = al + q f 1

g0 = b0 + q gO gl = bl + q gl g = b + q g

0≤ C0 = ∑ cO 0≤ Cl = ∑ cl

 D0 = ∑ d0 = 0 or 1 Dl = ∑ dl = 0 or 1

 F0 = ∑ fO Fl = ∑ f 1 G0 = ∑ gO Gl = ∑ gl

F0 _∞ rather than 0 <Floo GOcc rather than 0 <Gl∞

 If no intellectual disturbance other than totally closed means is used, the item d is omitted. The following equation comes out during the explanation.

 FU- cU '= E [X, Y] U = 0,1

This equation is (V) described in the background art, and if the stability of the response function is confirmed, the inverse matrix method or the optimal control method can be used. If you do not want to check the stability, you can use the multipoint settling method. In the case of the multipoint settling method with the minimum number of terms in the manipulated value (including the finite settling method as a special form), the solution is as follows. 'FU ω a, FU wa, * * * i FUdia' E ω a U

FU ω a U +, FU ω a U FUwa U-(jq + l E ω a U -t-

CU q U ωa U + ωj FUfiia U, ··· FUo, a UJE ωa U q From now on, the operation pair will be both closed (0) and the fully closed pair will be both open (1). To calculate the predicted value. The operation at this time is CO ' ₀ cl'. And the fully closed pair d0 dl are

0 = C0 ° = C0 c0 ° o; 0 = Cr _o = Cl-one + cl 'o

 · '· C0 o = — CO-; cl o = — CI- 1 = DOo = DO + dOo; 1 = Dlo = Dl + dlo

 . '. dOo = 1-DO; dlo = 1— Dl

In addition, it is necessary to change the value of the fully closed pair d0 and dl and re-estimate the control value. This change can be made, for example, by estimating d0 dl and then changing dV by dV, R '+ GV'dV.

r ° = f 0c0 ° + f1cl '+ g0 d0 + gldl + g d

r = fO-cO '+ f 1 · c0 "+ g0- (d0 + d0,) + gl-(dl + dl,) + gd = r ° + g0-d0 R ≡∑ r = R ° + dO ∑ g0 + dl ∑ gl = R '+ d0 G0 + dl ^ Gl

The method of implementing push-pull predictive control can be implemented as follows. The response functions of the operation pair and the fully closed pair are obtained, and the variance E is calculated based on the prediction of the control value when both the operation pair is closed and both the fully closed pair are open in each operation cycle. The operation value settled by only one of the operation pairs (operation means having the same value of the deviation and the same sign) that is appropriate for canceling is obtained, and if inconvenient, the operation value settled by only the other is obtained. In either case, check whether the fully closed means on the other side of the pair can be closed, and if it can be closed, close it. However, the operation of a fully closed pair has the trouble of finding as many response functions as possible, and involves some control fluctuations immediately after the operation of a fully closed pair due to hysteresis, etc. For less effective means or higher control accuracy, one or both of the fully closed pairs may be left open.

Consider the case when fully closed means 1 is changed from open to closed. Then, the effect of operation 1 that is paired with the fully closed means is reduced by the amount that cannot be set. The offset of this effect can only be compensated for by reducing the value of step 2. If the setting of step 2 is negative, the closing operation cannot be performed. That is, the closing operation of the fully closing means 1 is limited to the case where the operation 2 can cancel out. Similarly, the closing operation of the fully closing means depends on the operating means.

In this way, when considering the fully closed means and the operating means as a set, it is impossible to perform a pure push-pull operation in which at least one effect value of the operating pair is set to 0. It is possible to set at least one of the setting values of at least one of the operation pairs except for the fully closed means to zero. This is explained using FIG.4.

Using the following transfer equation, the response function a0, al, bl, b2, b, q is identified by the sequential identification method, the least squares method, etc. (F).

r = fO- cO + f1cO + gldl1 + g2-d2 + g-d

 = aO-cO + al-cO + bl-dl + b2-d2 + b d + q r

The data matrix X, data vector y, and unknown z when using the least squares method are as follows, and the observation equation is y = X z.

 x „= (c0„ • · ', c0 „1 .., Cl„, C 1, al 1 dl „

 -1, b,)

Χ = '(χο, Χ-ι, · ·, Χ y =' (ro, ri,, r- _ra )

^{z = 1 (aOi, · ·} ■, aO wa o, all, · · ·, al i, blx, · · ·, bl.b !,

_{b2i, · · ·, b2 2} , bi, · ·, ba, b, qi, · · ·, q Mq)

 Therefore, the response function is obtained as z = X X) _ X y. Of course, it is possible to use various types of improved least squares method, sequential identification method, and finite identification method.

