JPH02249003A - Adaptive controller - Google Patents

Abstract

PURPOSE:To freely set a target vector by means of a time locus by installing an unknown part negating signal output means, a known part negating signal output means, a target differential signal output means and a target error characteristic signal output means. CONSTITUTION:The unknown part negating signal output means 108 generates an unknown part negating signal based on an unknown part estimation value which an unknown part estimation means 106 has obtained by using a time delay circuit, and the known part negating output means 109 generates a known part negating signal. The two signals negate the undesirable characteristic of an object to be controlled. Furthermore, the target differential signal output means 110 and the target error characteristic signal output means 111 insert a target error characteristic into the object to be controlled. Finally, conversion into a p-dimensional input vector value is executed by a signal conversion means 113. Thus, the target value can be given by the time locus of a state vector.

Description

DETAILED DESCRIPTION OF THE INVENTION Field of the Invention The present invention relates to an adaptive control device for controlling an object that is significantly affected by unknown characteristics or disturbances.

Conventional technology In recent years, the specifications of equipment and systems have been required to be even more precise and intelligent. An adaptive control device that allows equipment and systems to always exhibit desired characteristics by estimating these unknown factors in real time from input/output signals and adjusting the control system in real time based on the results. is attracting attention.

An example of a conventional adaptive control device will be described below with reference to the drawings. FIG. 2 is a perspective view of a servo motor taken as an example of the object to be controlled by the adaptive control device. Second
In the figure, 201 is a servo motor body, 202 is a load, 203 is a viscous friction member, 204 is a spring member, and 205 is a disturbance member. The input torque and rotation angle of the servo motor body 201 are T(t) and θ(t), respectively, and the load 2
02's moment of inertia is 1, the unknown friction coefficient of the viscous friction member 203 is a, and the unknown spring constant of the spring member 204 is b.
, the unknown disturbance torque caused by the disturbance member 205 is T, (t)
Then, the differential equation governing the motion of the servo motor can be written as follows.

(d/dt) x D) = f (xdt) + h (xdt) +
B (xdt)u (t)+d (t)・・・・・・(
1) That is, here, x-[θ, b]T is the state vector, f=[b,
0]T is a known characteristic vector, h=[0°-a・θ-b
・θ]T is an unknown characteristic vector with unknown parameters a and b, and B-[0,1]' is its pseudo inverse matrix B" = [0
, 1] exists, a known input allocation matrix, d=[0,Td
(t)]' is an unknown disturbance vector.

Next, FIG. 3 shows a block diagram of a conventional adaptive control device configured to control such a servo motor. In Fig. 3, 301 is the servo motor of Fig. 2;
02 is a standard model circuit, 303 is a potentiometer, 3
04 is a tachometer, 305 is a differentiation circuit, 306 is an unknown part calculation circuit, 307 is a time delay circuit, 308 is an unknown part cancellation circuit, 309 is a known part cancellation circuit, 310 is a reference model characteristic insertion circuit, and 311 is an error characteristic adjustment circuit. , 312
313 is an adder circuit, 313 is a conversion circuit, and 314 is an output circuit. Further, it is assumed that the reference model 302 has the following characteristics.

('d/d t )xd=Am=xmm×BII+
・...(3) That is,...(4) Also, the error vector e=[θ., θ'IT is the state vector of the reference model 302 xIll=[θm+'im]
State vector X of T and servo motor 301 = [θ, δ]
It is defined by the difference in T as shown in the following equation.

e=xm=xm...
...(5) In other words, the target error characteristic is (d/d t)e (t)= (Am+K)e (t)
(7) A matrix K is provided as an adjustment term so that the characteristic matrix (Am+K) can be selected independently of the characteristic matrix Am of the reference model.

The operation of the conventional adaptive control device configured as described above will be explained. First, the tachometer 304 detects the rotational angular velocity θ of the servo motor 301, and then
05 gives the rotational angular acceleration θ. Using the value of the rotational angular acceleration θ and the value of the input torque T(t), the unknown part calculation circuit 306 calculates w (t)=(d/d t)x=f(xdt)B
(xd t) -u (t) --(8) That is, based on the equation, the hector value Wo (t) = h (xd t) -1-d ( t
) --(10) That is, the unknown part estimate z (t) z (t) -w (t-L) ・
-...03). Here, the unknown part W. If the delay time is chosen to be sufficiently small compared to the speed at which (1) changes, Wo (t) = Wo (t L) −
-04) holds true. θri ~ To summarize the measurements, z (t) #wo (t) ・・
...05), and from this formula, it can be seen that the estimated value z (t) has high accuracy for a sufficiently small delay time... (11) Calculate the value at time t. do. Here, w(t)−w
0(t)...02) is easily confirmed from equations (1) and (2).

The unknown part calculation value w(t) obtained by the unknown part calculation circuit 306 in this way is delayed by the delay time by the time delay circuit 307. Based on the equation (10), Using the value of the rotational angular acceleration G δ (t-L) at time t-L and the value of input torque T (t-L), the unknown friction coefficient a and the unknown spring constant at time t and the unknown disturbance torque Td ( Servo motor 3 consisting of +,)
W represents the unknown part of 01. ([) can be estimated.

Now, the unknown part estimate z (t) obtained in this way
The sign of is inverted by the unknown portion cancellation circuit 308 and output to the addition circuit 312. In addition, the servo motor 301
Undesirable known part of the molecule (x t)−[b,
The sign of "Ol" is also inverted by the known partial cancellation circuit 309 and output to the addition circuit 312.The reference model characteristic insertion circuit 310 calculates the rotation angle θ obtained by the potentiometer 303 and the rotation angular velocity θ obtained by the tachometer 304. Using A1□・x (t) ten B,
- The characteristic signal of the reference model represented by r (t) is also output to the adder circuit 312. Further, the error characteristic adjustment circuit 311 adjusts the rotation angle θ of the reference model 302. and the rotation angle error θ from the rotation angular velocity θ□, the actual rotation angle θ of the motor 301, and the rotation angular velocity δ. and rotational angular velocity error θ.

is calculated and multiplied by the error feed bank gain matrix to create an error characteristic adjustment signal -K.e, which is output to the adder circuit 312. The addition circuit 313 adds the above four types of signals, and furthermore, the two-dimensional vector value is the pseudo inverse matrix B'' of the conversion circuit 313 = (
The input torque T is a one-dimensional scalar value by 0,11
(t), and that value is finally given to the servo motor 301 by the output circuit 314.

