JPH0612103A - Learning control device - Google Patents

Abstract

PURPOSE:To obtain a learning device which controls a centrolled system of which an input/output relation is difficult to be preliminarily and exactly recognized, using a normal model predicting the input/output relation, is capable of controlling also the controlled system having the characteristic which is impossible to be controlled by a conventional normal control and is further capable of reducing the number of times of control till the output value of the controlled system is converged to a target value. CONSTITUTION:This learning control device is provided with an output detection means 102 detecting the output for a controlled system 100, a target value output means 104 outputting the target value of the output, an error output means 106 calculating the error of the target value and the output and outputting it, a change width determination means 107 setting gain according to the characteristic of the object to be controlled 100, and an input change determination means 108 operating an input increment, using the set gain and outputting it. Further, by providing an input update means 110 determining a new input using the obtained input increment and the input of the previous time, the output of the controlled system 100 is controlled so that it may coincide with the target value.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a learning control device for controlling a control target, such as a copying machine or a chemical plant, in which it is difficult to accurately grasp the input / output relationship in advance.

[0002]

2. Description of the Related Art First, as a conventional example, Japanese Patent Application No. Hei 2-202.
The learning control device 180 will be briefly described. FIG. 8 is a perspective view showing a main part of a copying machine having an analog electrophotographic process, which is taken as an example of a control target for explaining a basic learning control device. Figure 8
801 is a photoconductor, 802 is a charger, 803 is an exposure lamp, 804 is a developing unit, 806 is a copy document, and 80
7 is the first reference concentration plate (concentration = DIN.H), 808 is the second reference concentration plate (concentration = DIN.L, where DIN.H> DI)
N and L. ) And 809 are the first toner image (image density = D) on the first reference density plate 807 on the photoconductor 801.
OUT · H), 810 is a second toner image (image density = DOUT · D) on the second reference density plate 808 on the photoconductor 801.
L), 811 is a copying machine having an electrophotographic process composed of the above-mentioned elements, and 812 is a density sensor.

Next, the operation of the electrophotographic process thus constructed will be described. First, by inputting the charger voltage u2 to the charger 802, the surface of the photoconductor 801 is charged to the initial potential corresponding to u2. Next, the exposure lamp 803 irradiates the copy original 806, the first reference density plate 807, and the second reference density plate 808 with light according to the exposure lamp voltage u1. This light is imaged on the photoconductor 801, and the surface potential of the photoconductor 801 which was uniform before exposure is attenuated by receiving light energy corresponding to each density, and the potential distribution on the photoconductor 801 is reduced. To form an electrostatic latent image. Further, by the developing device 804 set to the developing bias voltage u3, a toner amount corresponding to the surface potential of the photoconductor 801 adheres to the surface of the photoconductor 801 to form the first toner image 809 and the second toner image 810. Form.

The quantitative relationship in the above explanation of operation is
It is expressed by the following equation.

[0005]

[Equation 10]

Here, DIN corresponds to the input image density (DIN.H or DIN.L), DOUT corresponds to the output image density on the photoconductor 801 (DOUT.H or DOUT.L), and E corresponds to the input image density DIN. Light energy, V is the surface potential on the photoconductor 801 attenuated by the light energy E, p1 is a positive parameter determined by the characteristics of the exposure lamp 803, p
2 is a positive parameter determined by the natural discharge characteristics of the photoconductor 801, p3 is a positive parameter determined by the sensitivity of the photoconductor 801 and the transmittance of the optical system, and p4 is the developing unit 80.
5 is a positive parameter determined by the toner density of 5 and the dielectric constant of the photoconductor 801.

The relationship between the input density DIN and the output density DOUT determined by [Equation 10] generally has a characteristic curve as shown in FIG. That is, FIG. 9 is a graph showing the relationship between the input image density and the output image density in the copying machine shown in FIG. Now, in order to simply express this characteristic curve, consider two outputs y1 and y2 expressed by the following equations.

[0008]

[Equation 11]

Here, y1 represents the midpoint in the straight line portion of the characteristic curve of FIG. 9, and y2 represents the slope of the straight line portion. As described above, the parameters p1 to p4 depend on various characteristics of the copying machine 811 and also vary depending on the temperature and humidity of the environment, so that it is actually extremely difficult to accurately obtain them. Therefore, for the purpose of control, the output y1 is set to the target intermediate density yd1 and the output y2 is set.
To match the target concentration gradient yd2. Then, as shown in the following [Equation 12], yd1 and yd2 are the target density DT.H for the density DIN.H of the first reference density plate 807 and the density DIN.L of the second reference density plate 808, respectively. Can be calculated from the target concentration DT.

[0010]

[Equation 12]

FIG. 7 is a block diagram showing the structure of a basic learning control device. In FIG. 7, 700 is a control target (that is, the copying machine 811 shown in FIG. 8), 702 is output detection means, 704 is target value output means, 706 is error output means, 708 is input change determination means, and 710 is Input updating means, 712 is a qualitative model correcting means, 714 is an input applying means, 716 is an output code detecting circuit, and 718 is an error code detecting circuit.

The operation of this learning control device is as follows. First, the output from the controlled object 700 is Y = (y1, y
2) is detected by the output detection means 702. Then, the output detected by the output detecting means 702 is Y = (y1, y
2) and the target value Yd output from the target value output means 704.
= (Yd1, yd2) and the error output means 706
Outputs the error e = Yd−Y. Then, the error code output circuit 718 detects the code [e] of the output error e. Here, the code [e] has data representing any one of "+", "-", and "0". That is, the code [e] has information on whether to increase or decrease the output Y in order to bring the output Y closer to the target value Yd, or to hold the current value. Further, the output code detection circuit 716 uses the output Y output from the output detection means 702 to output the sign [ΔY] of the change direction of the output (however, the change direction of the output is the output actually generated as a result of control. It is a qualitative value of change and its sign is
The fixed direction is defined as positive or negative) is detected and output.

