JPH01237701A - Control system to optimumly follow periodical target value - Google Patents

Abstract

PURPOSE:To obtain a control algorithm, with which control quantity optimumly follow a target value to have a constant period by simple four rules operation, and to obtain the control system of satisfactory following accuracy with a general digital circuit, etc., by using part deviation, present deviation, past increase part correcting quantity, a past control input and a constant, which is determined in advance, when a machine tool and a robot, which are repeatedly operated, are controlled. CONSTITUTION:A target value r(i) at a present time (i) is generated by a command generator 1 of the control system and deviation e(i) is obtained by a computing element 2 and stored. The control system from this computing element 2 to a hold circuit 12, which is in the front step of a controlled system 13, is composed of the general digital circuit. A control input u(i) at the present sampling time (i) is expressed by an equation I and increase part correcting quantity a(i) at the present time is determined by using information concerning the characteristic of the controlled system, control deviation during present and past 1 period and past deviation correcting quantity. Then, the (i) expresses the sampling time which is 1 period before the present time, the a(i) expresses the increase part correcting quantity at a sampling time (j) and an i0 expresses a setting time for the initial value of the increase part correcting quantity.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a control system for machine tools, robots, etc. that perform repetitive operations.

[Conventional technology]

Repetitive control is considered as a method of designing a control system for a repetitive target value (for example, "High-precision control in repetitive operation of proton synchrotron electromagnet power supply" by Inoue et al., Journal of the Institute of Electrical Engineers of Japan C, Vol. 100, Vol. 7-1, etc.) . The basic configuration of this method is shown in FIG. Here, r, e, u,
x is a target value, a control deviation, a control input, and a control output, respectively. In addition, L is the period of the target value (Fig. 24(a)
), e-Ls is a dead time element that causes a delay by the amount of time.

Therefore, the control force u (t) at time t is u
(t) = u (t-L) + e (t-L), and a major feature is that the control input from one cycle before and the control deviation from one cycle before are used.

This has the advantage of enabling highly accurate tracking and further eliminating periodic disturbances.

This method can also be applied when the target value repeats the same pattern intermittently (see Figure 24, etc.), and in that case, the control human power u (t) at time t is expressed as u(t) = u(
t') + e(t'). Here, to is the time of the previous trial corresponding to time t.

Further, as a predictive control method that minimizes the weighted sum of squares of predicted values of future control deviations, there is a method described in Japanese Patent Application Laid-Open No. 118405/1983, which was previously filed by the present applicant.

In this method, the control force u (i) at the current sampling time l is given as follows using an incremental control input. Here, the incremental control human power m(
This method predicts the future control deviation from the sampling value of the individual response of the controlled object, the past incremental control power, the current output, and the future target value, and calculates the weighted 2 of the predicted value.
It is determined so that the sum of the products is minimized.

Since this method uses future target values, it has the advantage of providing better response characteristics than a control system that uses only current target values, and can be realized using simple arithmetic operations. There is.

Furthermore, in JP-A-62-118406,
For target values that repeat the same pattern, the control deviation from one trial before is used, characterized in that the above-mentioned incremental control input plus a constant times the control deviation from one trial before is given as an incremental control input again. A predictive control method has been proposed.

[Problem to be solved by the invention]

In both of the above-mentioned design methods for the repetitive target value, that is, the repetitive control method and JP-A-62-118406, the control deviation at the time one cycle before, or the time t corresponding to the current time t at the previous trial. '
(See Figure 24 (5))
Deviation or time t from the time before the cycle up to the present
Although the deviation after 0.0° is extremely useful when determining the current control input, it is not utilized.

[Means to solve the problem]

In order to solve the above-mentioned conventional problems, in the first invention of the present application, a control input at each sampling time is applied to a controlled object having a target value that repeats the same pattern at a constant cycle. Control deviation between cycles, ■Past incremental correction amount, ■Information about the dynamic characteristics of the controlled object (individual response), ■Weighting of the predicted value of future control deviation using the control input at the time one cycle before. It is characterized by determining the sum of squares to be the minimum.

In the second invention of the present application, for a controlled object having a target value that repeats the same pattern at a constant period, the control human power at each sampling time is determined by: ■ Deviation in the past 1rR period, ■ Past correction amount, ■ Controlled object information regarding the dynamic characteristics of (individual response); (1) The control manual input at the time one cycle before is used to determine the weighted sum of squares of predicted values of future control deviation to be the minimum.

In the third invention of the present application, for a controlled object having a target value that repeats the same pattern, the control inputs at each sampling time are: ■ control deviation in the current and previous trials, ■ past incremental correction amount, ■ control It is characterized by determining the weighted sum of squares of the predicted values of future control deviation using information regarding the dynamic characteristics of the target, ■ the control human power from the previous trial so as to minimize it.

