JP2008165674A - Pid control method and pid control device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a PID control device with less overshoots and fewer computing processes, and to provide a PID control method. <P>SOLUTION: In the PID control method, an operation amount is computed by a deviation between a target value, set beforehand, and a measured value obtained from a control target. The PID control method and device are such that within a controllable range determined by a parameter established based on the control target, rate of deviation change is determined from the deviation between the target value and the measured value; a maximum value of the deviation change speed is determined from the rate of deviation change; and an ideal deviation change speed which can reach the target value without producing overshoots based on the deviation, ARW and a proportional band is computed, a corrected deviation is computed based on the deviation change speed and the ideal deviation change speed; and this corrected deviation is used for I calculation. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a PID control method and a PID control device, and more particularly to a PID control method with less overshoot and fewer calculation steps, and an optimum PID control device for implementing the method.

  In Patent Document 1, “... in the feedback control method, the deviation e (i),... Δe (i),... Δu (i) is represented by a fuzzy variable. ... From e (i) and .DELTA.e (i)... .DELTA.u (i) is calculated by fuzzy set operation and added to the previous process control output value to obtain a new control output value. "Feedback control method based on fuzzy rule".

  Further, Patent Document 2 states that “... in the PID control method based on fuzzy inference, the fuzzy set of the input variable is: the deviation at which the membership function grade of the fuzzy set is maximized and the rate of change of the deviation. The deviation obtained from a desired response model of the measured value with respect to the change of the target value and the value of the change speed, the antecedent part of the fuzzy inference is a logical product of the deviation and the change speed, and the consequent of the fuzzy inference A fuzzy control rule group in which a part is a fuzzy set of correction amounts of the respective PID coefficients, and the consequent part in which the deviation of the antecedent part is equal to the label of the fuzzy set of the changing speed is ... Using a fuzzy control rule group as a fuzzy set, performing the fuzzy inference based on a membership function of the response model, and at least one of the PID coefficients Are described in the PID control method according to fuzzy inference, characterized in that modifying the PID calculation result ".

  Further, Patent Document 3 states that “... in the PID control method, a plurality of inflection points in the known characteristics related to the controlled object are selected, and the value of the operating condition at these selected points is the maximum grade. A function is obtained as an input fuzzy set, a PID coefficient corresponding to the operation condition at the selected point is obtained, and a membership function having the PID coefficient as a maximum grade is obtained as an output fuzzy set, and the input fuzzy set is obtained. Fuzzy inference using fuzzy inference rules with a set as an antecedent part and the output fuzzy set as a consequent part, and the PID coefficient is determined. Has been.

  As described above, in the past, PID control did not adopt the fuzzy (sometimes referred to as “fuzzy”) theory, but fuzzy reasoning was applied in the method of improving PID control in recent years. In many cases, the technology used is used.

  However, when the calculation is performed by applying fuzzy reasoning, the calculation process increases. Especially when performing calculations using a microcomputer, the ROM capacity, the number of clocks, and the type of assembler instruction prepared in the microcomputer are limited depending on the type of microcomputer, and the processing speed varies greatly with a single division instruction. To do. Therefore, a PID control device and a PID control method that can be controlled with fewer calculation steps while reducing the occurrence of overshoot have been desired.

JP-A-1-76202 JP-A-7-281710 Japanese Patent Laid-Open No. 9-311703

  The problem to be solved by the present invention is to provide a PID control method and a PID control device with less overshoot and fewer calculation steps, without adopting fuzzy theory.

