JP2635786B2 - 2-DOF adjustment device - Google Patents

Description

The present invention relates to a two-degree-of-freedom adjustment apparatus that simultaneously optimizes both disturbance suppression characteristics and target value tracking characteristics, and more particularly to a target value filter. And a two-degree-of-freedom adjusting device that realizes an optimal two-degree-of-freedom by simplifying the above.

(Prior Art) Conventionally, PI or PID control devices have been widely used in all industrial fields, and they form the basis of plant control even today when digital control is the mainstream.

The basic equation of such PID control is It is represented by Here, C ₀ (s) is a PID basic expression, MV (s) is an operation signal, E (s) is a deviation, K _P is a proportional gain, T _I is an integration time, T _D is a differentiation time, and s is a Laplace operator. , Η are coefficients,
(1 / η) is a differential gain.

In the basic expression of the PID control, the D operation is used or not used depending on the characteristics of the control target. Therefore, the PI operation will be described below from the viewpoint of facilitating understanding. Of course, the device of the present invention is not directly affected by the presence or absence of the D operation.

Therefore, from the above equation (1), the basic equation of PI control is expressed as follows: C (s) = MV (s) / E (s) = K _P {1 + 1 / (T _I · s)} (2) .

In general, in a control system using PI or PID control, it is necessary to satisfy both functions of a disturbance suppression characteristic and a target value tracking characteristic. The former disturbance suppression characteristic is how to optimally suppress the influence of disturbance when the disturbance changes, and the latter target value tracking characteristic is how the process value follows the target value optimally when the target value is changed It is to show you. In a general PI or PID control system, the PI or PID parameter value for optimally suppressing the influence of disturbance changes and the PI or PI for optimally following target value changes
It is significantly different from the D parameter value. As a result, if the PID parameter value is set so as to optimally suppress the influence of disturbance change, the target value tracking characteristic becomes oscillatory. Conversely, if the PID parameter value is set so as to optimally follow the target value change, disturbance The suppression properties become very sweet.

However, the PI or PID control shown in the above equations (2) and (1) is a so-called one-degree-of-freedom system in which only one type of PI or PID parameter can be set. Both cannot be optimized at the same time.

In contrast, in 1963, 1ssac, M, Horowitz,
Two degree of freedom PI or PID algorithm (Two Degrees PI (PID) Al
gorithm: hereinafter referred to as 2DOF PID), and the two-degree-of-freedom adjusting device has come into the limelight. In recent years, in Japan, 2DOF
PIDs have been put into practical use and have greatly contributed to the advancement of plant control.

FIG. 8 is a diagram showing a block configuration of such a conventional 2DOF PI adjustment device. This device adds a target value filter 1 to the target value of a conventional general PID adjustment device, and performs 2DOF PI
A realizes a, the target value filter 1 Specifically, lead / lag element 1 _1, a first-order lag element 1 _2, consists inexact differential section 1 ₃ and subtracter 1 _4, etc., the target value SV the lead / lag element 1 ₁ through leads to the subtracting unit 1 _4, 1 the target value SV
Next delay elements 1 _2, inexact differential section 1 ₃ Similarly subtraction means via a 1
₄ to lead, the lead / lag element 1 ₁ of 'the inexact differential output is subtracted from the resulting subtraction output SV _0' output SV DOF the
It is introduced into the deviation calculating means 2 as a target value for performing the PI adjustment calculation.

The deviation calculation means 2 calculates a target value SV ₀ ′ for 1DOF PI adjustment calculation.
E ′ (= SV ₀ ′ −P) between the control amount PV and the control amount PV from the control target 3
After calculating V), the operation signal MV 'is guided to the PI adjustment means 4, where the PI adjustment operation is performed to obtain an operation signal MV'. Further, the addition means 5 adds and synthesizes the disturbance signal D to the operation signal MV '. 3, the deviation E ′ = 0, that is, the target value SV ₀ ′
= Control amount PV is controlled.