Furthermore, in the fourth invention of the present application, for a controlled object having a target value that repeats the same pattern, the control input at each sampling time is calculated based on: ■ the control deviation from the previous trial; and ■ the control human power from the previous trial. It is characterized in that the weighted sum of squares of predicted values of future control deviations is determined to be the minimum using (1) information regarding the dynamic characteristics of the controlled object, and (2) the amount of correction for one trial.

〔Example〕

Hereinafter, the present invention will be specifically explained based on Examples.

A specific embodiment of the first invention of the present application is shown in FIG. 1 in the figure is a command generator, which has a target value r at the current time i.
(i). 2 is a subtracter, which is used to calculate and store the deviation e(ri). 3 is a constant Q++Qa+...
・, QM, Q, g+, ...1gE1's memory, 4 is the deviation e of the current time i and one cycle in the past 0)(
j=i, i-1, . . . , 1°+t, l'). However, it is assumed that V=1-1.

In addition, 5 is the incremental correction amount a (j) (j=i-1, i-2,
....

i-N+1), and 6 is the control human power u (D(j=i-1
, i-2°...+''+1+'°).

Further, 7 is an arithmetic unit, which calculates the current incremental correction amount a (i) by the following operation.

8 is an integrator that calculates the current correction amount Σa (j).

J”l.

9 is an adder that adds the control input u (i') at the time one cycle before and the current correction amount Σa (j) to obtain j:i.

The current control force u (i) is output. At the start of control, u (Io) = O, a (Io) = 0.

10 and 11 are samplers that close at the sampling period T, and 12 is a hold circuit.

13 is a controlled object, the input is u (t), and the output amount of machining is x (t).

In the control system, 2 to 12 are parts usually called controllers, which can be easily realized using general-purpose digital circuits or micro combinators. Further, the controlled object 13 may already include some kind of control system (compensator, etc.).

Here, equation (1)) is derived.

From FIG. 1, the human output relationship to be controlled at the current time i is as shown in FIG. 2. However, the sampler and hold circuit shall be included in the control target. Furthermore, at time l° one cycle before, the relationship shown in FIG. 3 holds, so the relationship shown in FIG. 4 is obtained from FIGS. 2 and 3.

In Fig. 4, the correction amount Σa (j)F at time l
l.

The output for δ(1), that is, δC1) x (i) −x (i')...
・・・・・・・・・・・・・・・(2) is defined, and time i
Incremental correction amount a(j) after +1 (j=i+l.1+2.
...) are all zero, the prediction m? of the output for the correction amount after time i+l? j (ink) (K=1
．． 2. ...) is given by the following formula.

However, HJ (J=1.2...,N) is the sample value at the sampling interval T of the individual response of the controlled object, and N is set so that the response is sufficiently stable, that is, H*' = It is assumed that HII (N'> N) is selected (Figure 5).

Here, the predicted value of the output at time i+? (ink
) is from equation (2), ? (ink) =2i(i
nk)+x(i'+k) ...-...=(4), so the predicted deviation value @ (ink) is @
(ink) = r (ink) - t (ink) =
r (ink) - x (i'+k) - 71 (ink)
...(5). Furthermore, since r (i' + k) = r (ink),
In the end, @ ('1nk) = e (i' +k) - δ(+
+k) ・・・・・・・・・−(6).

Now, the weighted sum of squares J of the predicted deviation values up to future time i+M is used as the evaluation function, and this incremental correction is made so that this J becomes the minimum! a (i) shall be selected. Here, Wk is a weighting coefficient applied to the predicted deviation value @ (ink) at future time l+k, and an example thereof is shown in FIG.

a(i) that minimizes J is given by aJ/aa(i)=O... (8), and formulas (7), (6), and (3) Therefore, from equations (8) and (9), it becomes.Also, δ(i)
From equation (2), δ(i) = x(i)−χ(1′
) = (r(i')-x(i')) -(r(i)-z
(i))=e (i') −e (i)
・・・・・・・・・・・・(11) can be rewritten as (1
0) and (11), a (i
) is given by the following equation.

however, , and let H,'=H and (N'>N).

Above, the incremental correction N a (i) given by equation [1)
was shown to minimize the evaluation function J defined by equation (7).

Also, the constants qk, Q and g in equation (13). is the fifth
It is calculated in advance by measuring the individual response of the controlled object shown in the figure and giving an appropriate weighting function W.

As is clear from equation (5), the control algorithm according to the present invention uses the future target value r (ink) and the past output x (i' + k), but these pieces of information are used in equation (6). It is stored in the memory 4 of FIG. 1 as the past deviation e(i''k).

