JPH0430607B2 - - Google Patents

Description

[Detailed description of the invention] [Technical field to which the invention pertains] The present invention is applicable to various industries in which the static characteristic curve representing the relationship between input and output has an inflection point due to a sudden change in output near a specific value of input. This invention relates to a method for controlling the output of a process near an inflection point.

[Prior art and its problems]

Among the various processes in which the input-output relationship is nonlinear, there are many that have inflection points in their static characteristics. For example, in the process of continuously neutralizing water containing acid, the PH changes suddenly at the equivalence point between acid and alkali, so if the alkali injection rate is input and the PH is output, the static characteristics between the two will change at the equivalence point. It becomes a curve with curved points. Such a relationship is also seen in redox processes, and the redox potential (ORP) has an inflection point at the point of equivalence between oxidizing and reducing substances.
Processes that exhibit inflection points are not limited to chemical processes such as those mentioned above; for example, when detecting a sludge interface using changes in the amount of ultrasound or light transmitted in a solid-liquid separation tank, Because of this, there is an inflection point in the characteristic curve of the amount of permeation versus water depth.

From the above examples, the common feature of inflection points is that in many cases, inflection points can be viewed, in a broad sense, as the breaking point of a process that responds to rapid changes in state. This shows that when trying to control a process to its limit point, if the inflection point can be detected reliably and the process can be controlled to this inflection point, control will be extremely easy and effective.

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

The output value at the inflection point is determined in advance, and the output is controlled so that it becomes that value.

The input is adjusted so that the first derivative of the output with respect to the input is maximized or the second derivative is zero.

These methods are the 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 at a constant value without particularly considering the inflection point. However, it is better to consider that such cases are rather rare. For example, the above
The inflection point of PH or ORP is affected by coexisting substances, and if the characteristics of the electrode change, the inflection point will also change. This also applies to detecting the sludge interface, and there are many factors that can cause the position of the inflection point to vary, such as changes in sludge density, changes in the light source, and dirt on the light receiving surface. Therefore, the method cannot be expected to be effective.

Next, the method using differentiation has the most serious noise problem. In order to find the differential coefficient of the output with respect to the input, it is necessary to find the time derivatives of the input and output and find their ratio. However, since differential calculation is a type of high-pass filter, noise is magnified, and it is extremely difficult to obtain effective information from such a signal. Furthermore, for process control,
Factors that make differential calculations difficult include the fact that both input and output cannot be varied over a wide range, and the output responds with a delay to changes in the input, and the time constant varies depending on the conditions. ing.

[Purpose of the invention]

It is an object of the present invention to provide a method capable of eliminating the above-mentioned drawbacks and controlling various process outputs to inflection points with stability and high reliability.

[Key points of the invention]

The present invention is applied to a process in which the input/output characteristics are expressed by a curve having an inflection point due to a sudden change in the output near a specific value of the input, and a method for controlling the output near the inflection point. The control system comprises a first control loop that controls the output to a target value by manipulating the input, and a second control loop that maximizes the input/output gain by manipulating the target value. ,
The second control loop divides the output fluctuation region into an upper fluctuation region and a lower fluctuation region, and determines an input/output gain g ₁ when the output is in the lower fluctuation region and an input/output gain g 1 when the output is in the upper fluctuation region. This is achieved by identifying the input/output gain g ₂ at the time and sequentially changing the target value so that g ₁ and g ₂ are equal.

[Embodiments of the invention]

The present invention will be described in detail below based on examples.

First, the basic concept of the present invention will be described, and then specific embodiments will be shown.

The inventors first needed to solve the problem of output time delay, and for that purpose, they approximated the input-output relationship of the process with a model equation that included a dynamic characteristic term, and used this model equation to find the inflection point. We considered ways to explore. However, in reality, in order to approximate a nonlinear relationship that has an inflection point, the model equation naturally becomes nonlinear, which increases the number of parameters and complicates the identification calculation method. judged to be impractical.