As means for solving the problems,
Claim 1 is a PID control method for calculating an operation amount based on a deviation between a preset target value and a measured value obtained from a control target.
Within the controllable range determined by the parameter set based on the control object, the deviation change rate is determined from the deviation between the target value and the measured value,
Determine the maximum value of the deviation change rate from the deviation change rate,
Based on the maximum value of the deviation change rate, the deviation, the ARW and the proportional band, an ideal deviation change rate that can reach the target value without causing an overshoot is calculated.
A PID control method characterized in that a correction deviation is calculated based on the deviation change rate and the ideal deviation change rate, and the correction deviation is used for I calculation.
Claim 2 is a PID control device that calculates an operation amount by a deviation between a preset target value and a measured value obtained from a control target.
An anti-reset windup memory and a proportional band memory that determine a controllable range from parameters set based on the control object;
Within the controllable range, a deviation change rate calculator that determines the deviation change rate from the deviation between the target value and the measured value;
A maximum deviation change rate memory for determining a maximum value of the deviation change rate from the deviation change rate;
An ideal deviation change rate calculator that calculates an ideal deviation change rate that can reach the target value without causing overshoot based on the maximum value of the deviation change rate, the deviation, the ARW, and the proportional band;
A PID control device comprising: a deviation corrector that calculates a correction deviation based on the deviation change speed and the ideal deviation change speed and outputs the correction deviation to an I calculation.

  The present invention obtains a deviation at the time of measurement based on a measured value and a target value that are measured every moment in a controlled object, and further calculates a correction deviation for achieving the target value without causing overshoot. The control object is controlled based on the control amount of P, D and I obtained by performing the I operation based on the correction deviation, the P operation and the D operation based on the I deviation, and the overshoot. It is possible to provide a PID control method and a PID control device that can be prevented and can reduce the time required to reach the target value even if an overshoot occurs.

  Furthermore, the present invention can reduce the number of calculation steps because there is no need to set a membership function or the like as compared with the PID control method and PID control apparatus to which fuzzy reasoning is applied, thereby reducing the amount of programs. It is possible to provide a PID control method and a PID control device that can reduce the calculation time.

  An embodiment of the PID control apparatus and PID control method of the present invention will be described with reference to the block diagram shown in FIG.

In FIG. 1, PV indicates a measured value in the controlled object, SV indicates a preset target value, e indicates a deviation between the PV and the SV, Δe indicates a change rate of the e, Δe _max represents the maximum value of the .DELTA.e, I ₀ is the I ₀ when the target value SV ± I ₀ a value in the range that allows the I control. This I ₀ is given, for example, as a product of a proportional band Pb determined by the control target and an anti-reset windup (hereinafter also referred to as “ARW”). R _IDEAL indicates Δe (hereinafter, sometimes referred to as “ideal deviation change speed”) that can reach the target value while preventing overshoot, and e ′ is a ratio between Δe and R _IDEAL. The correction deviation weighted accordingly is shown, and MV shows the manipulated variable. Here, the term “ideal” is “to reach the target value so as not to cause overshoot, and even if overshoot occurs, the overshoot is reduced to a negligible level. Say that you can.

First, before performing a control calculation according to the block diagram of FIG. 1, a definition of values used for the calculation is created. The definition is shown below.
(1) the controllable range of the range of the prescribed value I ₀ around a target value SV by adding or subtracting.
(2) I ₀ is, for example, the product of Pb and ARW, and when ARW takes the maximum value of 100%, it is assumed to be the same value as Pb.
(3) On the premise of the above conditions, it is assumed that the change in the optimum measured value within the controllable range is in a form that follows a first order lag.
(4) When the above (3) is satisfied, the relational expression between the time t after the measured value PV reaches the controllable range and the measured value y (t) is as follows. This is a condition for the measured value that can reach the target value while preventing overshoot, and FIG. 2 shows a graph of the equation (1).

（式（１）中、Ｉ_０は目標値と制御可能範囲内の下限値又は上限値との偏差、すなわち制御可能範囲の１／２であり、ｅはネイピア数を表し、Ｔは一次遅れ時定数を表す。）
（５）前記式（１）から、時間ｔでの測定値の変化速度Ｒは以下の式となる。

(In Expression (1), I ₀ is the deviation between the target value and the lower limit value or the upper limit value within the controllable range, that is, ½ of the controllable range, e represents the number of Napiers, and T is the first order delay Represents a constant.)
(5) From the above equation (1), the change rate R of the measured value at time t is as follows.

（式（２）中、ｅはネイピア数を表す）
（６）前記式（２）から、測定値ＰＶが制御可能範囲に達した時点での測定値変化速度Ｒ_０は以下の式となる。

(In formula (2), e represents the number of napiers)
(6) From the equation (2), the measured value change rate R ₀ when the measured value PV reaches the controllable range is expressed by the following equation.