 Using A0, a0, and q, the next sequence is calculated from the first term to the jth term (G).

f0 = a0 + q fO F0 = ∑ fO f 1 = al + qf 1 Fl = ∑ fl gl = bl + q gl Gl = ∑ gl g2 = b2 + q g2 Q2 = ∑ g2 When the operation pair is closed and the fully closed pair is opened

c0 ° ₀ = — CO-cO ヽ_{ώ 1} = 0; cl ' ₀ = — CO-cl' _{k =; 1} = 0

dlo = 1-Dl, dlk≥ 0; d2 ₀ = 1-D2-!, d2 _kai = 0

Calculate the predicted values r °, R 'and the deviation E from the first term to the Yth (I).

r '2 {r' _n } = aO'cO '+ al' cr + bl-dl + b2-d2 '+ b-d + q-r *

= {aOi · cO _n -i + · · + aO _Ma o · c0 „-ω ₈ o + ali · cl _n -i + ... ten al ^ i-cl„ i

1 -d -r + ••• + q < _uq -r _n - _iuq }

R ° = {R ° „} = {R + r} = A R * + r ° ·

E = {Ε _η } = {S „-R \} = S-R"

Using this E, assuming N = 0, determine the operating value in the following procedure (J to R). If J 0 ≤ Ei, then (U, V) = (1,0), otherwise (U, V) = (0,1),

Let cV ' _o = 0. (Note: 0 <Ei may be used.)

Solving K FU- cU '= E [X, Y] gives cU'. And get cV '. = 0, N = N + 1. If L cUO <0, then cU '. = 0 (Note: cU ' ₀ ≤ 0 may be used)

 If M N = 2 go to R,

 If N N = l, U = V, V = 1-U and return to K.

 If 0 0 ≤ cU ', save cU' (CU "= CU '), and if non-negative, try to close all other means (dV,. =-1).

(Note: If cU ' ₀ ≤ 0 in L, it may be set to 0 and cU')

 R '= {R' „-GV„} = R ° — GV

 E = S-R '= E + GV = {E „+ GV„}

 Solving FU- cU '= E [X, Y] gives cU'. Get.

 If P cU '<0, do not use the trial result, and set cU' = cU ",

 If Q 0 ≤ cU ', adopt the trial result and DV. = 0.

R Finalize the most recent operation value, COo = cO 'o, CI o = cl'

S Operation value C0. , C1. , D0. , D1. Output

 If it becomes M, it is due to a mismatch in the dynamic characteristics of the operation pair, and in most cases, it will be resolved with a delay of one control cycle.

This method does not always close at least one of the fully closed means pairs, but can always close at least one of the operation pairs.

For E of J, use one of Ex to E _Y or a linear combination of these non-negative coefficients (one or more are positive). Ε _{ω 3} . , Ε _{ω 3 で す} . J preferentially examines operation pairs (operation means having static characteristics with the same sign as E,) that are appropriate to cancel the prediction error.

The above is summarized as follows. Assuming that the fully closed pair is both open and the operation pair is both closed, the predicted value is obtained, and the operation pair corresponding to the sign of the predicted value is selected. Calculate the MV of the selected operation pair. If negative, set the MV of the selected operation pair to ◦. If the operation amount of the opponent's operation pair has not been determined yet, select the opponent's operation pair and recalculate the operation amount, and if it has already been obtained, leave the operation amount of both operation pairs at 0 . If the selected manipulated variable is non-negative, retract the computed manipulated variable and find the manipulated variable of the platform with the other party's fully closed pair closed. If this value is non-negative, this value is used and the partner's fully closed pair is closed. If it is negative, the retracted value is used and the partner's fully closed pair is opened. The values of the fully closed pair and the operation pair determined in this way are output. However, for a fully closed pair that is not used, leave the open trial open.

 Fig.3 shows the case where both closed pairs are not operated.

Programs that have the same effect can be transformed in many ways. BRIEF DESCRIPTION OF THE FIGURES

 Fig.1 is a graph that shows the characteristic curve of the operating means on the horizontal axis and the effect value on the vertical axis.

