JPH0740203B2 - Process control method - Google Patents

Description

Description: TECHNICAL FIELD The present invention relates to a method for controlling the output of various industrial processes in which a static characteristic curve representing the relationship between input and output has an inflection point near the inflection point.

[Prior art and its problems]

There are many processes in which the static characteristics have an inflection point among various processes in which the input-output relationship is non-linear.
For example, in the process of continuously neutralizing water containing acid, the pH changes abruptly at the equivalent point of acid and alkali, so if the alkali injection rate is input and the pH is output, the static characteristics between the two change at the equivalent point. It becomes a curve with inflection points. Such a relationship is also found in the redox process, and the redox potential (ORP) has an inflection point at the equivalence point between the oxidizing substance and the reducing substance. The process showing the inflection point is not limited to the above chemical process, and for example, when detecting the sludge interface by utilizing the change in the amount of ultrasonic waves or light transmission in the solid-liquid separation tank,
There is an inflection point in the characteristic curve of the permeation amount with respect to the water depth because the permeation amount changes rapidly at the interface.

From the above examples, the commonality of the inflection points can be regarded as a limit point of the process corresponding to the abrupt change of the state in a broad sense in many cases. Therefore, when trying to control the process to its limit point, if the inflection point can be detected reliably and the process can be controlled to this inflection point, the process control becomes extremely easy and effective. I understand.

On the other hand, the following two methods are mainly used to control the process output at the inflection point.

The value of the output at the inflection point is obtained in advance, and the output is controlled so as to be that value.

The input is adjusted so that the first derivative of the output with respect to the input becomes maximum and the second derivative becomes zero.

Of these methods, the method is most reliable if the relationship between the inflection point and the output value is always constant, and in this case, the output can be controlled to a constant value without particularly considering the inflection point. However, such cases should be considered rather rare. For example, the inflection point of the above-mentioned pH or ORP is affected by the coexisting substance, and the inflection point also changes if the characteristics of the electrode change. This also applies to the case of detecting the sludge interface, and there are numerous factors that change the position of the inflection point, such as changes in sludge density, changes in the light source, and stains on the light-receiving surface. Therefore, all methods cannot be expected to be effective enough.

Next, the method of using differentiation has the most serious problem of noise. In order to obtain the differential coefficient of the output with respect to the input, it is necessary to obtain the time derivative of the input and the output and obtain the ratio thereof. However, since the differential operation is a kind of high-frequency filter, noise is magnified, and it is extremely difficult to obtain effective information from such a signal. Furthermore, in the case of process control, it is impossible to change the input and output in a wide range, and the output responds to the input change with a delay, and its time constant also changes depending on the conditions. It is a factor that makes it difficult.

On the other hand, the inventors set a reference value for the process output, and the slope of the input / output static characteristic curve when the output is smaller than this reference value, that is, the gain K _1, and the input / output when the output is larger than this reference value. By identifying the slope of the static characteristic curve, that is, the gain K ₂ online, and controlling the inputs so that K ₁ and K ₂ are equal, stable and reliable control of various process outputs at inflection points is achieved. A method (hereinafter referred to as "inflection point control method") capable of achieving this is found, and the method is disclosed in JP-A-60-251402.
It is disclosed in Japanese Patent Publication No. However, in this publication, K ₁ is g ₁ and K ₂ is g ₂
It is described as.

Next, the outline of this inflection point control method will be described with reference to FIG. Figure 6 shows the static characteristic curve of input and output with inflection point and K ₁
The thickness inflection point in the diagram showing the relationship between K ₂ and is a point where the curvature of the curve is zero. Now, in FIG. 6, it is assumed that the average value of the output is on the point B and the output fluctuates above and below the average value. Therefore, if we identify the gain K ₁ when the output is below the average value and the gain K ₂ when it is above the average value,
These gains K ₁ and K ₂ correspond to the slopes of the two straight lines shown in FIG. Therefore, the difference between K ₁ and K ₂ represents a kind of curvature, and the output can be controlled at the inflection point by adjusting the output level so that K ₁ and K ₂ are equal. Such a method of performing the nonlinear characteristic linear approximation on-line is hereinafter referred to as adaptive polygonal approximation.

The method disclosed in JP 60-251402 by the present inventors is based on the above principles, error factors included in common to both for using the difference between the strong noise, also K ₁ and K ₂ Have the advantage that they are eliminated. In this method, the process output is compared with the reference value corresponding to point B in FIG. 6, and the identification of K ₁ and K ₂ is switched depending on the magnitude relationship, but what is important here is what the output and reference value are. In terms of whether to use, the present value of the output and the moving average are used according to the invention of the present inventors.

However, with the progress of research thereafter, it was found that the above method causes the following problems.

The moving average is delayed because it is calculated using past data. Therefore, if there is a load change or the change in the control set value for adjusting the output level to the inflection point is large, the moving average cannot be the true average value for the current output value. The area corresponding to K ₁ and the area corresponding to K ₂ cannot be fairly divided.

Another problem relates to the removal of low frequency components. When performing the adaptive broken line approximation, in order to maintain the identification performance of the gain, the process must be constantly excited with a signal having a period that is about the same as the time constant of the process or 2 to 3 times that. Therefore, unless the noise added to the process is available to excite the process, the test signal for process excitation is used for identification. That is, the input signal of the process is a superposition of a relatively large low frequency component based on a disturbance such as a load change or a change in a set value and a high frequency component due to the test signal. It is necessary to remove low-frequency components from the input / output signals because the signal components due to the test signals are necessary for gain identification. For that purpose, the method of subtracting the reference value from the output is the most appropriate. I also understand. However, as long as the current value is used as the output and the moving average is used as the reference value, the influence of the disturbance appears with a time lag between the two, so even if it is a low-frequency disturbance, it is not possible to remove it sufficiently. It's difficult. In other words, it is necessary to lengthen the averaging time in order to use the moving average as the reference value, but doing so lowers the performance as a high band filter for removing low frequency components, and it is relatively long term. It means that the influence of the external disturbance cannot be eliminated. Therefore, in performing the above-mentioned adaptive polygonal line approximation according to the invention of the present inventors, a high band filter is newly provided, an input / output signal is passed through this filter, and the output is used to identify parameters. . However, increasing the filter pass frequency means that the characteristics of the filter have a stronger differential character, and therefore, there is the disadvantage that only when the input / output signal changes suddenly is greatly amplified.

[Object of the Invention]

The present invention was made in order to solve the problems of the process control method according to the invention of the present inventors disclosed in the above-mentioned Japanese Patent Laid-Open No. 60-251402. An object of the present invention is to provide a method capable of performing good gain switching even when the value changes and enabling stable inflection point control.

[Main points of the invention]

As described above, the problem of the method of subtracting the moving average from the current value of the signal is that the influence of the disturbance appears on both sides with a time lag. As a result of various studies on the characteristics of the moving average in order to solve this problem, the inventors have come to the conclusion that this time difference is approximately equal to 1/2 of the moving average time.

Therefore, instead of the current value of the signal, 1/2 of the moving average time
However, if the past value is used, the above-mentioned time lag is eliminated, and the low frequency component can be removed extremely efficiently.

Generally, when configuring a control system, it is common knowledge to use a value close to the current value, but the present invention, conversely,
The past value is used only for the time corresponding to 2. Although this does not mean that the performance will not decrease, it can be almost ignored when applying inflection point control.

Therefore, an object of the present invention is to define a reference value of C in a process in which a static characteristic curve representing a relationship between an input (F) and an output (C) has an inflection point, and a gain (when C is smaller than the reference value A process control for controlling C near the inflection point by identifying the gain (K ₂ ) when K ₁ ) and C are larger than the reference value and adjusting the output level so that K ₁ and K ₂ are equal. In the method, a moving average () of F in a constant time section and a moving average () of C in the same time section are calculated to obtain a value F _h of F and a value C _{h of} C at an intermediate point of the time section, Using the above-mentioned reference value, u = F _h − and y = C _h − data are sequentially measured, and the coefficient of the difference equation representing the relationship between y and u is calculated when y ≦ 0 and y> 0. By separately determining with and, the above K ₁ and K ₂ are obtained, and the output level is adjusted so that the K ₁ and K ₂ are equal. It is achieved by

Example of Invention

First, the basic concept of the present invention will be described, and then the present invention will be described in detail based on specific examples.

The above-mentioned two problems of the process control method according to the inventors of the present invention, that is, the problem of division of the K ₁ region and the K ₂ region and the problem of removal of low frequency components, are both moved from the current output value. This is because the method of subtracting the average value cannot sufficiently remove the influence of low-frequency disturbance from the input / output signal. Therefore, the present inventors have focused on the frequency characteristic of the moving average in order to solve this problem.

If the moving average of the time section L is expressed by a transfer function, Here, G _L (s) is the transfer function of the dead time element of the delay time L, and G _L (s) = e ^−sL (2). In addition, s is a Laplace conversion parameter.

Now, the reason why the above formula (1) is obtained will be described in detail below.

The moving average f _MAL of the time function f (t) in the time section L is generally defined by the following equation (a), where t is the present time.

Here, if the Laplace transform form of f (t) is F (s), the Laplace transform form of f (t−L) is G _L (s) F
(S). However, G _L (s) = e ^-sL (Equation (2) above)
Is.

Next, when Laplace transform is performed on both sides of the expression (a), f _MAL (s) = F (s) / sL− _GL (s) F (s) / sL = G _MAL (s) F (S) In the above, G _MAL (s) = (1-G _L (s)) / s
L, and the above formula (1) is obtained.

Substituting s = jω into equation (1) to examine the frequency characteristics, Is obtained. Where ω is the angular frequency, Is. When the equation (3) is transformed by using e ^−jωL = cosωL−jsinωL, And sin ωL = 2sin (ωL / 2) ・ cos (ωL /
2), 1−cos ωL = 2sin ² (ωL / 2), Becomes When sin (ωL / 2) is expanded in series, equation (5) becomes Can also be expressed as Where T is the period. As you can see, the signal is longer than the average time,
That is, for the signal of (1/31) (πL / T) ² << 1, the ^{second and} subsequent terms of equation (6) can be ignored, Becomes That is, the moving average works as a dead time element having a half of the average time for a signal having a period longer than the average time. Also, from equation (5) Is obtained and is represented in a graph, the gain curve of the moving average element is obtained as shown in FIG. From Fig. 1, the gain of the moving average drops sharply at L / T, especially L / T = n
It can be seen that the signals of (n = 1,2, ...) Are completely extinguished by the moving average operation.

The present invention utilizes the characteristics of the moving average described above. That is, the point that the moving average is used as the reference value is the same as the previous method, but in the present invention, not the current value but the past value is used as the process output for a time corresponding to 1/2 of the average time. When a test signal is used, its cycle can be specified, so the average time is set to be an integral multiple of that cycle. Here, the average time is a moving average time, where L is the current time and t is the current time, the moving average is the average of data from time t-L to t. now,
Since the current value C _o of the output is expressed by a sum of variation [Delta] C by the low-frequency components C _d and test signals _{C o = C d + ΔC (} 9), when passed through this moving average component of the G _MAL ( s) C ₀ (s) = G _MAL (s) Cd (s) + G _MAL (s) ΔC (s) G _{L / 2} (s) Cd (s) (10) Here, the reason why the term ΔC (s) can be deleted is as follows. When the average time L is set to be an integral multiple of the cycle T, the variation ΔC due to the test signal
Since (s) also has the same period T, ΔC (s)
L / T = n holds, and ΔC (s) disappears by the moving average operation as described above. On the other hand, the signal passed through the dead time element is G _{L / 2} (s) C ₀ (s) = G _{L / 2} (s) Cd (s) + G _{L / 2} (s) ΔC (s) (11) , both the difference y of _{y (s) = G L /} 2 (s) C 0 (s) -G MAL (s) C 0 (s) G L / 2 (s) ΔC (s) (12) , and the Only the variation due to the test signal is obtained.
By performing the same processing for the input, u (s)
G _{L / 2} (s) ΔF (s) (13) is obtained. Here, ΔF is the variation of the input due to the test signal. That is, for example, the first term G on the right side of Expression (12)
_{L / 2 (s) C 0} (s) denotes the value of the midpoint of the L / 2 only past values of C _0, i.e. the moving average time L. The second term G
_MAL (s) C ₀ (s) represents the moving average of C ₀ . Expression (1
The same applies to 3).

The present invention obtains the curvature of the input / output characteristic curve by adaptive polygonal line approximation using y and u, and performs the inflection point control.

Hereinafter, the method of the present invention is applied to the activated sludge process of dissolved oxygen (hereinafter
An example applied to the density control will be specifically described.

The activated sludge process is a kind of mixed culture system of aerobic microorganisms, and in order to keep the process stable, sufficient aeration must be performed and the DO concentration must be maintained at an appropriate level. However, from the viewpoint of power saving and the like, it is desirable to operate the process with as little air as possible within the range where the properties of microorganisms do not deteriorate.

A curve shown in FIG. 2 is obtained by measuring the DO concentration C as an output at a certain position in the air sludge tank in the activated sludge process and obtaining the relationship with the air flow air flow rate F as the input. Since the DO concentration C rapidly increases at a certain point with the increase of the air flow rate F, the second
An inflection point IP appears on the characteristic curve shown in the figure. In order to control the output to the inflection point, the present inventors have found that the minimum required air amount is maintained by controlling the DO concentration C so as to match the value of C at the inflection point IP. The present invention is applied to. Although the actual location of the inflection point varies slightly depending on the state of the process, it is almost certain that it is within the shaded area shown in FIG.

FIG. 3 is a system diagram showing an outline of the equipment configuration and functions of the activated sludge process to which the present invention is applied. In FIG. 3, the flow of water and air is shown by a solid line, and the electric signal system is shown by a broken line.
In each case, the direction of flow is indicated by an arrow.

In FIG. 3, the air sent from the air blower 1 is aerated by the air diffuser 4 from the bottom of the air tank 3 via the flow meter 2. The raw water that has been primarily treated by a device (not shown) is used in the air tank 3
After being decomposed by the pollutants, the pollutants are decomposed and stored in the final settling basin 5, and the supernatant water is discharged as secondary treated water, but the settled sludge is returned to the aeration tank 3 again.

On the other hand, the electric signal is the DO located in the air tank 3.
The output of the sensor 6 is converted into a transmission signal by the signal converter 7, and is input to the arithmetic unit 8 together with the signal of the air flow air amount measured by the flow meter 2. The arithmetic unit 8 performs the control calculation according to the present invention and inputs the target air amount as a set value to the controller 9. The operation signal for controlling the air quantity of air from the controller 9 to the set value is sent to the inverter.
By inputting 10 to the inverter 10, the rotation speed of the air blower 1 is adjusted by the inverter 10.

FIG. 4 shows the function of the arithmetic unit 8 of FIG. 3 as a block diagram. In Fig. 4, 21 is the activated sludge process, 22 is the proportional for controlling the DO concentration C to the set value +
An integral (PI) controller, 23 is a high-pass filter for removing low-frequency components from input / output signals, 24 is an arithmetic unit for performing adaptive line approximation, 25 is a divider, and 26 is for adjusting a set value. Integrator, 27 is a test signal generator.

This control system consists of a DO control loop for controlling the DO concentration C to Cr '(set value Cr + test signal) and a gain maximization loop for controlling the set value at the inflection point. The processing for removing low frequency components from the input F and the output C is performed by the high frequency filter 23. The calculation here is y (k) = C _h − (14) u (k) = F _h − (15). Here, C _h = C (k−m / 2) F _h = F (k−m / 2) = [C (k) + C (k−1) + ... + C (k−m +)
l)] / m = [F (k) + F (k-1) + ... + F (k-m +
l)] / m In addition, m is the number of data to be sampled to obtain the moving average. m is set to be an even number. F
(K) and C (k) are F and C at the k-th step, respectively, and these are the current values. Therefore and are moving averages of m data, including the current values of C and F, respectively, and _Ch and F
_h is the value of C and F of the midpoint of the time section which is the target of the moving average, respectively.

The adaptive polygonal line approximation calculation unit 24 performs calculation based on u and y. With this, the gain can be obtained. Generally, the input / output characteristics of a process can be expressed as the following difference equation using u and y.

Q ₀ Δy (k) + Q ₁ Δy (k−1) + …… + Q _n−1 Δy (k−n−1) + y (k) = Ku (k) + Q ₁ ′ Δu (k−1) + …… + Q ' _n-1 Δu (k-n-1) (16) where Δy (k) = y (k + 1) -y (k), Δy (k-1) = y (k) -y (k -1), ... Δu (k) = u (k + 1) -u (k), Δu (k-1) = u (k) -u (k-1) ,. In the case of the activated sludge process, since the input / output characteristics can be expressed by the primary delay, the equation (16) can be simplified as follows: QΔ (k) + y (k) = Ku (k) (17) .

Q and K change due to the non-linear characteristics of the process, which can be considered as the relationship of the DO concentration C. And the idea of adaptive polyline approximation is that the values of these parameters take two discontinuous values depending on the DO concentration C. Can be expressed as Where r (k) = y (k + 1)
+ Y (k). Equation (18) is the parameter vector And signal vector Can also be expressed as follows.

Therefore, the equation error e is Becomes here Is an adjustable parameter vector [Q _e1 (k), Q _e2 (k),
−K _e1 (k), −K _e2 (K)]. If you subtract equation (19) from equation (20), Is obtained. Therefore, the parameters can be identified by the following incremental equation.

Where e ₀ is a temporary value of e, Is a gain matrix for adjusting the sensitivity of the identification operation.

Since K _e1 and K _e2 thus obtained correspond to K ₁ and K ₂ in FIG. 6, the difference between K _e1 and K _e2 represents the curvature of the characteristic curve, and this difference is zero. The output level can be controlled to an inflection point by adjusting the set value so that The adaptive polygonal line approximation calculation unit 24 performs the calculation of Expression (22),
Output K _e1 and K _e2 . Then, a value (K _e2 −K _e1 ) / K _{e obtained} by dividing the difference between K _e2 and K _e1 by their average K _e is input to the integrator 26, and the set value Cr is adjusted. The control signal is controlled by the PI controller 22 so that the addition of the test signal to Cr is (C ^′ _r), and the DO concentration follows (C ^′ _r ).

In order to maintain the performance of the adaptive polygonal line approximation, it is desirable that the output C fluctuate within a certain range. For that, ▲ C ^'
_The closed loop transfer function from _r ▼ to C must be constant. Therefore, in this embodiment, the PI control parameter is adjusted based on the identified value of the process parameter. If the PI control operation is expressed by a z-transform type transfer function, Becomes Where k _p is the proportional gain and k _i is the integral gain. In this embodiment, k _i and k _p are Determined by Therefore And d is specified by the designer. When k _i and k _p are determined in this way, the order of the closed-loop transfer function is reduced by one due to pole-zero cancellation, and the system becomes an apparent first-order system, and the pole can be designated as the value of d. Ie Where G _p (z) is the transfer function of the process and is given by equation (16)
From G _p (z) = (1−a) K / (z−a).

In this example, the data sampling time was set to 5 minutes, and a rectangular wave whose value randomly changes every 30 minutes was used as the test signal. Therefore, the signals included in the test signal are those of one hour period and their harmonics. Therefore, the average time was set to 2 hours. That is, m in equations (14) and (15) is 24.

Since the load of the activated sludge process changes according to human life patterns, the main cycle of the waveform included in load fluctuation is 12
Hours and 24 hours. If the load changes every 12 hours, then in equation (6) Therefore, it can be seen that the method of the present invention works effectively.

FIG. 5 is a diagram showing changes in various data obtained with the passage of time when the control of the activated sludge process shown in FIG. 3 is performed by the control system described above. Control is Cr =
It started at 0.5mg / and continued for about 300 hours. Since Cr is low at the start of control, K _e1 <K _e2 , and as a result, Cr is corrected upward. Cr reaches a constant value after about 50 hours, and thereafter fluctuates within the range of 1.0 to 1.5 mg /. Although the amount of inflow water fluctuates greatly, the adjustment operation of the set value is performed extremely stably without being disturbed by this load fluctuation, and it can be seen that the control function according to the present invention is sufficiently achieved. .

Although the above description of the embodiment has been made on the case of being applied to the activated sludge process represented by the primary delay, the present invention is such that the input / output characteristics become a high-order difference equation such as equation (16). The same is applicable to the case. In this case, the signal vector of Equation (22) And adjustable parameter vector Similarly, the present invention can be implemented by increasing the order of s as necessary.

〔The invention's effect〕

As described above, according to the method of the present invention, it is possible to efficiently remove low-frequency disturbance from the input / output signals of the process, so that it is not necessary to newly provide a high-frequency filter, and u and y can reduce low-frequency disturbance. The fact that they are not included means that they change around zero due to the test signal and that there is no bias, so that the K ₁ and K ₂ regions are equally divided.
Therefore, the inflection point control method of the present invention having such high performance is extremely effective when applied to various industrial processes.

[Brief description of drawings]

FIG. 1 is a gain curve diagram of a moving average element, FIG. 2 is a diagram showing the relationship between the air flow amount F and the DO concentration C of the activated sludge process, and FIG. 3 is the equipment of the activated sludge process to which the present invention is applied. FIG. 4 is a system diagram showing the configuration and function, FIG. 4 is a block diagram showing the control calculation by the method of the present invention, and FIG. 5 is a graph showing changes over time of various data obtained by the activated sludge process control by the method of the present invention. The diagram shown in FIG. 6 is a diagram showing the input / output characteristic curve having an inflection point and the relationship between K ₁ and K ₂ . 1 …… Air Racer Blower, 2 …… Air Flow Meter, 3 …… Air Racer Tank, 4 …… Diffuser, 5 …… Final Settling Tank, 6…
… DO sensor, 7 …… Signal converter, 8 …… Computer, 9 …… Controller, 10 …… Inverter, 21 …… Activated sludge process, 22 …… P
I control device, 23 …… High-range filter, 24 …… Adaptive broken line approximation calculation unit, 25 …… Divisor, 26 …… Integrator, 27 …… Test signal generator, C …… DO concentration (output), F …… Air flow rate, y …… C signal with low frequency components removed, u …… F signal with low frequency components removed, Q _e1 , Q _e2 , K _e1 , K _e2 …… Process model parameters, Q _e … Average of Q _e1 and Q _e2 , K _e … Average of K _e1 and K _e2 , Cr …… Set value, ▲ C ^′ _r ▼ …… Cr + test signal, Qw …… Inflow water quantity.

Claims (2)

[Claims] 1. A gain (K ₁ ) when a static characteristic curve representing a relationship between an input (F) and an output (C) defines a reference value of C in a process having an inflection point and C is smaller than the reference value. And C
There were identified gain (K ₂₎ when greater than the reference value, and K ₁
In a process control method in which C is controlled near the inflection point by adjusting the output level so that K ₂ becomes equal, a moving average of F in a constant time section () and a moving average of C in the same time section () Is calculated to obtain the F value F _h and the C value C _{h at} the midpoint of the above-mentioned time interval, and the above reference values are used as the values to sequentially measure the data of u = F _h − and y = C _h −. , Y and u, the coefficient of the differential equation is expressed as y ≦ 0
Process of determining the K ₁ and K ₂ by separately determining the time of y and the time of y> 0, and adjusting the output level so that the K ₁ and K ₂ are equal. Control method. 2. The process control method according to claim 1, wherein the time interval of the moving average is an integral multiple of the period of the main frequency components included in F and C.