The above operations can be summarized as follows.

u (t)-B' (xdt}{-z (t)f (
xdt) +Am=xm (t) +Bm-r (t)K-e(t
)) ・・・・・・08) That is, ・・・・・・Q9) Or rearranging, T(t)=−(υ(t−L)−T (t−L))−am
・θ-bI11・θ+Cll1-rka-te-k ・
θ8...Ql, O[9-G! The @formula becomes the final control law.

At this time, by substituting equation 08), which expresses the control law, into (1) 2, which expresses the characteristics of the controlled object, and further rearranging 2 by using equation 05), which is an approximate expression regarding the unknown estimated value, as a complete equation, , the characteristics of the error vector e are obtained as shown below.

(d/d t)e-(AI,l+K)e+ {I-B-
B” ) (=f−h−d+Ae・χ+Bm −r−
(21) Here, in order for the above equation to match the target error characteristic defined by equation (7), the second term on the right side of equation (21) must be zero. There needs to be. That is, (1-B-B") (=f-h-d+Am=xm+
BIllr-K・e)-0 (22) Here, the range of targets to which the adaptive control device can be applied by the above equation is limited to some extent by the state vector x (t
) is generally larger than the number of elements of the control vector u (t), the conversion circuit 313
This is because when calculating (t), the inverse matrix of the input distribution matrix B must be approximated by a pseudo-inverse matrix B'. Therefore, if the numbers of elements of both are equal, the pseudo-inverse matrix B' will be equal to the inverse matrix B'l, so the limiting condition of equation (22) should have no practical meaning. In fact, in this case, it can be easily confirmed that I-B-B" = I-B-B' = O, and the formula (22) is definitely satisfied. In other words, the formula (22) is This can be interpreted as requiring that the number of elements of the state vector x (t) of the controlled object and the number of elements of the control vector u (t) be "substantially" equal. In this conventional example, the elements of the state vector are the rotation angle θ and rotation angular velocity θ of the servo motor 301, but once the rotation angle is determined, the rotation angular velocity is uniquely determined by differentiating it, so the state vector The "substantive" number of elements is 1. Furthermore, since the only element of the control vector is the human torque T(t), the number of elements is 1 (unpaid). Therefore, in this conventional example, the number of elements of the state vector and the number of elements of the control vector are "substantially" equal, which means (2), (4
), it can be confirmed by substituting Equation 09 into Equation (22). Note that the error characteristics in the conventional example are (4), 0
By substituting Equation 9 into Equation (7) and rearranging it, it can be written as the following equation.

i8+(aIIl+ka)δ,,+(bnl+, )
θe-0 (23) From the above, the main operations of the conventional adaptive control device can be summarized as follows.

■ Unknown part calculation circuit 306 and time delay circuit 307
As a result, the unknown portion of the servo motor 301 is estimated by the formula OI;1, and the unknown portion estimated value z (t) is obtained.

(2) The unknown part cancellation circuit 308 generates an unknown part cancellation signal (-2).

(2) The known portion cancellation circuit 309 generates a known portion cancellation signal (=f).

(2) The standard model characteristic insertion circuit 310 generates a standard model characteristic signal (Ae=xm+Bm-r).

(2) The error characteristic adjustment circuit 311 generates an error characteristic adjustment signal (-K·e).

(2) Addition circuit 312 adds the above four signals.

■ The conversion circuit 313 converts the addition signal, which is a two-dimensional hector value, into inputs 1 to Rk, which are one-dimensional scalar values, using the pseudo inverse matrix (B), and finally (20)
Obtain the control law for Eq.

(For example, ■ Ito, page 55-56 of the 32nd System and Control Research Presentation Proceedings, published in May 1988.
The paper “TimeDelay C” by Joseph 1--mi
ontrol (TDC) proposal"", ■ American Control Con, published June 1988.
"A Time Dela" paper by Joseph Tomi and Ito on pages 904-911 of the ference Lecture Proceedings.
y Cont-roller for Systems
Problems to be Solved by the Invention of With Unknown Dynamics However, the above configuration has the following three problems.

That is: (1) Since the setting of the target vector is restricted by the normative model, the target vector cannot be freely given by the time trajectory.

■ Since the necessary and sufficient conditions to be satisfied by the signal processing in the unknown part estimating means have not been clarified, the selection of the unknown part estimating means is limited to time delay, making it difficult to realize an adaptive control device.

■ Differential value of state vector (d/d t) x (t),
Known characteristic vector f (xdt) and known input distribution matrix B
When (xdt) changes rapidly, the estimation accuracy of the unknown portion deteriorates.

In view of each of the above-mentioned problems, the present invention provides the following adaptive control device. That is, (1) an adaptive control device that can freely provide a target vector based on the time trajectory of the state vector without being restricted by a reference model;

■ Adaptive control device that is easy to implement by making it possible to use signal processing means other than time delay.

■ Differential value of state vector (d/d t) x (t),
Known characteristic vector ((xdt) and known input distribution matrix B (
An adaptive control device that can estimate unknown portions with high accuracy even when the change in speed (xdt) is rapid.

Means for Solving the Problems In order to solve the above problems, the adaptive control device of the present invention has the following configurations. That is, (1) W is the value of the unknown part of the controlled object. (1)-h(x
d t)+d(t) using the value of the known part of the controlled object, W (t) −(d/d t)x (t)
= f (
a value z that is partially equal but not identical to t)
(t) as an unknown part estimated value, and an unknown part cancellation signal z (t) of the controlled object using the unknown part estimated value z (L) obtained by the unknown part estimation means. unknown part cancellation signal output means for outputting a known part cancellation signal=f(xdt) of the controlled object from the known characteristic vector f(xdt); target differential signal output means for outputting a vector signal (d/dt) xd (t); and target error characteristic signal -A8·e (t
), each signal output from the unknown part cancellation signal output means, the known part cancellation signal output means, the target differential signal output means, and the target error characteristic signal output means. Addition signal -z(t)f (xd t)+(d/d t)xd
(t)-Ae・e (t) and a pseudo inverse matrix B(xd t) of the known input distribution matrix B(xd t), The n-dimensional addition signal is converted into the p-dimensional input vector u (t) u(t)=B'' (xd t)
(-z(t) =f (xd t)+(d/d
t) signal conversion means for converting by xd (t) - Ae - e (t) 1; and target differential signal output means for outputting a differential vector signal (d/dt) xd (t) of the constituent target vectors. and target error characteristic signal -A8e
and target error characteristic signal output means for outputting (t).