 Explanation of reference numerals

 A Rise area B Linear area

 C Saturation region D Non-settable region

 Fig.2 is a graph in which the characteristic curve of the operating means is linearized, the horizontal axis represents the set value, the vertical axis the effect value, and the set value is represented by a small circle.

 Explanation of reference numerals

 A Rise area B Linear area

 C Saturation region D Non-settable region

 FIG.3 is a flow chart in sequence representation when not using fully closed pairs.

 Explanation of reference numerals

 A Start (including necessary processing such as initialization)

 B Reading basic response function from non-volatile memory

 C Control cycle timing

 D Enter target values, measured values, and other information

 E Calculation of change (difference)

 F Basic response function identification / correction

 Calculate G-derived response function

 H Setting the forecast criteria

 I Forecast calculation and calculation of deviation E between target value and forecast value

 J Select priority operation

 K Calculation of the latest operation value

 L Check the suitability of the latest operation value

M Immediate action (set operation value to 0) Check whether both operation pairs have been considered

 R Finalize the most recent operation value.

 (Including measures to set the operation value to 0 during control standby, etc.)

 s Output of the last operation value

 Update at τ

 u Determine whether to end

 V Store the basic response function in non-volatile memory.

 w End (including end processing)

F I G. 4 is a flow chart in a sequence representation of a platform using fully closed pairs.

 Explanation of code (except for 0, P, and Q, common to FIG.3)

 0 When the operation value is appropriate, calculate the platform with the other party's fully closed means closed ο

 p Determines whether the fully closed means can be closed.

 Q Use the calculation results.

BEST MODE FOR CARRYING OUT THE INVENTION

Control varies depending on the required accuracy, required speed, computing unit speed, storage capacity, peripheral devices, economics, etc., and is not always the best form. Here, we will explain a platform that does not use a fully closed pair and a relatively simple embodiment that uses both.

Example 1

In an embodiment of a platform that does not use both fully closed pairs, it is assumed that the memory effect, the operation pair considering the memory effect, and the end point of the disturbance response function can be 1, 3, and 3, respectively. If you use it, and there are causal sequences that are not enough with 1 or 3 terms, increasing the number of terms in the response function should be easy in this example.

Operation pairs, static characteristic F0 _∞, since F 1 _∞ is the reverse of the combination, the absolute value divided If not, the sign is known.

Therefore, operation pairs 0 and 1 are assigned so that F0 _∞ <0 <Floe holds. The end

The selection of 1, 3, and 3 is based on the experience that sufficiently high accuracy and high speed control can be achieved if the control cycle is not incorrectly selected.

Then the transfer equation is

r = f 0-c0 + f 1-cl + g-d = q r + aOc0 + alcl + b-d

r „= qi r„-1 + aOi c0 „-1 + aOa cO _n -2 + a0 ₃ c0„ -3

+ ali cln -1 + al ₂ cln -2 + ala cl _n -3

+ bi d „-1 + b2 dn -2 + b ₃ d„ -a

In step response tests, etc., for each of the above n, for each of cO, c1, and d, four or more consecutive points in time immediately after the signal amplitude Z noise amplitude (SZN ratio) changed significantly to 100 or more. Select 10 or more sets of data including. Since d is an intellectual disturbance, the data before and after the disturbance is observed is adopted. If you do not use d, omit the section on d.

Ignore the data for small SZN ratios when seeking and correcting during control. In addition, data when the relationship between the operation value and the control value cannot be expressed by the response function is used. For example, when a safety limiter circuit is activated. A platform that can only provide low SZN ratio data requires more data, but a small number of digits does not help improve the accuracy of the response function, even with a large number of digits. . Based on this data, qi, we look at _{aOi, a0 2, a0 3,} a, al 2, al 3, bi, how favorite a b _2, b _3. A platform using the successive update least squares method is as follows. Let ε be a small positive amount (eg 0.01). Let X be the matrix of the 10-line, 10-column normal equation, y be the 10-dimensional normal vector, z be the 10-dimensional unknown vector, u be the 10-dimensional overnight vector, and be the data at time 0. You add it.

u = '(r-1, c0-1, cO-2, c0-3, cl-1, cl -2, cl-3, d-1, d-2, d-3) z = '(qi, aOi, _{A_rei_2, a0 3, al i, al} 2, al 3, bi, b 2, b 3)

