JPS63167907A - Unknown function estimating device - Google Patents

Abstract

PURPOSE:To obtain an unknown function estimating device which can estimate its characteristic function, as long as a variable is known, even if a function format of a characteristic function of an object plant is unknown. CONSTITUTION:From element functions generated by element function generators 22, 141-14N, and 211-21M and a known output, a function corresponding to an unknown characteristic function of an object plant 11 is generated by multipliers 13, 151-15N, 171-17N 20 and 231-23M. Thereafter, an operator 1/s+mu to an unknown characteristic and a known output is calculated by filters 161-16N, 181-18N and 241-24M. Also, by using a result which has calculated an operator mu/s+mu by a filter against the known output, and said known output, a function corresponding to the unknown characteristic function is generated and given to a parameter regulator 29. A parameter and an output of said multiplier are multiplied and added, and outputted as an estimation function of the unknown characteristic function. As a result, an operation for estimating the unknown characteristic function by which it is only clear that it is a function of a known output of an object plant 11 is executed.

Description

Detailed Description of the Invention (1) Purpose of the Invention [Field of Industrial Application] The present invention relates to an unknown function estimating device, and in particular, the present invention relates to an unknown function estimating device, and in particular, the present invention relates to an unknown function estimating device, and in particular to an unknown characteristic function (for example, a transfer function or a dynamic characteristic) of a target plant in which only variables are known. This relates to an unknown function estimator that estimates equations, etc.).

[Prior art] Conventionally, this type of unknown function estimating device uses the parameter as a coefficient even if the parameter of the target plant changes and maintains linearity with respect to the parameter, even if the form of the function is known as a whole. For example, methods have been proposed that can estimate the characteristic function of the target plant.

[Problems to be solved] However, conventional unknown function estimators have the disadvantage that they cannot handle cases where there is a phenomenon such as friction inside the target plant and the functional form of the characteristic function is not known. It had the disadvantage that it could not be used to estimate the characteristic function of

Therefore, the present invention aims to eliminate this drawback and provide an unknown function estimation device that can estimate the characteristic function of a target plant even if the functional form of the characteristic function is unknown as long as the variables are known. It is.

(2) Structure of the Invention [Means for Solving Problems] The solution provided by the present invention consists of "a plurality of elemental function generators that generate elemental functions in response to known outputs of a target plant; a plurality of multipliers that create a function corresponding to an unknown characteristic function of the target plant, which is a function of the known output, from the output of the function generator and the known output; and a plurality of multipliers that each operate on the output of the plurality of multipliers. a filter, an adder that creates another function corresponding to the unknown characteristic function using the known output and the known output of the target plant, and outputs of the plurality of filters, the other filter, and the adder. a parameter adjuster that receives an input, performs least squares calculation processing, and outputs a parameter corresponding to the unknown characteristic function, and a plurality of multipliers that mutually multiply the parameter and the output of the plurality of multipliers; and a plurality of adders that add together the outputs of the other multipliers to output an estimation function corresponding to the unknown characteristic function.''

[Operation] The unknown function estimating device according to the present invention calculates a function of the known output using a plurality of multipliers from the known output and an element function generated by a plurality of element function generators corresponding to the known output of the target plant. Create a function corresponding to the unknown characteristic function of the target plant, and use another filter and an operator adder to create a function corresponding to the unknown characteristic function for the known input of the target plant and the known output of other plants. By creating the parameter, the outputs of the plurality of filters, other filters, and the adder are respectively given to the parameter adjuster, and the parameter corresponding to the unknown characteristic function created by performing the calculation process of the least squares method and the multiplication The function is to multiply the outputs of the transformers and the outputs of the target plant, and then add them using another adder to output the estimated function of the unknown characteristic function. The function is to estimate an unknown characteristic function that is only a function.

[Example] Next, the present invention will be specifically described with reference to the accompanying drawings.

FIG. 1 is a circuit diagram showing an embodiment of an unknown function estimating device of the present invention. 2 to 5 are respectively explanatory diagrams of the same operation, and in particular, FIG. 5 is an explanatory diagram of the operation when an unknown function is specifically estimated according to an embodiment of the present invention.

First, the configuration of the unknown function estimating device of the present invention will be explained.

+I is a target plant with U as input and actual position lx and actual speed - as output, and using unknown functions f, (x) and ft(x) and actual speed with actual position alx as a known variable, The characteristic function is a dynamic characteristic equation expressed as x=f+(x)x+ft(x)x+f,j(x)signx+bu.

