JPS5916002A - Pi controlling method - Google Patents

Abstract

PURPOSE:To simplify algorithm and to improve control precision by finding parameters of a PI control expression from a gain, time constant, process variables, and overshoot control time of control response as parameters of a first- order lag system. CONSTITUTION:The measured value (u) of an air capacity detector 7 and measured value (x) of a DO detector 6 are inputted to a controlled system identifying part 12. The identifying part 12 calculates the gain K and time constant T of the first-order lag system from the measured values (u) and (x). A PI control constant adjusting part 13 calculates the proportional gain KP and integral time T1 of a PI controller from the gain K and time constant T. The controlled system identifying part 12 performs the arithmetic at every control period. The PI control constant adjusting part 13 performs the arithmetic so that an attenuation constant xsi and overshoot time tP are constant. Even when the characteristics of a controlled system vary, the overshoot time is constant, so quick response is satisfied and gain characteristics to frequency response are desirable all the time.

Description

[Detailed Description of the Invention] [Technical Field of the Invention] The present invention provides PI (
The present invention relates to a PI control method that performs control using a proportional/integral (proportional/integral) control device.

[Technical background of the invention and its problems] In general, input U (
8) and the output X(S) expressed by equation (1) is called a first-order lag system.

Here, K is the gain of the first-order lag system, T is the time constant of the first-order lag system, and Sif>plus operator.

When performing feedback control to match the controlled variable to the target value for such a first-order lag system controlled object,
As the control device, a so-called proportional-integral (PI) control device is often used, which multiplies the deviation between the controlled variable and the measured value and its derivative by a certain constant, and uses the sum as the output of the manipulated variable.

FIG. 1 shows an example of the configuration of a control device in the above case.

As an example for explanation, the control system is a dissolved oxygen concentration control system in an aeration tank in a sewage treatment process.In general, in a sewage treatment process, polluted water is introduced into an aeration tank, and the aerobic microorganisms in the aeration tank V1 treatment is performed using the activated sludge method, which decomposes organic matter in polluted water and separates wastewater and sludge. At that time, dissolved oxygen concentration in the aeration tank (hereinafter referred to as I)
(referred to as 0) is not necessary or necessary. In Fig. 1, the air supplied by the blower 1 passes through the pipe 2 and the air volume control valve 3, is sent to the aeration tank 4, and is released into the polluted water in the aeration tank by the aeration pipe 5. 1 and 7 are air volume detectors, which are installed on the inlet side of the air volume control valve 3, and are installed in the aeration tank 4 to measure Do in the aeration tank. Measure Ik. As a result, the measured process quantities are input to the control device 8. Control device 8
Then, calculation is performed using a built-in function in advance, and as a result, an opening degree control command is output from the control device 8 to the wind 1 control valve 3.

The functions of the control device 80 consist of an input/output interface section 9, a DO control section 10, and an air volume control section 11 for each dog. The input/output interface unit 9 has a function of inputting signals measured by the Do detector 6 and the air volume detector 7, and issuing an opening degree control command to the air volume control valve 3. The DO control unit lo determines that the Do measurement value X added by the Do detector 6 is
It has a function of calculating the air flow rate target values u, k so that they match the preset 7'cI) o target value Xr. Air volume control section 11
is, the air volume measurement value U measured by the air volume detector 7 is D
The DO control unit 10 has a function of calculating the opening degree control signal 2 for the air volume control valve 3 so as to match the air volume target value ur calculated by the control unit 10.The DO control unit 10 calculates the response of Do to the air volume. shows a response almost like that of a first-order lag system, so Do measurement value X and DO
From the target value xr, the air flow target value U is calculated using the following PI calculation formula.

ur(n): Current air volume target value ur(n-1)' Previous air volume target value Δu,: Air volume target value variation k: Proportional gain p TI: Integral time eI,: Current deviation en-1' Previous time Deviation - control period In a control device having such a configuration, conventionally, the DO control section 1
Proportional gain l, which is a parameter of the PI control equation at 0
cp and integration time T1 are fixed values, and the desired value E
The operator made adjustments through trial and error to obtain a good control response [7
It was a good value. Generally, if the characteristics of the controlled object do not always change, the desired control response cannot always be obtained by adjusting the PI control constant once.
If the characteristics of the controlled object are changing from time to time, the PI
If the control redundancy is set to a fixed value, it is impossible to always obtain a desired control response. Even in front DO control, the response of DO to air flow rate is close to that of a first-order lag system, but the responsiveness varies depending on changes in operating conditions, and the time constant is generally between 5 and 30 minutes. It is said that things are changing. Therefore, if the PI control constant k,,T1 in the conventional Do control unit 10 is set to a fixed value,
Since it is not possible to always obtain the desired control response,
The operator had to periodically observe the control response and readjust the P■ control constant.

[Purpose of the invention]

An object of the present invention is to follow changes in the characteristics of a controlled object approximated by a first-order lag system, so that P
An object of the present invention is to provide a PI control method that performs control by automatically adjusting an I control constant.

[Summary of the invention]

The present invention provides P for a controlled object approximated by a first-order lag system.
When performing control with the I control device, the values of the gain K and time constant T, which are the parameters of the first-order lag system, are determined by using an equation that linearly approximates a nonlinear function representing the characteristics of the controlled object. The PI control formula is calculated from the process quantities U and X corresponding to the input and output of p, and the PI control formula is calculated using the results, a separately determined damping coefficient ξ, and an overshoot control time t for the control response. Find the values of proportional gain Kp and integration time T1, which are the parameters of
A PI control method is characterized in that PI control is performed using this value.

[Embodiments of the invention]

The present invention will be described in detail below with reference to an embodiment shown in the drawings. FIG. 2 shows the configuration of a Do control device to which the control method according to the present invention is applied. Note that the same symbols as in FIG. 1 indicate the same functions. A feature of the control device of the present invention is that it includes a controlled object identification section 12 and a PI control constant adjustment section 13.

The controlled object identification unit 12 has a function of calculating the gain K and time constant T of the first-order lag system from the current air volume measurement value U and DO measurement value X. The PI control constant adjustment unit 13 determines a proportional gain Kp and an integral time T. of the PI control constant that will provide a desirable control response from the gain K and time constant T of the first-order lag system calculated by the controlled object identification unit l2. Next, the specific functions of the same leg part l2 to be controlled and the PI control constant adjusting part 13, which have the function of changing the PI control constant of the DO control part 10, will be explained.

(1) Function 1 of the controlled object identification unit I2: The characteristics of the controlled object change from time to time due to changes in operating conditions, etc. This is due to the non-linear relationship between the number of people to be controlled and the way they appear. . And for general control objects,
This relationship between the direction of entry and the direction of exit is often expressed by some kind of nonlinear function. In the controlled object identification unit l2, the nonlinear function of the controlled object is linearized within minute changes in the vicinity of the equilibrium point, and the gain K and time of the first-order lag system are calculated from various process quantities using an arithmetic expression that is expressed as a first-order lag system. A detailed method will be explained below using the L)0 control system as an example, which has the function of calculating the constant T.

It is generally known that there is a relationship between the air flow density u and the DO value X as shown in equation (5).Here, X: DO value (PPM) d. ■． Time differential U: Air flow rate (1/hour) D.O.
The value X is a known value, Rr is an undetectable process quantity, a,
n is a plant-specific constant. In equation (5), it can be seen that the time change in the Do value is determined by the nonlinear relationship between the air flow rate U, which is a characteristic of the controlled object, and the DO value X. This nonlinear function is linearized within minute changes in the vicinity of the equilibrium point.

Now, assuming that the control target range is near the equilibrium point, the following equation holds true.

Here, xo = Do when the process is at the equilibrium point
Value (PPM) ΔX: Deviation from 1) O value (PPM) when the process is at a certain equilibrium point u0. Blast silk (n?) when the process is at a certain equilibrium point
/hour) △U: Deviation CnlZ from the air flow rate when the process is at a certain equilibrium point) Rr0: Oxygen consumption rate (PPM/hour) when the process is at a certain equilibrium point ΔRr: Equilibrium where the process is Deviation from the oxygen consumption rate at the point (PPM/hour) (ignoring the term ΔU.ΔX in the force equation and substituting equation (6), equation (8) is obtained.

Equation (8) relates to U and X (1 and linear), and if this is expressed in a block diagram, it will be as shown in FIG. 3. However, K1, 1 K2, 100 are as follows.

Therefore, this model is expressed as a first-order lag system and a disturbance, and the gain K and time constant T of the first-order lag system are expressed by the following equation.

(lυ Equation. (In Equation 12, a, n, and x are constants, so the controlled object identification unit 12 was measured by the DO measurement value X measured by the Do detectors 6 to 9 and the air volume detector 7. The gain K and time constant T of the first-order lag system are calculated for each control cycle by substituting the measured value U of the wind wave into Equation 13.

f2) Function of PI control constant adjustment unit l3 The PI control constant adjustment unit 13 performs PI control that satisfies the lower design goals based on the gain K1 and time constant T of the first-order lag system calculated by the controlled object identification unit 12. It has a function to calculate the proportional gain Kp and integration time TI of the device.

Design goal 1: Make the damping coefficient ξ constant (for example, 0.8) and 9.

Design goal 2: Make the overshoot time tp (timetopeek) of the response of the controlled variable to a step change in the target value constant. Design goal 3: Make the gain characteristics in the frequency response of the open-loop transfer function desirable. do. That is, the slope of the gain characteristic is set to -20 dB/dec near the intersecting frequency wc, and set to -40 dB/dec in the low frequency range to increase the low frequency gain.

Here, the damping coefficient ξ and the overshoot time t are preset values. FIG. 4 shows an algorithm showing the function of the PI control constant adjustment section l3. In FIG. 4, first, the set values of the damping coefficient ξ and the overshoot time 1p are input (step l4), and the gain K1 time constant T of the first-order lag system calculated by the controlled object identification unit 12 is input ( Step 15).

In order to make the gain characteristic in the frequency response of the open loop transfer function desirable, a limit is placed on the relationship between the overshoot time 1p and the time constant T of the first-order lag system (steps 16 and 17).

An operation 'N of the α-order formula is performed (step 18).

Then, the proportional gain Kp% integration time Tzt of the Pl controller
Each (14), ti! Calculate using Equation 19 (Step 1
9).

In this algorithm, Co,C,,C, is a constant that depends on the damping coefficient ξ, for example, C at ξ-0.8. -1
．． IC+-2.14C2=0.52. The PI control constant adjustment unit 13 determines the proportional gain Kp1 integral time TIk of the PI controller that maintains a desired control response by calculating Doki's algorithm for each control cycle, and determines the proportional gain Kp1 integral time TIk of the PI controller to maintain a desired control response
Change the PI control constant to the value calculated this time.

Next, the operation of the present invention will be explained. The characteristics of the controlled object approximated by a first-order lag system, that is, the gain K of the first-order lag system
and time constant T fluctuate from moment to moment due to changes in operating conditions, etc., whereas the controlled object identification unit 12
The two equations are calculated for each control period to calculate the gain K and time constant T of the first-order lag system at that point in time. The PI control constant adjustment unit l3 adjusts the set damping coefficient ξ and overtravel time tP for the calculated gain K and time constant T of the first-order lag system.
The proportional gain Kp1 integral time TI of the PI controller such that is constant is calculated according to the algorithm shown in FIG. 4, and the PI control constant of the DO control section 10 is changed.

The Do control unit 10 uses the calculated PI control constant in equation (3), and calculates the air flow target value U: using equations (2>, f3) and f41.

As a result, even if the characteristics of the controlled object change, the overtravel time 1
, is constant, so the quick response is satisfied, and the damping coefficient ξ
In one step, the gain characteristic in the frequency response of the open-loop transfer function becomes a constantly desirable characteristic. Therefore, stability is also satisfied, and a desirable control response can always be obtained.

In the above-mentioned embodiment, the dissolved oxygen concentration control system in the aeration tank in the sewage treatment process was explained. However, the present invention is not limited to this, and the controlled object is approximated by a first-order lag system in a general process control system. , it is possible to apply all processes in which parameters of a first-order lag system can be calculated using a functional formula that linearly approximates a nonlinear function to be controlled.

〔Effect of the invention〕

According to the present invention, a simple algorithm is used to automatically adjust the P
The I control constant can be adjusted to always obtain the desired control response. The fact that the algorithm is simple means that it is highly practical, and the ability to automatically adjust the control constant reduces the time required for testing and adjusting the product, and furthermore, it means that the desired control answer can always be obtained. It is possible to improve product quality by improving control accuracy.

[Brief explanation of the drawing]

Fig. 1 is a block diagram showing the relationship between the dissolved oxygen concentration control system and a conventional PI control device, Fig. 2 is a block diagram showing the configuration of a device that executes the PI control method according to the present invention, and Fig. 3 is a linearized FIG. 4 is a block diagram showing a dissolved oxygen concentration model, and FIG. 4 is a schematic flowchart of an algorithm showing the function of the PI control constant adjustment section in the present invention. ■...Blower 2...Pipe line 3...Air volume control valve 4...Aeration tank 5...Diffuser pipe 6...DO detector 7...Air volume detector 8...Control device 9... Input/output interface section 10... Do control section (PI control section) 11... Air volume control section 12... Controlled object identification section l3.
...PI control constant adjustment section X...DO measurement value/x,...DO target value ur...
Air volume target value U... Wind velocity measurement value Z... Opening control signal Kp... Proportional gain II of PI control type... Integral time K of PI control type... Gain T of first-order lag system ... Time constant ξ of first-order lag system ... Damping coefficient 1p ... Overtravel time -12-

Claims (1)

[Claims] When controlling a controlled object approximated by a first-order lag system using a PI control device, the first-order lag The values of the gain K and time constant T, which are system parameters, are calculated from the process quantities U and X corresponding to the input and output of the first-order lag system, and the results are calculated using the separately determined damping coefficient ξ and control response. PI using the overshoot control time tp of
Proportional gain Kp and integral time T, which are parameters of the control equation
A PI control method characterized in that the value of 1 is determined by the following formula, and PI control is performed using this value. Also C,,C. is a constant that depends on the damping coefficient ξ.