X and y are updated with X = (l — s) X + su 'u, y = (l — £) y + sr ₀ u. When X is a regular sequence, z = X — ¹ y The response function is obtained. When X is not a regular sequence, it is when linearly independent data is lacking. This method effectively uses the most recent 1Zs data set. Since X and y are multiplied by 1-ε, numerical overflow can be avoided. The inverse matrix can be obtained by well-known methods such as the cofactor method and the sweeping method. fCh using _{ζ, ίθ2, ί0 3, f0} 4,, Π 2, Π 3, Π 4; sequentially calculated _{FCh, F0 2, F0 3,} F0 4, Fli, the F1 _2, F1 _3, F by the following equation To do.

f0 = aO + qf 0, F0 = Λ FO + fO, f 1 = al + q- f 1, Fl = Λ Fl + f 1 fOi = aOi FOi = aOi f li = li Fl, = f li f0 ₂ = a0 ₂ + qi · fO, FO2 = FOi + fOi f 1 = al + qi · f1: FI2 = Fli + f1: f0 ₃ = aOa + qi · f0 _; F0 ₃ = F0 ₂ + f0; f1 ₃ = al _{3 + qi · f 1: Fl} 3 = Fl 2 + f 1: f0 4 = qi · fO- FO4 = F0 3 + fO 'f = qi · f 1: in the Fl ₄ = Fl ₃ + f 1. Thus Using the obtained response function, the operation value C is determined by the finite settling method so that the control value R matches the target value S at each control cycle.

At present, past and present measured values R, past set values C0 and C1, disturbances d in a known range (assuming future values by schedule are available), and target values S are available. The required values are listed below.

Ro, R- i, R ~ 2, R- 3; = Ro— R-, r— 1 = R- 1 — R-2, r— ₂ = R 2 — R— 3

 CO-i, C0, C0; cO-i = CO-i-C0, cO = CO-CO

CI -丄, CI one _2, CI one; cO-i = CO-i - CO, cO = CO - C0

D ₄ , D ₃ , D ₂ , Di, Do, Di, D- 2, D- ₃ ; d ₄ = D ₄ — D ₃ , d ₃ = D ₃ — D ₂ , d ₂ = D ₂ —,

d ₁ = Di-Do, do = Do-Di, di = D- i-D- 2, d- 2 = D- 2-D- ₃

S, S, S, S i

Based on this, find the predicted value when both operation pairs are closed in the future. From C0o = 0 = C0-i + cO ° o, Clo = 0 = + clo

r ° = qr ° + aOc0 ° + alcl '+ b-d

R '= Λ R' + r ', E = S-R'

r ° i = qi • ro + bido + b 2 d-i + b 3 d- 2 + a0i c0 0 + a0 2 cO "-i + a0 3 cO '- 2

+ al i cl o + al2 cl 'one i + al ₃ cl'— 2

^{R l = R o + rl,} E l = S l- R l

r. ₂ = qi · Γ. i + bi di + b ₂ do + b3 d— i + aOacO "o + aC cO. i + al ₂ cl o + al ₃ c — i

R 2 ⁼ R 1 + Γ 2, E 2— S 2— R 2

r '3 = qi-r ° 2 + bi d ₂ + b ₂ di + b ₃ do + a0 ₃ cO' o + al ₃ cl ° ₀

R 3 ⁼ R 2+ r 3, E 3 — 3− R 3

r '= qi r ° 3 + bi d3 + b2 da + b3 di

Based on these, the operation value cO 'that makes the control value match the target value at the third and fourth time points. , C Γ. Is determined by the following procedure.

Assuming that 0 N = 0, E _{3 is} 0, and if it is 0, it moves to 1.

 1 cO '0 = 0,

 F1 · cl '= E [3.4]

_{Fl 3 · cl Ό + Fl 2} · cl Ί = E 3

_{Fl 4 · cl Ό + Fls ·} cl Ί = E 4

... cl Ό = (E ₃ 'F1 ₃ — E ₄ ' F1 ₂ ) / (F1 ₃ ² — F1 ₂ 'F1 ₄ )

 If 0≤cl '0, solve this, otherwise N = N + 1, if 1, cl'. = 0 is solved, and if N = l, move to 2.

 2 cl '0 = 0, and

 From FO- cO '= E [3.4]

FOsc0'o + FO2cO'i = E ₃ 35

_{F0 4 · cOO + F0 3 ·} CO 'i = E 4

_{·· cOO ^. (E 3 ·} F0 3 - E 4 · FO2) / (F0 3 2 - F0 2 · F0 +)

 0≤ c0 '. If this is the case, then solve it, if not, set N = N + 1, and if 1, set c0 '. = 0 is solved, and if N = 1, it moves to 1.

This results in C0. = cO ' ₀ , Clo = cl'. Is output, the data is updated at one point, and the process moves to the next control cycle. CO in the next control cycle ^ Cl-, is, this C0o, Ri You Do to Cl _o.

 Example 2

In the embodiment in which both the fully closed pairs described in the disclosure of the invention are used, the memory effect, the operation pair considering the memory effect, and the end points of the fully closed pair and the response function of the disturbance are 1, 2, 2, and 2, respectively. 2, 2. Choosing 1, 2, 2, ² , ² chose a simple example because the formula would be complicated. For example, when controlling the temperature by sending the heat quantity w to the heat capacity C cooled by the heat conduction of the heat resistance k, and letting the temperature be _r ,

C (r / dt) + k r = w

It becomes. This equation can be solved as

e ^{k 1} ' ^c (dr / dt) + (k / C) re ^{k 1} ' ^c = (w (t) / C) e ^k '' ^c

-(t) e ^ktc ) = (F (t) / C) e ^{kl / c}

r (t) e "= $ (w (x) / C) e ^k dx

r (t) = $ (w (x) / C) e ^k 'ヽ-"^; dx

Therefore, if ε = 0 using the result of the background art,

 τ

r = fwf _n >. = (e — ^{/ C} dt / C = k (l- e ~ ^{k T / c} ) e

 "One"

qi≡ e- ^{k T} '" ^c q ≡ qi Λ f = kUn) A / (l-q)

 r = q r + a w q e [l, l] a ≡ k (l-qi) A e [l, l]

Such a simple control system does not require many terms in a finite sequence. Considering that aO, a1, b1, b2, and b have two terms for reasons such as loosening and deflection, even this number of terms is sufficiently practical. If you use it, and there is a cause sequence that is not enough with 1 or 2 terms, increasing the number of terms in the response function should be easy in this example.

Operation pair, static characteristics FOcc, since Fl _∞ is the reverse of the pair stand Align, the absolute value rather than from the minute also, the sign has been found.

Where you pretend divide the 1, 2, as FOco rather than 0 rather Fl _∞ stand become.

Then the transfer equation is

r = fOcO + f Icl + g0d0 + gldl + gd = qr + aOcO + alcl + bOdO + bldl + bd

If the current time is term 0, then:

ro = qi r- 1 + aOi cO-l + aC cO- ₂ + ali cl-i + al _z cl-2

+ bOidO i + b0 ₂ dO 2 + blidl alacl one 2 + bid one i + b ₂ d— 2 + b ₃ d

Three consecutive points immediately after a large change in signal amplitude / noise amplitude (S / N ratio) of 100 or more for each of c0, cl, dl, d2, and d in trial control, etc. Select more than 20 sets of data, including each.

It is advisable to ignore the data for small signal-to-noise ratios when seeking and correcting during control. If you get only a small signal-to-noise ratio, you need more data. Based on this data, a (, aOa, a, a, bC, b0 ₂ .bl !, bl ₂ , b, and b ₂ are obtained by a preferred method (for example, the least square method).

After the response function is determined by the preliminary method, if it is modified in parallel with the control, if the sequential identification method is used, the following is performed. Let the small positive amount be ε (for example, 0.02).

 ■ η ― ro-qir- 1-aOicO- i-a02 c0- 2-alicl-1-a cl- 2

-bOidO 1-b0 ₂ d0 2-blidl 1-al ₂ cl 2-bid 1-b ₂ d

Ask for. Also, adjust the degree of noise in the control system. will do. "." Is the value obtained by adding the value corresponding to several digits of the control value to the long-term root mean square of "". For example,. ^{2 = (1- ε) ".} 2 + ε 2 + (3-dgt) can be obtained with ^2.