Here fi(x)X, fz(x)x, f3(x)sig
The reason why X is expressed as the sum of nx and bu is simply to give generality to the dynamic characteristic equation, and even if this dynamic characteristic equation is "x=f, (x)+bu," from the following explanation, As is clear, the present invention is applicable.

Reference numeral 12 denotes an adder, one input end (i.e., the input terminal) is connected to a bias source (not shown) that supplies the bias Xb, and the other input terminal (i.e., the other input terminal) is connected to the bias source (not shown).
is connected to one output end of the target plant 11 (that is, the output end that outputs X), and outputs x+xb from the output end. X is the minimum value x1. ．． ~maximum value X, □, and Xb is -x, 1. ．． , the output x+xb of adder 1z is X Xmz. becomes.

13 is a multiplier, one input terminal is connected to a constant source (not shown) that supplies a constant X, the other input terminal is connected to the output terminal of the adder 12, and from the output terminal x = x
=(x + Xb) is output. Constant X.

If is 1/(Xma*Xain), the output X of the multiplier 13 is (X-Xal+)/(x+-□
-Xmta) and varies in the range of θ to l.

14+, 142, =., 14% are element function generators, whose input ends are both connected to the output end of the multiplier 13, and from which they each receive ft(x).

fs(x), . . . , tit(x) are output. Here, the element function generator 14. , 14. , . . . , 14o are pyramid functions such that f, (x)=O(x<x+-+) =0 (X≧X, .1) as shown in Fig. 2 for 1=l−N, respectively. is sending out the output of

For example, if you collect multiple ft(x), it becomes as shown in Figure 3, and any function f(x) can be expressed as Σt r ti(x) as shown in Figure 4 (ft is f,
(indicates the value of (x gate)).

15, ,15□,...+, 15. are multipliers, one input end of which is both connected to the other output end of the target plant 11 (that is, an output end that outputs Q), and the other input end of each of which is connected to the element function generator 14 . .

142,..., 14. is connected to the output end of
f1(X)X-f1 from the output end, respectively. +(x) Output x+. The input terminals of LL, 16*, . , Is□,・++
, 15Il, and each of the output terminals indicates "S" of the S transformation, and the pot indicates a constant (the same applies hereinafter).

17, ,17. , -, 17% are each a multiplier, one input end of which is connected to one input end of the target plant 11 (
(that is, the output terminal that outputs X), and the other input terminal is connected to the element function generator 14. .

142, . . . , 14, and outputs each from the output end. The input terminals of 18+, 18*, ``-, 18, and l are respectively multipliers 17., 17□, ・
..., is connected to the 17% output terminal, and outputs each from the output terminal.

19 is an adder, one input terminal (i.e., − input terminal) is connected to a bias generation source (not shown) that supplies bias It is connected to the other output terminal (that is, the output terminal that outputs Q), and outputs ;-shi from the output terminal. x is the minimum value X, i. ~Maximum value Q11. When Xb is +X@i yl, the output XXb of the adder 19 becomes X-X5ia. 20
is a multiplier with one input connected to a constant source (not shown) supplying a constant X, and the other input connected to an adder 19.
is connected to the output terminal of x = X @I(X −
Output X b). Constant X is 1/(X66g
X1lllll), then f! The output of the calculator here is (k-crosswin)/(Xwaax-Xsi.), which varies in the range of O to l.

21, ,21. , .-, 21, are element function generators whose input terminals are both connected to the output terminal of the multiplier 20, and are f+(x)1 number generators whose input terminals are connected to the target plant 11. is connected to the other output terminal of (i.e., the output terminal that outputs ;), and
Output ignx.

23, ,23. , . . . , 23M are multipliers, one input end of which is connected to the output end of the element function generator 22, and the other input end of which is connected to the element function generator 21 . , 21yo, . . . +, 21m are connected to the output end, and each is output from the output end. 24. , 24□, ・”, 24 & 1 have input terminals as multipliers 23., 23., ・”
, 23m, and outputs each from the output end.

25 is an S+ filter that calculates the operator □ on the input, and the input end is connected to the other output end of the target plant U (
In other words, one input end (i.e., the -manual power end) is connected to the output end of the filter 25, and the other input end (i.e., 10-man end) is connected to the target plant 11. is a filter connected to the other output terminal (i.e., the output terminal that outputs ;
Outputs to the input terminal of 1.

29 is a parameter adjuster, and a plurality of input terminals are respectively filters 16s, IL, ", 16N; 1
88.18. .

...+, tan; 24t, 24m, -,
24w: Connected to 27 and the output end of the adder 26, so z,.