（７）前記式（１）及び前記式（２）から、次式を導出する。

(7) The following formula is derived from the formula (1) and the formula (2).

（８）一次遅れの式に従うため、前記式（４）は、次のように表せる。

(8) In order to follow the first-order lag equation, the equation (4) can be expressed as follows.

（９）前記式（５）を理想的な偏差変化速度とし、制御範囲内における実際の偏差変化速度の割合に応じてＩ演算に用いる偏差を補正するとする。

(9) The above equation (5) is assumed to be an ideal deviation change rate, and the deviation used for the I calculation is corrected according to the ratio of the actual deviation change rate within the control range.

The values calculated according to the above definitions (1) to (9) are calculated according to the block diagram shown in FIG.
Here, in the PID control device and the PID control method of the present invention, the calculations performed by the P calculator, the I calculator, and the D calculator are the conventional PID controller and PID control method as shown in FIG. This is almost the same as the calculation performed in (1). More specifically, the calculation performed by the conventional PID control device and the PID control method is as follows. In the P calculator, the control operation amount is determined based on the proportional band Pb and the deviation e between the measured value PV and the target value SV. The I calculator determines an amount of control operation based on an integral value obtained by integrating the deviation e, that is, the total deviation and the integration time It, and the D calculator calculates the deviation e for each preset differential sampling time ΔDt. This is an operation for determining the control operation amount based on the differentiated differential value and the differential time. In the PID control device and the PID control method of the present invention, it is important that the deviation e input to the I calculator is changed to a correction deviation e ′.

First, as shown in FIG. 1, the target value SV output from the target value storage means 2 and the measurement value PV output from the measurement value storage means 3 are input to the deviation calculator 4, and PV is subtracted from SV. To calculate the deviation e.
Here, the target value is a value to be realized for the physical quantity to be controlled in the controlled object. Examples of the physical quantity include temperature and pressure. Control objects include, for example, devices that require temperature control, such as a constant temperature bath, a reaction bath, a room that must be maintained at a constant temperature, such as a freezer room, a living room, or a machine that must be maintained in a constant temperature environment. , Instruments, devices, and the like.
The target value is normally input by the input means for inputting the target value and stored in the target value storage means. In other words, the target value storage means includes a memory for storing a set value input as a target value through input means such as communication or a keyboard.
The measured value storage means includes a memory that temporarily stores a physical quantity measured over time in a measurement target as a measured value for a certain period. The physical quantity in the measurement object is measured by various sensors. For example, when the physical quantity to be measured in the measurement object is temperature, the measured value is measured by a temperature sensor that can output the temperature as an electrical signal. The deviation calculator compares the set target value for the measurement object stored in the target value storage means with the measured value and outputs the deviation. The deviation is calculated for each measured value and stored in a memory provided in the deviation calculator for a certain period.

  Next, the deviation e is output from the deviation calculator 4 to the P calculator 5, the D calculator 6, the deviation change rate calculator 10, and the ideal deviation change rate calculator 12. As described above, the P calculator uses the proportional band Pb and the deviation e input from the deviation calculator 4 to output a control output amount corresponding to the ratio of the deviation e to the proportional band Pb. Similarly, as described above, the D calculator calculates a deviation change amount for each differential sampling time ΔDt using the differential time Dt and the deviation e input from the deviation calculator 4, and according to the change amount. Output the amount of control output.

  The deviation change rate calculator 10 calculates a deviation change rate Δe from the input deviation e. This deviation change rate Δe is generally the difference between the deviation at the measurement time and the deviation at the measurement time immediately before the measurement time, and the time difference between the measurement time and the measurement time before the measurement time. The value divided by. The deviation change rate Δe calculated by the deviation change rate calculator 10 is output to the maximum deviation change rate storage unit 11 and the deviation corrector 15.

  Generally speaking, the maximum deviation change rate storage device can selectively store the maximum value from the deviation change rate calculated at each time point in the measurement time from the measurement start time point. If the deviation change rate at the next measurement time is higher than the current maximum deviation change rate, the value of the maximum deviation change rate is updated to the value of the deviation change rate at this point. The change rate storage unit incorporates a calculator that updates the value.

That is, as shown in FIG. 1, the maximum deviation change rate storage unit 11 calculates the maximum deviation change rate Δe _max . In various actual control systems, the speed at which the measured value PV rises and the speed at which the measured value PV rises are not necessarily the same depending on the control target, so the maximum deviation change speed Δe _max is divided into the rising time and the falling time. Specifically, when the target value SV is larger than the measured value PV and the deviation e is positive, the maximum deviation change rate Δe _max at the time of ascent is adopted, and the target value SV is smaller than the measured value PV and the deviation e is negative. Adopts the maximum deviation change speed Δe _max when descending. Incidentally, the calculated deviation change rate .DELTA.e is if exceeding the maximum deviation change rate .DELTA.e _max until it updates the maximum deviation change rate .DELTA.e _max to the deviation change rate .DELTA.e.

The maximum deviation change rate Δe _max is input from the maximum deviation change rate storage unit 11 to the ideal deviation change rate calculator 12. In the ideal deviation change rate calculator 12, the deviation e, the maximum deviation change rate Δe _max , and the controllable range. A value I ₀ (for example, the product of the proportional band determined by the control object 9 in the proportional band memory 13 and the ARW output from the ARW memory 14) is input, and an ideal deviation change from the equation (5) The speed R _IDEAL is calculated. Here, generally speaking, the proportional band memory is a memory that stores a preset proportional band. This proportional band indicates a control range of proportional control, that is, control called P control, and is a value determined in advance by the measurement target. This proportional band is stored in the proportional band memory through input means such as communication or a keyboard. In general, the ARW memory is a memory for storing a deviation value for starting integration of deviations in the integration operation in order to prevent overshoot in advance by limiting the range in which the integration operation is effective. This value is determined in advance according to the measurement target. The ARW is input by input means such as communication or a keyboard. Here, the proportional band and ARW are determined by auto-tuning or the like that automatically calculates PID control parameters. For example, when the PID control device and the PID control method of the present invention are used for temperature control, It is determined in consideration of heating or heat dissipation characteristics.

Further, the deviation corrector 15 receives the obtained R _IDEAL and the deviation change speed Δe, and calculates a correction deviation e ′ according to the ratio thereof. At this time, when the deviation change rate exceeds the ideal deviation change rate, e ′ <e, so that the correction deviation input to the I calculator is made small, and when the deviation change rate is lower than the ideal deviation change rate, e ′> e. e, so that the correction deviation is increased. As an example, Formula (6) is given.

（式（６）中、Ｃは重み付けを示す定数であり、Ｆは制御対象によって決定される定数Ｃの補助係数を表す）
式（６）の補助係数Ｆは、式（５）から導出される理想的な偏差変化速度Ｒ_{ＩＤＥＡＬ}が、実際の偏差変化速度Δｅと比べてどの程度差異があるかに応じて決定される。例えば、前記補正偏差ｅ’を算出する場合に、仮に偏差ｅが正の値であっても、重み付けを大きくすることにより補正偏差ｅ’を負にすることができ、偏差変化速度Δｅを理想的な偏差変化速度Ｒ_{ＩＤＥＡＬ}に近づけることができる。

(In Expression (6), C is a constant indicating weighting, and F represents an auxiliary coefficient of the constant C determined by the control target)
The auxiliary coefficient F in Expression (6) is determined according to how much the ideal deviation change speed R _IDEAL derived from Expression (5) differs from the actual deviation change speed Δe. For example, when calculating the correction deviation e ′, even if the deviation e is a positive value, the correction deviation e ′ can be made negative by increasing the weighting, and the deviation change speed Δe is ideal. The deviation change speed R _IDEAL can be approached.

  Next, the I calculator 7 performs an operation using the correction deviation e ′.

  The I computing unit calculates the total sum of deviations based on the corrected deviation e 'input to the I computing unit, and outputs the control output amount in the I computing unit from the sum of the deviations and the integration time It.

  Furthermore, the control operation amount MV is determined by the control operation unit 8 by summing the operation result of the I operation unit 7 and the operation results of the P operation unit 5 and the D operation unit 6 calculated using the deviation e. To do.

  The calculated control operation amount MV has a value of 0 to 100%, and the controlled object is controlled by means for adjusting the output of a power regulator or the like. Examples of the power regulator include an electromagnetic relay using a time-sharing control output, a thyristor using a solid state relay control or a current output.

  The PID control apparatus and the PID control method of the present invention do not need to create a plurality of membership functions and inference rules by fuzzy inference, and can greatly reduce the calculation process. As a result, it is possible to quickly respond to changes in the controlled object, and since the number of calculation steps is small, the PID control device and the PID control method of the present invention can be implemented even with a computer with low calculation capability.

  Furthermore, when creating a plurality of membership functions and inference rules by fuzzy inference, a large amount of data is experimentally accumulated and the deviation is calculated through a complicated calculation process. In the PID control device and the PID control method, an ideal deviation change rate is determined by a simple calculation formula by obtaining a deviation at a certain time point and the deviation change rate. Can be calculated by correcting the deviation used in the I calculation.

When the measured value exceeds the target value, or when the measured value exceeds the target value from the beginning, the PID control device and the PID control method to which fuzzy inference is applied, in addition to the default membership function and inference rule Further, it is necessary to create and deal with a plurality of membership functions and inference rules. However, in the PID control apparatus and the PID control method of the present invention, the maximum deviation is appropriately divided into cases where the deviation e is positive and negative. By using the change rate Δe _max , it is possible to cope with the condition where the measured value exceeds the target value.
Furthermore, the PID control device and the PID control method of the present invention do not control along the graph shown in FIG. 2, but compares the actual deviation change rate Δe with the ideal deviation change rate R _IDEAL. By correcting the deviation e at the time of measurement, the measured value PV eventually approaches the displacement of the graph shown in FIG.

(Example)
Using the PID control device and the PID control method of the present invention, temperature control was performed according to FIG.
Control conditions / control object Brass square block of 25 × 20 × 100mm Heater capacity 200W
-Initial temperature 25-28 ° C
・ Control device setting Target value (SV) 100 ℃
Proportional band (Pb) 30 ° C
Integration time (It) 100 seconds Differential time (Dt) 12.5 seconds ARW 100%
Control level (weighting) 5
The operation procedure of the embodiment will be described below.
Deviation e between measured value 3 and target value 2 obtained from the control object is calculated by deviation calculator 4, P calculator 5, D calculator 6, deviation change rate calculator 10, ideal deviation change rate calculator. 12 is output.
The P calculator 5 performs general P control.
The D calculator 6 performs general D control.
The deviation change rate calculator 10 compares the deviation obtained in the previous sampling with the deviation obtained this time, calculates the deviation change rate Δe, and outputs it to the maximum deviation change rate storage unit 11 and the deviation corrector 15.
The maximum deviation change rate storage unit 11 compares the largest deviation change rate at this time with the deviation change rate obtained this time. If the current deviation change rate is large, the maximum deviation change rate is updated and an ideal deviation change rate calculator is obtained. Output to.
The ideal deviation change rate calculator 12 calculates an ideal deviation change rate R _IDEAL from the deviation, the deviation change rate, the maximum deviation change rate, and I ₀ (in this case, the product of the ARW storage unit 14 and the proportional band storage unit 13). Calculate and output to the deviation corrector 15.
The deviation corrector 15 compares the deviation change rate with an ideal deviation change rate, obtains a correction deviation e ′ with the weight obtained by the control level storage 16, and outputs it to the I calculator.
The I computing unit adds the obtained deviation e ′ to the total deviation Σe, calculates an operation amount by I control from the integration time It, the total deviation Σe, and the proportional band Pb, and outputs it to the control computing unit 8.
The control arithmetic unit 8 performs the same general PID control process as in the comparative example.

(Comparative example)
A simulation was performed using the conventional PID control method and PID control device shown in FIG. Specifically, the deviation change rate calculator 10, the maximum deviation change rate calculator 11, the ideal deviation change rate calculator 12, and the deviation corrector 15 in FIG. 1 are not employed, and the deviation e is not corrected from the deviation calculator 4. A temperature control simulation was performed by directly outputting to the I calculator 7.
Control conditions / control object Brass square block of 25 × 20 × 100mm Heater capacity 200W
-Initial temperature 25-28 ° C
・ Control device setting Target value (SV) 100 ℃
Proportional band (Pb) 30 ° C
Integration time (It) 100 seconds Differential time (Dt) 12.5 seconds ARW 100%
The operation procedure of the comparative example will be described below.
A deviation e between the measured value 3 and the target value 2 obtained from the controlled object is calculated by the deviation calculator 4 and output to the P calculator 5, the D calculator 6, and the I calculator 7.
The P calculator 5 compares the obtained deviation e with the proportional band (Pb) stored in the proportional band storage 13, calculates the operation amount by the P calculation, and outputs it to the control calculator 8.
For each differential sampling ΔDt (D control has its own sampling time), the D calculator 6 calculates the variation in deviation for each differential sampling from the deviation e and the previous deviation e ₂ obtained at the previous sampling. An operation amount is calculated from the change amount, the differential time Dt, the operation amount Der ₂ by the previous D control, and the proportional band Pb, and is output to the control calculator 8.
The I computing unit adds the obtained deviation e to the total deviation Σe, calculates an operation amount by I control from the integration time It, the total deviation Σe, and the proportional band Pb, and outputs it to the control computing unit 8.
The control arithmetic unit 8 adds the operation amounts output from the P, D, and I arithmetic units, and outputs the result to the control target through processing such as a limit.

  The results of Examples and Comparative Examples are shown in FIG. In addition, a continuous line is an Example and a broken line is shown by a comparative example.

  In FIG. 3, it can be seen that overshoot could be prevented by using the PID control device and the PID control method of the present invention. In addition, the target value is reached in a short time compared to the comparative example, and is stable thereafter.

FIG. 1 shows a block diagram of an operation procedure which is an embodiment of the PID control device and the PID control method of the present invention. FIG. 2 shows the conditions of the measured values that can reach the target value while preventing the schematic overshoot. FIG. 3 shows simulation results of the example and the comparative example. FIG. 4 is a block diagram showing a PID control device that is outside the scope of the present invention.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 PID control apparatus 2 Target value memory | storage means 3 Measured value memory | storage means 4 Deviation calculator 5 P calculator 6 D calculator 7 I calculator 8 Control calculator 9 Control object 10 Deviation change speed calculator 11 Maximum deviation change speed calculator 12 Ideal Deviation Change Speed Calculator 13 Proportional Band Memory 14 ARW Memory 15 Deviation Corrector 16 Control Level Memory

Claims (2)

In a PID control method for calculating an operation amount by a deviation between a preset target value and a measured value obtained from a control target,
Within the controllable range determined by the parameter set based on the control object, the deviation change rate is determined from the deviation between the target value and the measured value,
Determine the maximum value of the deviation change rate from the deviation change rate,
Based on the maximum value of the deviation change rate, the deviation, the ARW and the proportional band, an ideal deviation change rate that can reach the target value without causing an overshoot is calculated.
A PID control method, wherein a correction deviation is calculated based on the deviation change speed and the ideal deviation change speed, and the correction deviation is used for I calculation. In a PID control device that calculates an operation amount based on a deviation between a preset target value and a measurement value obtained from a control target,
An anti-reset windup memory and a proportional band memory that determine a controllable range from parameters set based on the control object;
Within the controllable range, a deviation change rate calculator that determines the deviation change rate from the deviation between the target value and the measured value;
A maximum deviation change rate memory for determining a maximum value of the deviation change rate from the deviation change rate;
An ideal deviation change rate calculator that calculates an ideal deviation change rate that can reach the target value without causing overshoot based on the maximum value of the deviation change rate, the deviation, the ARW, and the proportional band;
A PID control apparatus comprising: a deviation corrector that calculates a correction deviation based on the deviation change speed and the ideal deviation change speed and outputs the correction deviation to an I calculation.

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