= ri ² + A0 ² (cO-! ² + c0- ₂ ² ) + Α1 ² (cl-) ² + cl- ²² ) + B0 ² (dO—, ² + d0-) + Bl ² (dl— ₂ ² ) + B ² (d- + d— 2 ² ) _{+ 77} o ²

Is calculated, and when data with a large S / N ratio is obtained, the response function is modified as follows. Where AO- aC + aO Al = all + al ₂ , Β0 = bOi + b0 ₂ , Bl = bli + bl ₂ , Β = bi + b ₂ , k = f] / λ. q ₀ = (1- ε) q + kr-aOi = (1- ε) aOi + kAO ² cO-i, a0 ₂ = (1- ε) a0 ₂ + kAO ² cO-i,

all = (1-ε) ali + kAl ² cl- i, al ₂ = (1-ε) al ₂ + kAl ² cl-i,

bOi = (1-ε) bOi + kB0 ² dO-i, b0 ₂ = (1-ε) b0 ₂ + kB0 ² dO

bli = (1- ε) bl! + kBl ² dl- i, bl ₂ = (l- ε) bl ₂ + kBl ² dl- i,

b) = (1-ε) bi + kB ² d →, b _a = (1-ε) b2 + kB ² d- i

This sequential identification method provides an unbiased estimator at the expense of slower identification times. Based on these, ίθ ί0 ₂ f0 ₃ f, il ₂ , f 1 ₃ gOi g0 ₂ g0 ₃ , gl i, gl ₂ , gl ₃ ; FOi, F0 ₂ , F0 ₃ , Fli, F1 ₂ , F1 ₃ , G0 ,, G0 ₂ , G0 ₃ , Gli G 1 ₂ Gl ₃ are calculated sequentially. f0 = aO + qfO, F0 = Λ FO + fO, fl = al + qf 1, Fl = Λ Fl + f 1 fOi = aOi FOi = aOi f li = li Fli = f li f0 ₂ = a0 ₂ + qi f 0 F0 ₂ = FOi + f0 ₂ f 12 = al 2 + qi f 11 Fl ₂ = Fli + f 1 ₂ f0 ₃ = qi fO FOs = F0 ₂ + f 0 ₂ f 13 = qi fl 2 Fl ₃ = Fl ₂ + f Is g0 = bO + qgO, G0 = Λ GO + gO, gl = bl + qgl Gl = Λ Gl + gl gOi = bOi FOi = bOi gli = bl, Fli = gli g0 ₂ = b0 ₂ + qi gO FO2 = FOi + g0 ₂ gl2 = bl 2 + qi gl i Fl ₂ = Fli + gla g0 ₃ = Qi gO F0 ₃ = F0 ₂ + g0 ₂ gl3 = qi g FI3 = Fl ₂ + gl _{3 The} response function obtained in this way Using, determine the operation value C by finite settling so that the control value R matches the target value S at each control cycle.

 At present, past and current measured values R, past set values CO CI, DO, Dl, disturbance D within a known range (current and past can be obtained by measurement), and target value S are available. The required items are listed below.

Ro, Ri, R ~ 2; r ₀ = Ro-Ri, r- i = R- i-R-2 CO-1 "CO-1 2; cO-i = CO-i-CO-2 Cl-i, Cl-2; cO-i = CO-i-CO-2

DO-!, DO- 2; dO- i = DO- i-DO- 2 Dl- j, Dl- ₂ ; dO- i = DO- i-D0- ₂

D ₃ , D ₂ , Di, Do, Di, D- 2; d3 = D ₃ -D2, d ₂ = D ₂ -Di, di = Di-Do,

 do = Do-D-i, d- i = D-i-D- 2

 S 3, S 2, S 1 J

Based on this, we will obtain a predicted value when both operation pairs are closed in the future and the fully closed means is opened.

cO '0 = — CO-i i, cl ° o =-CO- i, d0 ₀ = 1-DO- i, dlo = 1-DO- i

r ° = q- r '+ aO-cO "+ alcl' + bO-dO + bl-dl + b-d

 R '= Λ R' + r °, E = S-R °

r ° l = qi-ro + bi do + ba d- i + aOi cO o + aOs cO — ι + ali cl o + al 2 c 1-1

+ bOi dOo + b0 ₂ d0- i + bli dlo + bl ₂ dl- i

R * 1 = Ro + r 'i, E i = S i-R "1

r '2 = qi r ° 1 + bi di + b2 do + aOa cO' Q + & I 2 cl 'o + b0 ₂ d0 ₀ + bl ₂ dl ₀

° 2 = R '1 + r ° 2, E ₂ = S 2 — R' 2

R '3 = R 2 + r * 3, E ₃ = S _3- ° 3

Based on these, the operation values cO'0, cO'i, cl'0, cl'i that match the control values to the target values at the second and third time points are determined in the following procedure.