■ Wo (t), which is the value of the unknown part of the control target
-h(xdt)+d(t) using the value of the known part of the control target, W(t)-(d/d t)x(t)
=f(xdt) -B (xt)u'(t) The unknown part calculation means obtains the unknown part calculation value, and the unknown part calculation value w(t) obtained by the unknown part calculation means and partially Unknown part estimating means outputs a value z (L) that is equal but not identical as an unknown part estimated value, and the unknown part estimated value z (t) obtained by the unknown part estimating means is used to calculate the above. unknown part cancellation signal output means for outputting an unknown part cancellation signal -z (t) of the controlled object; and the known characteristic vector f (xd t).
From the known part cancellation signal of the controlled object = f (xdt)
and a characteristic signal of the reference model Am=xm (t) +Bm-r (t).
a reference model characteristic signal output means for outputting an error characteristic adjustment signal -K.e(t); an error characteristic adjustment signal output means for outputting an error characteristic adjustment signal -K.e(t); The respective signals output from the reference model characteristic signal output means and the error characteristic adjustment signal output means are added to produce an added signal -Z (t)f (X, t).
+Am−X(t)+Bmr(t)−K·e(t); and the known input allocation matrix B(x
dt), the n-dimensional addition signal obtained by the signal addition means is added to the p-dimensional input vector u(t) by u (t)-B''
(xdt}{-z (t)f(xdt)+A,,=
xm (t)+Bm-r(t)K-e(t)).

■In place of the unknown part calculating means and the unknown part estimating means in the above two configurations, a signal processing means that outputs v (t) which is partially equal to the input vector u(t) but not identically is used. , W, which is the value of the unknown part of the controlled object. (
1) = h (xdt) + d (t) using the output value v (t) obtained by the signal processing means and the value of the known part of the controlled object to calculate the unknown part estimated value z (t)
-(d/d t)x (t)f (xdt)-B (
xdt)v(t).

Effects The effects of the above-described configuration of the present invention are as follows. That is, ■ First, based on the unknown part estimate Z (t) obtained by the unknown part estimating means using a time delay circuit,
The unknown part cancellation signal (
−Z) is generated. Furthermore, the known portion cancellation signal output means generates a known portion cancellation signal (=f), and these two signals cancel out undesirable characteristics of the controlled object. Further, the target differential signal output means and the target error characteristic signal output means respectively output the target differential signal (d/dt) xd and the target error characteristic signal (-Ae・-
e) and insert a target error characteristic into the controlled object using these two signals. Finally, the signal converting means converts the addition signal, which is an n-dimensional vector value, into a p-dimensional input vector value using a pseudo inverse matrix (B), and thereby, the control target has the target error characteristic. It becomes possible to realize an adaptive control device that allows the state vector to follow the target value of the state vector.

■ Adaptive control is achieved by using unknown part estimating means that outputs as an estimated value z (t) which is partially equal to the input value w(t) obtained from the unknown part calculation value, but is not identical to it. The closed-loop gain present in the device can be kept finite, which makes it possible to realize an adaptive control device using signal processing means other than time delay.

■ First, by using signal processing means, human power and
partially equal to (t) but not identically v
Outputs (+,). Next, using the output value v (t), the unknown part estimation means calculates z (t) = (d/d
t) x (t)=f (xt)-B (xdt)v
(t) to obtain the unknown part estimate. At this time, the differential value of the state vector (d/d t) x (t), the known characteristic vector f (xd t), and the known input distribution matrix B (
xL), since there is no delay due to signal processing, it is possible to realize an adaptive control device that can estimate unknown parts with high accuracy even when those characteristics change rapidly.

Embodiment The purpose of the adaptive control device in the first embodiment of the present invention is to
An object of the present invention is to provide an adaptive control device that can provide a target value based on a time trajectory of a state vector.

The basic idea will be explained below using mathematical formulas. "A" on the right side of θB) 2, which shows the control law in the conventional example.
m=xm+Bm-r-K.e" is transformed as follows.

A =xm+B -r-K・e (5) Using the second definition of the error vector, =Am=xm
+Bm-r-K ・ (xd=xm}{Am=xmm-
Am =xm□) Add =0, -Am=xm+Bm
−r−K ・ (xm=xm)+(Am=xmLI}=
AII}=xm) rearranged, −(Am=xmff,+B,・r) −(AII}=
1-K} {xm=xm) Using the definition of the normative model in equation (3), -(d/dt)
xm-(A,,, +K}{xm x}{5) Using the definition of the error vector in the formula, -(d/d t)xm-(A
m+K)e...(24) Also, as shown in equation (7), "(AIIl+K)" in equation (24) is the characteristic matrix of the target error characteristic, so this can be rewritten. is defined as A8.

That is, Ae=Am+K...--1
25) Also, by substituting equation (25) into equation (7), (d/
d t)e (t)=Ae−e (t)−・・−(26
) represents the target error characteristic.

(24), (25) Putting both equations together, Am = xm + B, -r-K・e- (d/d t ) xm-Ae-e −= (27) Here obtained (27) By substituting the equation into the adaptive control law expressed by equation 08), a new adaptive control law expressed by the following equation is obtained.

u (t)=B" (xdt}{-z (t)f
(xdt) 10 (d/dt) xm(t) A8・e (t) ) −・−(28}
Although the control law of equation {28) and the control law of equation θ8) are equivalent in pure mathematics, their meanings are very different in terms of application to a control device. That is, in equation (28), parameter matrices Am and B defining the reference model
Since m does not exist, by using this adaptive control law, there is no need to define a norm model when setting the target vector xl1, (t), and the target vector can be freely set according to the time trajectory. There is an advantage.

In order to clearly express that there is no need to define a normative model, xd(t
) will be used, and the definition of the error vector based on equation (5) will also be changed accordingly. That is, Xd (t)-xm (t)...
...(29) e=x =xm
(30}{29) By substituting equation (30) into equation (28), an equation representing the control law in the first embodiment of the present invention is obtained.

u (t)−B” (xdt}{z (t)f (x
dt) + (d/d t)xd(t) Ae-e(t)l -...-(31) The above is the basic idea of the adaptive control device of the first embodiment of the present invention. This will be explained in more detail below with reference to the drawings. FIG. 1 shows a block diagram of an adaptive control device in a first embodiment of the present invention. In FIG. 1, 101 is the servo motor of FIG. 2, 102 is a target signal output circuit, 103 is a potentiometer, 104 is a coccometer, 105 is a differentiation circuit, 106 is an unknown part calculation circuit, 107 is a time delay circuit, and 108 is an unknown 109 is a known partial cancellation circuit; 110 is a target differential signal insertion circuit; 111 is an error characteristic insertion circuit; 112 is an addition circuit; 113 is a conversion circuit; and 114 is an output circuit.

The operation of the adaptive control device according to the first embodiment of the present invention configured as described above will be explained below. The unknown part calculation circuit 106 uses the rotational angular acceleration δ(1) of the servo motor 101 detected by the tachometer 104 and the differentiation circuit 105 and the input torque T(t), and calculates the value based on equation (9) as in the conventional example. The unknown portion of the servo motor 104 is calculated, and the unknown portion calculation value w(t) is output.

The unknown part calculation value w(t) is turned into an unknown part estimated value z (t) by the time delay circuit 107 , and the sign is further inverted by the unknown part cancellation circuit 108 and output to the adding circuit 112 . Also, the sign of the undesirable known part molecule (xdt)-[01'' of the servo motor 101 is inverted by the known part cancellation circuit A!8109 and output to the adder circuit 112, similarly to the conventional example. Next, the target vector xd (t) given by the target signal output circuit 102 is changed to (d/at)xd (t) by the target differential signal insertion circuit 110 and output to the addition circuit 112 .

Further, the error characteristic insertion circuit 111 includes the target signal output circuit 1
Rotation angle error θ from the target rotation angle θ6 and target rotation angular velocity θ6 of 02 and the actual rotation angle θ and rotation angular velocity θ of the servo motor 101. and rotational angular velocity error θ. By calculating and multiplying by the error feedback gain matrix, an error characteristic signal -Ae-e is created and outputted to the addition circuit 112. The adder circuit 112 adds the above four types of signals, and furthermore, the two-dimensional vector value is converted to the pseudomorphic inverse matrix B'' of the converter circuit 113 = [
0, I], the input torque T is a one-dimensional scalar value
(t), and this value is finally given to the servo motor 101 by the output circuit 114.

The above operations can be summarized as the equation (31) already explained, and if this is specifically written to correspond to the equation 09), C) 0, it will be as follows.

(Left below) ・・・・・・(33) Or rearranged, T (t)=-(i (t-+-) -T (L-L)
)+i d ao ・θQ ”+1 ・θ. ・・・・・
・(34) At this time, by substituting equation (31) representing the control law into equation (1) representing the characteristics of the controlled object, and using equation 09, which is an approximate equation regarding the unknown part estimate, as a complete equation, By rearranging 2, the characteristics of the error vector C can be obtained as shown in the following equation.

(d/d t)e=A8 ・e + (1-B-B゛l (-r-h-a+ (d/d
t)xd-Ae-e) (35) Here, in order for the above equation to match the target error characteristic defined by equation (26), must be zero. That is, (1-B-B') (=f-h-d+(d/dt)
x 6 A 6 ・el −0 (36) Here, the range of objects to which the adaptive control device of the present invention can be applied is limited to some extent by the above equation, as in the conventional example, the conversion When calculating the control vector u (t) by the circuit 313, the inverse matrix of the input allocation matrix B is converted into a pseudo inverse matrix B
This is due to the fact that it must be approximated by . In other words, equation (36) shows that the number of elements in the state vector x (t) of the controlled object and the number of elements in the control vector u (t) are "substantially"
It can be interpreted as requiring equality.

Furthermore, in this embodiment, as in the conventional example, the number of elements of the state vector and the number of elements of the control vector are "substantially" equal, which means (2), (4), (32
) can be confirmed by substituting equation (36) into equation (36).

Note that the error characteristics in this example are expressed by converting equation (32) into (26
) can be written as the following equation by substituting it into the equation and rearranging it.

go+a8・θ. +b.・θ. −〇 ・・・・・・(
37) From the above, the main operations of the adaptive control device according to the first embodiment of the present invention can be summarized as follows.

■ Unknown part calculation circuit 106 and time delay circuit 107
As a result, the unknown part of the servo motor 101 is estimated by equation (10), and the unknown part estimated value z(t) is obtained.

(2) The unknown part cancellation circuit 108 generates an unknown part cancellation signal (-Z).

(2) The known part cancellation circuit 109 generates a known part cancellation signal (-1).

(2) The target differential signal insertion circuit 110 generates the target differential signal (d/dt) xd.

■ The error characteristic insertion circuit 111 inserts the error characteristic signal (-
Ae・-e) is generated.

(2) The adding circuit 112 adds the above image signals.

■ The conversion circuit 113 converts the addition signal, which is a two-dimensional vector value, into an input torque, which is a one-dimensional scalar value, using the pseudo inverse matrix (B), and finally the input torque is 12 (11
Obtain the control law for Eq.

Comparing these operations (1) to (2) with operations (1) to (2) described in the conventional example, the major differences between the two are in (1) and (2). That is, the target differential signal (d/dt)x is used instead of the characteristic signal Am-X+Bm-r of the reference model, and the error characteristic signal -A is used instead of the error characteristic "adjustment" signal K.e.
This embodiment differs greatly in its configuration from the conventional example in two respects: ee is used "directly".

As a result, the target vector can be freely set according to the time trajectory without being restricted by the reference model.

Next, a second embodiment of the present invention will be described.