Next, the input change determining means 708 will be described. First, the input change determining means 708 first determines all input changes ΔUi (specifically, [ΔU1] = (+, 0, −)).
And [ΔU2] = (+, 0, −) all combination patterns), as a qualitative value of the prediction output,

[0014]

[Equation 13]

(Note that the hat "^" above a character represents the predicted data of the data represented by that character).
Then, the prediction output is expressed as a vector using the signs of "+", "-", "0", and "?" As in [Equation 13] = (+,-). Then, the sign of the change direction of the output is represented by each sign such as "+" for the increase prediction, "-" for the decrease prediction, "0" for no change, and "?" For unpredictable.

Next, the input change determining means 708 selects one predicted output from the predicted outputs, the sign of which matches the sign [e] of the error value output from the error code detection circuit 718. . Further, input change determining means 708
Outputs the input change ΔUi corresponding to the selected prediction output. Therefore, the input update unit 710 performs an addition operation on the input change ΔUi output from the input change determination unit 708 and the current input U, and outputs the updated new input U.

Further, the qualitative model correction means 712 has a prediction output [Equation 1] output from the input change determination means 708.
3], the exposure lamp voltage u1 which is the output from the input applying unit 714, and the code change [ΔY] that represents the change direction of the output from the output code detection circuit 716. Here, the code change [ΔY] output from the output code detection circuit 716 and the predicted output [Equation 1] output from the input change determining means 708.
3] are compared, and if they are not equal, the corrected output Q (a boundary parameter described later) is input to the input change determination means 708 as described later.

As described above, the qualitative model correction means 712 corrects the qualitative model (a model used to obtain a predicted output, the details of which will be described later), and the input change determination means 708 corrects the qualitative model. An input change ΔUi for outputting a prediction output that matches the code [e] output from the error code detection circuit 718 is selected. The input update means 710 then selects the selected input change ΔUi.
To obtain a new input U. Therefore, the control target 7 is
The input U actually obtained is applied to 00. The above operation is repeated until the output Y matches the target value Yd.

Next, the qualitative model in the input change determining means 708 used for obtaining the predicted outputs [Equation 13] for all the input changes ΔUi, and the qualitative model correcting means 712 for correcting this qualitative model will be described in more detail. explain. Generally, control based on qualitative inference is performed as control of a copying machine having an analog electrophotographic process. That is, when you move the operating parameters,
The control is performed by extracting a qualitative causal relationship in which direction the output moves. Now, change the operation parameter U to u
_{If 1} (exposure lamp voltage), u ₂ (charger voltage), and output parameters Y are y ₁ and y ₂ (see [Equation 11]), the following equation can be obtained from [Equation 10].

[0020]

[Equation 14]

Here, in order to extract the qualitative causal relationship between the operation parameter U and the output parameter Y, the above equation is u ₁ ,
Partial differentiation with u ₂

[0022]

[Equation 15]

In the above equation, the underlined portion is zero or more due to the characteristics of the photoconductor, so ∂y ₁ /
∂u ₁ ≦ 0, that is, if u ₁ increases, y ₁ will decrease. Also,

[0024]

[Equation 16]

Since DIN · L <DIN · H, 1
0- ^{DIN ・ L-} 10- ^{DIN ・ H} > 0, and ∂y ₁ / ∂u
_{If 2} ≧ 0, that is, if u ₂ increases, y ₁ will increase. This relationship can be expressed by the following equation.

[0026]

[Equation 17]

On the other hand,

[0028]

[Equation 18]

In addition,

[0030]

[Formula 19]

Here, 10 ^{−DIN · L} + 10 ^{−DIN · H} ≧
Since it is 0, ∂y ₂ / ∂u ₂ ≧ 0, and if u ₂ increases, y ₂ increases. Further, in [Equation 18], if {}> 0, ∂y ₂ / ∂u ₁ > 0, and if u ₁ increases, y ₂ increases. Therefore, these relationships can be expressed by the following equation.

[0032]

[Equation 20]

When {} = 0, ∂y ₂ / ∂u
₁ = 0, and y ₂ does not change even if u ₁ increases. Therefore, these relationships can be expressed by the following equation.

[0034]

[Equation 21]

When {} <0, ∂y ₂ / ∂u
₁ <0, and if u ₁ increases, y ₂ decreases. Therefore, these relationships can be expressed by the following equation.

[0036]

[Equation 22]

When the above results are summarized, the predicted output

[0038]

[Equation 23]

And input [ΔU] = ([Δu1], [Δu]
2]) is obtained by the following equation.

[0040]

[Equation 24]

Here, Q is a boundary parameter represented by the following equation.

[0042]

[Equation 25]

That is, Q is a solution for u _{1 with} {} = 0 in the equation for finding ∂y ₂ / ∂u ₁ .
Further, Table 1 shows a summary of the contents of [Equation 24], which is a qualitative model for controlling a copying machine having an analog electrophotographic process. That is,
This model shows a qualitative relationship between input and output.

[0044]

[Table 1]

Next, the control operation using the qualitative model will be described according to [Table 1]. As shown in [Table 1], the difference between the input value u1 given to the copying machine and the boundary parameter Q It is divided into three areas (1) to (3). [U1-Q]
= (+) Area (1 It has become.

[0046]

[Equation 26]

Similarly, regarding the areas (2) and (3),
It is possible to specify the increase or decrease of the output using the above calculation rule. 2] = −, [Δu1] = −, [Δu1]
By setting u2] = 0 It becomes possible by controlling.

However, as described above, the parameter p
Since 1, p2, and p3 are difficult to measure and cannot be predicted, the boundary parameter Q including them cannot be predicted accurately, and the prediction in [Table 1] is correct. Not exclusively. Therefore, when this prediction is incorrect, the actual output code [ΔY] and the predicted output [Equation 13] detected by the output code detection circuit 716 are calculated.
Will not match. In such a case, it is determined that the qualitative model is not appropriate, and the qualitative model correction means 712 changes the boundary parameter Q of the qualitative model. Then, the area of the qualitative model in the input change determining means 708 is changed.

For example, the actual input to the copying machine is Ui =
If (u1, u2) = (75v, 700v) and the value of the boundary parameter Q is Q = 70v,

[0050]

[Equation 27]

Therefore, the area (1) in [Table 1]
Is selected. At this time, for example, the following data is input as the input change ΔUi.

[0052]

[Equation 28]

In this case, the predicted output [Equation 13] is (+,
+). Next, in the copying machine to which the above-mentioned input change ΔUi is given, when the output code [ΔY] becomes (+, −) after the end of the process operation, it is expected that the area selection is wrong. To be done. Therefore, in [Table 1], the area where the predicted output [Equation 13] is (+,-) is searched for. As a result, it can be seen that the matching area is (3). Therefore, a boundary parameter Q that fits the boundary function of the region (3) is obtained. That is,

[0054]

[Equation 29]

To satisfy the above equation, the value of Q'can be set as follows.

[0056]

[Equation 30]

However, "ε" is a positive real number. Here, when the predicted output [Equation 13] and the output code [ΔY] match, the boundary parameter Q is not modified.

[0058]

By the way, in the above learning control device, the qualitative model of the controlled object 700 in the above-mentioned region (3) is as follows.

[0059]

[Equation 31]

In this case, as described above, the outputs y1 and y
Since qualitative models of 2 are different, it is possible to control y1 and y2 independently. However, in the area (1), the qualitative model is as follows.

[0061]

[Equation 32]

In this case, since the qualitative models of the outputs y1 and y2 are the same, when using a qualitative control law (that is, a procedure in which error detection is added to the qualitative model and the error is reduced to 0). Moreover, it is impossible to control y1 and y2 independently, for example, increasing y1 and decreasing y2. Here, in the analog copying machine as in the conventional example, it is confirmed that almost the area (3) is taken as such a qualitative model, so it is not necessary to consider the qualitative model in the area (1). A problem arises that the conventional control law cannot deal with the control target that takes only the area (1).

Further, in the conventional example, there is no specific setting standard for the change width of the input ΔUi, and it is necessary to make the input change width very small in order to prevent oscillation. Therefore, there is a problem that the number of times until the output Y converges to the target value Yd becomes large. That is, according to the conventional qualitative control law, although results such as [Δu1] = + and [Δu2] = 0 can be obtained, specifically, to what extent u1 should be increased Can't get the instructions. Therefore, when the input change width is small, the change in the output per one time becomes small, and the control operation must be repeated many times before the target value is reached. On the contrary, the input change width is too large. In this case, the target value will be exceeded too much, causing divergence and vibration.

The present invention has been made in order to solve the above problem, and controls a control target whose input / output relationship is difficult to be accurately grasped by using a qualitative model predicting the input / output relationship. In addition to the above, it also enables control of a control target that has characteristics that could not be controlled by conventional qualitative control, and the number of control times until the output value of the control target converges to the target value. It is an object of the present invention to provide a learning control device capable of reducing the number of times.

[0065]

In order to achieve the above object, the learning control device according to the present invention inputs inputs u1 and u.
2. Output is represented by y1 and y2, and the static characteristics are

[0066]

[Expression 33]

Output detecting means for detecting the output of the controlled object represented by and obtaining detection values y1 and y2;
The target value output means for outputting the output target values yd1 and yd2 and the error between the target values yd1 and yd2 and the detected values y1 and y2 are calculated by the following equation.

[0068]

[Equation 34]

Error output means for calculating and outputting by:
When k1, k2, k3, and k4 are constants that give a gain, and the characteristic of the controlled object is always a · d−b · c> 0, the following equation

[0070]

[Equation 35]

When k1 and k4 satisfying the condition of are set and the characteristic of the controlled object is always a.db.cc <0,

[0072]

[Equation 36]

The change width determining means for setting k2 and k3 satisfying the condition of (3) and the characteristic of the controlled object are always a · d−b.
When c> 0, the input increase is calculated by the following equation using the error output from the error output means and the gain output from the change width determining means.

[0074]

[Equation 37]

When the characteristic of the controlled object is always a.db.c <0, the error output from the error output means and the gain output from the change width determining means are used. , Input increment is

[0076]

[Equation 38]

By using the input change determining means calculated by the above, the input increment obtained from the input change determining means and the previous input,

[0078]

[Formula 39]

The input updating means for obtaining a new input by means of and the input applying means for applying the new input outputted from the input updating means to the controlled object are provided, and the outputs y1 and y2 of the controlled object are set to target values. The feature is that control is performed so as to match yd1 and yd2. Further, in the learning control device according to the present invention, when the inputs are represented by u1 and u2 and the outputs are represented by y1 and y2, the static characteristic is
[3] output control means for detecting the output of the controlled object, target value output means for outputting the target value of the output, and detected value y of the output detection means.
1, y2 and the target value y output from the target value output means
While the error output means for calculating and outputting the error between d1 and yd2 by [Formula 34] is provided, the sign of a, d, b, and c as the characteristic of the controlled object is output from the output detection means. When the output or the history value thereof, the characteristic determining means for determining using the input or the history value thereof, and k1, k2, k3, or k4 are constants giving a gain, the output of the characteristic determining means is When positive, k1 and k4 that satisfy the condition of [Equation 35] are set, and when the output of the characteristic determining means is negative, [Equation 3]
[6] The change width determining means for setting k2 and k3 that satisfy the condition [6], and the output from the error output means and the change width determining means when the output of the characteristic determining means is positive. Using the gain, the input increment is calculated by
7], the input increase is calculated by using the error output from the error output means and the gain output from the change width determining means when the output of the characteristic determining means is negative. ] Input change deciding means which calculates and obtains, input update means which obtains a new input by said [Equation 39] using the input increment obtained from said input change deciding means, and said input, and said input update means Input control means for applying a new input output from the control target to the control target, and controlling the outputs y1 and y2 of the control target to match the target values yd1 and yd2.

Further, the learning control device according to the present invention is k
When 1, k2, k3, and k4 are constants that give a gain, the change width determining means is

[0081]

[Formula 40]

K1, k2, k3, k4 satisfying the condition of
And the input change determining means uses the error output from the error output means and the gain output from the change width determining means to calculate the input increment by the following equation:

[0083]

[Formula 41]

It is characterized in that it is calculated and calculated by. Further, the learning control device according to the present invention is provided with k1, k
When 2, k3, and k4 are constants that give a gain, the variation width determining unit satisfies k that satisfies the condition of [Equation 40].
At least one of 1, k2, k3, and k4 is set for each case where the signs of a, d, b, and c are positive and negative, and gains k1 to k4 are given from the output value of the characteristic judging means. The input change determination means uses the error output from the error output means and the gain output from the change width determination means to calculate the input increase amount as described in [Equation 4].
1] is used for the calculation.

[0085]

According to the above construction, the inputs are represented by u1 and u2, the outputs are represented by y1 and y2, and the static characteristics are as follows.

[0086]

[Equation 42]

The outputs y1, y of the controlled object represented by
2 is detected by the output detection means. Moreover, the target value output means outputs the target values yd1 and yd2 of the output. Furthermore, the error output means is

[0088]

[Equation 43]

The error is calculated and output by. Then k
When 1, k2, k3, and k4 are constants that give a gain, and the characteristic of the controlled object is always a · d−b · c> 0, the change width determining unit determines

[0090]

[Equation 44]

K1 and k4 satisfying the condition of are set.
In addition, when the characteristics of the controlled object are always a · d−b · c <0,

[0092]

[Equation 45]

K2 and k3 satisfying the condition of are set.
In addition, when the characteristic of the controlled object is always a · d−b · c> 0, the input change determining unit uses the error output from the error output unit and the gain output from the change width determining unit. , Input increment

[0094]

[Equation 46]

It is calculated by Similarly, when the characteristic of the controlled object is always a · d−b · c <0, the input change determining means uses the error output from the error output means and the gain output from the change width determining means. , Input increment

[0096]

[Equation 47]

Calculated and calculated by Therefore, the input updating unit obtains a new input by using the input increment obtained from the input changing unit and the previous input. Subsequently, the input applying unit applies the new input thus obtained to the control target.
Further, according to the present invention, the characteristic determining means determines at least the sign of a, d, b, and c as the characteristic of the controlled object from the output and its history value output from the output detecting means and the input and its history value. Use one to judge.

In the present invention, k1, k2, k3, k4
Is a constant that gives a gain,
The following formula

[0099]

[Equation 48]

K1, k2, k3, k4 satisfying the condition of
To set. In addition, the input change determining means uses the error output from the error output means and the gain output from the change width determining means to determine the input increment.

[0101]

[Equation 49]

Calculated and calculated by In the present invention,
When the change width determining means sets k1, k2, k3, and k4 to constants that give a gain, k that satisfies the condition of [Equation 48]
At least one or more of 1, k2, k3, and k4 are set respectively when the signs of a, d, b, and c are positive and negative, and gains k1 to k4 are given from the output value of the characteristic judging means.
Then, the input change determining means calculates and obtains the input increase amount by using the error output from the error output means and the gain output from the change width determining means by [Equation 49].

As a result, when the qualitative models of the outputs y1 and y2 are the same, the characteristic of the controlled object is a.d-
When b · c> 0, it is impossible to control by the conventional qualitative control, but by providing an input change determining means for connecting each input and each error as in [Equation 46], It is possible to control each output independently. Furthermore, gains k1, k4 or k satisfying the stability condition
By providing the change width determining means for setting the set of 2 and k3, the optimum gain can be used for the controlled object, and the number of times the output is converged to the target value can be reduced.

Further, by providing the characteristic judging means for judging the characteristic of the controlled object, it is possible to appropriately select an appropriate gain in the case where the characteristic of a, d, b, and c is not constant and the characteristic is largely changed. Is possible. Further, the number of gains to be used is increased, and the gains k1 and k satisfying the stability condition are satisfied.
By providing the change width determining means for setting at least one of 2, k3, and k4, it becomes possible to perform control in accordance with the state of the controlled object. Further, by providing the input change determining means for calculating the input increment by using the two output errors and the respective two gains corresponding thereto, the input increment can be more appropriately calculated, and the number of convergences can be further increased. Can be reduced.

Further, by combining the change width determining means in which the number of gains used is increased, the input change determining means using the gains, and the characteristic determining means for determining the characteristic of the controlled object, the controlled object whose characteristic largely fluctuates. Even with respect to the above, it is possible to select an appropriate gain and perform control in accordance with the state of the control target, and it is possible to further reduce the number of times of convergence.

[0106]

First, the concept will be described so that the structure of the present embodiment can be easily understood. That is, consider the qualitative model in the area (1) of the conventional example expressed as follows.

[0107]

[Equation 50]

In the above equation, if u1 → -u1 is set and the influence of each input on each output is set as a, b, c, d> 0, the static relationship of the controlled object is expressed by the following equation.

[0109]

[Equation 51]

The above equation is expressed by the following equation when expressed using a matrix.

[0111]

[Equation 52]

Here, A represents the following matrix.

[0113]

[Equation 53]

Further, U = [u1, u2] ^T is an input, Y =
[Y1, y2] ^T is the output, and a, b, c, d are the characteristics of the controlled object that fluctuates. Furthermore, Yd = [yd1, yd
2] If ^T is a constant target value of output, output error e = [e
1, e2] ^T is given by the following equation.

[0115]

[Equation 54]

Next, the control law is expressed by the following equation.

[0117]

[Equation 55]

Here, Φ represents the following matrix.

[0119]

[Equation 56]

It should be noted that (i) and (i-1) represent the present and previous values, respectively. Then, each relationship can be expressed as follows using the shift operator z.

[0121]

[Equation 57]

The shift operator Z delays the output once in the digital circuit. That is, the following equation A = y
A represented by (i) + y (i-1) can be represented as A = (1 + Z- ¹ ) y (i) in the format by using the shift operator Z. Further, Z ⁻¹ can be configured with a delay element. [Equation 52], [Equation 55],
If [Formula 57] is rearranged,

[0123]

[Equation 58]

[0124] In contrast to the above equation, Jury's stability determination method, which is a stability determination condition in a discrete control system (when the output to be controlled is to be converged to a certain target value, the conditions for stable convergence are derived as mathematical expressions. Is used, the condition of [Equation 48] is obtained. Here, in [Equation 48], if a · d−b · c> 0 is set, k1 = k4 = 0 is set, and transformation is performed using sufficient conditions so as to simplify the equation, [Equation 44] is obtained. . Similarly, a
If k2 = k3 = 0 is set in the case of d−b · c> 0 and transformation is performed using sufficient conditions so as to simplify the equation, [Equation 4]
5] is obtained. In this way, by setting the gains that satisfy the above conditions in accordance with the characteristics of the controlled object, the control system can be operated stably.

An embodiment of the learning control device according to the present invention will be specifically described below with reference to the drawings. FIG. 2 is a perspective view showing a main part of a copying machine having a digital exposure type electrophotographic process, which is taken as an example of a control target of the learning control device according to the present invention. In FIG. 2, 201
Is a photoconductor, 202 is a charger, 203 is exposure means, and 204
Is a developing device, 205 is an image signal inputting means, 209 is a first toner image (image density = DOUT.M) on the photoconductor 201 for the first input reference density, and 210 is a photoconductor for the second input reference density. A second toner image (image density = DOUT.L) on 201, a copying machine 211 having an electrophotographic process composed of the above-mentioned elements, and a density sensor 212. However, the first input reference concentration is
M, the second input reference concentration is DIN · L, DIN · M> D
Suppose IN and L.

Next, the operation of the electrophotographic process thus constructed will be described. First, by inputting the charger voltage u2 to the charger 202, the surface of the photoconductor 201 is charged to the initial potential corresponding to u2. Next, the exposure unit 203 irradiates the photosensitive member 201 with light according to the input voltage u1 of the exposure unit 203, based on the image signals of the respective reference densities input from the image signal input unit 205, to perform exposure. The surface potential of the photoconductor 201, which was uniform before exposure, is attenuated by receiving light energy corresponding to each density, and an electrostatic latent image is formed on the photoconductor 201 by the potential distribution. Further, by the developing device 204 set to the developing bias voltage u3, a toner amount corresponding to the surface potential of the photoconductor 201 adheres to the surface of the photoconductor 201, and the first toner image 209 and the second toner image 210 are formed. Form.

By the way, the process difference between the analog copying machine using the electrophotographic process and the digital printer lies in the exposure process. That is, when considering the exposure distribution of a density patch having a constant density, an analog copying machine can obtain a uniform and uniform exposure intensity distribution corresponding to the density of an original document, whereas a digital printer can obtain a pulse width modulation or a dither pattern. Since the density is expressed by the gradation method, the exposure intensity distribution is not uniform and uniform. In addition, the corresponding formula in the digital printer, which is the formula [Formula 10] of the sub-process in the analog copying machine, is

[0128]

[Equation 59]

[0129]

[Equation 60]

[0130]

[Equation 61]

It is represented by [Equation 59] is the formula of exposure energy, E is the total exposure energy per pixel, u1 is the input laser light intensity, x is the coordinate in the main scanning direction, y
Is the coordinate in the sub-scanning direction, WX is the radius of the laser spot obtained on the photoconductor 201 in the main-scanning direction, WY is the radius of the laser spot in the sub-scanning direction, and Δt is the input density (DIN.H
Alternatively, the time during which the laser is turned on, that is, the pulse width, is proportional to DIN.L), and v is the scanning speed. This equation is unique to digital printers that use polygon mirrors. [Equation 60] is a formula for forming an electrostatic latent image on a selenium-based photoconductor, which is the same as in the case of an analog copying machine. In [Equation 61], DOUT is the density on the photoconductor 201, and V is the surface potential on the photoconductor 201 attenuated by the light energy E.
Note that [Equation 61] is a formula indicating reversal development, and the sign is reversed from the formula in the analog copying machine.

Here, p1 is a positive parameter determined by the input / output characteristics of the exposure means 203, and p2 is the photoconductor 201.
Is a positive parameter determined by the spontaneous discharge characteristic of the photoconductor 201, p3 is a positive parameter determined by the sensitivity of the photoconductor 201 and the transmittance of the optical system, and p4 is a positive parameter determined by the toner density of the developing unit 205 and the dielectric constant of the photoconductor 201. Is.

At this time, the relationship between the input density DIN and the output density DOUT determined by [Equation 59] to [Equation 61] is
Generally, the characteristic curve is as shown in FIG. That is, FIG.
4 is a graph showing the relationship between the input image density and the output image density in the copying machine shown in FIG. In this characteristic curve, the output y1 is changed to a low concentration (DOUT
), The output y2 is set to a medium density (DOUT · M). Here, the parameters p1 to p4 depend on various characteristic parameters of the copying machine 211 as in the case of the conventional example, and greatly vary depending on the temperature and humidity of the environment. y1 is the target low concentration yd1 (D
Therefore, y2 is made to coincide with the target medium concentration yd2 (DT * M). Here, yd1 and yd2 are the target densities D with respect to the first input reference densities DIN · M, respectively.
T · M and the target concentration DT · L for the second input reference concentration DIN · L.

The qualitative model for the above digital printer is derived as follows. First, [Equation 59]
From [Equation 61], knowledge that can be easily derived when the output y1 is low concentration and the output y2 is medium concentration is as follows. Laser light intensity u1 (that is, corresponding to the exposure voltage)
If is increased, both the output image densities y1 and y2 are increased.

2. When the charger voltage u2 is increased, both output image densities y1 and y2 are decreased. Is obtained. Then, based on this knowledge, the qualitative model of the digital printer is obtained by the following equation.

[0136]

[Equation 62]

That is, if u1 is increased, y1 is increased,
If u2 is increased, y1 is decreased. Here, it should be noted that in this qualitative model, the boundary parameter Q does not exist as in the case of the analog copying machine (see [Equation 24]). Then, in the above equation, u2 →
-U2, the influence of each input on each output is a, b,
When c and d> 0 are set, the controlled object is statically expressed by [Equation 52]. Here, a to d are fluctuating parameters, and the parameters a to d satisfy the relationship of the following equation even if the characteristic fluctuation of the digital printer occurs.

[0138]

[Equation 63]

That is, in [Equation 59] to [Equation 61],
Δt is Δt1 (low concentration) <Δt2 (medium concentration) <Δt3
(High density), exposure lamp voltage u1 and charger voltage u
When numerical simulation is performed with 2 slightly changed, a
-D-b-c <0 is maintained. Further, when the concentration does not saturate due to the phenomenon, a.d-b.c <0 is maintained by numerical simulation from [Equation 59] to [Equation 61]. When the concentration is saturated, a ・ d ・ b ・
It is not possible to specify the sign of c.

FIG. 1 is a block diagram showing the configuration of the first embodiment of the learning control apparatus according to the present invention for controlling the above copying machine. In FIG. 1, 100 is a control target (that is,
2), 102 is output detection means, 104 is target value output means, 106 is error output means,
107 is a change width determining means, 108 is an input change determining means,
Reference numeral 110 is an input updating means, and 114 is an input applying means.

The operation of this learning control device is as follows. First, the output from the controlled object 100 is Y = (y1, y
2) is detected by the output detection means 102. next,
Output detected by output detection means 102 Y = (y1, y
2) and the target value Yd output from the target value output means 104
= (Yd1, yd2) and the error output means 106
Calculates and outputs the errors e1 = yd1-y1 and e2 = yd2-y2. The change width determining unit 107 is a control target 100.
Since the characteristic of is always a · d−b · c <0, [Equation 4
5], k2 and k3 that satisfy the condition [5] are set. That is, k2 and k3 are output according to the characteristics of the controlled object 100.
Note that k2 and k3 are constants that give a gain. next,
The input change determining means 108 uses the errors e1 and e2 output from the error output means 106 and the gains k2 and k3 output from the change width determining means 107 to calculate the input increment by [Equation 47] and output it. To do. Therefore, the input update means 110 uses the input increment output from the input change determination means 108 and the input during the previous control,

[0142]

[Equation 64]

A new input is obtained and output by. Finally, an input is actually applied to the controlled object 100 by the input applying means 114 composed of a high voltage power supply circuit or the like. By repeating the above series of operations, the outputs y1 and y2 of the controlled object 100 can be made to match the target values yd1 and yd2. Next, a second embodiment of the learning control device according to the present invention will be described. This learning control device, when the characteristics of the controlled object changes significantly (that is,
Even when the signs of a, d, b, and c change), control can be performed by selecting an appropriate gain according to the change in the characteristic. Here, with respect to the controlled object similar to that of the first embodiment, similarly, [Equation 59] to [Equation 60]
Is established. Therefore, if the output y1 is set to a low concentration (DOUT.L) and the output y3 is set to a high concentration (DOUT.H) as shown in FIG. 3, the following knowledge is obtained as in the case of the first embodiment.

1. If the laser light intensity u1 is increased, the output image densities y1 and y3 are increased. 2. If the charger voltage u2 is increased, output image densities y1 and y3
Go down together. Based on this knowledge, the qualitative model of the digital printer is similar to that of the first embodiment.

[0145]

[Equation 65]

[0146] In [Equation 65], u2 → −u
2 and the influence of each input on each output is a, b, c,
When d> 0 is set, the controlled object is statically expressed by the following equation.

[0147]

[Equation 66]

Here, a to d are fluctuating parameters, and unlike the first embodiment, the sign of a.d.b.c is the laser light density u1 (that is, corresponding to the exposure voltage). Depending on the value, the following two cases, positive and negative, are taken.

[0149]

[Equation 67]

L is a boundary parameter and can take any value. FIG. 4 is a block diagram showing the configuration of the second embodiment of the learning control device according to the present invention for controlling the digital printer. In FIG. 4, 100 is a control target (that is, corresponds to the copying machine 211 shown in FIG. 2), 1
Reference numeral 02 is output detection means, 104 is target value output means, 106
Is an error output means, 407 is a change width determining means, 408 is an input change determining means, 110 is an input updating means, 412 is a characteristic determining means, and 114 is an input applying means. It should be noted that the same numbers as in the case of the first embodiment are attached to the means for performing the same operations as in the first embodiment.

The differences from the first embodiment will be mainly described below. First, the output Y from the controlled object 100 =
The output detection means 102 detects (y1, y3). Then, the output Y detected by the output detection unit 102 is Y =
Using (y1, y3) and the target value Yd = (yd1, yd3) output from the target value output means 104, the error output means 106 causes the errors e1 = yd1-y1 and e3 = yd3-.
Calculate and output y3.

Here, first, by the characteristic judging means 412,
As the characteristic of the controlled object 100 using the current input,
The sign of dbc is determined. If the current input is u1 ≧
If L is satisfied, it can be considered that the characteristics of the controlled object 100 are always a · d−b · c> 0. Therefore, the change width determining unit 407 sets k1 and k4 that satisfy the conditional expression [Equation 44] when a · d−b · c> 0. That is, the gain is output according to the characteristics of the controlled object 100. Note that k1 and k4 are constants that give a gain. Further, the input change determining unit 408 uses the error output from the error output unit 106 and the gain output from the change width determining unit 407 to calculate and output the input increment by [Equation 46].

On the contrary, u1 <in the characteristic judging means 412
When the condition of L is satisfied, the change width determining unit 407 sets k2 and k3 that satisfy the condition of the conditional expression [Formula 45]. That is, k2 and k3 are adjusted according to the characteristics of the controlled object 100.
Is output. Similarly, k2 and k3 are constants that give a gain. Further, the input change determining means 408 determines the error output from the error output means 106 and the change width determining means 40.
Using the gain output from 7
7] to calculate and output.