Therefore, according to the above configuration, the external disturbance control algorithm is as follows: C _D ′ (s) = K _P {1 + 1 / (T _I · s)} (3) as, Becomes In this equation, α is a two-degree-of-freedom coefficient of the proportional gain, β ₀ is a two-degree-of-freedom coefficient of the integration time, and the disturbance suppression characteristics are optimized based on the above equation (3).
After determining K _P and T _I , it is possible to determine the two-degree-of-freedom coefficients α and β ₀ that optimize the target value following characteristic based on the above equation (4). Accuracy can be achieved.

(Problems to be Solved by the Invention) However, while the above-described 2DOF PI adjusting device has various features, it has the following defects.

Originally, the two-degree-of-freedom coefficients α and β ₀ must be related to each other, but in the conventional control method, α and β ₀ are completely independent as shown in equation (4). When the conversion factor α is changed, β ₀ must be changed independently, and it takes much time to adjust.

In addition, for the purpose of 2DOF PI conversion, the target value filter 1 has three temporal elements (lead / lag element 1 ₁ , primary delay element)
1 _2, but using the inexact differential section 1 _3), usually when a lot using several tens to several thousand control loops in this type of plant, per loop these time factor 1 If the number is reduced, tens to thousands are reduced as a whole plant, which can contribute not only to the cost but also to the reduction of the load on the entire system, the speeding up of the data processing, and the reduction of the capacity.

In particular, in the future, higher precision, quicker response, optimization and safety of the plant operation control system will be increasingly required. However, the fundamental PID 2DOF which is frequently used in the plant to sufficiently meet these demands PID conversion is essential,
For that purpose, the above-mentioned defects must be removed.

The present invention has been made in view of the above circumstances, and when the two-degree-of-freedom coefficient of the proportional gain is changed, the integration operation output is changed in accordance with the change of the two-degree-of-freedom coefficient, and the two-degree of freedom of the integration time is changed. Configuration that is easy to adjust by making it equivalent to changing the optimization coefficient, and has two degrees of freedom that enables complete two degrees of freedom, reduced load, and high-speed processing of the PI using fewer time elements. It is an object to provide an adjusting device.

[Means for Solving the Problems] In order to solve the above problems, the present invention provides a two-degree-of-freedom adjusting apparatus using a target value filter, wherein the target value filter has a proportional gain to the target value. A coefficient multiplying means for multiplying the output signal of the coefficient multiplying means from the target value, and at least one signal obtained as a result of the subtraction has a two-degree-of-freedom coefficient for integration time. A first-order delay means for outputting a delay with two series-connected first-order delay elements; an output of the coefficient multiplication means and an output of the first-order delay means; And a means for obtaining a signal.

That is, in order to make the proportional gain of the target value filter used in the conventional method into two degrees of freedom, the apparatus of the present invention decomposes the lead / lag element to obtain a static compensation component proportional to the input and an input related to the input. Additive separation into the dynamic compensation component that changes with the first-order delay and adding the first-order delay element in series with the first-order delay component for the dynamic compensation, that is, complete 2DOF with only two first-order delay components By realizing PI and changing the integral operation output with the change of the proportional gain 2 degree of freedom coefficient,
The configuration is equivalent to changing the integration time two-degree-of-freedom coefficient.

(Operation) Accordingly, by taking the above-described means, by changing the two-degree-of-freedom coefficient for the proportional gain of the coefficient multiplying means, the proportional gain parameter of the disturbance suppression optimization is maintained as it is and the target value is proportional to the target value. You can change the gain
By changing the two-degree-of-freedom coefficient for integration time of the next delay means, it is possible to equivalently change the integration time with respect to the target value while keeping the disturbance integration time as it is, thereby realizing complete two-degree-of-freedom of the PI. When the two-degree-of-freedom coefficient of the proportional gain is changed,
The integration operation output is changed along with the change of the two-degree-of-freedom coefficient to make the integration time equivalent to changing the two-degree-of-freedom coefficient, thereby facilitating adjustment. By making the number smaller, it is possible to realize two degrees of freedom of the PI, reduce the load, and achieve high-speed processing.

(Example) Hereinafter, an example of the present invention will be described with reference to FIG. 1 and FIG. FIG. 1 is a block diagram showing an embodiment of a two-degree-of-freedom adjusting device, and FIG. 2 is an equivalent circuit diagram derived from a conventional target value filter to realize the adjusting device of FIG. In these drawings, the same parts as those in FIG. 8 are denoted by the same reference numerals, and detailed description thereof will be omitted.

First, the lead / lag element 1 shown in FIG. 2 (a) is incorporated in the target value filter 1 shown in FIG. 8 of the conventional example. It becomes like b). That is, when this lead / lag element 1 is decomposed, Can be converted as follows. Then, if this equation (5) is represented by a functional block, it becomes as shown in FIG. 2 (b).

FIG. 1 is a diagram showing a 2DOF PI adjusting device using a target value filter 10 incorporating the functional blocks of FIG. 2 (b). That is, the target value filter 10
Coefficient multiplying means 11 for multiplying the target value SV by a two-degree-of-freedom coefficient α of a proportional gain, subtraction means 12 for subtracting the output of the coefficient multiplication means 11 from the free value SV, and a subtraction output obtained by the subtraction means 12 First-order lag elements 13 and 14 to provide appropriate first-order lags
And an adding means 15 for adding and combining the output of the coefficient multiplying means 11 and the output of the primary delay element 14.
The output of 15 is configured to the target value SV ₀ of the PI regulation means 4. Therefore, the target value filter 10 has a configuration in which a first-order lag element 13 is added to the circuit of FIG. 2 (b).

Therefore, in the present adjusting device, the target value SV is received by the target value filter 10 so that the proportional gain and the integration time are calculated.
After obtaining the target value SV ₀ of DOF PI arithmetic processing performed free degree, leads to the target value SV ₀ to the deviation calculation means 2, wherein the control amount PV from a controlled object 3 from the target value SV ₀ The difference E is obtained by subtraction. Further, the PI adjustment means 4 performs a PI adjustment calculation based on the deviation E to obtain the operation signal MV, and then adds the operation signal MV.
In operation signal disturbance signal D by adding synthesized MV, applying the resulting combined signal to the control target 3, and controls so that the target value SV = SV ₀ = PV.

Next, the operation of the adjusting device configured as described above will be described. Now, when the target value SV changes stepwise as shown in FIG. 3A, the equivalent conversion circuit shown in FIG. An output SV 'as shown in (b) is obtained. After the output characteristic of (b) of FIG. 3 changes proportionally by the coefficient α,
In the portion of (1−α), the characteristic changes depending on 1 / (1 + T _I · s). Therefore, for example, when the response characteristic of (b) in FIG.
If the first-order lag element 13 is added in the portion of -α), the characteristic becomes as shown in FIG. 3C, and it is easy that the overshoot of the step response to the change in the target value becomes smaller than the characteristic in FIG. Can be predicted.

Next, it will be proved that when the target value filter 10 and the PI adjusting means 4 are combined, the PI has two complete degrees of freedom.

First, from FIG. 1, the disturbance control algorithm C _D (s) is expressed as follows: C _D (s) = C (s) = K _P {1 + 1 / (T _I · s)} (6) Target value control algorithm Csv (s)
Is Becomes

Therefore, as is apparent from the above equations (6) and (7), K _P and T _I are determined from the above equation (6) so that the disturbance suppression characteristics are optimal, and the proportionality is determined from the equations (7). Gain 2
Pairs disturbance proportional gain by varying the free cathodic coefficient alpha remain K _P, can be used to adjust the pair target value proportional gain as alpha · K _P, whereas, varying the second free cathodic coefficient β of the integration time Thus, the target value integration time β · T _I can be equivalently varied while the external disturbance integration time is kept at T _I, and complete two degrees of freedom of PI can be realized.

Thus, if the integral term for target value is Isv (s), It is represented by That is, from this equation (8), when β = 0, Isv (s) = 1 / (T _I · s)... Integral time invariant When β> 0, Isv (s) <1 / (T _I · s) …… Integral time → Large β <0, Isv (s)> 1 / (T _I · s)… Integral time → Small, and by changing the two-degree-of-freedom coefficient β of the integral time, It can be seen that the disturbance integration time β · T _I can be equivalently varied while keeping the disturbance integration time T _I.

Therefore, according to the configuration of the embodiment described above, for example, the transfer function G (s) of the control target 3 is set to e− ^2s / (1 + 5s), and the PID parameters are adjusted to the optimum disturbance suppression characteristics. When the target value is changed stepwise, a response characteristic as shown in FIG. 4 is obtained. First, (a) of FIG.
= 1, β = 0, that is, the response in the case of the one-degree-of-freedom PI control without the target value filter, and the response characteristic has a large overshoot. Next, when α = 0.4 and β = 0, that is, when only P has two degrees of freedom, a response characteristic as shown in FIG. 4B is obtained. Further, when α is set to 0.4 and β is set to 0.25, and β is included to make the PI two degrees of freedom, the result becomes as shown in FIG. 4C, and the overshoot is considerably reduced. Next, FIG. 4 (d) shows a case where α = 0 and β = 0, the one-degree-of-freedom IP control is performed, and the response is greatly delayed. Therefore, as is clear from the above response characteristics, the response characteristics shown in FIG. 4 (c) are the best, and the effect of two degrees of freedom is remarkably exhibited.

Moreover, as is apparent from the above equation (7), when the two-degree-of-freedom coefficient α of the proportional gain is changed, the integration time becomes equivalently a reasonable size, that is, when α → large, the integration time → small. On the other hand, when α → small, the integration time → large, and the direction is the same as the response speed increases / decreases. Further, the points described above will be specifically described. That is, the basic expression of the integral operation with respect to the disturbance is expressed by K _P / T _I · s from the expression (6), and the expression of the integral operation with respect to the target value is expressed by the formula (7)
From the formula, it is represented by K _P [{1 / (T _I s)} − {(1-α) · β / (1 + β · T _I s)}]. FIG. 9 shows the output of the integration operation when there is a constant deviation input. However, 2 free cathodic coefficient alpha ₁ of the proportional gain shown in the figure, alpha ₂ is, alpha ₁
> And are intended to be α ₂ of the relationship.

From the characteristic curve (a) shown in FIG. 9, when the integration time T _{I is} increased, the integration operation output becomes small (weak).

If the integration time T _I becomes smaller, the integration operation output becomes larger (stronger).

On the other hand, from the characteristic curves (b) and (c), when α → large, the integration operation output becomes large (strong).

When α → small, the integration operation output becomes small (weak).

Therefore, what can be said from the relationship between the characteristic curves (a), (b), and (c) is that if α → large, the integration operation output increases, which is equivalent to integration time T _I → small. .

If α → small, the integration operation output becomes small, which is equivalent to integration time T _I → large.

Therefore, from equation (7), the two-degree-of-freedom coefficient α
→ If the value is large, the proportional gain α · K _P results in a direction in which the proportional operation output becomes large (strong) and the response becomes fast, and the integral operation output also becomes large (strong) from the above description.
And the response becomes faster, and the two agree.

If the directions are reversed, they will interfere with each other, making adjustment impossible. Therefore, it is desirable that both directions be the same.

When α is fixed, only β can be independently varied to vary the integration time.

Further, the target value filter 10 has a minimum number of two 1
Two-degree-of-freedom can be reliably realized by using the next-delay elements 13 and 14, and the configuration is simple. The load can be reduced in a plant having tens to tens of thousands of control loops, and high-speed signal processing can be achieved. Can be expected.

Next, FIGS. 5 to 7 are block diagrams showing other embodiments of the present invention. These are examples in which the target value filter 10 is configured using two first-order delay elements.

First, FIG. 5 shows that a primary delay element 16 and an addition means 17 are provided on the output side of a subtraction means 12 for subtracting the output of the coefficient multiplication means 11 from the target value SV. After the outputs of 16 are added and synthesized by the adding means 17, they are introduced into the first-order lag element 14. Thereafter, the output of the first-order lag element 14 is subtracted by the output of the first-order lag element 16 in the subtraction means 18 and is introduced into the addition means 15.

Therefore, according to this configuration, as an equation corresponding to the above-described equation (7), Thus, two degrees of freedom can be realized by the two first-order delay elements 14 and 16.

Further, FIG. 6 also uses two first-order lag elements 13 and 14, and specifically, a subtraction means is provided on the output side of a subtraction means 12 for subtracting the output of the coefficient multiplication means 11 from the target value SV. 19
The subtraction means 19 subtracts the signal obtained by subtracting the target value SV from the output of the subtraction means 12 through the primary delay element 13 and introduces the obtained signal into the primary delay element 14. is there.

According to this configuration, as an equation corresponding to equation (7), Is obtained.

Further, FIG. 7 corresponds to a modification of FIG. 5, in which the input side of the primary delay element 16 is not the output of the subtraction means 12, but the target value SV.
Is input.

In this case, the equation corresponding to equation (7) is This is similar to the conventional equation (4), and two degrees of freedom can be realized only by the two first-order delay elements 14 and 16. In addition, the present invention can be implemented with various modifications without departing from the scope of the invention.

[Effects of the Invention] As described above, according to the present invention, a PI that optimizes disturbance suppression characteristics using a smaller time delay element than in the past.
While holding the D parameter, the two-degree-of-freedom coefficient of the proportional gain and the integration time can be varied to change the proportional gain with respect to the target value and the integration time with respect to the target value. Therefore, the load can be reduced and the signal can be processed at high speed, which can greatly contribute to cost reduction. Further, when the two-degree-of-freedom coefficient of the proportional gain is changed, the two-degree-of-freedom coefficient of the integration time needs to be changed. Without
In addition, it is possible to provide a two-degree-of-freedom adjusting device capable of changing the integral operation output to an appropriate magnitude.

[Brief description of the drawings]

1 to 4 show an embodiment of a two-degree-of-freedom adjusting apparatus according to the present invention. FIG. 1 is a block diagram of the apparatus of the present invention, and FIG. 2 is an apparatus of FIG. Fig. 3 is a diagram showing a response comparison of a target value filter when a target value is changed stepwise, and Fig. 4 is a tuning of a disturbance suppression characteristic. FIG. 5 is a configuration diagram showing another embodiment of the present invention, and FIG.
FIG. 8 is a configuration diagram of the conventional device, and FIG. 9 is a characteristic diagram for explaining the relationship between the integral operation outputs when the two-degree-of-freedom coefficient of the proportional gain is changed. 2... Deviation calculating means, 3... Controlled object, 4... PI adjusting means, 5... Adding means, 10... Target value filter, 11. 16: primary delay element, 15: adding means.

Claims (1)

(57) [Claims] At least a PI (proportional + integral) parameter optimum for disturbance suppression is set in advance, and a deviation between a target value signal for adjustment calculation obtained through a target value filter upon receiving a target value and a control amount of a control object is determined. A two-degree-of-freedom adjusting apparatus that performs an adjustment operation using the PI parameter and applies an obtained operation signal to the control target to control the target value, wherein the target value filter has two degrees of freedom for a proportional gain to the target value. A coefficient multiplying means for multiplying a coefficient, and an output of the coefficient multiplying means subtracted from the target value, and the resulting signal of the subtraction is connected in series to two series having at least one integration time two-degree-of-freedom coefficient. First-order delay means for outputting a signal with a delay by a first-order delay element; and means for adding and combining the output of the coefficient multiplication means and the output of the first-order delay means to obtain the adjustment calculation target value signal. Equipment 2 degrees of freedom adjustment device, characterized in that the.