Z2 * ””+ ZN ; Ztwt * Zw*z
* -”* Ztw; Z engineering *l+ Z2N+t+・”
+ Z 2N*M + Z 2N*ゎ, and U are given. The parameter adjuster 29 executes the least squares calculation process for the input 2 and sends out the output P (T indicates a transposed matrix), where the input Z is and the output P is f +++ ( x i) + f 2. t(xt)+f
It shows the value of z, j(X +)+ (i=1~N;j
=1 to M), b indicates the estimated value of b.

30, , 30□, ·−, 30, are multipliers, respectively.
One input end is a multiplier 15□, 15m, ・
....

15, and the other input terminal is connected to the first to Nth output terminals of the parameter adjuster 29, respectively, and outputs each from the output terminal.

31, , :+t, , -..., 31N are multipliers, and one input terminal is the multiplier 17. , 17
□ +++.

17.4, and the other input terminal is connected to the (N◆1) to the second N◆1 of the parameter adjuster 29, respectively.
is connected to the output terminal of ' f
fi+l f t, +(x) Xf 2.2 f 2
1! Outputs (X) X f t,, 1f t, H(X ) X.

32, , 32□, ·-, 32, are multipliers, respectively.

Each input terminal has two multipliers, 232. =
・.

23, and the other input terminal is connected to the (2N◆l) to (2nd)th of the parameter adjuster 29, respectively.
8411), and from the output terminal fff+l f*, +(M) signxf x, * respectively.
f s, *(M) signxf 3+M f 3+
M(X) Outputs SjgnX.

33,,-,33.1 is a multiplier 30. One input terminal (that is, the manual input terminal) is connected in series to the output terminal of the adder, and the other input terminal (that is, the manual input terminal) is connected to the multiplier 302 .・-, 30, is connected to the output terminal of the multiplier 30+, 30*, ”・, :1OH(
7) Add the outputs together and add the sum, that is, adder 3
3. It is output as an estimation function for the first term of the unknown characteristic function of the target plant 11 from the output terminal of l-1. 34. ,
. . , Ko4, -1 is the multiplier 31. One input terminal (i.e., manual input terminal) is connected in series to the output terminal of the adder, and the other input terminal (i.e., manual input terminal) is the output terminal of the multiplier 31□, . . . -, 31, respectively. is connected to 1
Multipliers 311, 31. ,-.

31, are added together, and the summation, that is, Σ f
*, + f 5ot(x) X to adder 34%
-1 output terminal as an estimation function for the second term of the unknown characteristic function of the target plant 11. 35. ,・++
, :15. -, is the multiplier 32. One input terminal (i.e., manual input terminal) is connected in series to the output terminal of the adder, and the other input terminal (i.e., manual input terminal) is the output terminal of the multiplier 32□, ``'', :12m. multiplier 32 . , 32□,...

The outputs of 32 and 32 are added together, and the sum, that is, the sum is outputted from the output terminal of the adder core 5 as an estimation function for the third term of the unknown characteristic function of the target plant 11.

36 is a multiplier, one input terminal is connected to the input terminal of the target plant 11, the other input terminal is connected to the (2N◆l1l-1)th output terminal of the parameter adjuster 29, and the output From the end, it is output as an estimation function of the fourth term of the unknown characteristic function of the bu target plant 11.

37 is an adder, and one input terminal (i.e., 10 people) is an adder: 13. 1, and the other input terminal (i.e., 100 million yen) is connected to the output terminal of 34. ~． is connected to the output end of the output end, and outputs from the output end.

38 is an adder, one input end (i.e., Junin Mandan) is connected to the output end of the adder 37, and the other input end (i.e., Junin Mandan) is connected to the adder: 15. is connected to the output end of , and outputs from the output end.

39 is an adder, one input end (i.e., Junin Mandan) is connected to the output end of the adder core, and the other input end (i.e., Junin Mandan) performs addition: +5. , and outputs +bu from the output end as an estimation function for the unknown characteristic function of the target plant 11.

Here, the multipliers 3G, , 3G□,..., 30.
; 31. .

312, -, 31,; 32. ,32m,・-,
32, and an adder 33. ,-, :13. ,; 3
4. ,...-,34,4-,;ko51,-,35. ,
; 37 ; 38 performs an operation to reconstruct the unknown characteristic function to be estimated using element functions.

Furthermore, the operation of the unknown function estimating device of the present invention will be explained.

X+Xb, which is obtained by adding the known output X of the target plant U and the bias Xb using the adder 12, is multiplied by the constant X using the multiplier I3 to output 3(=x-(x+xb).Here, Xb
= Xm1n big X @ =1 /(Xaax
w+in), then x=(x-X,i.)/(X,
□-Xai. ), which varies in the range of 0 to 1. X is an element function generator '41.1%, -.

It is input to 14Thl, and the element function generator +
4+, 14t, "", f + (x) at 14H,
f t(x).

...+, f, (x) and are output.

f + (x), ft (x), −, f, 4 (x)
is 1 multiplier I5. , is, ,...=,15x, then the filter IS, , 16□,...+,
16. 2. ．． 2. , -,2, are given to the parameter adjuster 29.

271, 17□, -, 17H, filter tat, 18□, -, 18
, and are given to the parameter adjuster 29 as Z-1, Zs-*, =, Z-H, respectively.

The multiplier 20 multiplies x-Xb, which is obtained by adding the known output X and bias Xb of the target plant 11 by the adder 19, by a constant Q, and outputs c=is (c-Mb).

Here xb= + X wa i big X m =
1 / (X whaxXmtn), then X =
(X −X +++zn)/ (X whaxXmt
n), which varies in the range from 0 to l, is generated by the element function generator 21. , ztg, ·−,21, and is input to the element function generator 21. , 21. .

-f1(x), fg(
x), -.

fig(x) is the multiplier 23. ,232,-,23-
7 a) b924+, 24t
, -, 24m = f3.10C)! 1 ign*.

S Tokachi-f: +, v (M) sign; C5 ten end, respectively Z, N+□I Z2H+t*・”+Z
211, etc. are given to the parameter adjuster 29.

The known input U of the target plant 11 is input to the parameter adjuster S Tokachi 29 via the filter 27 as 22N6ゎ,=□U.

Also, the known output of the target plant 11 is given to the filter adjuster 29.

The parameter adjuster 29 performs a least squares calculation process on the input Z and sends out an output P. Here the input Z is and the output P is.

The outputs f l + + of the parameter adjuster 29 are provided to multipliers 3G, 302, -, 30.1 (i=1 to N), respectively, and multipliers 15. , 15. ,,-, After the appearance of Summer 5.1 and the multiplication are combined, f Ill f +, + (X) X.

as adder 33. ~33H-r. As a result, the output terminal of the adder 33N-r is outputted as an estimation function for the first term of the unknown characteristic function of the target plant 11.

The output f21 of the parameter adjuster 29 is applied to the multipliers t, , 3t, .-, 31, respectively (i
=1~N), multiplier 17+, 172, ”',
After the output of 17N and the multiplication are combined, f mol f t, +(X ) X f *, z f *, t(X ) X f 1% f 2. N(X)X is applied to adders 41 to 3411-1.

This allows the adder: 14) from the output end of l-1 to Σ
f 2+i f 2+i(X ) X is output as an estimation function for the second term of the unknown characteristic function of the target plant 11.

Output f31 of parameter adjuster 29. are multipliers 32 . , 32. ,...,32, (i
=1~M), multiplier 23+, 23t,...'', 2
After the output of 3v and the multiplication are combined, f ff + l f *, t(c) signxf !
+! f*,t(M)signxf3. M f
z, v c) adder 35 as signx. ~:1
5M-1. As a result, from the output terminal of the adder 35, Σ f :I+i f *, +(M
) sign)c is output as the estimation function for the third term of the unknown characteristic function of the target plant 11.

The output of the parameter adjuster 29 is given to the multiplier 36, and the multiplier is combined with the input U of the target plant 11 to give b
After being set as u, it is output as the estimated rA number for the fourth term of the unknown characteristic CjJ numbers of the target plant 1■.

The output of the adder: 13m-1, 34%-1, :1Sv-+ and the output of the multiplier 36 are added together by the adders 37 to 39 and added together to obtain 2 + bu, and then the unknown characteristics of the target plant 11 are calculated. Output as the estimated function for the function.

In order to further understand the unknown function estimating device of the present invention described above, a case will be described in which one vehicle with a vertical multi-joint arm is used as a specific example of a target plant, and its coefficient of friction af(θ) is estimated.

The dynamic characteristic equation for one vertically articulated arm is the moment of inertia I, mass m, length 1 rotation angle 0 of the vertically articulated arm.
．． Using tip position X and gravitational acceleration g, ■θ=mgl 5inO+ f (0) signx
It can be shown as + bu. The friction coefficient f in this dynamic characteristic equation
(δ) was estimated using the present invention, and the results shown in FIG. 5 were obtained. That is, according to the present invention, it has been found that even friction, which has conventionally been simply assumed as Coulomb friction or viscous friction and has not been actually considered, can be estimated as a subordinate.