The purpose of the adaptive control device in the second embodiment of the present invention is to
It is an object of the present invention to provide an adaptive control device that is easy to implement by making it possible to use signal processing means other than time delay.

In the conventional example, it was shown that an adaptive control device can be realized by using a time delay circuit 307 as an unknown part estimating means for obtaining an unknown part estimated value z (t) from an unknown part calculation value w (t). .

However, the general conditions that an unknown part estimating means should have were unclear, so it is unclear whether there is any unknown part estimating means other than time delay that can be used, and if so, what kind of method is it? It wasn't clear if there was. This point will be explained below.

First, the signal processing performed by the unknown portion estimating means is represented by the general form "G(.)". That is, z (t) =
G (w (t) ) --(38). As explained in the conventional example, according to equation 02), the unknown part calculation value w (t) is the value W of the unknown part of the servo motor 301. Equal to (1). Therefore, the unknown part estimate K
(t) is the value W of the unknown part. In order to faithfully represent (1), the unknown part estimation means is G(・)=1 ・Old...(39
) is desirable. If the only purpose is to estimate the unknown part of the controlled object, then this equation (39) is the only basic condition that the signal processing means G(.) should satisfy. Next, when the unknown part estimation value z (t) obtained in this way is also used in the F control 1J in real time, that is, when trying to realize an adaptive control device, the unknown part estimation means G (・) Consider the conditions that must be met.

Generally, for a feedback control device to be realizable, it is necessary that the magnitude of the closed-loop gain is bounded. In the conventional adaptive control device shown in FIG. 3, there are four closed loops. That is, ■ known part cancellation part ■ error feedback part ■ unknown part cancellation part (output side) ■ unknown part cancellation part (input side), and each closed loop part is shown in FIGS. Simplified block diagrams are shown in FIGS. 8 to 11. However, in these figures, the output circuit 314 and the servo motor 301 are
, the transfer function of the controlled object that reaches the rotation angle θ(1) through the potentiometer 303 is simply indicated by H.

As shown in FIG. 8, the closed loop of the known partial cancellation section is essentially cut off, but this is due to the known characteristic vector f created from the output of the servo motor and the transformation matrix B1 that determines the input torque T(t). The product of B゛・f−[0,1]・[
a, Q]tmiO... (40) Since it is always zero, a zero signal is fed back to any signal.

From FIGS. 9 to 11, the conditions for the gain of each closed loop to be bounded are as follows.

1+ <k, +to, ・s) H(0...
...(41)1+s”・G-HI3・Old・(
42) 1-G〆0...
...(43) Equations (41) and (42) include the transfer function H of the controlled object, which is an actual physical system, in the conditional expressions, and the left sides of both equations are ``exactly'' and ``identity.'' Normally, it is impossible for the value to become zero. That is, (41), (42)
It can be considered that both conditions are always satisfied. Therefore, equation (43) that does not include H becomes a substantially effective conditional equation for realizing the adaptive control device. (43
) expression, we get G(・)〆1 ・・・・・・
(44). Now, the conditional expression (39) is for making the estimated value of the unknown part of the controlled object highly accurate, and the conditional expression (44) is for making it possible to realize an adaptive control device using the estimated value. Comparing the formulas, the conditions of both formulas are clearly contradictory, and it is impossible to satisfy them simultaneously. Therefore, after securing the conditions for realizing the adaptive control device in equation (44), it is necessary to compromise on equation (39), which is a condition for increasing the accuracy of the estimated value, within a range that does not cause any practical problems. It is a practical solution for realizing a control device. That is, G(・)L=, and G(・)〆l
(45) becomes the final conditional expression that must be satisfied by the unknown portion estimating means. That is, the unknown part estimating means in this adaptive control device needs to be an unknown part estimating means that "outputs an output value that is partially equal to the input value but not identically equal." In addition to time delay circuits, there are various unknown part estimating means that satisfy such conditions. As an example, an embodiment of an adaptive control device using a low-pass filter circuit as unknown portion estimating means will be described below with reference to the drawings.

FIG. 12 is a block diagram of an adaptive control device showing a second embodiment of the present invention. In FIG. 12, 1201 is the servo motor of FIG. 2, 1202 is a reference model circuit, and 1201 is the servo motor of FIG.
03 is a potentiometer, 1204 is a tachometer', 1
205 is a differentiation circuit, 1206 is an unknown part calculation circuit, 12
07 is a low-pass filter circuit, 1208 is an unknown part cancellation circuit, 1209 is a known part cancellation circuit, 1210 is a reference model characteristic insertion circuit, 1211 is an error characteristic adjustment circuit, 12
12 is an adder circuit, 1213 is a conversion circuit, and 1214 is an output circuit. Further, it is assumed that the reference model 1202 has the characteristics of equations (3) and (4) similarly to the adaptive control device of the prior art.

The operation of the adaptive control device according to the second embodiment of the present invention configured as described above will be described below. The unknown part calculation circuit 1206 operates on the servo motor 120 detected by the tachometer 1204 and the differentiation circuit 1205.
Using the rotational angular acceleration υ(1) of 1 and the input torque T(t), the motor 1 is calculated based on equation (9) as in the conventional example.
The unknown part of 201 is calculated and the unknown part calculation value w(t) is output. High frequency components of the unknown part calculation value w (t) are attenuated by the low-pass filter circuit 1207, and the unknown part calculation value w (t) becomes the unknown part estimated value z (t). That is, z (t)= (
1/(Ts+1)l w (t) (46). Here, the unknown part W. (1) If the time constant τ of the low-pass filter is chosen sufficiently small compared to lt which changes, wo (t) = (1/ (τs+1)) w(, (t)
...(47) holds true. 02) ~ To summarize the opening ceremony, z (t)”i
wo (t) ・・・・・・(48
), and from this formula, for a sufficiently small time constant τ,
Based on the assumption that the estimated value z (t) has high accuracy, it is calculated by calculating the value of the rotational angular acceleration i (t) and the input torque T (t
) is processed using a low-pass filter to generate a servo motor 1201 consisting of an unknown friction coefficient a, an unknown spring constant, and an unknown disturbance torque Td-(t).
W represents the unknown part of. (1) can be estimated.

The unknown portion estimated value z(t) obtained in this way has its sign inverted by the unknown portion cancellation circuit 1208 and is output to the addition circuit 1212. Further, the sign of the undesirable known part molecule (xt)-[b,0]0 of the servo motor 1201 is inverted by the known part cancellation circuit 1209,
It is output to the adder circuit 1212. The reference model characteristic insertion circuit 1210 uses the rotation angle θ obtained by the potentiometer 1203 and the rotation angular velocity θ obtained by the tachometer 1204 to calculate Am=xm (t)+8m.
- Output the characteristic signal of the reference model represented by r (t) to the addition circuit 1212 as well. Furthermore, the error characteristic adjustment circuit 1211 calculates the rotation angle error θe and rotation angular velocity error θe from the rotation angle θ□ and rotation angular velocity θ□ of the reference model 1202 and the actual rotation angle θ and rotation angular velocity θ of the servo motor 1201, and calculates the rotation angle error θe and rotation angular velocity error θe using the formula 09. By multiplying the error feedback gain matrix K of the error characteristic adjustment signal −K・e
is created and output to the adder circuit 1212.

The addition circuit 1213 adds the above four types of signals, and furthermore, the two-dimensional hector value is converted to the one-dimensional scalar input 1-lux by the pseudo inverse matrix B''-[0,1 of the conversion circuit 1213. It is converted into a value of T(t), and that value is finally given to the servo motor 1201 by the output circuit 1214.

The above operations can be summarized as follows.

u (t)=B” (xdt}{−z (t)f (
xdt) +Am=xm (t) +Bm-r (t)K-e(t
)l ・・・・・・(50) That is, (hereinafter the margin) ・・・・・・(51) Or rearranged, T (t)=−(1/(τs+1))(y(t )−
T (t)) a-'71-b ・θ''-c-r ka-j)e-J, ・θe ・-・・-(52)
Therefore, equations (50) to (52) become the final control law.

At this time, by substituting equation (50) representing the control law into equation (1) representing the characteristics of the controlled object, and using equation (48), which is an approximate equation regarding the unknown estimated value, as a complete equation, To summarize, the characteristics of the error vector and the conditions for limiting the range of the controlled object are (21) to (23) as in the prior art.
) is given by the formula.

From the above, the main operations of the adaptive control device according to the second embodiment of the present invention can be summarized as follows.

■ The unknown part calculation circuit 1206 and the low-pass filter circuit 207 estimate the unknown part of the servo motor 1201 using equation (49), and the unknown part estimated value z (
t) is obtained.

(2) The unknown part cancellation circuit 1208 generates an unknown part cancellation signal (-z).

(2) The known portion cancellation circuit 1209 generates a known portion cancellation signal (=f).

(2) The reference model characteristic insertion circuit 1210 generates a reference model characteristic signal (Am=xm-1-BIT, -r).

(2) The error characteristic adjustment circuit 1211 generates an error characteristic adjustment signal (-K·e).

(2) The above-mentioned image signals are added by the addition circuit 1212.

■ The conversion circuit 1213 converts the addition signal, which is a two-dimensional vector value, into an input torque, which is a one-dimensional scalar value, using the pseudo inverse matrix (B), and finally (52)
Obtain the control law for Eq.

Comparing these operations (1) to (2) with operations (2) to (2) described in the conventional example, the major difference between the two is in (2). In other words, while conventional time delay circuits are used to obtain the unknown part estimation value, this embodiment uses a low-pass filter circuit that is easy to circuit (different from the conventional method). .

As a result, an adaptive control device with equivalent performance can be realized using an easy-to-implement low-pass filter circuit. Furthermore, the low-pass filter circuit can also exhibit the effect of removing high-frequency measurement noise included in the unknown partial calculation value.

In addition, as an unknown part estimating means that satisfies equation (45),
In addition to the low-pass filter circuit described in the second embodiment, there are various means that have unique effects. for example,
By using the bandpass filter according to claim (4), when the frequency band of the unknown part of the controlled object is known, the special effect is that measurement noise included in the unknown part calculation value can be removed very effectively. is obtained. Further, by using the zero-order sample and hold circuit according to claim (6), there is an effect that an adaptive control device of a digital circuit system can be easily constructed. Furthermore, by combining the zero-order sample and hold circuit with a shift circuit as described in claim (7), it is possible to have the effect that the configuration of the adaptive control device using a computer program is extremely easy. In addition, claims (8) and (9)
) By using the unknown part estimating means of multiplying by a coefficient of 1, it is possible to completely cancel out the phase of the unknown part of the controlled object and most of the magnitude as well. The effect of this can be obtained.

Furthermore, the various unknown part estimating means described above are applicable not only to the standard model following type adaptive control device described in the second embodiment, but also to the trajectory following type adaptive control device described in the first embodiment. It goes without saying that the same effect can be achieved even when combined with

Next, a third embodiment of the present invention will be described.

The purpose of the adaptive control device in the third embodiment of the present invention is to
The differential value of the state vector (d/dt)
An object of the present invention is to provide an adaptive control device that can estimate an unknown part with high precision even when changes in

Of the four closed loops considered in the second example,
We will focus on two closed loops that are directly related to the unknown part estimating means, that is, the closed loop of the unknown part cancellation unit (output side) and the closed loop of the unknown part cancellation unit (input side). As shown in Figures 6 and 7, the same signal processing G(・) is performed on both the output side signal and the input side signal, but these are processed separately. G, (・), G2 (
・) Consider replacing it with By doing so, the condition for increasing the precision of the estimated value expressed by equation (39) is changed as follows.

G, (・)=1 ・・・・・・
(53)G2 (・)=1
(54) Furthermore, the conditions for realizing the adaptive control device expressed by equations (42) and (43) are changed as follows.

1 +s -G, ・HmO... (55) 1-
G2〆0・・・・・・(5
6}{It is possible to satisfy equations (53) and (55) at the same time, but since equations (54) and (56) are contradictory conditions, (54) is satisfied as in the second embodiment. ) must be relaxed to the extent that there is no practical problem. As a result, the final conditional expression that G, (.) and G2 (.) should satisfy is as follows.

C, (・)=1 and G2 (・)', 1 and G2 (
・)〆1 ・・・・・・(57) Similar to the second embodiment, there are various G2 (・) that satisfy the above conditions.・)
An example of an adaptive control device used as an example will be described with reference to the drawings. Note that the point V between the second embodiment and the third embodiment is limited to the configuration of the unknown portion estimating means, so the following explanation will focus on this point.

FIG. 13 is a block diagram showing unknown part estimating means in an adaptive control device showing a third embodiment of the present invention.

In Figure 13, 1301 is a constant multiplier circuit (constant -1)
, 1302 is a time delay circuit, 1303 is an addition circuit, 13
04 is an unknown part estimating means composed of 1301 to 1303.

The operation of the unknown portion estimating means in the third embodiment of the present invention configured as described above will be explained below.

The rotational angular acceleration θ of the servo motor to be controlled is output as is to the addition circuit 1303 by the constant multiplier circuit 1301. Further, the input torque T (L) is multiplied by the input distribution matrix B, further has its sign inverted, and is then delayed by the time delay circuit 1302 by the amount of time -T(t-
L) and is output to the adder circuit 1303. The adding circuit 1303 adds the above two signals and outputs the unknown portion estimated value z (t). The unknown portion estimated value obtained in this manner is used in the same manner as in the second embodiment to configure an adaptive control device.

Comparing the configuration of the unknown part estimating means of the third embodiment with that of the first embodiment, it is found that from equation (57), in the second embodiment, the accurate value of the rotational angular acceleration θ is set as G1-1. can be used. Due to this structural feature, in the third embodiment, when the rotational angular acceleration δ changes very quickly, the differential value (d/
dt) x (t) or known characteristic vector f (xd t
) or when the known input allocation matrix B(χ, 1) changes very quickly, a special effect can be obtained in that the unknown part estimated value can be made highly accurate. Furthermore, the rotational angular acceleration b, generally the differential value of the state variable of the controlled object (d/dt) x (
t) often includes high-frequency measurement noise that cannot be ignored, but in such cases, G1 can be used as a low-pass filter to effectively remove the measurement noise and provide even more accurate adaptive control. This has the effect that the device can be realized.

Effect of the invention As described above, the present invention has the following effects.

■ By providing the unknown part cancellation signal output means, the known part cancellation signal output means, the target differential signal output means, and the target error characteristic signal output means, the target vector can be set according to the time trajectory without being restricted by the reference model. The effect is that it can be set freely.

■ Equipped with unknown part estimating means that outputs a value z (t) that is partially equal but not identically equal to the unknown part calculated value w(t) obtained by the unknown part calculating means as an unknown part estimated value. By doing so, means other than time delay can be used as a signal processing means in the unknown portion estimating means, and an adaptive control device can thereby be easily configured.

■ A signal processing means that outputs v (t) that is partially equal to the input vector u (t) but not identically, and an unknown part estimated value z (t) using the output value v (t).
) = (d/d t) x (t) = f (xdt) - B
(xdt)v(t), the differential value of the state vector of the controlled object (
d/dt) x (t) or known characteristic vector f (xdt
) or the effect that the unknown part estimated value can be made highly accurate even when the known input distribution matrix B(xdt) changes very quickly.

[Brief explanation of drawings]

FIG. 1 is a block diagram of an adaptive control device according to a first embodiment of the present invention, FIG. 2 is a perspective view of a servo motor taken as an example of the object to be controlled by the adaptive control device, and FIG. 3 is a conventional adaptive control device. Figures 4 to 7 are block diagrams of the four closed loop parts present in the adaptive control device, and Figures 8 to 11 are simplified blocks of Figures 4 to 7, respectively. 12 is a block diagram of the adaptive control device according to the second embodiment of the present invention, and FIG. 13 is a block diagram of the unknown part estimating means in the adaptive control device according to the third embodiment of the present invention. be. 101... Servo motor in Figure 2, 102...
...Target signal output circuit, 106...Unknown part calculation circuit, 107...Time delay circuit, 10B
...Unknown part cancellation circuit, 109...Known part cancellation circuit, 110...Target differential signal insertion circuit, 111...Error characteristic insertion circuit, 302.
... Normative model circuit, 310 ... Normative model characteristic insertion circuit, 311 ... Error characteristic adjustment circuit, 1207 ... Low-pass filter circuit, 13
01...Constant multiplier circuit (constant -1), 1302.
...Time delay circuit. Name of agent: Patent attorney Shigetaka Awano

Claims (11)

[Claims] (1) t is time, x(t) is n-dimensional state vector,
Let f(x, t) be an n-dimensional known characteristic vector, h(x, t
) is an n-dimensional unknown characteristic vector, B(x, t) is an n×p-dimensional known input allocation matrix in which its pseudo-inverse matrix B^+(x, t) exists, and u(t) is a p-dimensional input Vector, d(
t) is an n-dimensional unknown disturbance vector, (d/dt)
x(t)=f(x,t)+h(x,t)+B(x,t)
For a controlled object that can be expressed by u(t)+d(t), x_d(t) is the n-dimensional target vector of the state vector x(t), and e(t) is the target vector x_d(
t) and the state vector x(t), e(t)=
Let A_e be an n-dimensional error vector defined by
)e(t)=Ae・e(t), and further I as n×n
dimensional identity matrix, with 0 as an n-dimensional zero vector, {I
-B(x,t)B^+(x,t)}(-f(x,t)-
h(x,t)−d(t)+(d/dt)x_d(t)−
A_e・e(t)}=0, that is, when the number of elements n of the state vector x(t) in the controlled object and the number of elements p of the input vector u(t) are substantially equal. , w_0(t
)=h(x,t)+d(t) using the value of the known part of the control target, W(t)=(d/dt)x(t)-f
(x, t) - B(x, t) u(t) to calculate the unknown part calculation value as the unknown part calculation means, and the unknown part calculation value w(t) obtained by the unknown part calculation means and the partial unknown part estimating means for outputting a value z(t) that is equal to but not identical to as an unknown part estimated value, and using the unknown part estimated value z(t) obtained by the unknown part estimating means. and the unknown part cancellation signal of the controlled object.
unknown part cancellation signal output means for outputting z(t); and known part cancellation signal output means for outputting a known part cancellation signal -f(x, t) of the controlled object from the known characteristic vector f(x, t). and the differential vector signal (
d/dt)x_d(t); target error characteristic signal output means for outputting a target error characteristic signal -A_e・e(t); The respective signals output from the partial cancellation signal output means, the target differential signal output means, and the target error characteristic signal output means are added to produce a sum signal -z(t)-.
f(x,t))+(d/dt)x_d(t)−A_e・
e(t) and the pseudo inverse matrix B^+(x,t) of the known input distribution matrix B(x,t), the n-dimensional signal obtained by the signal addition means is The added signal is input to the p-dimensional input vector u(t).
=B^+(x,t){-z(t)-f(x,t)+(d
/dt)x_d(t)-A_e・e(t)}, and the input vector u(t) obtained by the signal converting means
An adaptive control device that controls the state vector x(t) of the controlled object. (2) The unknown part estimation means assumes that L is a positive time and calculates z
The adaptive control device according to claim 1, characterized in that the unknown portion estimating means satisfies (t)=w(t-L). (3) t is time, x(t) is n-dimensional state vector,
Let f(x, t) be an n-dimensional known characteristic vector, h(x, t
) is an n-dimensional unknown characteristic vector, B(x, t) is an nxp-dimensional known input distribution matrix in which its pseudo inverse matrix B^+(x, t) exists, u(t) is a p-dimensional input vector, d(
t) is an n-dimensional unknown disturbance vector, (d/dt)
x(t)=f(x,t)+h(x,t)+B(x,t)
For a controlled object that can be expressed by u(t) + d(t), A_m is an n×n-dimensional normative characteristic matrix, and B_m is n×
Let r(t) be a q-dimensional normative input distribution matrix and a q-dimensional normative input vector, and (d/dt)x_m(t)=A_m・
Let x_m(t) of the normative model defined by x_m(t)+B_m−r(t) be an n-dimensional normative vector, and e(t) be the relation between the normative vector x_m(t) and the state vector x(t). As the difference e(t)=x_m(t)−
An n-dimensional error vector defined by x(t), K
is an (n×n)-dimensional error feedback matrix, and the target error characteristic of the error vector e(t) is (d/dt)e
Let (t) = (A_m+K)・e(t), further let I be an n×n-dimensional unit matrix, and 0 be an n-dimensional zero vector, then {I-B
(x, t)B+(x,t)} {-f(x,t)-h(x,t)-d(t)+A_m・
x(t)+B_m・r(t)−K・e(t)}=0, that is, in the controlled object, the number of elements n of the state vector x(t) and the input vector u(t) When the number of elements p is substantially equal, w_0(t)=h(x,t)+d(t), which is the value of the unknown part of the controlled object
Using the value of the known part of the controlled object, w(t)=(d/dt)x(t)-f(x,t)-B(
x, t) u(t) as an unknown part calculation value, and the unknown part calculation value w(t) obtained by the unknown part calculation means is partially equal but identical. unknown part estimating means that outputs an unequal value z(t) as an unknown part estimated value, and canceling the unknown part of the controlled object using the unknown part estimated value z(t) obtained by the unknown part estimating means. unknown part cancellation signal output means for outputting a signal -z(t); and a known part cancellation signal -f of the controlled object from the known characteristic vector f(x, t).
(x, t), and a characteristic signal A_m·x(t)+B_m·r of the reference model.
(t), an error characteristic adjustment signal output means that outputs an error characteristic adjustment signal -K.e(t), the unknown part cancellation signal output means, and the known part cancellation signal. The respective signals outputted from the output means, the reference model characteristic signal output means, and the error characteristic adjustment signal output means are added to produce a sum signal −z(t)−f(x
,t)+A_m・x(t)+B_m・r(t)−K・e
(t) and a pseudo inverse matrix B^+(x,t) of the known input distribution matrix B(x,t), the n-dimensional Addition signal to the p-dimensional input vector u(t) u(t)=
B^+(x,t){-z(t)-f(x,t)+A_m
x(t)+B_m・r(t)−K・e(t)}, and the input vector u(
t), the state vector x(t) of the controlled object
An adaptive control device that controls the (4) The unknown part estimation means sets the gain to approximately 1 and the phase difference to approximately 0 for a predetermined frequency or frequency band of w(t), and sets the gain to be smaller than 1 for other frequency bands. The adaptive control device according to claim 1 or 3, characterized in that the adaptive control device is an unknown part estimating means that processes and obtains z(t). (5) The adaptive control device according to claim (4), wherein the predetermined frequency band is a continuous low frequency band including direct current. (6) The unknown part estimating means satisfies z(t)=w(k・L) for the time range k・L≦t<(k+1)L, where L is a positive time and k is an integer. The adaptive control device according to claim 1 or 3, characterized in that the adaptive control device is unknown portion estimating means. (7) The unknown part estimation means calculates z(t)=w((k-1)L for the time range k・L≦t<(k+1)L, where L is a positive time and k is an integer. ) Claim (1) or (3) characterized in that the unknown part estimating means is
The adaptive control device according to any one of. (8) Claim (1) characterized in that the unknown part estimating means is an unknown part estimating means in which z(t)=(1+δ)w(t), where δ is a positive value smaller than 1. or the adaptive control device according to any one of (3). (9) Claim characterized in that the unknown part estimating means is an unknown part estimating means in which z(t)=(1-δ)w(t), where δ is a positive value smaller than 1. The adaptive control device according to either 1) or (3). (10) An unknown part calculation means, a signal processing means for outputting v(t) which is partially equal to the input vector u(t) but not identically equal to the input vector u(t) in place of the unknown part estimation means, and a controlled object. w_0(t) = h(x, t
)+d(t) using the output value v(t) obtained by the signal processing means and the value of the known part of the controlled object, and calculate the unknown part estimated value z(t)=(d/dt)x (t)-
Adaptation according to any one of claims (1) or (3), characterized in that the adaptation device comprises unknown part estimating means for outputting f(x,t)−B(x,t)v(t). Control device. (11) Differential vector (d/
With dt) (d/dt)x(t) in the unknown part estimating means;
Claim (1) characterized in that the output value s(t) obtained by the second signal processing means is used instead of s(t).
0) The adaptive control device described above.