When the deviation converges within a desired value after sufficient repetition, memory operation may be performed using the sequence of control inputs for one past cycle. The configuration at this time is shown in FIG.

In addition, if the trial calculation time of equation (1) takes a non-negligible amount compared to the sampling time T, then the incremental correction 1a (i+1>) after one sampling at the current time l is calculated, and the incremental correction after time i+2 is calculated. Correction amount a (i
) (j=i+2. i+3....) are all zero, then the predicted value δ(ink) at future time i+k
is J(ink) = δ(i) + a (++1) L
-However, H,=0. In the same manner, a('i+1) that minimizes the evaluation function J of equation (7) can be found.

A specific embodiment of the second invention of the present application is shown in FIG. In the figure, 21 is a command generator with a constant period l, and the current time 1
A target value r (i) at is generated. 22 is a subtracter, which is used to obtain and store the deviation e (i). 2
3 is constant Q'+, Q, non, Qx, f In
f2. j-1j.

The memory 24 of fN-1 is the deviation e (
j) (''・1-1. . . il4 il +l) memory. However, it is assumed that i°=1−β.

In addition, 25 is the past correction amount σ(D (j=i-1, i-2,...
, i-N+1), and 26 is the memory for the control human power u(J) (j=i-1, i-2, .
'+l,i') memory.

Further, 27 is an arithmetic unit, which calculates the correction amount σ(i) at time X by the following calculation.

28 is an adder that adds the control human power u(i'') at the time one cycle before and the current correction amount σ(1), and outputs the current control human power u(i).At the start of control. The past deviation, correction amount, and control human power may be all given as zero, for example.

29 and 30 are samplers that close at the sampling period T, and 31 is a hold circuit. 32 is a controlled object, and u(t) and χ(1) are input and output, respectively.

In the control system, 22 to 31 are parts commonly called controllers, which can be easily realized using general-purpose digital circuits or microcomputers. In addition, some control system (compensator, etc.) already exists in the controlled object 32.
It doesn't matter if it is included.

Here, equation (21) is derived.

From FIG. 8, the human output relationship of the controlled object at the current time l is as shown in FIG. 9. However, it is assumed that the sampler and hold circuit are included in the control target. At time l' one cycle before, the relationship shown in FIG. 10 holds, so the relationships shown in FIGS. 9, 10, and 11 are obtained.

In FIG. 11, the correction amount σ(i) at the current time l
Let the output for δ(1) be δ(i) and χ(+)
-x (+') ・・・・・・・・・・・・・・・
...(22) is defined, and the amount of correction σ after time i+l is
(D'(J=i+1゜l+2....) are all σ(
1), the predicted value after time i+1 of the output for the correction amount 8 (ink) (K4.2
．． ...) is given by the following formula.

However, HJ (j=1.2..., N) is the sample value at the sampling period T of the individual response of the controlled object, and N is set so that the response is sufficiently stable, that is, in the first embodiment. Similarly, HN' = HN (N'
>N) (Figure 5).

Here, at time i+, the predicted value T (ink
) is from equation (22), ? (ink) =7I(
ink)+z(i'+k)"""...(24), the predicted deviation value δ(ink) is given by
nk) = r (ink) - t (ink) =
r (ink)-1x (i°+k)-J (ink)
... (25) becomes. Furthermore, since r (i'+k) = r (ink), in the end, @ (ink) = e (pi k) - δ (ink)''...
...(26).

Now, it is assumed that the weighted sum of squares J of the predicted values of deviations up to a future time i0M is used as an evaluation function, and the correction amount σ(i) at time l is selected so that this J is minimized. Here, Wk is the predicted deviation value @ (ink) at future time i+k
It is a weighting coefficient to be applied to, for example, the sixth
The values are chosen as shown in the figure.

σ(1) that minimizes J is a J/aσ(i)=0...
...Given by (28), equation (27), (26
) and (23), so, (28),
From equation (29), we get σ(
1) is given by the following equation.

however, , and H1l'=HN (N'>N).

Above, the correction amount σ(i) given by equation (21) is (
27) It was shown that the evaluation function J defined by the formula is minimized.

In addition, the constants q and ", in equation (32) are determined by measuring the individual response of the controlled object shown in FIG.
It is calculated in advance by giving k appropriately.

As is clear from equation (25), the control algorithm according to the present invention uses the future target value r (ink) and the past output z (i°+11), but these pieces of information can be expressed by equation (26). The past deviation e (i' + k)
is stored in the memory 24 in FIG.

Furthermore, when calculating the correction amount σ(i) at time i in equation (1), information at time l (output of the controlled object, etc.) is not used, so the correction amount σ(1) is calculated at time l. can be calculated previously. Therefore, in this method, there is no problem of manual delay due to calculation time, which is a problem when designing a sampling control system with ordinary output feedback.

When the deviation converges within a desired value after sufficient repetition, memory operation may be performed using the sequence of control inputs for one past cycle. The configuration at this time is shown in FIG.

A specific embodiment of the third invention of the present application is shown in FIG. 13(a). In the figure, reference numeral 41 denotes a command generator, which generates a target value r (+) at the current time i. 42 is a subtracter, which calculates the deviation e (i). An example of the target value is shown in Figure 13(b).
Shown below. Here, 10(i, °), i, (i,,')
are the control start time and control end time of the current (previous) trial, and furthermore, L = ir, +M (L' = i
n' + M).

43 are constants Ql, Q2 . ..., Qll, Q,
gl, g2. ....

The memory of gN-+, 44 is the memory of control deviations, and the deviations from the previous trial are e(io), e(i'+1), e
(i'+2), ---.

After outputting the value of e(i''10k) to the arithmetic unit 47, e(
i') with the current deviation e (i).

45 is a memory for the amount of incremental correction from 1 sampling number before the current time to N-1 sampling number before the current time;
6 is a control input memory, which is the input u (i
'), then convert u(i') to the current input u(1)
Replace with

Also, 47 is an arithmetic unit 1, a(i)=Σqke(i'+k)+Q (e(i)
-e(i')), the incremental correction amount a(1) at time i is calculated.

48 is an integrator that calculates the correction amount Σa (j) at time 1. 49 is an adder that calculates the amount of correction Σa (j) at time 1.
(i') and the correction amount Σa (D) to obtain the control J:l at time 1.

Outputs the power u(1).

50 and 51 are samplers that close at the sampling period T, and 52 is a hold circuit. 53 is a controlled object, and u (t) and x (t) are input and output, respectively.

In the control system, 42 to 52 are parts usually called controllers, which can be easily realized using general-purpose digital circuits or microcombiners. In addition, some control system (compensator, etc.) already exists in the controlled object 53.
It doesn't matter if it is included.

Here, equation (41) is derived.

From FIG. 13(a), the input/output relationship of the controlled object at the current time of summer in this trial is as shown in FIG. 14.

However, the sampler and hold circuit shall be included in the control target. Furthermore, at time l° of the previous trial corresponding to current time i (see FIG. 13(b)), the first
Since the relationship shown in FIG. 5 holds, the relationship shown in FIG. 16 can be obtained from FIGS. 14 and 15.

In FIG. 16, the amount of correction Σa (J) at time l
J”l.

The output for is δ(1), that is, δ(i) Qχ(i)−χ(i')...
・・・・・・・・・・・・(42) is defined, and time i+
Incremental correction amount a(j) after l (j=ill, l+2+
...) are all zero, the predicted value J(ink) after time i+l of the output for the correction amount (to=1.2
．． ...) is given by the following formula.

However, H4 (''・1.2..., N) is the sample value at the sampling interval T of the individual response of the controlled object, and N is set so that the response is sufficiently stable, that is, in the first embodiment. Similarly, H, □=HN(N'>N)8
(Figure 5).

Here, at time i+, the predicted value of the output at time X (i + k
) is from equation (42), ! (ink) = 8
(ink)+x (i'+k)..."..."
・Since it is given by (44), the predicted value of deviation @ (in
k) is @ (ink) = r (ink)
-X (i + k) = r (ink) - x (i'+k
)−? I (ink)...(45). Furthermore, since r (i' + k) = r (ink),
In the end, @(ink) = e(+'10k)-i(ink)=・
・It becomes (46).

Now, the weighted sum of squares J of the predicted deviation values up to the future time i0M is set as the evaluation function, and the current time i is set so that this J is the minimum.
Let us choose the incremental correction amount a (i) of . here wk
is the predicted deviation value @ (in
k) is a weighting coefficient to be applied to, and can be selected as shown in FIG. 6, for example, as in the first embodiment.

a (i) that minimizes J is aJ/θa (i) = 0 """ (48
), and are given by equations (47), (46) and (43
) From the equation, a J / a a (i), so from the equations (48) and (49), it becomes. Also, from equation (42), δ(i) is δ(i)−x (+
) −x (io)” (r(+')−x (1°))
(r(i)−χ(1))=e(1°)−e(
i) ..."" (51), so from equations (50) and (51), a (i) that minimizes J is given by the following equation.

however, , and HN'=Hn (N'>N).

Above, the incremental correction it a (
It was shown that i) minimizes the evaluation function J defined by equation (47).

Furthermore, the constants qk, Q, and g7 in equation (53) can be calculated in advance by measuring the individual response of the controlled object shown in FIG. 5, and appropriately giving the weighting function wk as shown in FIG. It is something that will be done.