Although the adder 9 multiplier, filter, element 08a generator, etc. are described as fixed electrical circuit elements in the above description, they may be replaced by a microprocessor or computer.

In addition, in the above description, the known variables are X and X, which are essentially one variable, but even if there are two or more variables, it is only necessary to select or add/remove element function generators as appropriate. Included in the range.

(3) Effects of the invention As is clear from the above, the unknown function estimating device according to the present invention includes a plurality of element function generators that generate element functions corresponding to known outputs of a target plant, and a plurality of element function generators that generate element functions in accordance with known outputs of a target plant. a plurality of multipliers that create a function corresponding to an unknown characteristic function of the target plant, which is a function of the known output, from the output of the multiplier and the known output; a filter, and an adder that creates another function corresponding to the unknown characteristic function using the known output and the result of performing S Tokachi operation on the operator □ using another filter on the known output of the target plant; a parameter adjuster that receives the outputs of the plurality of filters, other filters, and adders, performs a least squares calculation process, and outputs a parameter corresponding to the unknown characteristic function; and a parameter adjuster that outputs a parameter corresponding to the unknown characteristic function; and a plurality of adders that add together the outputs of the other multipliers to output an estimation function corresponding to the unknown characteristic function.

(i) If only the characteristic function of the target plant or its known output is known, the characteristic function can be estimated, and (ii) the characteristic function can be estimated even if there is friction in the target plant. In addition, (iii) there is no need to handle the noisy second-order differential of the output of the target plant, reducing the estimation work and achieving high accuracy.

[Brief explanation of the drawing]

FIG. 1 is a circuit diagram showing an embodiment of the unknown function estimating device of the present invention, and FIGS. 2 to 5 are explanatory diagrams of the same operation. 11・・・・・・・・・・・・・・・・・・Target plant 12・・・・・・・・・・・・・・・・・・・・・
Adder 13・・・・・・・・・・・・・・・・・・
Multiplier 14+, l'b,'', 14H...Element function generator 15,, Is□,..., 15.1...
...... Multiplier ia,,ts□,-,ts,i...
...Filter 17, . 17. ,・7”,IL+
...... Multiplier 1B,, 1B,...-, 1B,
l・・・・・・Filter 19・・・・・・・・・・
・・・・・・・・・Adder 20・・・・・・・・・・
. . . Multiplier 21, . 21□,””,2
1m...Element function generator 22...
・・・・・・・・・・・・Element function generator 23, .
23□, -, 23,... Multiplier 241.2
4t, "", 24es...Filter 25.
・・・・・・・・・・・・・・・・・・Filter 26
・・・・・・・・・・・・・・・・・・ Adder 27
・・・・・・・・・・・・・・・・・・・・・Filter Z
9・・・・・・・・・・・・・・・・・・Parameter adjuster 30s, 30g,...-, 30,...
... Multiplier 311.312. −． 31.・・・・・・・・・
・Multiplier 32+, 32t, ・-, 32t...
... Multiplier 331, ..., 33N-1 ...
... Adder 34I, ...", 34H-1" ...
... Adder 351, ...", 35u-r...
・・・Adder 36 ・・・・・・・・・・・・・・・
・・・1st base 37-39・・・・・・・・・・・・・・・
... Adder patent applicant Kumamoto Technopolis Foundation agent Patent attorney Takashi Kudo Mistakes Figure 2, Figure 3, Figure 4

Claims (1)

[Claims] a plurality of elemental function generators that generate elemental functions corresponding to the known outputs of the target plant; and an unknown characteristic function of the target plant that is a function of the known outputs from the outputs of the plurality of elemental function generators and the known outputs. a plurality of multipliers that create corresponding functions; and a plurality of filters that respectively calculate an operator 1/(s+μ) on the outputs of the plurality of multipliers;
Operator 1/(s+μ
), and another filter corresponding to the unknown characteristic function using the known output and the result of calculating the operator μ/(s+μ) using another filter for the known output of the target plant. an adder that creates a function; a parameter adjuster that receives the outputs of the plurality of filters, other filters, and the adder, performs least squares calculation processing, and outputs a parameter corresponding to the unknown characteristic function; another multiplier that mutually multiplies the parameters and the outputs of the plurality of multipliers; and another adder that adds the outputs of the other multipliers to each other to output an estimation function corresponding to the unknown characteristic function. An unknown function estimating device comprising: