JPH07210212A - Control system - Google Patents

Abstract

(57) [Summary] [Objective] To provide a control system for rapidly stabilizing a system in a chaotic state to an arbitrary periodic state. [Structure] By extending the SOGY algorithm so that it can target any region on the chaotic attractor, it was successfully connected to the OGY algorithm for stabilization to periodic states. We also introduced nonlinear prediction to ensure the effectiveness of the SOGY algorithm. Furthermore, by considering the uncertainty of the prediction, unnecessary control was omitted and the effectiveness of the SOGY algorithm was improved.

Description

Detailed Description of the Invention

[0001]

FIELD OF THE INVENTION The present invention relates to a control system utilizing chaotic states.

[0002]

2. Description of the Related Art As a control technique utilizing a chaotic state,
Controls based on the OGY algorithm and the SOGY algorithm are included. The OGY algorithm is that when the controlled system is near an unstable periodic point on the Poincaré section in phase space, a slight perturbation is applied to the system to stabilize it at this periodic point (Reference [1] : Physical Review Letters, 64, 1196-1199 (1990); Phys. Rev.
Lett. 64, 1196-1199 (1990)). The periodic point is the point where the orbit of the system in the periodic state penetrates the Poincaré cross section. OGY
In the algorithm, the Poincare map is the control parameter p
Since it is assumed that the control parameter p is linearly dependent on, the adjustable range of the control parameter p is a finite region I _p (= [p _min , p
_max ], that is, p _min ≤p≤p _max ). As a result, in order to OGY algorithm works effectively is restriction that must be within the area I _t which is the system is imposed. On the other hand SOGY
The algorithm adds a slight perturbation to the system and rapidly shifts the system state to an arbitrary state (target) on a chaotic orbit (Reference [2]: Physical review
Letters, 65, 3215-3218 (1990); Phy. Rev. Lett., 6
5, 3215-3218 (1990)). These OGY algorithms and SOGY
It was thought that rapid control would be possible by combining algorithms (Reference [3]: Journal of Physical Chemistry 95, 4957-.
4959 (1991); J. Phys. Chem., 95, 4957-4959 (1991).
).

[0003]

However, how to combine the OGY algorithm and the SOGY algorithm has not been concretely clarified. There was also a problem in how to secure the effectiveness of the SOGY algorithm itself.

[0004]

[Means for Solving the Problems] In the original SOGY algorithm, the target is a single point in the phase space, and thus the consistency with the OGY algorithm was poor. Therefore, in the present invention, SOGY
Algorithm expands if the target is a region I _t. This allows the OGY and SOGY algorithms to be combined well.

Since the SOGY algorithm is a feedforward type control algorithm, its implementation requires information on the future of the system. If the law of mechanics is known, as in the literature, it is easily obtained. However, in reality, there are few cases where the laws of dynamics are known.
Therefore, the present invention uses a method of non-linear prediction to obtain information about the future. That is, a large amount of past output data of the system is stored and a chaotic attractor is constructed by embedding. Feature extraction is performed based on it, and the future value (future state) is estimated. Specific methods include non-parametric zero-order or first-order local approximation, parametric global or local approximation, and a neural network model. Parametric global approximation includes polynomial expansion and radial basis function expansion, and parametric local approximation includes polynomial expansion.

Due to the nature of the SOGY algorithm, it is desirable to make accurate predictions. In the commonly used time delay coordinates,
The reliability of prediction can be improved by using a distance evaluation method that takes into consideration the uncertainty included in the coordinate component. The use of such an improved prediction method will increase the effectiveness of the control itself.

[0007]

[Action] extension of the area I _t to SOGY algorithm that targets can be as follows. The state variable on the Poincaré cross section in the phase space is represented by ξ _i . i means that the Poincaré section was visited the i-th time. Parameter p
The if may freely changed in the range of I _p is the state xi] _k after k steps when the current state and xi] ₀ region I
will be in _k . Therefore, Ik
, The smallest value n such that I _t and I _k overlap
You should ask. n is

[0008]

[Equation 1]

Can be expressed as That is, the parameter whose current value is p ₀ can be adjusted within the range of I _p so that ξ _n can be within I _t . The parameter correction value δp is given as follows. The area of the parameter corresponding to the overlapping portion of I _t and I _k is obtained, and the parameter p * corresponding to the center of gravity of the area is set as the modified parameter. The correction value is obtained by δp = p * -p ₀ . It has been explained that the SOGY algorithm can be combined with the OGY algorithm by expanding it.

Next, it is shown that the reliability of the prediction can be improved by using the distance evaluation method in consideration of the uncertainty included in the coordinate component in the prediction using the time delay coordinate. In the local approximation of nonlinear prediction, we construct an attractor from past data {x _-i },
The future value x _k is estimated from the behavior of a point near the point X ₀ corresponding to the current value x ₀ . Euclidean distance is usually used. However, when the time-delayed coordinate is used, since the data at different times are used to represent the coordinate of one point, the uncertainty included in each coordinate component is different. When the point X _-i is in the d-dimensional time delay coordinate space, specifically, X _-i = (x _-i , x _-i-τ , x _-i-2τ , ....., x _{-i- ( m-1) τ} , .....,
x _{-i- (d-2) τ} , x _{-i- (d-1) τ} ). Where τ is a time delay. When the uncertainty contained in x _-i is ε ₀ , the uncertainty ε contained in x _{-i- (m-1) τ} is related to the maximum absolute value K of the Lyapunov exponent, and ε ~ ε ₀ exp [K (m-1) τ], K ~ max (| λ _j |; j = 1,2,3, ..., d). λ _j is the Lyapunov exponent. Therefore, in the distance calculation, each component is weighted by 1 / ε.

[0011]

[Equation 2]

The prediction can be made more accurate by using. We used the Euclidean norm here,
Other norms can be used, such as the maximum norm.

FIG. 1 shows an example of a prediction result using this distance evaluation formula. The chaotic time series generated by the Henon map is predicted based on nonparametric zero-order local approximation, and the correlation coefficient between the predicted value and the actual value is obtained. (a) is the case of using Euclidean distance, (b)
Is the case where the above distance evaluation formula is used. (b) d = 1
Except for the case, the variation due to the dimension d has almost disappeared. If the prediction step is 1, the correlation coefficient is (a)
Became 0.999891 (b) became 0.999965. This corresponds to an improvement in accuracy of about 3 times. Similar improvements are seen for first-order local approximations. Thus, the prediction using the above formula provides a more accurate predicted value.

[0014]

【Example】

(Example 1) An example in which the present invention is applied to a control system in alloy plating will be described. The configurations considered here are of two types: a current regulation type and a potential regulation type. In alloy plating, component ratio distribution and film thickness are given as target values. Regarding the film thickness control, the conventional control is sufficiently effective, and here, the control of the component ratio distribution will be mainly taken up. The metal ions in the plating solution deposit faster as the potential of the electrode is lower than the redox potential of itself. Therefore, when the potential changes periodically, the component ratio changes periodically in the thickness direction of the plating layer. If the potential is constant, the component ratio will also be constant. Therefore, the component ratio distribution can be controlled by controlling the potential.

(1) Current Control Type FIG. 2 shows the configuration. The controller 201 controls a current-regulating alloy plating apparatus including a galvanostat 202 and an electrolytic cell 203. The electrolytic cell 203 has a reference electrode 20 inside.
4, a working electrode 205 and a counter electrode 206 made of a component metal of an alloy. Further, the inside of the tank is filled with an electrolyte solution containing metal ions as an alloy component. The plating proceeds in such a manner that the metal of the counter electrode 206 is eluted and deposited on the working electrode 205. At this time, the current value i set by the controller 201 flows between the working electrode 205 and the counter electrode 206. Potential E = E _W -E _R relative to the reference electrode of the working electrode 205 varies with a change both of the electrode surface condition. This potential E is sent to the controller 201 via the galvanostat 202. In this example, when the potential of the working electrode oscillates chaotically, the current value i is slightly changed to obtain a desired periodic potential fluctuation. There are innumerable unstable periodic states near the chaotic state. When the one periodic state is realized as the potential of the working electrode, it forms one component ratio distribution. It is possible to know in advance what kind of component ratio distribution these unstable periodic points correspond to by analyzing the Poincare section. The control algorithm is as shown in FIG. 3 in order to speed up the transition from the chaotic state to the target periodic state.

The potential E which is the output from the controlled object 301
Is sampled and discretized in the Poincare section by the discretization means 302. Below, the discretized potential E _i is regarded as the output. The component ratio distribution is designated as the designation of the periodic points to be stabilized. Therefore, the range of potential that can be stabilized
I _t = [E _min , E _max ] is determined. Control instruction unit 303 sends a representative voltage E ⁰ and I _t object periodic point. At the current value i = i ₀ before the start of control, the potential E _i changes chaotically.
The current value i is adjusted within the range of [i ₀ -Δi, i ₀ + Δi], and the control is performed as follows.

When the potential E _i is included in I _{t according} to the determination 304, control for speeding up is not necessary, and the stabilization algorithm 305 enables the current value i to be stabilized at the target periodic point in the next step. To fix. Stabilization can be achieved by adding a correction δi proportional to the deviation of the periodic point from the typical potential E ⁰ .

If the potential E _i is not included in I _{t according} to the determination 304, prediction is performed. Change the current value i to [i ₀ -Δ
The prediction unit 306 estimates the section I _k of the potential after k steps when changing in the range of i, i ₀ + Δi]. The correction value δi is calculated by the speed-up algorithm 307.
When I _n overlaps with I _t for the first time, n is adjusted by adjusting δ _i.
It can be migrated to I _t after the step. As a result, the stabilization algorithm 305 becomes effective in the nth step, and the target periodic point can be stabilized in the next step. The OGY and SOGY algorithms are used for the stabilization and speed-up algorithms, respectively. The results of applying the present invention to Cu-Ag alloy plating will be described. Current value 1.2 in this system
At 5 mA, the potential E showed chaotic fluctuation. Current value i
Was controlled in the range of [1.2, 1.3] (mA).
For the prediction, a parametric first-order local approximation was used, and 2000 points were used for i = 1.2, 1.25, and 1.3 mA as past data. As a result, an alloy plating layer as shown in FIGS. 4 (1) to (5) could be produced. Potential E in the corresponding plating process
The variation of is shown in Fig. 5 (1) to (5). In the drawing, where the start and the end are indicated by arrows, new control commands are issued and the control targets are reached. (1) of FIG. 4 shows the case where chaos → cycle 1 (2) is chaos → cycle 2 (3) is chaos → cycle 1 → cycle 2 → cycle 1 → ... …… → cycle 2 In the figure, a, b, and c indicate that the distributions of the component ratios are different. That is, a, b, and c are distributed in the alloy layer
The proportions of Cu and Ag are different. These are shown in Figure 5, respectively.
This corresponds to the precipitation in the potential range of a, b, and c shown in (1) and (2). The shaded area in FIG. 4 corresponds to the transitional state when the chaotic state changes to the periodic state. Here, almost average component ratios were obtained. Fig. 4 (4) shows the case where the SOGY algorithm does not work under the control of chaos → cycle 1, and Fig. 4 (5) shows the control of chaos → cycle 1.
This section presents the results when prediction is performed using a distance evaluation formula that considers the uncertainty included in the coordinate components. Figure 5 (4),
(5) shows potential fluctuations corresponding to the cases of FIGS. 4 (4) and 4 (5), respectively. When the control method is changed, the time of the transient state changes, and the thickness of the shaded portion changes correspondingly. From these facts, i) it is possible to change the distribution of the component ratio by changing the period, ii) the SOGY algorithm works effectively, the part corresponding to the transient state can be reduced, and iii) the uncertainty contained in the coordinate component It was clarified that the portion corresponding to the transient state can be further reduced by making a prediction using the distance evaluation formula in consideration of the size.
Further, even if the states corresponding to the same cycle are used, it is possible to change the component ratio distribution by changing the position of the Poincare section to be controlled. The result is an almost infinite number of variations.

As described above, in the above example, the potential is directly monitored, but it is also possible to install a crystal oscillator as a sensor to monitor the frequency. The configuration in that case is as shown in FIG. The crystal oscillator sensor 61 is designed so that the electric potential of the electrode attached to the sensor surface becomes equal to that of the working electrode 205. The difference from the case of FIG. 2 is that the frequency f 62 is monitored instead of the electric potential E. Since the frequency of the crystal oscillator depends on the mass of the deposited metal, its time change directly reflects the composition ratio of the alloy. Therefore the potential E
Has the same effect as monitoring. Furthermore, if the composition ratio distribution of the alloy deposited on the surface of the working electrode deviates from the ideal composition ratio distribution estimated from the potential E, this system that can directly monitor the metal deposited on the electrode surface is excellent. ing.

The film thickness is controlled so that the amount of electricity flowing is monitored and the plating is completed when the target value is reached.
When forming a multilayer film of alloy plating, for example, the operator is allowed to specify the total film thickness and the finishing type as shown in FIG. 4, and the periodic state and film thickness corresponding to the component ratio distribution to be formed by the microcomputer are set. The sequence shall be automatically generated. Since this is the same as the conventional method,
The description is omitted.

(2) Potential regulation type In the potential regulation type, the potential is directly controlled. The configuration is shown in FIG. The chaotic potential changes in the chaos generator 71.
Caused by. The chaos generator 71 may be hardware such as an electronic circuit or software. Here, a chaotic train is generated by the map E _i = p E _i-1 [1-E _i-1 ], and the result of scale conversion according to the metal deposition potential range is newly set as Ei and sent to the potentiostat 72. This value is held until the next E _{i + 1} is sent. During this time, the electric potential E based on the reference electrode of the working electrode is also held at E _i . This E _i corresponds to the electric potential E _i discretized in the Poincare section of FIG. p is the control parameter 73. Therefore, the controlled object is the chaos generator. p =
Chaos was generated at 3.87 and parameters were adjusted at I _p = [3.84, 3.89]. The control algorithm is the same as in FIG. However, in this example, since the mapping which is the dynamic law of the system is known, this mapping can be used as the prediction means 306. Further, since the chaos generator generates a discretized chaos sequence, the discretizing means 302 is omitted. For example,
By stabilizing the cycle 1 state (fixed point), a plating layer having a uniform component ratio is formed in the film thickness direction. The film thickness is controlled by monitoring the integrated value of the current I74.

FIG. 8 shows the result when a Cu-Ag alloy plating layer was produced by controlling the period to 4 states. FIG. 8 (1) is a schematic diagram of the produced plating layer structure. The shaded area corresponds to the transient state when transitioning from the chaotic state to the periodic state. In fact, it was so negligible. Figure 8 (2) shows the variation of the discretized potential Ei. The time interval of occurrence of chaotic sequences was 5 seconds. Different component ratios (d, e, f, g
) Are alternately stacked. In the figure, each point corresponds to one discretized potential. In the cycle 4 state, the dots are closely arranged, so that the dots cannot be distinguished from each other. The arrow in the figure indicates the point at which control is started. The point of reaching the target is the beginning of the cycle 4 state and is clear.

In this example as well, it is possible to monitor the frequency by directly installing a crystal oscillator as a sensor instead of directly monitoring the potential. The configuration in that case is as shown in FIG. This case is the same as the case of the current regulation type (FIG. 6).
The control algorithm is also the same as in FIG. However, as in the case of FIG. 7, the discretization means 302 is omitted. Here, the prediction was performed using a neural network, and the effectiveness was confirmed. Specifically, we used a 4-4-1 type neural network and learned by backpropagation.
The past data used are three parameter values p = 3.84,3.
There are 2000 points for 87 and 3.89 respectively. In the potential regulation type example, the case where the chaos generator 71 generates a discrete chaos sequence is taken up. Of course, the same can be done when a continuous chaotic sequence is generated. However, in that case, the discretization means 302 cannot be omitted in the control algorithm (FIG. 3).

(Embodiment 2) The present invention will be described by taking a control system in the thin film production of multi-component materials as an example. FIG. 10 shows an example in which the present invention is applied to a multilayer film manufacturing apparatus by vapor deposition of binary materials. The opening / closing time of the shutter of the vapor deposition source is determined according to the chaotic sequence T _i 101 generated by the chaos generator 71. In this example, when shutter A 102 is open, shutter B 103 is closed, and vice versa.
Shutter A is closed when B is open. In this way, raw material A 104 and raw material B 10
Deposition of No. 5 on the substrate 106 is controlled. The control target is the film thickness of each layer. In the chaos row T _i, the odd number represents the time when the shutter A is open, and the even number represents the time when the shutter A is closed. Therefore, in order to fabricate a multilayer film having a periodic structure in a binary system, it is necessary to utilize a high periodic state of period 2 or more. The chaos generator 71 is controlled. A film thickness meter 107 provided near the substrate 106
The film thickness t _i 108, which is the output from, is monitored. The control algorithm is the same as in FIG. 3 here. The change in film thickness t _i Δt _i (＝ t _i −t) corresponds to the discretized potential E _i.
i-1 ). Therefore, the discretizing means 302 is omitted.

FIG. 11 shows the results when applied to an Au—Ag system multilayer film. Au and Ag were alternately laminated by using the stabilization from chaos to cycle 4 state. The structure of the multilayer film in that case,
The shutter open / close sequence is shown in Fig. 10 (1) and (2) respectively.
Shown in. A periodic structure is obtained.

(Embodiment 3) FIG. 12 shows an example in which the present invention is applied to a control system in a cardiac pacemaker. In this pacemaker, a chaos generator 71 is used as an oscillator.
Is equipped with. The chaos generator 71 is composed of chaotic elements. Examples of chaotic elements are described in "Chaos" Science Co. (1990) edited by Kazuyuki Aihara. Here again, control from the chaotic state to the periodic state is used. A high heart rate condition is used to maintain a resting heart rate, for example, a cycle 15 condition,
If you use 0 to 14 states, it will be 6 with a slight parameter change.
It is possible to control the heart rate in stages. If you set 60 times / minute at rest, you can set up to 90 times / minute in 6 steps (60, 6
5, 69, 75, 82, 90). The chaotic sequence generated by the chaotic generator 71 at regular time intervals is controlled, and a pulse is output in accordance with the largest value in a certain periodic state. For example,
In the period 15 state, it takes 15 discrete values, but a signal is sent to the oscillator 121 in accordance with the maximum value, and the oscillator 121 generates a pulse at that timing. The pulse acts as a cardiac pacemaker.

It is already known that the heart rate variability of healthy humans without heart disease is chaotic. If an oscillating element that reproduces this chaos is used, it becomes a pacemaker that has natural fluctuations even in a control-off state or in a transient state when switching paces. It is also possible to construct an autonomous pacemaker by combining it with sensing of the amount of sweat, the oxygen concentration in blood, and the like.

It has been described above that the control system of the present invention functions effectively in some typical embodiments. However, in the SOGY algorithm, the effectiveness of the algorithm may not be guaranteed if the above n becomes large. This is probably due to the prediction error. SO
Regarding how to secure the effectiveness of the GY algorithm itself, in addition to the improvement of the prediction method described above, there are several solutions as below, and it was confirmed that any of them is effective.

1) A limit value of n is set, and when it exceeds the limit value, the parameter is set to the current value (nominal value), and the control is continued with n = 1.

[0030] 2) Alternatively It of each step k the estimated uncertainty of the prediction Δ a _{(k) I t (= [} E min, E max]) (k)
(= [E _min + Δ (k), E _max -Δ (k)]) is used to activate the SOGY algorithm. As a result, if I _t (k) ~ empty set, the parameter is set to the current value (nominal value) and control is continued with n = 1.

3) Make Ip wide so that n does not become large. But at this time, the linearity of the map F with respect to p may be lost. Although the OGY algorithm assumes linearity of the map F with respect to p,
The algorithm can be extended if the map F is one-dimensional. That is, solve a linear equation for p (references)
[3]) Instead, solve higher order equations. No changes are required in the SOGY algorithm part.

[0032]

As described above, the control system of the present invention can quickly and accurately make a transition from the chaotic state to various periodic states and maintain the state in a stable manner.

[Brief description of drawings]

1A and 1B are diagrams showing prediction results when a distance evaluation formula considering uncertainty included in a coordinate component is used.

FIG. 2 is a configuration diagram of a current-regulating alloy plating system when monitoring a working electrode potential.

3 is a block diagram showing the contents of control in the system of FIG.

FIG. 4 is a formula diagram showing a cross section of the produced alloy plating layer.

FIG. 5 is a diagram showing corresponding potential fluctuations when the alloy plated layer of FIG. 3 is produced.

FIG. 6 is a configuration diagram of a current-regulating alloy plating system when monitoring a signal from a crystal oscillator.

FIG. 7 is a block diagram of a potential-regulating alloy plating system for monitoring the working electrode potential.

FIG. 8 is a schematic diagram showing a cross section of the produced alloy plating layer and a diagram showing potential fluctuations at the time of producing the corresponding plating layer.

FIG. 9 is a configuration diagram of a potential-regulating alloy plating system when monitoring a signal from a crystal oscillator.

FIG. 10 is a configuration diagram of a control system for a multilayer film manufacturing apparatus by vapor deposition of binary materials.

FIG. 11 is a schematic diagram showing a structure of a manufactured multilayer film and a diagram showing an opening / closing sequence of a shutter.

FIG. 12 shows a block diagram of a pacemaker.

[Simple explanation of symbols]

201 ... Controller, 202 ... Galvanostat, 2
03 ... Electrolyzer, 204 ... Reference electrode R, 205 ... Working electrode W,
206 ... Counter electrode C, 207 ... Current value i, 208 ... Reference electrode potential ER, 209 ... Working electrode potential EW, 210 ... Working electrode potential E (= EW-ER) based on the reference electrode potential, 301 ... Control object, 302 ... Discretizing means using Poincare section, 3
03 ... Control command device, 304 ... Judgment step, 305 ...
Periodic point stabilization algorithm, 306 ... Prediction means, 30
7 ... Algorithm for speeding up, 61 ... Crystal oscillator sensor
S, 62 ... Frequency f, 71 ... Chaos generator, 72
… Potentiostat, 73… Control parameter p, 74
… Current value I, 101… Chaotic train Ti, 102… Shutter
A, 103 ... Shutter B, 104 ... Raw material A, 105 ... Raw material B, 106 ... Substrate, 107 ... Thickness gauge, 108 ... Thickness t
i, change in film thickness Δt _i .

 ─────────────────────────────────────────────────── ─── Continuation of the front page (72) Inventor Masami Naito 2520 Akanuma, Hatoyama-cho, Hiki-gun, Saitama Stock Company Hitachi Research Laboratories (72) Inventor Hiroshi Okamoto 2520 Akanuma, Hatoyama-cho, Hiki-gun, Saitama Prefecture Stock Company Hitachi Research Laboratory (72) Inventor Shinichiro Umemura 2520 Akanuma, Hatoyama-cho, Hiki-gun, Saitama Stock Company Hitachi Research Laboratory (72) Inventor Hiroaki Okuhira 292 Yoshida-cho, Totsuka-ku, Yokohama, Kanagawa Stock company Hitachi Manufacturing Technology Institute

Claims (8)

[Claims] 1. An algorithm for stabilizing a transition target from a chaotic state to a periodic state, which has a part for performing a chaotic time series prediction operation, and an algorithm for quickly achieving stabilization. A control system comprising: 2. The speed-up algorithm quickly transfers the controlled object to a state in which the stabilization algorithm effectively operates by feed word control based on a time-series prediction result. The control system according to claim 1. 3. The control system according to claim 1, wherein the algorithm in the chaotic time series prediction unit is based on nonparametric zero-order or first-order local approximation. 4. The control system according to claim 1, wherein the algorithm in the chaotic time series prediction unit is based on parametric global or local approximation. 5. The control system according to claim 1 or 2, wherein the algorithm in the chaotic time series prediction unit is based on a neural network model. 6. When the algorithm in the chaotic time series prediction unit is based on non-parametric zero-order or first-order local approximation using time-delayed coordinates, distance evaluation is performed in consideration of uncertainty included in coordinate components. The control system according to claim 1 or 2, characterized in that. 7. When the algorithm in the chaotic time series prediction unit is based on a parametric 0th-order or 1st-order local approximation using time-delayed coordinates, distance evaluation considering uncertainty included in coordinate components is performed. The control system according to claim 1 or 2, which is characterized. 8. The control system according to claim 1, wherein the operation amount is given in consideration of the prediction error of the chaotic time series prediction.