In the control algorithm according to the present invention, as is clear from equation (45), the future target value r (i 0 k) and the output z (i'' 1 k) from the previous trial are used; The information is the deviation e from the previous trial as shown in equation (46).
(As i' +IO, the memory 44 in FIG. 13(a)
is stored in the .

When the deviation converges within a desired value after sufficient repetition, memory operation may be performed using one trial's worth of manual control sequences. The configuration at this time is shown in FIG.

In addition, if the calculation time of equation (41) takes a non-negligible amount compared to the sampling time T, the incremental correction amount a(++1) after l sampling shall be calculated at the current time l, and the incremental correction amount after time l+2 Correction amount a (j)
Assuming that (j=i+2. ++3....) are all zero, the predicted value δ(ink) at future time i+k is δ(ink) = δ(+) + a (++1) L
-5 However, HO=0. Hereinafter, a(++1) that minimizes the evaluation function J of equation (47) may be found in the same manner.

A specific embodiment of the fourth invention of the present application is shown in FIG. In the figure, 61 is a command generator that intermittently generates the same pattern, and the series of target values for one trial (r (D) (J =
' o + ' o '' 1 r..., 1.) is generated.The series of target values is as shown in Figure 13 of the previous embodiment)
It is similar to In Figure 18, lo (lo')
+ In (In') is the control start time and control end time of the current (previous) trial, and l a'' I n
”!J (1m' = I n' +!J).

62 is a subtracter, and the deviation series (e (J)) (j=io, io+1..., 1
．． ).

63 is a constant Q1. q2. ..., Q)1. f I
n fa, . . . , the memory 64 of fE1 is the correction amount σ(J) (J=IO.

A memory of 10"L..., In) is required for calculations in the arithmetic unit 66, but does not necessarily need to store all the correction amounts for one trial. 65 is the memory for the previous trial. deviation e (J) (j=1a', i0°+l, jll
l, 1. ') memory, and in this trial,
The output value of the subtracter 62, that is, the deviation e (D □=io,
io”l9m, i,) is stored.

Also, 66 is a calculation unit, and after the previous trial is over, u(i)=u(io)+ a(i) (i=i.

, io+1. ..., i, )+1 (61a), the control human power U('')(J''o
+ lo"l+..., 11). Here, lo
represents the previous time corresponding to time l at the time of the current trial (see Figure 13(b)), and furthermore, σ('') =
0 (J<10).

67 is a memory of control inputs for l trials, and in the previous trial, the human power u (D (J=lo',
lo°+1,...+'n') are stored, and the human power u (j) (J=IO1to"l,
..., 1o) are stored and output during the current trial.

68 and 69 are samplers that close at the sampling period T, 70 is a hold circuit, 71 is a controlled object, u (t)
and χ(1) are its manpower and output, respectively. Moreover, the control human power u(D(j・l'l'
l+lli, +2. ..., 1. ) can all be set to zero.

62-70 are control systems! Here, the part usually called a controller can be easily realized using a general-purpose digital circuit or a microcomputer. Also,
It does not matter if the controlled object 71 already includes some kind of control system (compensator, inner loop, etc.).

Here, equation (61) is derived.

From FIG. 1'8 and equation (61a), the input-output relationship of the controlled object at time l during the current trial is as shown in FIG. However, the sampler and hold circuit shall be included in the control target. Also, at time 1° during the previous trial, the relationship shown in FIG. 20 holds; therefore, as shown in FIG.
The relationship shown in FIG. 21 can be obtained from FIG. 20.

In Fig. 21, the output for the correction amount σ(]) at time I is δ(1), that is, δ(i) x (+) −x (i')...
・・・・・・・・・・・・・・・(62) is defined, and time 1
Correction amount σ(j) after +1 (j=i↓1゜1+2.・
) all take the value of σ(i), then
Predicted value of output after time i+l for correction amount? j (
ink) (K=1.2...) is given by the following equation.

However, Hh (j=1.2..., N) is the sample value at the sampling interval T of the individual response of the controlled object, and N is set so that the response is sufficiently stabilized, that is, in the first embodiment. Similarly, HN' = H++ (N
'>N) (Figure 5).

Here, the predicted value T (ink) of the output at time i+ is calculated from equation (62) as T (ink
) = δ(ink)+x (i°+k)=・=・
(64), so the predicted value of deviation @ (in
k) is @ (ink) = r (ink)−
t(ink)=r(ink)−x(i'+
k)-'l (ink)''・(65) Furthermore, since r (i' + k) = r (ink),
In the end, @(ink) = e(i'+k)-3(ink)""
...(66).

Now, the weighted sum of squares of the predicted deviation values from time 1+1 to i0M is J = ΣWb (@ (ink) ) ”...
(67) is used as an evaluation function, and the correction amount σ(i) at time l is selected so that J is minimized.

Here, wk is the predicted deviation value @
(ink) is a weighting coefficient to be applied to, and can be shown in FIG. 6 as in the first embodiment.

σ(1) that minimizes J is aJ/θσ(i)=O (68), so from equations (68) and (69),
σ(i) that satisfies equation (70) is given by the following equation.

however, , and H,'=H, (N''>N).

Above, the correction amount σ(1) at time l in equation (61) is (
67) It was shown that the evaluation function J defined by the formula is minimized.

Also, the constants qk and f in equation (73). measures the individual response of the controlled object shown in Fig. 5, and calculates the weighting coefficient w
It is calculated in advance by giving k appropriately.

In the control algorithm according to the present invention, after the previous trial ends, the input u(j) (j=1o+i
o”L..., 11) can be calculated by the calculator 66, and then the current trial can be performed.This allows the value of the previous trial to be calculated without feeding back the output of the controlled object in real time. This is because it is used effectively, and there is no need for real-time human control calculations.

When the deviation converges within a desired value after sufficient trials, memory operation may be performed using the series of manual control operations for one trial stored in the memory 87. The configuration at this time is shown in FIG.

〔Effect of the invention〕

As explained above, according to the first invention of the present application, by using the past deviation, the current deviation, the past incremental correction amount, the past control input, and the predetermined constant, four simple arithmetic operations are performed. , a control algorithm has been obtained in which the controlled variable optimally follows a target value with a constant period, and by realizing this using a general-purpose digital circuit or a microcombiner, the tracking accuracy is much better than that of conventional methods. A control system can be realized.

According to the second invention of the present application, by using past deviations, past correction amounts, past control human power, and predetermined constants, through simple arithmetic operations, the output is optimally adjusted to a target value with a - constant period. By using a general-purpose digital circuit or a microcomputer to implement this control algorithm, it is possible to realize a control system with much better tracking accuracy than conventional ones.

According to the third invention of the present application, by using the deviation and control human power from the previous trial, the current deviation, the past increment '2 positive amount, and a predetermined constant, by simple four arithmetic operations, A control algorithm has been obtained in which the output of the controlled object optimally follows the target value that repeats the same pattern, and by realizing this using a general-purpose digital circuit or a microcombiner, the tracking accuracy is much higher than that of conventional methods. A good control system can be realized.

According to the fourth invention of the present application, the output of the controlled object is optimized to the target value that repeats the same pattern by using the deviation from the previous trial, the control input, and a predetermined constant through simple arithmetic operations. By obtaining a tracking control algorithm and implementing it using a general-purpose digital circuit or micro combinator, a control system with much better tracking accuracy than conventional systems can be realized. Furthermore, the above-mentioned calculation only needs to be performed between each trial, and no calculation is required at the time of trial, so it is possible to perform control with a shorter sampling period than in the conventional method. This also leads to improvement in tracking accuracy.

[Brief explanation of the drawing]

Fig. 1 is a block diagram showing the configuration of an embodiment of the first invention of the present application, Figs. 2 to 4 are block diagrams showing the input/output relationship of the controlled object, and Fig. 5 is the individual response of the controlled object. FIG. 6 is an explanatory diagram showing one example of weighting coefficients, FIG. 7 is a block diagram showing an example of the configuration during memory operation, and FIG. 8 is a configuration of an embodiment of the second invention of the present application. Block diagram, No. 9
11 are block diagrams showing the relationship between the human outputs of the controlled object, FIG. 12 is a block diagram showing an example of the configuration during memory operation, and FIG. A block diagram showing the configuration, FIG. 13(b) is an example of the target value at that time, FIGS. 14 to 16 are block diagrams showing the relationship between input and output of the controlled object, and FIG. 17 is the configuration during memory operation. A block diagram showing an example, FIG. 18 is a block diagram showing the configuration of an embodiment of the fourth invention of the present application, FIGS. 19 to 21 are block diagrams showing the relationship between input and output of the controlled object, and FIG. FIG. 23 is a block diagram showing a configuration example of a memory operation after sufficient trials, FIG. 23 is a block diagram showing a configuration of a repetitive control system, and FIG. 24 is an example of a repetitive target value. Command generator 2: Subtractor 3: Memory for constants 4: Memory for past one cycle's worth of deviation 5: Memory for past incremental correction amounts 6: Memory for past control inputs 7: Arithmetic unit 8: Integrator 9: Adder to, 11: Sampler 12:
Hold circuit 13: Control object 14: Memory for one cycle of optimal control input 21: Command generator 22: Subtractor 23: Memory for constants 24: Memory for deviation for one past cycle 25: Memory for past correction amounts 26 : Memory of past control inputs 27: Arithmetic unit 28: Adder 29.30: Sampler 31: Hold circuit 32: Controlled object 33: Memory for one cycle of optimal control human power 41: Command generator 42: Subtractor 43: Constant memory 44: Deviation memory 45: Past incremental correction amount memory 46': Control input memory 47: Arithmetic unit 48: Integrator 49: Adder
50.51: Sampler 52: Hold circuit
53: Controlled object 54: Optimal control Memory for one trial of human power 61: Command generator 62: Subtractor 63: Memory for constants 64: Memory for correction amount 65: Memory for control deviation for one trial 66: Arithmetic unit 67 : Memory for control inputs for l trials 68, 69 : Sampler 70 : Hold circuit, circuit 71 : Patent applicant for control object Ayuo Electric Manufacturing Co., Ltd. Representative Person Small
Masu Hori (and 2 others) Figure 2 u (i') Figure 3 Figure 4 Figure 5 0123 N Figure 7 Figure 9 u (i'') Figure 10 Figure 11 Figure 12 Figure 14 u (i') Figure 15 Figure 16 Figure 17 Figure 13 (b) (+) Figure 19 u (i Figure 20 Figure 21 Figure 22 Figure 23 Figure 24 (a)