Further, the characteristic judging means 412 inputs this time u
1 (i) and the previous input u1 (i-1), a · d−
Judge the signs of b and c. Then, if u1 (i) ≦ L and u1 (i−1) ≦ L, then a · d−b · c <
It is determined to be 0. Further, the characteristic determining unit 412 uses the current output y1 (i) and the previous output y1 (i-1) to obtain a.
・ Judge the signs of dbc. And y1 (i) ≦ m
When y1 (i−1) ≦ m (where m is an arbitrary value), it is determined that a · d−b · c <0. As described above, in determining the signs of a, d, b, and c, various determination methods according to the controlled object are used.

Therefore, the input updating means 110 obtains and outputs a new input according to [Equation 64] using the input increment output from the input change determining means 408 and the previous input. Finally, an input is actually applied to the controlled object 100 by the input applying means 114 composed of a high voltage power supply circuit or the like. By repeating the above series of operations,
The outputs y1 and y3 of the controlled object 100 are set to target values yd1 and
can be matched to yd3.

Next, the third learning control apparatus according to the present invention will be described.
An example will be described. This learning control device, when the characteristics of the controlled object are within a certain range (that is, a.d.b.
Even when the sign of c is constant), by increasing the number of control gains to be used, it is possible to stabilize and further reduce the number of convergences as compared with the first embodiment. Here, if similar outputs y1 (low concentration) and y2 (medium concentration) are selected for the same controlled object as in the first embodiment, the qualitative model also becomes [Equation 62]. Similarly, the static expression of the controlled object is [Equation 52], and the characteristic of the controlled object is [Equation 6].
3].

When a certain output y1, y2 is affected by two inputs u1, u2, respectively, the output y1,
Since y2 interferes with each other, each input u1,
In order to obtain u2, the convergence is improved by using the error of the output y1 and the error of the output y2. FIG. 5 is a block diagram showing the configuration of the third embodiment of the learning control device according to the present invention. In FIG. 5, 100 is a control target (that is, corresponds to the copying machine 211 shown in FIG. 2), 102 is output detection means, 104 is target value output means, 106 is error output means, 507 is change width determination means, 508. Is an input change determining means, 110 is an input updating means, and 114 is an input applying means. Incidentally, the same numbers as those in the first embodiment are attached to the means for performing the same operations as in the first embodiment.

The differences from the first embodiment will be mainly described below. First, the output Y from the controlled object 100 =
The output detection means 102 detects (y1, y2). Then, the output Y detected by the output detection unit 102 is Y =
By using (y1, y2) and the target value Yd = (yd1, yd2) output from the target value output means 104, the error output means 106 causes the errors e1 = yd1-y1 and e2 = yd2-.
Calculate and output y2.

As described above, [Equation 52], [Equation 55]
When the Jury's stability determination method is applied to the discrete control system represented by, the conditional expression of [Equation 48] is obtained. The change width determining means 507 has a gain k1 that satisfies this condition,
All of k2, k3, and k4 are set. That is, the controlled object 10
Output k1, k2, k3, and k4 according to the characteristic of 0. Note that all elements of the gain matrix Φ (see [Equation 56]) are used here.

The input change determining means 508 determines the error and change width determining means 50 output from the error output means 106.
Using the gain output from 7
9] to calculate and output. Then, the input updating means 1
10 uses the input increment output from the input change determining means 508 and the previous input to obtain a new input according to [Equation 64] and output the new input. Finally, an input is actually applied to the controlled object 100 by the input applying means 114 composed of a high voltage power supply circuit or the like. By repeating the above series of operations, the outputs y1 and y2 of the controlled object 100 are obtained.
Can be made to match the target values yd1 and yd2.

Next, the fourth learning control apparatus according to the present invention will be described.
An example will be described. This learning control device is used when the characteristics of the controlled object change significantly (that is, a · d−b ·
In the case where the sign of c changes), the control can be performed by appropriately selecting the control gain according to the change of the characteristic, and by increasing the types of the control gain, it is stable and the second embodiment is possible. The number of times of convergence can be further reduced as compared with. Here, if similar outputs y1 (low concentration) and y3 (high concentration) are selected for the same controlled object as in the second embodiment, the qualitative model also becomes [Equation 65]. Similarly, the static expression of the control target is [Equation 66]. Similarly, the characteristics of the controlled object also take two positive and negative cases of [Equation 67] according to the value of the exposure voltage u1.

FIG. 6 is a block diagram showing the configuration of the fourth embodiment of the learning control device according to the present invention. In FIG. 6, 100 is a control target (that is, the copying machine 211 shown in FIG. 2).
102, output detection means, 104 target value output means, 106 error output means, 607 change width determination means, 608 input change determination means, 110 input change means, 412 characteristic determination means, Reference numeral 114 is an input applying means. Incidentally, the same numbers as those in the second embodiment are attached to the means for performing the same operations as those in the second embodiment.

The differences from the second embodiment will be mainly described below. First, the output Y from the controlled object 100 =
The output detection means 102 detects (y1, y3). Then, the output Y detected by the output detection unit 102 is Y =
Using (y1, y3) and the target value Yd = (yd1, yd3) output from the target value output means 104, the error output means 106 causes the errors e1 = yd1-y1 and e3 = yd3-.
Calculate and output y3. Next, the characteristic judging means 412 judges the signs of a, d, b, and c as the characteristics of the controlled object 100 using the current input (see [Equation 67]).
The change width determining unit 607 determines the gains k1, k2, and k that satisfy the condition of [Equation 48] according to the signs of a, d, b, and c.
Set only one set of 3 and k4. That is, k1, k2, k3, and k4 are output according to the characteristics of the controlled object 100. Note that all elements of the gain matrix Φ are used here.

Further, the input change determining means 608 determines the error output from the error output means 106 and the change width determining means 60.
Using the gain output from 7
1] to calculate and output. Then, the input updating means 1
10 uses the input increment output from the input change determination means 608 and the previous input to obtain a new input according to [Equation 64] and output the new input. Finally, an input is actually applied to the controlled object 100 by the input applying means 114 composed of a high voltage power supply circuit or the like. By repeating the above series of operations, the outputs y1 and y3 of the controlled object 100 are obtained.
Can be made to match the target values yd1 and yd3.