 0 N = 0, M = 0, cO '. = cl '. = 0, DO. = Dl. = l as the initial value,

If E ₂ <0, go to 1;

 1 N = N + 1 and Flcl '= E (n = 3 to 4)

Fl ₃ cl Ό + FI 2 cl '1 = E ₃

... cl '. = (E ₂ · Fl ₂ — E ₃ · Fli) / (Fl ₂ ² _ · Fl ₃ )

If 0≤ cl 'o, If D0 _o = 0, solve this and

If not, D0. = 0, and 'save the _{o (C "= C 1'} cl 0) and,

_{E 2 = E 2 - G0 2} , E 3 = E 3 - G0 3 and to repeat the 1.

 If you do,

Also D0 _o = 0 if _c r. = _c ", D0. = 1 as a solution, and then cl '. = 0,

If ΝΦ 1, solve this, then go to 2 _c N = N + 1 and F0c0 '= E (n = 3 to 4)

F0 ₃ cO 'o + F0 ₂ c0' i = E ₃

. · C0. 'O = ( E 2 -F0 2 - E 3 - FOi) / (F0 2 2 - FOi · F0 3) 0≤ cO'. Then

 If D1. If = 0, solve this,

D1. = 0 and save cO 'o (c "= c0' _o ).

E ₂ = E ₂ — Gl ₂ , E ₃ = E ₃ — Repeat 2 for Gl ₃ .

 Otherwise,

If D1 ₀ = 0, solve for cO ' ₀ = c ", Dl ₀ = l, and if not, CO' = 0,

If N 1, then solve this, then go to 1. Dlo, D ² . , COo = cO '0, Cl = C1'. Is output, the data is updated at one time, and the process moves to the next control cycle. Industrial applicability

 Control is an indispensable technology for the use of machines and devices.It is based on the calculation using a computing unit, that is, a computer, instead of the mechanical control using a conventional cam or gear wheel. Now replaces the action of equipment parts.

Alternatives have shifted from classical control, which digitally approximates analog control, to more accurate and faster MRAS. The technology that solves the push-pull control, which has been an obstacle to MRAS in the course of technology, along with the problem of non-configurable areas is extremely useful from an energy-saving standpoint.

Claims

The scope of the claims

1. For a control system having a pair of operation means (operation pair) acting in opposite directions, the future control value is determined by the past and present control values, usable disturbance values, past operation values, and future operation values. In the control method of predicting and calculating the future operation value as a value that matches the control value to the target value at several points in the future, when the setting range of the operation value is set to a non-negative value, the response to each operation pair A function is calculated, and the control value when assuming that both operation values of the operation pair are kept closed is predicted, and only the means having the static characteristic of the same sign as the difference between the target value and the predicted value is assumed. If the last operation value is a non-negative value, the value is determined as the operation value.If the operation value is a negative value, the operation value is assumed to be the operation of only the other party and the operation value is determined. If the last operation value is a non-negative value, that value is used as the operation value. If then determined negative value, the control method characterized that you are closed to both pairs.

2. For a control system that has a pair of operation means (operation pair) acting in the opposite direction and a pair of means for fully closing the output of the operation pair (fully closed pair), use the past and current control values and values. Predict future control values based on possible disturbance values, past operation values, and future operation values, and calculate future operation values as values that match control values to target values at several points in the future When the setting range of the operation value is set to a non-negative value, the response function for both the operation pair and the fully closed pair is obtained, and the operation value of both the operation pair is kept at 0 and the fully closed pair is The control value when both are assumed to be open is predicted, and the operation value is obtained by assuming the operation of only the means having the static characteristic of the same sign as the difference between the target value and the predicted value, and If the most recent operation value is a non-negative value, the value is provisionally determined as the operation value. The operation value is calculated assuming the operation of only the other party, and if the latest operation value is a non-negative value, the value is provisionally determined as the operation value. In both cases, the operation value is determined to be o, and for the operation pair whose operation value is not set to 0, the operation value is calculated assuming that the fully closing means of the pair is closed, and the latest operation value is non-negative If the value is a value, the operation value is used to close the other party's fully closed means, and if the value is negative, the original operation value is used to open the other party's fully closed means. Control method