WO1999049370A1

WO1999049370A1 - Control method and controller

Info

Publication number: WO1999049370A1
Application number: PCT/JP1998/001224
Authority: WO
Inventors: Takehiko Futatsugi; Hiroo Sato
Original assignee: Adtex, Inc.
Priority date: 1998-03-23
Filing date: 1998-03-23
Publication date: 1999-09-30
Also published as: JP3352699B2; AU6421098A

Abstract

In order that a manipulated value which makes the estimated value of a controlled value agree with a target value (1) is calculated, a limit value which is obtained by subtracting a liner expression of the sign of the difference of the target values from the weighted mean of the target values is found at a plurality of timings using the controlled value, the manipulated value and usable disturbance value. If the target value is not between the target value or the limit value of the next timing and the limit value of the present timing, the target value (A) is changed to the limit value (B). By calculating the manipulated value by using the changed target value, a control by which the increase before a sudden decrease, the decrease before a sudden increase (2), the overshoot when the target value (3) is reached, the delay of follow up (3), etc. can be suppressed is realized.

Description

Description s Control method and device

According to the present invention, in a control in which a control value follows a target value that changes in a time series, an operation value is calculated by changing a target value that rapidly changes beyond an allowable gradient to within an allowable limit. It relates to a control method that more accurately matches the target value and a control device using that method. Background art

As shown in FIG. 1, the control device inputs a target value (S), a control value (R), and a disturbance value (B), and stores a storage device (M) using these and an operation value (C). Finds and outputs C that matches S and R with the arithmetic unit (X) that has it.

In many cases, the values used in control calculations differ from the input / output values from the device. For example, a value measured as a voltage value or a current value is converted into a power value and then operated, and the value calculated as the power value is converted into an AC phase value and output. Calculation is performed by converting the electromotive force of the thermocouple into a temperature. In order to increase the signal-to-noise ratio, the measurement values are averaged before calculation. Converts the result obtained by real number arithmetic into an integer and outputs it. And so on.

The conversion by such input / output is performed by using a well-known method or a trivial method by selecting the control system. Will also mean.

Recently, in order to realize more precise and high-speed control, instead of the conventional PID control, a response function has been obtained, and the usefulness of the control has been predicted. Calculating the control value that matches the target value is being performed. Learn how to match forecasts to goals.

Control values, manipulated values, disturbance values, etc., form a time series that continues from the past, passes through the present, and continues into the future.

These relations are expressed using a bi-infinite sequence in which the term numbers continue infinitely on both the positive and negative sides, the past is represented by small term numbers, and the future is represented by large term numbers.

However, the control has a starting point, and it is not necessary to mention an infinite past within a reasonable approximation.

Therefore, we consider only the next sequence as both infinite sequences.

A) A sequence (left regular sequence) with non-zero terms (called the first term, and the term number is called the first place), where all the terms with smaller term numbers become 0

{•••, 0,0,0, aA

_{S +} t, aAs + 2, '*-}

B) A sequence in which all terms are 0 (represented by 0)

0≡ {··, 0,0,0, ···}

Addition (+), subtraction (1), multiplication (·), and division () are defined by the following formula.

a · b = b · a = {} mi {· · ·, 0, CA s + e s, · · ·, ", ♦ ·}

^{= {···, 0, dA S} be S, · · · aA s bk -. A S + AS + l bk - AS - l + '^' + ak- B s BS, · · ·} a / b = { c} = {· ♦ ·, 0, CA _S -BS, CA S -BS +, ♦ ·, CA s -es + k, ♦ ·}

M {•••, 0, aAs / bBs, (aAs + i-bes + iCAs-BS) zobes, *-*

, (3A S + k-bB S +, CAS-BS + k-1-· ·-bB S + k CA S-BS) Zbe S, * * *} Multiplication is defined by the so-called hammering convolution .

Division is obtained by solving the multiplication method from the first term side.

This operation does not divide by zero, satisfies the rules of distribution, associative, and multiplication, and can be calculated like ordinary algebraic expressions. Defines positive and negative powers as if they were real numbers by repeating multiplication and division. If a'b = 0, then a = 0 or b = 0.

A sequence in which all but the 0th term is 0 is identified with the numerical value (scalar) of the 0th term, and the numerical value represents the sequence.

For example, 1 represents a sequence where the 0th term is 1 and all other terms are 0. By this identification, the definition of multiplication is the definition of scalar product.

N represents a sequence where the first term is 1 and all other terms are 0.

The m-th power of N is 1 only for the m-th term and 0 for the other terms, and the product N ^m · {aj = {a „—„} with an arbitrary sequence a is a sequence that represents the time point m before a. You.

Since the first power of N is the Z operator of the Z transformation, it is represented by Z.

Z ョ 1 // N-N— 'Z ^m · {a _n } = {a „ _{+ m} } (2) Sequence ≡ 1 The difference between N and any sequence a is the difference between the sequence a .

A * a = a — Ν · a = {a _n — a (3) The product of a reciprocal of Δ and an arbitrary sequence a is the sum of a.

∑ 1 ΖΔ = 1 / (1 — Ν) = {···, 0,0,1,1,1, ··· First place = 0} (4)

∑ · a = {aA s + aA s ₊ , + * · · + (AS is the first place of a) (5) Although the term itself is not 0, the term whose future side is all 0 than that term (final term and A sequence with the term number and its terminator is called a finite sequence. Since a finite sequence is not zero, it has a first term and the number of nonzero terms is finite. Next, this sequence is used to express the transfer equation.

The transfer equation is an equation that relates the cause (operation value c, disturbance b) and the result (control value r).

In order to express zero that there is no change, the cause and effect shall represent the difference (change amount) at each time point.

c = i · · · 0, ccs, · · ·, co, c,, · · ·} b = {· ·, 0, ss, · · ·, bo, bi, ♦ · r} { . ·, 0, r _RS ,…, r ₀ , r ′,…} (6) Assuming the principle of linearity and superposition, the sequence f, g whose first rank is 1 or more is defined as a response function (a time series representing the effect after the cause occurs), and

f = i · ·, 0, f,, f ₂ , f 3,…}, g = {…, 0, g,, g ₂ , g ₃ ,…}, 7) The transfer equation is .

r = {r „} = f-c + g-b

= {f 1 · C r>-1 + T 2 'C n-2 + • • * + fr-CS ^, Cc S

+ gi * bn-i + g 2 * bn-2 + • • • + gn-B s ^, bB s} (8) For example, the second item is the change in c that occurred two times before time n (- _This indicates that the effect (f ₂ ) after two points in ₂ ) is realized at the n-th point (). As the available energy (exergy) in the natural world is constantly decreasing, the resulting change caused by the finite changes will eventually stop exponentially. (Energy theorem)

Expressing this theorem as a transfer equation,

f ^, = (.--, 0 ₎ f ^, ₁ ,--- ₎ f ^, PE, 0, ---} = f-(l-d ') finite sequence

g '= {''', 0, g ' _,, ''', g ' _QE , 0,'''} = g '(1—d') finite sequence

(! '= {··, 0, d',, · ·, d ' _DE , 0, ···}} Finite sequence (9) 1-d' = (1 d, · N) · (1 - d ₂ · N) (1 one d [N)

0 <d,, d ₂ , ···, CIDE <1 (10) r = {rn} = f '· c + g' · b + d '· r

= {f ^, 1 * C n-l + f ^, 2 * C n-2 +

+ g,-, + g, 2 ·-2 + + g 'b-Q

+ d ^, fr „-i + d ^, 2 T n-2 +---++ d 0 'DD EE T' T _n n-DD ₆ e}} (11) (10) (9) expresses that the damping occurs within a finite time, (9) is substituted into the transfer equation and rearranged to (11), and (10) becomes the absolute value if the vibrational damping is included. Is changed to a condition less than 1. Since the result always comes after the cause, the first order of the response function is 1 or more. Since the first order of the finite sequences d 'and f g' are also 1 or more, they can be considered as response functions and interpreted as follows.

(11) has r on both the left and right sides.

We call the cause and the resulting r the internal cause.

(11) indicates that external causes c and b change to internal causes. The result remains even after the external cause disappears due to the internal cause.

In other words, internal causes represent memories of past external causes. d 'can be called the response function of the memory effect, and f' and g 'can be called the response functions of the operation and disturbance considering the memory effect.

Since (8) must be calculated from the first term of the cause, the amount of calculation becomes enormous as control progresses.

However, (11) only needs to go back a certain amount in the past.

It is known to use (11) to find the response functions d 'and f g'.

By Takato Yasuto System and control Shimoiwanami store 19778 f, g is calculated from d ', f', g 'using the relationship of (9).

Normally, for each control cycle, increase the parameter π representing the current time by one, or fix the current time to the 0th term and shift the sequence of cause and effect by one term. Here, the expression that represents the present time is used in Section 0.

Rather than expressing the target value or control value as a difference, it is easier to express the raw value to be measured or set: the actual value (sum of the difference), so the sum of the transfer equation is used.

∑-r = ∑-f-c + ∑-g-b

= ∑ -f '· c + ∑ -g' · b + ∑ -d '· r (12) The yield of three sequences, for example ∑' g * b, is the product of ∑ · g and b Can be thought of as the product of g and ∑ · b.

b is the amount of change (difference) of the cause, ∑ · b is the sum of the The raw value (actual value) to be generated.

The time series that represents the result when the cause is increased by 1 during the point in time in terms of a pulse and is returned at the next point in time is called the pulse response function, and the time series when the cause is not returned is called the step response function.

d ', f', g ',; f, 9, h are the changes (differences) in the result (step response function) when not returned, and are a pulse response function.

The relationship between the pulse response function and the step response function, and the relationship between the amount of change in the cause or result and the actual value (the raw value of the measurement or setting) is the relationship between the difference and the sum. The pulse response function and the amount of change in cause and effect are expressed in lowercase letters, and the step response function and the actual value of the cause and effect are expressed in uppercase letters.

R≡ ∑ · rr = A «= R-N-RR = N 'R 10 r (13) Operate values C and c are the last time points and the manipulated values when the manipulated values are not changed in the future (no operation) If R and R are measured values from the past to the present and control values indicating the prediction when no operation is performed, it can be calculated sequentially from the first time point to any Q time point.

R = N · R + d '· mm · R + f' 'c + g' 'b (14) At this time, if the disturbance b If the disturbance is caused by, the past value, present value, and future value can be used.

The effect of such intellectual disturbance can be eliminated by g '* b in (14).

Let C, c 'be the manipulated value from the present time (past 0), and R' the control value when c 'is performed after c (measured values in the past and present, predicted values in the future), F 'c'-R'— R (15), but if the operative control value R 'matches the target value from the Pth point to the Qth point, the following equation is established.

{F 'c' = {S-R n = P ~ Q (16) Assuming that the end of the future manipulated value c 'is CE, the unknowns c' ₀ , c ''''',c' _CE , In the case of CE = Q-P, by considering (16) as a system of linear equations,

In the case of CE Q Q — P, it can be obtained by using the least squares method with (16) as the observation equation.

The last (current) manipulated value Co = C- + c '. Is output and controlled. The finite settling method is known as the former example, and the optimal control method is known as the latter example. However, in the finite settling method, the target value is invariable from the present time S == S. · In the case of ∑, time series of target values is not considered.

In the finite settling method, P = FE, Q = FE + DE, CE = DE.

Both methods are explained in the book by Yasuto Takahashi mentioned above.

However, if a programmed time series is used for the target value S of (16), the increase before the rapid decrease or decrease before the rapid increase shown in FIG. Inconveniences such as overshoot when reaching the value (3: excessive response, overshoot), and delay in following (4) may occur. This disadvantage occurs even when the operating values are within the limit range.

Disclosure of the invention

The delay caused by the operation means being at the limit value, the delay caused by a sudden change of the target value so that the response cannot be made in time, and the excessive response (overshoot) caused by noise or insufficient accuracy of the response function are stopped. It is a phenomenon that cannot be obtained. However, if the programmed values follow the programmed and known targets, but the operating values have not reached their limits, there should be some improvement.

Assuming that the control value and the target value So are the same at this point, connecting the points that should match with a smooth curve results in a thick solid curve of FIG.2. In this way, the manipulated value that causes a fallback before the time point P is the solution of the most natural settling equation (16) and is actually realized.

In a car, when turning at a right angle, it is similar to a situation in which the driver must turn off the handle once in the opposite direction of the turn to lose the wheel due to the inner ring difference.

If cutbacks are not desired, you must cut corners. By adding a corner cut (change from A to B) in the target value program, switchback (2) can be reduced.

Overshoot ( ₃₎ is a recoil caused by turning back, so it is automatically reduced by corner cutting.

Since this corner cut is ahead of the change in the target value at the part with a large curvature, the carry (4) can also be reduced.

There are two basic ways to do kumari, and you can combine these two methods.

One is the weighted average of the target values

ΤΡ ₊ Ι = ∑, (a,, i -SP ₊ j) ∑ ”(a ,,)) = 1 (17) is used as the limit value to smooth the change.

Here, ∑, () indicates that the sum is taken for j in (). This method calculates the value corresponding to the P + i time point of a curve such as a quadratic curve or a cubic curve that passes through some time points near the P + i time point (sometimes excluding the P + i time point). Includes the method of limiting, or using the method of least squares to limit the value corresponding to the point P + i of such a curve.

Determining the weights (a, J) that fit these curves is a well-known method that can be obtained by finding a linear equation with the weights as unknowns (the former) or the inverse matrix of the least squares structural equation (the latter). is.

The other is the value obtained by subtracting the maximum allowable slope from the time point P + i + 1, starting from the time point before the time point Q + 1 before the time point P.

TP +, = SP +, +1-M, -sgn (sp ₊ ,) (18) sgn (X) = —〗 (X 0 0), 0 (X-0), +1 (0 <X) (19) Is taken as the limit value, and the cutback caused by the limit value is regarded as an allowable limit. If only the target value at the Pth point is corrected by this method, the target value is changed stepwise by the control up to now, and the change back of the target value (the change when the absolute value of the amount) and S _MAX, M. = S _MAX .

Considering the case where the target value S _{P +} , ₊ , of (18) is modified, in general,

T _{P + j} = S _{P +} i _{+ 1} -∑ j (M,, j 'sgn (sp _{+ i + j} )) (20).

The first term on the right side of (20) is a special case of weighted averaging.

Combining these two methods gives:

T _{P + i} = ∑ j ((a ', S _{P +} ')-M,, i -sgn (sp ₊ i _{+ i} )) ∑. (A,,;) = 1 (21) The value obtained by subtracting the linear expression of the sign of the difference between the target value from the weighted average of the values is the limit value.

When only equation (17) is used, Μ,, in (21) is all zero.

Perform this correction from point Q to point P. In either method, the target value at the P + i time is between the limit value at the P + i time point and the target value at the P + i + 1 time point (in some cases, the limit value has been corrected). You do not need to change it if the change is moderate. Therefore, usually

If (Tp _{+ i} -Sp ₊ ,)-(S _{P +} i-Sp ₊ , ₊ ,) <0 (22), replace the target value SP ₊ , with the limit value Τ _{Ρ +} , and After calculating the operation value, return the target value to the original value and move on to the next control cycle. Since the purpose of changing the target value is corner cutting, it is necessary to correct the target value at each point in time, including the first time point (time point Ρ) at which the control value matches the target value.

As a special case of (21), there are cases where the limit value is a target value only at a specific point in time and a case where the difference only at a specific point in time is used. The present invention includes this case. However, the coefficients a, ο = 1, a,, * o = 0, «I,, '= 0 (23) are always corner cut Therefore, it is out of the scope of the present invention.

FIG.2 shows the case where only the point in time was changed from A to B as necessary. The target value is indicated by a polygonal line, and the control value is indicated by a curve.

With this correction, the control value is improved from a bold solid line to a bold dotted line. BRIEF DESCRIPTION OF THE FIGURES

F I G. 1 is the block diagram of the control equipment »

Explanation of reference numerals

S: Target value R: Control value B: Disturbance value

C: Operation value X: Computing device »M: Storage device

FI G. 2 is a graph explaining the setting by the conventional method. 1: Target value 2: Switch back 3: Overshoot

4: Delayed Line: Target value Curve: Control value

A: Target value before correction B: Target value after correction Best mode for carrying out the invention

The realities of control vary, and there is no always the best embodiment. Therefore, the end point of the memory effect, which can be easily implemented, is selected as 1 and the target value changes in a time series. Here is an example of modifying.

It is assumed that the end of the response function considering the memory effect is 3 for both the manipulated value and the disturbance, and only one disturbance is available, and the response function can be identified by a known method.

Then, from (14), the measured value R. , R - ,, preset value c- _2, c - ,, planned value (past, present and future) or measured values (past and present and future is 0) using _b-2 ~b _2, the After the first time, it can be calculated as follows.

R, = Ro + d 'i' (Ro-Ri) + f '2 * c-. + F'3'C-2 + g 'i * bo + g, ₂ · b-! _{_{+ g, 3 · b - 2}} 2 = Ri + d '1 · (R.-Ro) + f'3'C-i + g 'i * bi + g' 2 -bo + g '3 * b -,

R ₃ = R ₂ + d '1 · (R ₂ -i) + g', 'bii + g' 2 * b, + g ' ₃ * bo Next, evacuation of target value, calculation of limit value and target value Fix

Ss = S ₂

T ₂ = ao ♦ So + ai * Si + a ₂ 'S2 + a3 * S 4-M ₂ · sgn (S ₃ -S2) (24) If (S ₂ — T ₂ ) (S ₃ — S ₂ ) < If 0, set S ₂ = T ₂

Follow the steps below.

For the coefficient of (24), if a quadratic curve that passes the target values at time 0, time 1, and time 3 is adopted as the limit value, the limit value is calculated using the following coefficient.

l = 0, a. = -1/3, at = 1, a ₂ = 0, a ₃ = 1/3 (16) is the operation value c '. , C ', is a binary system of linear equations.

(fi + f ₂ ) * C '0 + f 1 «c' 1 = S 2 -R2

(f, + f ₂ + f ₃ ) «C '0 + (f i + f 2)' C '1 = S 3 -R3

The solution to this equation is

C '0 = {(f, + f 2)' (S ₂ -R ₂ ) — f 1-(S 3 -R ₃ )} / {(f 1 + f ₂ ) ² -f, «(f, + f 2 + f ₃ )} The last operation value is the actual value C '. = C-1 + C'o and output.

c ', is also found, but is not needed for control other than displaying predictions.

Restore the target value and move on to the next control cycle.

Industrial applicability

At present, it is unlikely that no control measures will be taken to operate the machine. There is always a need for controls that are more faithful to target values and that do not behave undesirably. Computer control, in which conventional cams and gears are replaced by computer calculations, is the softwareization of equipment components themselves. The method of the present invention and the control device using this method for improving the fidelity of the target value by a simple means of changing the target value »have a high industrial value with little economic burden. I can say.

Claims

The scope of the claims

1. Predict future control values based on past and present control values, usable disturbance values, past operation values, and future operation values, and set future operation values as control values at several future points. In the control method of calculating as a value that matches the target value, the weighted average value of the target value at each time point, including the first time point at which the control value matches the target value The value obtained by subtracting the linear expression of the sign of the difference of the target value (including the case where the difference at only a specific time is used and including an equal 0) is subtracted from the value at that time. If the target value at each time point is not between the limit value at each time point and the target value or limit value at the next time point, replace the target value with the limit value and calculate the operation value. Characteristic control method.

2. Predict future control values based on past and current control values, available disturbance values, past operation values, and future operation values, and set future operation values as control values at several future points. In a control device that uses a control method that outputs a value that matches the target value, the weighted average value of the target value at each point in time, including the first point in time when the control value matches the target value And the linear expression of the sign of the difference between the target value and the target value at all points in time (excluding the case where the difference at only a specific point in time is used and the identity 0) If the target value at each time point is not between the limit value at each time point and the target value at the next time point or the limit value, the target value is replaced with the limit value. A control device for outputting the calculated latest operation value.