[0165]

As described above, according to the present invention, the conventional qualitative control is realized by providing the input change determining means for connecting the relationship between each input to the controlled object and the error between the output from the controlled object and its target value. It is possible to control each output independently, even for a control target that has the same qualitative model for each output that cannot be controlled. Further, by providing the change width determining means for setting the set of gains that satisfy the stability condition, it is possible to reduce the number of times of controlling the output of the controlled object to converge to the target value.

Further, by providing the characteristic judging means for judging the characteristic of the controlled object, it is possible to provide the learning control device which does not limit the controlled object. In addition, by providing the change width determining means in which the number of gains used is increased and the input change determining means, it is possible to perform control in accordance with the state of the controlled object, and to further reduce the number of convergences. Will be able to.

Further, by combining the change width determining means using four kinds of gains, the input change determining means, and the characteristic determining means for determining the characteristic of the controlled object, the controlled object is not limited but converges further. It is possible to provide a learning control device having a small number of times.

[Brief description of drawings]

FIG. 1 is a block diagram showing a configuration of a first embodiment of a learning control device according to the present invention.

FIG. 2 is a perspective view showing a main part of a copying machine having a digital exposure type electrophotographic process taken as an example of a control target of a learning control device according to the present invention.

3 is a graph showing a relationship between an input image density and an output image density in the copying machine shown in FIG.

FIG. 4 is a block diagram showing a configuration of a second embodiment of a learning control device according to the present invention.

FIG. 5 is a block diagram showing the configuration of a third embodiment of the learning control device according to the present invention.

FIG. 6 is a block diagram showing a configuration of a fourth embodiment of a learning control device according to the present invention.

FIG. 7 is a block diagram showing a configuration of a basic learning control device.

FIG. 8 illustrates a basic learning control device.
FIG. 6 is a perspective view showing a main part of a copying machine having an analog electrophotographic process taken as an example of the controlled object.

9 is a graph showing the relationship between input image density and output image density in the copying machine shown in FIG.

[Explanation of symbols]

 100 Controlled object 102 Output detection means 104 Target value output means 106 Error output means 107 Change width determination means 108 Input change determination means 110 Input update means 114 Input application means

 ─────────────────────────────────────────────────── ─── Continuation of the front page (72) Inventor Osamu Ito 1006 Kadoma, Kadoma City, Osaka Prefecture Matsushita Electric Industrial Co., Ltd.

Claims (4)

[Claims] 1. Inputs are represented by u1 and u2, outputs are represented by y1 and y2, and static characteristics are expressed by the following equation: The output is detected for the controlled object represented by
Output detection means for obtaining detection values y1 and y2, target value output means for outputting output target values yd1 and yd2, and target value y
The error between d1 and yd2 and the detected values y1 and y2 is expressed by the following equation: In the case where the characteristics of the controlled object are always a · d−b · c> 0, an error output unit for calculating and outputting by the following, and k1, k2, k3, and k4 are constants that give a gain, ] When k1 and k4 satisfying the condition of are set, and the characteristic of the controlled object is always a · d−b · c <0, the following equation And a change width determining means for setting k2 and k3 that satisfy the above condition, and an error output from the error output means and the change when the characteristic of the controlled object is always a · d−b · c> 0. Using the gain output from the width determining means, the input increment is calculated by the following equation: And the characteristic of the controlled object is always a · d−b.
When c <0, using the error output from the error output means and the gain output from the change width determination means, the input increment is calculated by the following equation: By using the input change determining means calculated by the following, and the input increment obtained from the input change determining means and the previous input, And an input applying unit for applying a new input output from the input updating unit to the control target, and an output y of the control target.
A learning control device that controls 1 and y2 so as to match the target values yd1 and yd2. 2. Output detection for detecting an output of the controlled object with respect to a controlled object having static characteristics when the inputs are represented by u1 and u2 and the outputs are represented by y1 and y2. Means, a target value output means for outputting the target value of the output, and an error between the detected values y1, y2 of the output detection means and the target values yd1, yd2 output from the target value output means, as expressed by the formula 2 ] While providing an error output means for calculating and outputting, the sign of a · d−b · c as the characteristic of the controlled object is
The output output from the output detection means and its history value,
When the characteristic judging means for judging using at least one of the input and its history value and k1, k2, k3, k4 are constants giving a gain, and the output of the characteristic judging means is positive, Change width determining means for setting k1 and k4 that satisfy the condition of [Equation 3], and setting k2 and k3 that satisfy the condition of [Equation 4] when the output of the characteristic determining means is negative, When the output of the characteristic determining means is positive, the input increase is calculated by the [Equation 5] using the error output from the error output means and the gain output from the change width determining means. When the output of the characteristic determination means is negative, the input increase is calculated by the above [Equation 6] using the error output from the error output means and the gain output from the change width determination means. Change determining means , An input update unit that obtains a new input according to [Equation 7] using the input increment obtained from the input change determination unit and the previous input, and a new input that is output from the input update unit. A learning control device comprising: an input application unit for applying to a target, and controlling outputs y1 and y2 of the control target so as to match target values yd1 and yd2. 3. When k1, k2, k3, and k4 are constants that give a gain, the change width determining means has the following equation: And k1, k2, k3, k4 satisfying the condition of (1) are set, and the input change determining means uses the error output from the error output means and the gain output from the change width determining means to increase the input. Minute is expressed by the following equation The learning control device according to claim 1, wherein the learning control device is calculated by 4. When k1, k2, k3, and k4 are constants that give a gain, the change width determining means sets k1, k2, k3, and k4 that satisfy the condition of [Equation 8] to a.
At least one or more is set for each of the positive and negative signs of dbc, and gains k1 to k4 are given from the output value of the characteristic determining means, and the input change determining means causes the error output to be increased. 3. The learning control device according to claim 2, wherein the input increment is calculated and calculated by the [Equation 9] using the error output from the means and the gain output from the change width determining means.