Claims (1)

[Claims] 1. In a control system that adds input to a controlled object so that the output of the controlled object matches a target value that repeats the same pattern at a constant cycle, the control input u(i) at the current sampling time i is set to ▲ There are mathematical formulas, chemical formulas, tables, etc. ▼ Here, i' Sampling time a(j) one cycle before the current time: Incremental correction amount at sampling time j i_o: Time at which the initial value of the incremental correction amount was set, The incremental correction amount a(j) at the current time is based on information regarding the dynamic characteristics of the controlled object, the control deviation between the current and past cycles,
It is determined using the past incremental correction amount. A control method that optimally follows a periodic target value. 2. The incremental correction amount a(i) at the current time is the predicted value of the control deviation from the current time to M sampling times in the future.
Weighted sum of squares of (j) (j=i+1, i+2,..., i+M) ▲There are mathematical formulas, chemical formulas, tables, etc.▼(W_k
is a weighting coefficient). Claim 1:
A control method that optimally follows the stated periodic target value. 3. A control method that optimally follows a periodic target value according to claim 1, wherein a sampling value of an individual response of the controlled object is used as information regarding the dynamic characteristics of the controlled object. 4. The incremental correction amount a(i) at the current time is expressed as:
There are chemical formulas, tables, etc. ▼ Here, e(i): Deviation at time i N: Number of sampling points for the individual response of the control system M: Number of predicted control deviation points {q_k (k=1,...,M) , Q, g_n (n=1
, . . . , M-1)} The periodic target value according to claim 1, wherein the periodic target value is a constant determined by a sample value of an individual response of the control system and a weight to be applied to a predicted value of the control deviation. Control method that follows optimally. 5. After the control deviation converges to a desired value or less through sufficient repetition, memory operation is performed based on one cycle's worth of input recorded in the memory, the periodic target value according to claim 1. A control method that optimally follows. 6. Claim 1, characterized in that a(i+1) is determined instead of the incremental correction amount a(i) at the current time i, taking into account the delay in calculation time, and that value is used at the time i+1.
A control method that optimally follows the stated periodic target value. 7. In a control system that applies input to a controlled object so that the output of the controlled object matches a target value that repeats the same pattern at a constant cycle, a memory that stores the deviation and input during the past cycle and the past correction amount is used. and the control input u(i) at the current sampling time i is u(i)=u(i')+σ(i), where i' represents the time one cycle before the current time i,
σ(i) is the amount of correction at the current time i, and is determined using information regarding the dynamic characteristics of the controlled object, the deviation during the past cycle, and the amount of correction in the past. A control method that optimally follows a periodic target value. 8. The correction amount σ(i) at the current time is expressed as the predicted control deviation value ■(j
) (j = i + 1, i + 2, ..., i + M) ▲ There are mathematical formulas, chemical formulas, tables, etc. ▼ (where W_k is a weighting coefficient) is determined so that it is minimized. Claim 7
Sampling control method described. 9. The sampling control method according to claim 7, wherein a sampled value of an individual response of the controlled object is used as the information regarding the dynamic characteristics of the controlled object. 10. Correction amount σ(i
), ▲There are mathematical formulas, chemical formulas, tables, etc.▼ Here, e(i'+k): Deviation at time i'+k N: Number of sampling points of the individual response of the control system M: Number of predicted control deviation points {q_k( k=1,...,M), f_n(n=1,...
. . , N-1)} Optimal for the periodic target value according to claim 7, characterized in that it is a constant determined by the sample value of the individual response of the control system and the weight to be applied to the predicted value of the control deviation. Control method to follow. 11. The sampling control method according to claim 7, wherein after the control deviation converges to a desired value or less through sufficient repetition, memory operation is performed based on one cycle's worth of input recorded in the memory. 12. In a control system that applies control input so that the output of the controlled object matches a target value that repeats the same pattern intermittently, it has a memory that stores the control input, deviation, and incremental correction amount, and controls the control at each sampling time i. Input u(i) ▲ There are mathematical formulas, chemical formulas, tables, etc. ▼ Here, i′: Time corresponding to i in the previous trial a(j): Incremental correction amount at time j i_o: Start of the current trial The incremental correction amount a(i) at time i is based on information about the dynamic characteristics of the controlled object, the deviation at time i, the deviation from the previous trial, and several sampling times before time i-1. is determined using the past incremental correction amount. A control method that optimally follows a periodic target value. 13. The incremental correction amount a(i) at time i is the predicted deviation value ■(j) from time i to M sampling times in the future.
A claim characterized in that the weighted sum of squares of (j=i+1, i+2,..., i+M) ▲There are mathematical formulas, chemical formulas, tables, etc.▼ (where W_k is a weighting coefficient) is determined to be the minimum Item 1
The sampling control method described in 2. 14. Claim 1, characterized in that the sampling value of the individual response of the controlled object is used as the information regarding the dynamic characteristics of the controlled object.
The sampling control method described in 2. 15. The incremental correction amount a(i) at the current time i is ▲ Numerical formula, chemical formula, table, etc. ▼ Where, e(i): Deviation N at time i: Number of sampling points M of the individual response of the control system: Predicted number of control deviation points {q_k (k=1, ..., M), Q, g_n (n=1
, . . . , N-1)} The periodic target value according to claim 12, wherein the periodic target value is a constant determined by a sample value of an individual response of the control system and a weight to be applied to a predicted value of the control deviation. Control method that follows optimally. 16. The sampling control method according to claim 12, wherein after the control deviation converges to a desired value or less after sufficient trials, memory operation is performed using the input for one trial recorded in the memory. . 17. The sampling according to claim 12, wherein the incremental correction amount a(i+1) is determined at time i, instead of a(i), in consideration of the calculation time delay, and that value is used at time i+1. control method. 18. It has a memory that stores the value calculated from the deviation from the previous trial and a predetermined constant, and the control input u(i
13. The sampling control system according to claim 12, wherein those values are used when determining . 19. In a control system that provides a control input so that the output of a controlled object matches a target value that repeats the same pattern intermittently, one trial's worth of control input, deviation, correction amount, and predetermined constants are stored. control input u(i) at each sampling time i as u(i)=u(i'
) + σ(i) Here, i' represents the time corresponding to time i during the previous trial, and σ(i) is the amount of correction at the current time i, which combines information about the dynamic characteristics of the controlled object and the previous trial. Deviation during trial and
The correction amount before time i is determined. A control method that optimally follows a periodic target value. 20. Sampling according to claim 19, characterized in that after each trial ends, a sequence of control inputs for one trial for the next trial is calculated and stored in memory, thereby performing memory operation at each trial. control method. 21. The correction amount σ(i) at time i is calculated from time i to M
Sampling count Predicted value of control deviation until the future■(j)
A claim characterized in that the weighted sum of squares of (j=i+1, i+2,..., i+M) ▲There are mathematical formulas, chemical formulas, tables, etc.▼ (where W_k is a weighting coefficient) is determined to be the minimum Item 1
9. The sampling control method described in 9. 22. Claim 1, characterized in that the sampling value of the individual response of the controlled object is used as the information regarding the dynamic characteristics of the controlled object.
9. The sampling control method described in 9. 23. The correction amount σ(i) at sampling time i is
▲There are mathematical formulas, chemical formulas, tables, etc.▼ Here, e(i'+k): Deviation at time i'+k N: Number of sampling points of the individual response of the control system M: Number of predicted control deviation points {q_k (k=1 ,...,M), f_n(n=1,.
. . , N-1)} Optimal for the periodic target value according to claim 19, characterized in that it is a constant determined by the sample value of the individual response of the control system and the weight to be applied to the predicted value of the control deviation. Control method to follow. 24. After the control deviation converges to the desired value or less after sufficient repetitions, the input sequence for one trial recorded in memory is used every time without changing between each trial, and memory operation is performed. 20. The sampling control method according to claim 19, wherein: