JPH0876804A - Digital pid controller - Google Patents

Abstract

PURPOSE: To provide a digital PID controller which can improve its control performance by correcting easily a differential operation against the change of control operation cycle. CONSTITUTION: The digital PID controller performs a digital PI operation to the controlled variable given from a system to be controlled and also to the deviation of the controlled variable and its target value, performs a digital D operation to the deviation or the controlled variable based on the control operation cycle and the differential time, and synthesizes these operation outputs to apply them to the controlled system as a manipulation signal. A differential operation correction coefficient computing means 11 is added to the PID controller to calculate a differential operation correction coefficient against the change of a control operation cycle Δt based on the differential time TD0 set in a control operation cycle Δt0 that has been best adjusted, together with a velocity type aifferential computing means 12 which calculates a differential member against the change of the cycle Δt by a prescribed operational expression and based on the differential operation correction coefficient calculated by the means 11.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION The present invention relates to PID (P: proportional,
Digital PID that corrects the D operation term in the I: integral, D: derivative) operation terms in response to changes in the control operation cycle.
Regarding the control device.

[0002]

2. Description of the Related Art This type of PID control system can be said to be an indispensable control system for performing feedback control of a plant even at the present time when the plant operation is being optimized or being made flexible. .

The basic equations of PID control are a P (proportional) operation which outputs an output proportional to the deviation, an I (integral) operation which outputs an output proportional to the integral of the deviation, and an output proportional to the derivative of the deviation. It can be expressed as the sum of the D (differential) calculation operation to be performed.

Therefore, when the arithmetic expressions in these PID arithmetic operations are expressed in the form of transfer functions, the following equations are obtained. C (s) = {MV (s) / E (s)} = K _P {1 + 1 / (T _I · s) + (T _D · s) / (1 + ηT _D · s)} ………… (1) , C (s): transfer function of PID, MV (s): manipulated variable,
E (s): deviation, K _P : proportional gain, T _I : integration time, T
_D : differential time, s: Laplace operator, 1 / η: differential gain. When this equation (1) is expressed as a velocity type digital arithmetic expression using data that changes every control arithmetic cycle Δt,
Expressions (2) and (3) are obtained.

[0005]

[Equation 1]

Where MV _n : current manipulated variable, MV
_n-1: the operation amount of the previous control operation period time, △ MV _n: the operation amount of the change of time until a current time from the last, e _n: deviation of current, e _n-1: previous control operation period time deviation, D _n : the differential output at the present time, D _n-1 : the differential output at the time of the previous control calculation cycle, ΔD _n : the change in the differential output from the previous time to the present time. Among them, the (3) the effective differential gain beta in the differential operation section type, expressed by _{β = T D / (△ t} + ηT D) ......... (4).

FIG. 4 is a diagram showing a configuration of a conventional digital PID control device using the equations (2) and (3). The controller directs the target value SV _n and controlled variable PV _n to the deviation operation means 1, wherein the deviation e _n = SV _n -PV
_{After n} is obtained, it is sent to the speed type proportional calculating means 2, the speed type integrating calculating means 3 and the speed type differential calculating means 4. The velocity type proportional calculation means _{2, △ P n = e n -e} n-1 becomes performs the operation, also in the velocity type integral calculation means _{3, △ I n = (△} t / T I) · e n becomes operational Further, the velocity-type differential calculation means 4 calculates ΔD _n by performing the calculation based on the equation (3).

Then, after the operation outputs obtained by the respective operation means 2 to 4 are guided to the addition means 5 and added and synthesized, the proportional gain means 6 multiplies the proportional gain K _P to obtain the operation amount from the previous time to the present time. The change amount ΔMV _n , that is, ΔMV _n = K _p (ΔP _n + ΔI _n + ΔD _n ) ... (5)

Thereafter, the change amount ΔMV _n of the manipulated variable thus obtained is applied to the speed type / position type signal converting means 7, and the manipulated variable MV _n-1 at the previous time point is added to the current control cycle time point. MV _n = MV _n-1 + ΔMV _{n is} calculated by using the change amount ΔMV _n of the manipulated variable obtained in step 3 to obtain the current position type manipulated variable MV _n ,
This position type manipulated variable MV _n is applied to the controlled object 8.

The control result for the controlled object 8 is detected by the control amount detecting means 9 as the control amount PV _n , and the control amount PV _n becomes equal to the target value SV _n , that is, the deviation e _n = SV. _n -PV _n is one that is controlled to be zero.

By the way, in the PID control operation method, the analog operation method is continuous, whereas in the digital operation method, discontinuous data is used to perform the PID operation at every constant control operation cycle. Will be done. Moreover, it can be said that the differential operation that handles abrupt changes is most affected by the discontinuous operation in this PID digital operation method. In other words, in the case of the analog operation method, the differential output waveform of continuous change is obtained, but in the case of the digital operation method, the larger the control operation cycle,
For each control calculation cycle, a large differential output different from that at the previous control calculation cycle is obtained.

Therefore, let us consider how the differential calculation is affected by the magnitude of the control calculation cycle Δt. Now, in the case of the analog calculation method, the magnitude of the differential control calculation output when the differential unit step is input, that is, the differential gain K _A

[0013]

[Equation 2] Can be obtained by the following formula.

On the other hand, in the case of the digital operation system, since the differential gain K _D corresponds to β in the equation (3), K _D = T _D / (Δt + ηT _D ) (7)

Therefore, if the differential gain K _D of the digital operation system of the equation (7) is Δt → 0, the value is the same as that of the equation (6). However, since the digital operation method generally has Δt ≠ 0, it is affected by the control operation cycle Δt. As a result, when the relationship of Δt << ηT _D is established, almost the analog calculation method can be applied, but in the digital controller currently used, there are many cases in which the size of the control calculation cycle Δt cannot be ignored.

[0016]

Therefore, as described above, in the conventional digital PID control device, the differential operation is greatly affected by the size of the control calculation cycle Δt, and the control response is greatly different accordingly. come. As a result, the following problems have been pointed out in the conventional device. (1) When trying to change to an analog type controller or a digital controller having a different control calculation cycle Δt, the PID parameter cannot be applied as it is, and it is necessary to tune the derivative time again. (2) For the differential time, general adjustment formulas such as the Ziegler-Nichols method and CHR method (actual digital control technology, published by Kogyo Kogyo Co., Ltd., Kazuo Hiroi, published October 1, 1992) are applied when adjusting PID parameters. Therefore, the PID parameter adjustment work is performed by repeating trial and error individually, which not only takes a very long time, but also wastes the plant during the adjustment work, resulting in a large economical loss. (3) A simulation or the like cannot be used unless it is the result when the control operation periods Δt of the digital PID control devices are matched.

As described above, since the conventional digital PID control device has various problems, it is the present situation that it is used without actually performing the differential operation while having the function of the differential operation. .

The present invention has been made in view of the above circumstances, and an object of the present invention is to provide a digital PID control device capable of easily modifying a differential operation according to a change in a control operation cycle. Another aspect of the present invention is a digital P that improves controllability even if the control calculation cycle changes.
It is to provide an ID control device.

[0019]

In order to solve the above-mentioned problems, the invention corresponding to the claims claims a digital PI for the deviation between the controlled variable from the controlled object and the target value of the controlled variable.
(P: Proportional, I: Integral) operation is performed, and a digital D (D: Derivative) operation is performed on the deviation or the control amount using the control operation cycle and the derivative time, and these operation outputs are combined. In the digital PID control device which is applied as an operation signal to the control target, the differential operation correction coefficient is used for the change of the control operation cycle Δt by using the differential time T _D0 optimally adjusted in advance in the control operation cycle Δt _0. and correction factor calculation means for obtaining the [rho, by using this differential operation correction coefficient [rho determined by calculating means _{D n = D n-1 +} {T D0 / (△ t + ηT D0)} (e n -e n-1) −ρ {Δt / (Δt + ηT _D0 )} D _n-1 (8) The speed-type differential operation means for obtaining the differential operation output D _n according to the change in the control operation cycle Δt by the operation expression The digital PID control device is provided.

However, in the above equation, D _n : the differential operation output at the present time, D _n-1 : the differential operation output at the time of the previous control operation cycle, e _n : the deviation at the current time, e _n-1 : the previous control operation cycle Time deviation, 1 / η: differential gain, ρ: differential calculation correction coefficient (= ρ (Δt−Δt ₀ ): Δt−Δt ₀ function).

When the control calculation period Δt changes, the differential calculation correction coefficient ρ to be used in the equation (8) is ρ = 1 + A {(Δt-Δt ₀ ) / ηT _D0 } (however, , A: coefficient) (9) or ρ = 1 + B {(Δt-Δt ₀ ) / ηT _D0 } + C {(Δt-Δt ₀ ) / ηT _D0 } ² (B, C: coefficient) (10) It is obtained by the following arithmetic expression.

[0022]

Therefore, according to the invention corresponding to the claims, by taking the above-mentioned means, the differential time T is obtained by performing the optimum adjustment at the control calculation cycle Δt ₀ at the time of installing the apparatus or at the time of regular inspection.
_D0 is determined, but thereafter, when the control operation cycle changes from Δt ₀ to Δt due to a device change or other replacement, the differential operation correction is performed using the differential time T _D0 and the predetermined coefficients A or B, C. After obtaining the coefficient ρ, the modified coefficient ρ is used to obtain the differential operation output based on the equation (8). Therefore, it is not necessary to retune when the control operation cycle changes, and after the change. A differential term suitable for the control calculation cycle can be calculated, so that the controllability can be improved and the differential calculation of the digital PID control device can be efficiently utilized.

[0023]

Embodiments of the present invention will be described below with reference to the drawings. FIG. 1 shows a digital PI according to the present invention.
It is a block diagram which shows one Example of a D control apparatus. In the figure, the same parts as those in FIG. 4 are designated by the same reference numerals, and particularly the constituent parts improved by this device will be described.

That is, the control device according to the present invention is provided with a new correction coefficient calculating means 11 and an improved speed type differential calculating means 12. This correction coefficient calculation means 1
1 indicates that when the control calculation cycle changes from Δt ₀ to Δt,
Using the predetermined coefficient A or B, C, the differential operation time T _D0 , the control operation cycle Δt ₀ , Δt, etc. optimally adjusted at the control operation cycle Δt ₀ at the time of equipment installation, periodic inspection, etc. The differential calculation correction coefficient ρ is calculated by the following equation and is sent to the velocity type differential calculating means 12.

Ρ = 1 + A {(Δt−Δt ₀ ) / ηT _D0 } ... (11) ρ = 1 + B {(Δt−Δt ₀ ) / ηT _D0 } + C {(Δt−Δt ₀ ) / ΗT _D0 } ² (12) where A, B, C are coefficients.

When the velocity-type differential operation means 12 receives the differential operation correction coefficient ρ from the differential operation correction coefficient operation means 11, D _n = D using the changed control operation cycle Δt and the differential time T _D0. the _{n-1 + {T D0 /} (△ t + ηT D0)} (e n -e n-1) -ρ {△ t / (△ t + ηT D0)} D n-1 ......... (13) becomes operational expression, The current differential operation output D _n , which is the differential term, is obtained.

Here, D _n-1 : differential operation output at the time of the previous control operation cycle, e _n : current deviation, e _n-1 : deviation at the time of the previous control operation cycle, 1 / η: differential gain, ρ: differential calculation correction coefficient (= ρ (Δt−Δt ₀ ): Δt−Δt ₀
Function).

Therefore, as an arithmetic expression for obtaining the differential operation output D _n as described above, paying attention to the fact that the differential gain changes depending on the control operation cycle Δt, the differential equation is obtained from the equation (3) and the simulation result. The calculation correction coefficient ρ is determined, and the calculation formula of the formula (13) is obtained.

It should be noted that the coefficient A is a value determined by the best condition of the simulation result when the linear first approximation is performed by the simulation, and the coefficients B and C are also the nonlinear second order approximation by the simulation. It is a value determined by the best condition of the simulation result when set to.

As an arithmetic expression of the differential operation output D _n ,
The following equations (14) and (15) are also conceivable,
From the simulation result, it was confirmed that the effect of the correction calculation formula for the change of the control calculation period Δt was small.

[0031] _{D n = D n-1 +} ρ 1 [{T D0 / (△ t + ηT D0)} (e n -e n-1) - {△ t / (△ t + ηT D0)} D n-1] ...... _{... (14) D n = D} n-1 + ρ 2 {T D0 / (△ t + ηT D0)} (e n -e n-1) - {△ t / (△ t + ηT D0)} D n-1 ......... (15) Incidentally, the simulation result when the control calculation period Δt changes will be described with reference to FIGS. 2 and 3.

FIG. 2 is a diagram showing the control response, and the condition of the response is that the transfer function G (s) of the controlled object = e ^−2s / (1+
5 s), when Δt ₀ = 0.01 sec and η = 0.1, the proportional gain K _{p is} set as the optimum value of the PID parameter.
= 3.04, T _I = 3.24 sec, T _D = 0.767
9 seconds can be obtained. Then, various control calculation cycles Δt
When the differential operation correction coefficient ρ is obtained by a simulation while considering the controllability with respect to, the following operational expression is obtained.

Ρ = 1 + 0.02617 {(Δt−Δt ₀ ) / ηT _D0 } (16) Therefore, the coefficient A = 0.02617 is obtained as the best condition by the linear first-order approximation by this simulation.

Then, with respect to the change of the control calculation cycle Δt,
Controllability evaluation function IT when ρ = 1 is fixed according to the conventional technique
Controllability evaluation function IT using AE (= t · edt) and the differential operation correction coefficient ρ obtained by the equation (16)
When compared with AE, the result shown in FIG. 3 is obtained. That is, as is clear from the figure, Δt = 0.4s
When ec, the present device can be improved by about 10% as compared with the conventional device.

Incidentally, in the case of the conventional apparatus, the disturbance of the response is large with respect to the change of the set value and the change of the disturbance, and it takes a settling time, but in the case of the apparatus of the present invention, the control response as shown in FIG. Show. In other words, the device of the present invention uses the set value (target value) S
With respect to changes in V and changes in disturbance (D), there is little disturbance, and control response can be improved. Further, the apparatus of the present invention has better PV overshoot and settling time.

Therefore, according to the configuration of the above embodiment, the differential operation correction coefficient is adjusted for the change in the control operation cycle Δt by using the differential time T _D0 which has been optimally adjusted in the control operation cycle Δt _0. After ρ is obtained, the differential operation output is obtained based on the equation (13) which is the operation equation for correction in consideration of the past velocity type digital operation equation which is the equation (3) and the simulation result. It is possible to prevent deterioration of controllability to a minimum with respect to the change. Moreover, the need for retuning is eliminated even if the differential times obtained by devices with different control operation cycles are set. The differential term of the digital operation is essentially affected by the control operation cycle Δt. However, according to the apparatus of the present invention, the differential term operation suitable for the control operation cycle Δt can be performed, and the problem of the conventional apparatus can be solved. Therefore, the differential operation of the digital PID control device can be efficiently utilized.

In particular, since the digital PID control device is frequently used for plant control, it has a very great industrial significance. In the above-mentioned embodiment, the velocity differential operation means 12 performs the differential operation based on the deviation. However, for example, instead of the deviation, the controlled variable PV _n is directly taken in to perform the differential operation, that is, a so-called measured value. It may be of the differential precedence type. In addition, the present invention can be modified in various ways without departing from the scope of the invention.

[0038]

As described above, according to the present invention, the differential operation can be easily corrected with respect to the change in the control operation cycle, and the controllability can be greatly improved.

[Brief description of drawings]

FIG. 1 is a configuration diagram showing an embodiment of a digital PID control device according to the present invention.

FIG. 2 is a diagram showing the control response of the device of the present invention.

FIG. 3 is a comparison diagram of controllability evaluation functions of the conventional device and the device of the present invention.

FIG. 4 is a diagram showing a configuration of a conventional device.

[Explanation of symbols]

2 ... Velocity type proportional computing means, 3 ... Velocity type integral computing means, 5
... adding means, 6 ... proportional gain means, 7 ... speed type / position type signal converting means, 8 ... controlled object, 9 ... control amount detecting means, 1
1 ... Differential calculation correction coefficient calculation means, 12 ... Velocity type differential calculation means.

Claims (3)

[Claims] 1. A digital PI (P: proportional, I: relative to a deviation between a controlled variable from a controlled object and a target value of the controlled variable).
(Integration) calculation is performed, and a digital D (D: differentiation) calculation is performed on the deviation or the control amount by using a control calculation cycle and a differentiation time, and these calculation outputs are combined to perform the control as an operation signal. Digital P applied to target
In the ID control device, when the control calculation cycle Δt changes, the control calculation cycle Δt is changed in advance.
A correction coefficient calculation means for obtaining a differential calculation correction coefficient ρ using the differential time T _D0 optimally adjusted at ₀ , and a differential calculation correction coefficient ρ obtained by this calculation means are used to calculate the control calculation cycle Δt A digital PID control device comprising: a speed-type differential operation means for obtaining a differential operation output D _n according to a change. _{D n = D n-1 +} {T D0 / (△ t + ηT D0)} (e n -e
_n-1 ) -ρ {Δt / (Δt + ηT _D0 )} D _n-1 where D _{n is} the differential operation output at the present time, D _{n-1 is} the differential operation output at the time of the previous control operation cycle, e _n : Current deviation,
e _n-1 : deviation at the time of the previous control operation cycle, 1 / η: differential gain, ρ: differential operation correction coefficient (= ρ (Δt−Δt
₀ ): function of Δt-Δt ₀ ) 2. When the control calculation cycle Δt changes, the differential calculation correction coefficient ρ is ρ = 1 + A {(Δt−Δt ₀ ) / ηT _D0 } (however,
The digital PID control device according to claim 1, wherein the digital PID control device is obtained by a calculation of A: coefficient. 3. When the control calculation cycle Δt changes, the differential calculation correction coefficient ρ is expressed as ρ = 1 + B {(Δt−Δt ₀ ) / ηT _D0 } + C {(Δt
The digital PID control device according to claim 1, wherein the calculation is performed by the following formula: -Δt ₀ ) / ηT _D0 } ² (B, C: coefficient).