Therefore, the present inventors focused on the fact that the purpose is to detect inflection points, rather than approximating curves with functions, and detailed the minimum requirements for detecting inflection points. We considered this. As a result, we divide the output fluctuation region into upper and lower regions, find the gain g ₁ when the output is in the lower fluctuation region, and the gain g ₂ when the output is in the upper fluctuation region, and calculate g ₁ = g ₂ . We came to the conclusion that it is best to determine that the boundary value that separates the two regions corresponds to an inflection point when the two regions are the same, and applied this to the method of the present invention. For example, a moving average value of the output over a certain period of time can be used as the boundary value.

FIG. 1 shows an example of an input-output relationship curve having an inflection point. In FIG. 1, the method of the present invention approximates the static characteristic curve with a broken line whose breaking point is a point P on the boundary value. It means that. However, the difference between the gain g ₁ when the output is smaller than point P and the gain g ₂ when the output is larger than point P is only the magnitude relationship between the output value and the boundary value, and the approximate interval is not determined.
g ₁ and g ₂ change depending on the fluctuation range of the output. In this way, the above method cannot approximate the characteristic curve with a function, but in order to detect the inflection point, g ₁ and g ₂
Since the only question is whether or not they are equal, it can be used to control the output to an inflection point. Moreover, since this method uses a linear model, the parameter identification calculation is simple, and g ₁
Reliability is improved by using the difference between and g ₂ .
In other words, if the process output contains noise or if the process input has feedback from the output, bias will often occur between the identified value and the true value of the parameter, but these effects
This is because g ₁ and g ₂ act in common, so the method of the present invention that uses the difference between g ₁ and g ₂ can eliminate the influence of bias.

Furthermore, the present inventors developed a Model Reference Adaptivs (System).
It is abbreviated as MRAS. ) was found to be suitable for carrying out the present invention. MRAS consists of an actual process and a model that approximates its dynamic characteristics.
When used for parameter identification, the model parameters are automatically adjusted so that the process output and model output match.

An example in which the method of the present invention is applied to controlling dissolved oxygen (hereinafter abbreviated as DO) concentration in an activated sludge process using MRAS will be specifically described below.

The activated sludge process is a mixed culture system of aerobic microorganisms, and in order to maintain a stable process, sufficient aeration must be performed to maintain the DO concentration at an appropriate level. However, from the viewpoint of power saving, etc., it is desirable to operate the process with as little amount of air as possible without deteriorating the properties of the microorganisms.

In the activated sludge process, when the DO concentration C is measured at a certain point in the aeration tank and the relationship with the aeration air flow rate f is determined, the curve shown in Figure 2 is obtained. As the aeration air flow rate f increases, the DO concentration C increases rapidly at a certain point, so there is an inflection point Q on the static characteristic curve shown in Figure 2.
appears. The present inventors set the DO concentration C to the inflection point Q
It was discovered that the minimum necessary amount of air can be maintained by controlling the amount of air to match the value of C in , and the present invention was applied to control the output to the inflection point.

FIG. 3 is a system diagram showing an overview 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 solid lines, and the electrical signal system is shown by broken lines, and the direction of flow is shown by arrows.

In FIG. 3, air sent from an aeration blower 1 passes through a flow meter 2 and is aerated from the bottom of an aeration tank 3 by an aeration pipe 4. Water that has been primarily treated by a device (not shown) passes through a flow meter 5 and flows into an aeration tank 3, where pollutants are decomposed and then stored in a final sedimentation tank 6, where the supernatant water is discharged as secondary treated water. However, the settled sludge is returned to the aeration tank 3 again.

On the other hand, the electrical signal is calculated by converting the output of the DO sensor 7 located in the aeration tank 3 into a transmission signal by the signal converter 8, and using the signals of the aeration air amount and inflow water amount measured by the flowmeters 2 and 5, respectively. input into device 9; The calculation device 9 performs control calculation according to the present invention and inputs a target air amount as a set value to the controller 10. Controller 1
By inputting an operation signal to the inverter 11 to control the aeration air amount from 0 to a set value, the inverter 11 controls the aeration blower 1.
The rotation speed is adjusted.

FIG. 4 shows a block diagram for performing control calculations in the configuration of FIG. 3. In FIG. 4, numeral 21 represents the process shown in FIG. 3, where the input is the aeration air flow rate f and the output is the DO concentration C. 22 is a first-order lag element of the time constant Tf that filters f; 23 is a first-order lag element of the time constant Tf that filters C; 2
4 is a proportional element with adjustable gain g, 25 is a first-order lag element with adjustable time constant T, and 26 is the output of 25.
A divider for finding the differential coefficient of xm, 27 a parameter adaptation mechanism for adjusting T to suit the actual process, and 28 an adaptation for adjusting the gain g ₁ when the DO concentration is in the lower fluctuation region. Mechanism, 29
is the gain g ₂ when the DO concentration is in the upper fluctuation region
30 is a moving average calculation unit for calculating the moving average of the signal Cf obtained by filtering the process output; 31 is a moving average calculation unit that compares the signal Cf with Cf and switches S ₁ and S ₂ according to their magnitude relationship; ，
A comparator for opening and closing _S3 ; 32 is an integrator that integrates g ₂ - _{g 1} and outputs it as the target value Cr of DO concentration;
33 is a target air amount calculation unit into which the difference ε between Cr and C and the inflow water amount signal W are input, and is used to control C to Cr; 34 is an identification process for the reference value f _b of the air flow rate signal output from 33; This is a sample hold section that holds a signal to which identification noise N has been added for a certain period of time to make it smooth. A portion 35 surrounded by a broken line consisting of 24 and 25 represents an adaptive model.

The above control calculations are roughly divided into two parts. That is, the first control loop for controlling the process output C below the dashed-dotted line to the target value Cr shown in Fig. 4, the parameter identification above the dashed-dotted line, and the operation of Cr are performed to maximize the input/output gain. This is the second control loop. Of these two parts, the former performs feedback control so that the output C matches the target value Cr, and the latter
It calculates g ₁ and g ₂ and manipulates Cr so that g ₂ - _{g 1} becomes zero.

Next, the control operation in this embodiment will be explained in order starting from the parameter identification part of the first control loop. The input f and output C of the process are required to identify the parameters. f and C first
Filtering is performed by second delay elements 22 and 23 to obtain respective smoothed signals. Next, the smoothed signals are subtracted from f and C to obtain u and y, respectively. In the case of an activated sludge process, the relationship between u and y can be expressed by a first-order lag model, so the adaptive model 35 that constitutes the MRAS can also be a first-order lag model consisting of 24 and 25. The role of this MRAS is to automatically adjust the time constant T and gain g of the adaptive model 35 so that the process signal y and the output xm from the adaptive model 25 match. Automatic adjustment of T and g is performed by parameter adaptation mechanisms 27, 28 and 29. 27 of these are adaptation mechanisms of T, y
_{The difference} e ^between To in equation (1) is the initial value of T, k _T
is the adaptation gain of T. The gain g identification operation in this embodiment is different from the normal case. In other words, in the method of the present invention, an identification mechanism is provided in response to the filtered output signal Cf so that the gains g ₁ and g ₂ can be separately identified when the signal Cf is smaller than the moving average and when it is larger than the moving average. It is divided into two parts: and 29. The identification algorithms are g ₁ = g ₁₀ + k _g ∫ ^t _p eudt (2) and g ₂ = g ₂₀ + k _g ∫ ^t _p eudt (3). In equations (2) and (3), g ₁₀ and g ₂₀ are initial values of g ₁ and g ₂ , respectively, and k _g is an adaptive gain. Furthermore, in the present invention, only one of the two adaptive mechanisms 28 and 29 is operated depending on the magnitude relationship with Cf, and the gain g of the adaptive model 35 is the gain calculated by the operating adaptive mechanism. By using (g ₁ or g ₂ ), it is possible to separately identify the gain g ₁ when Cf is smaller and the gain g ₂ when Cf is larger.

Three changeover switches S ₁ , S ₂ and S ₃ are opened and closed by the comparator 31 and perform switching operations for such a series of operations. Further, in this embodiment, in order to ensure the identification operation, the output xm of the adaptive model 35 is made to match the process signal y at the time when the three switches are switched and the air flow rate f is updated. The broken line arrow leading from the comparator 31 and sample hold unit 34 to the adaptive model 35 indicates this operation.

If the difference between g ₂ and g ₁ obtained in the above manner is integrated by the integrator 32 and the output is Cr, then by appropriately selecting the integral constant, Cr will change in the direction that g ₁ and g ₂ become equal. A kind of integral control action is performed,
Cr reaches a value corresponding to an inflection point on the characteristic curve representing the input-output relationship of the process. The thus calculated Cr is input as a target value to the DO control section, and feedback control is performed so that the DO concentration C is equal to the target value Cr. In order to perform this control operation, in this embodiment, in addition to the normal PI control, an auxiliary operation using the amount of inflow water W is used to improve the response to sudden changes in the inflow load. Then, an identification noise N is added to the reference value f _b of the air amount obtained by the control calculation so that the identification process is carried out smoothly, and this signal is held for a certain period of time to become the actual air amount f.

The results obtained by actually controlling the activated sludge process using the equipment configuration shown in FIG. 3 and the control system shown in FIG. 4 are shown in FIGS. 5a to 5d. Figures 5a to 5d are all diagrams showing changes in various data obtained over the course of 100 hours, and the vertical axis of each of these diagrams is divided by an appropriate full scale value (FS). The FS values are shown on each diagram.

Figure 5a shows the change in time constant T, Figure 5b shows the change in gain _g1 when the output is in the lower fluctuation region and _g2 when the output is in the upper fluctuation region, and Figure 5c shows the change in DO.
FIG. 5d shows changes in the concentration C and its target value Cr, and FIG. 5d shows changes in the amount of air and the amount of inflowing water W, respectively.
Among these, the effect of the present invention is particularly clear in Figure 5c. According to Figure 5c, starting with Cr = 0.5mg/ and the control of the activated sludge process, approximately
After 100 hours of operation, Cr decreased slightly immediately after the start of control, but after 5 to 6 hours it started to increase and was approximately 40
As time passes, it reaches an almost constant value. Then Cr
is maintained at 1.5 to 2 mg/, and the DO concentration C is controlled within a range of approximately ±1 mg/centering on Cr. Comparing the value of Cr after reaching a certain value and the value of C corresponding to the inflection point Q of the curve shown in Fig. 2, the two agree well, and this also shows that the purpose of the present invention is achieved. It can be seen that this has been fully achieved.

In addition, in the above embodiment, the effectiveness of applying the present invention to an activated sludge process and controlling the output near the inflection point by adjusting the output so that g ₁ = g ₂ was described, but the present invention This method is expected to be highly effective not only for activated sludge processes, but also for various processes in which the static characteristic curve representing the input-output relationship has an inflection point, and can be applied to process control in a variety of fields. . Further, in the above embodiment, the output fluctuation region is divided into upper and lower regions using a moving average of the output, but it is also possible to divide the fluctuation region into upper and lower regions according to a target value as another method. Furthermore, it is also possible to input the identification noise N into a model having the same dynamic characteristics as the process, and to divide the region according to when the model output is positive and when it is negative.

〔Effect of the invention〕

As explained above in the embodiments, the present invention is applied to a process in which the input/output characteristics are expressed by a curve having an inflection point due to a sudden change in the output near a specific value of the input, and the output is A method of controlling near an inflection point, the first control loop controlling the output to a target value by manipulating the input, and the second control loop manipulating the target value to maximize the input/output gain. The second control loop divides the output fluctuation region into an upper fluctuation region and a lower fluctuation region, and calculates an input/output gain g ₁ when the output is in the lower fluctuation region. Since this is a method of identifying the input/output gain g ₂ when the output is in the upper fluctuation region and sequentially changing the target value so that g ₁ and g ₂ are equal, the characteristic curve is approximated by a function. It is not necessary to make a determination based only on the magnitude relationship between g ₁ and g _2. Therefore, using a linear model makes it easy to perform parameter identification calculations. Moreover, since the difference between g ₁ and g _{2 is used, noise that commonly affects both g 1 and g 2} can be determined. It is possible to remove the influence of disturbances such as In addition, in the present invention, for example, MRAS is used for online parameter identification.
It is also advantageous in terms of practicality that it is suitable to carry out using .

From the above, the method of the present invention enables a stable control operation with significantly higher reliability than the conventional constant value control method or differential method. In particular, this method fully satisfies the purpose of process control in which improvements in stability and reliability are desired, and can be said to be a method of extremely high practical value.

[Brief explanation of drawings]

Figure 1 is a diagram showing the input/output static characteristic curve with an inflection point and the relationship between g ₁ and g _2. Figure 2 is a diagram showing the aeration air amount f and DO concentration C in the activated sludge process.
3 is a system diagram showing the equipment configuration and functions of the activated sludge process to which the present invention is applied; FIG. 4 is a block diagram showing control calculations according to the method of the present invention; FIG. 5 a to d show changes over time in various data obtained by controlling the activated sludge process using the method of the present invention, where a is set as the time constant T, b is set as g ₁ and g ₂ , and c is set as the DO concentration C. Value Cr,
d is a diagram showing changes in air amount f and inflow water amount W; 1...Aeration blower, 2...Air flow meter, 3...Aeration tank, 4...Aeration pipe, 5...Influent flow meter, 6...Final sedimentation tank, 7
...DO sensor, 8 ... Signal converter, 9 ... Arithmetic device, 10 ... Controller, 11 ... Inverter, 2
1...Activated sludge process, 22, 23, 25...
First-order delay element, 24... Proportional element, 26... Divider, 27, 28, 29... Parameter adaptation mechanism,
30...Moving average calculation unit, 31...Comparator, 32
...Integrator, 33...Target air amount calculation section, 34...
...sample hold section, 35...adaptive model, c
...DO concentration, f...aeration air amount, g ₁
... Gain when the output is smaller than the reference value, g ₂ ...
...gain when the output is greater than the reference value, xm...
...output of adaptive model, y...process signal, P...
...Output reference point, Q...Inflection point, W...Inflow water volume.

Claims (1)

[Claims] 1. Application to a process in which the input/output characteristics are expressed by a curve having an inflection point, where the output changes rapidly near a specific value of the input, and the output changes around the inflection point. The method includes a first control loop that controls the output to a target value by manipulating the input, and a second control loop that maximizes the input/output gain by manipulating the target value. The second control loop divides the output fluctuation region into an upper fluctuation region and a lower fluctuation region, and the input/output gain g ₁ when the output is in the lower fluctuation region and the output when the output is in the lower fluctuation region. 1. A process control method characterized by identifying an input/output gain g ₂ when the input/output gain is in an upper fluctuation region, and sequentially changing the target value so that g ₁ and g ₂ become equal. 2. In the method described in claim 1,
A process control method characterized by dividing an output fluctuation region by a moving average value over two periods. 3. In the method according to claim 1 or 2, a model reference adaptation system for parameter identification MRAS having an adaptation mechanism 28 for g ₁ identification and an adaptation mechanism 29 for g ₂ identification is used, and the output is When in the fluctuation region, only the adaptive mechanism 28 operates and the gain g of the MRAS adaptive model 35 is g ₁
is input, and when the output is in the upper fluctuation region, only the adaptive mechanism 28 operates, and g ₁ is input to the gain g of the adaptive model 35 of the MRAS. 4. In the method described in any one of claims 1 to 3, the adaptive model 3 of MRAS
A process control method characterized by matching the output signal (xm) of No. 5 with a process signal y excluding a DC component.