JP6380552B2 - Control device, program thereof, and plant control method - Google Patents

Description

  The present invention relates to a control device for a plant or the like.

  Temperature control devices, control devices such as PLC (Programmable Logic Controller) and DCS (Distributed Control System), and control devices mounted on personal computers and embedded control devices are widely used in the industry.

  Further, in the conventionally known control engineering, there are control methods such as PID control, model predictive control, internal model control, LQG control, H2 control, H∞ control, etc., which are control methods aiming at target value tracking of the controlled object. Is known (for example, Non-Patent Document 1).

Moreover, each method enumerated below is well-known as a control system aiming at suppression of overshoot.
A method for determining PID control parameters based on the idea of generalized predictive control (GPC) (Patent Document 1);
A method of shaping the target value according to the time when the peak occurs (Patent Document 2);
A method for determining PID control parameters so that an open loop is matched to a plant expressed by a second-order lag transfer function (Patent Document 3);
Further, model predictive control for obtaining a desired response by sequentially performing optimization calculations using a state space model to be controlled or a future time response model is known (for example, Non-Patent Document 2).
JP 2003-195905 A JP 2005-276169 A JP 2007-188322 A "Control system design" Asakura Shoten (1994) “Model Predictive Control”, Tokyo Denki University Press, 2005 “Process Control Engineering”, Asakura Shoten, 2002

  In industrial plant control, it is important to ensure stable operation of the plant and safety of machine operation. On the other hand, rapid follow-up to the target value increases plant operating efficiency and improves machine operation responsiveness. It is an indispensable requirement to do.

  However, in general, overshooting tends to occur when the follow-up performance is improved.

Overshoot is sometimes
-Liquid overflow in liquid level control;
-Boiler misfire;
-Robot hand and stage collisions;
・ Material modification due to excessive heating temperature;
In some cases, problems that must be avoided (such as operational problems, safety problems or quality problems) may occur.

  For this reason, there is a situation where it is necessary to set a conservative setting at the expense of control performance in order to obtain a safety margin, or to allow a certain degree of overshoot to prioritize control performance. Can happen frequently.

  In conventionally known control engineering, target function tracking performance, disturbance suppression performance, robust stability performance, etc. are expressed as objective functions such as quadratic norm and infinite norm by frequency function, and control system design by minimizing objective function The technique of performing is general (for example, the said nonpatent literature 1).

  In the evaluation of the frequency function, it is possible to suppress the gain in an average or worst case, but the target deviation at the actual online control instant cannot be treated as a constraint condition. Therefore, in principle, it is difficult to suppress overshoot.

  In addition, the conventionally known overshoot suppression method relies on a model-based method designed in advance, such as adjusting a target value when a PID control parameter adjustment or a peak is likely to occur. The target deviation at the moment of online control and the influence of operation cannot be considered. In addition, PID control generally cannot achieve sufficient control performance for plants that include dead time, reverse response, and higher-order modes of the second or higher order.

  In addition, in the conventionally known model predictive control, since constraint conditions can be handled, overshoot suppression can be handled as a constraint condition, but optimization problems such as quadratic programming problems must be solved in each control step. There is a problem that it can be implemented only by a control device having relatively abundant CPU computing capacity and installed memory capacity. In other words, there is a problem that overshoot suppression cannot be realized with a simple configuration (such as relatively small memory and CPU resources).

  As described above, in the conventionally known control method, it is possible to clearly suppress overshoot in the time domain according to the situation of the target deviation that changes every moment and the influence of the operation, and to be able to be easily implemented. It can be said that technology is not provided.

  The subject of this invention is providing the control apparatus etc. which can implement | achieve overshoot suppression exactly with a simple structure.

  In the present invention, a control device that outputs an operation amount to a control target device and causes the control amount of the control target device to follow an arbitrary target value has, for example, the following configurations.

Target deviation calculation means for obtaining a difference between the control amount and the target value as a target deviation current value;
Correction target deviation calculation means for calculating a correction target deviation based on a plant response model held in advance, the target deviation current value, and the amount of change in the manipulated variable;
Operation amount calculation means for determining a new operation amount based on the correction target deviation.

It is a block diagram of the control apparatus of this example. It is a figure for demonstrating operation | movement of a termination | terminus response correction | amendment part. It is FIG. (1) for demonstrating operation | movement of a termination | terminus response correction | amendment part. It is FIG. (2) for demonstrating operation | movement of a termination | terminus response correction | amendment part. It is FIG. (3) for demonstrating operation | movement of a termination | terminus response correction | amendment part. It is a figure for demonstrating the specific example of operation | movement of a termination | terminus response correction | amendment part. FIG. 10 is a diagram (part 1) illustrating a specific example of data stored in advance by the operation change amount calculation unit. It is a figure which shows the specific example of a plant response model. FIG. 12 is a second diagram illustrating a specific example of data stored in advance by the operation change amount calculation unit. (A)-(d) is a figure which shows the simulation result in the case of this method. (A)-(c) is a figure which shows the simulation result in the case of a prior art. It is FIG. (1) explaining operation | movement of the control apparatus of this example using a transfer function. It is FIG. (2) explaining operation | movement of the control apparatus of this example using a transfer function. It is a figure for demonstrating conventionally well-known internal model control for a comparison. It is a process flowchart figure of a control apparatus.

  Embodiments of the present invention will be described below with reference to the drawings.

  FIG. 1 is a configuration diagram of the control device of this example.

  The control device 1 is a device that controls the illustrated control target plant 2.

  The control target plant 2 is an example of an arbitrary device / apparatus to be controlled.

  The control device 1 outputs an arbitrary manipulated variable u to the controlled plant 2 based on an arbitrary target value r, and a controlled variable y that is data indicating the state of the controlled plant 2 and the like according to this. And the next operation amount u is determined based on the measured control amount y and the like. Note that the control amount y is, for example, the temperature of the control target plant 2. In this example, the target value r is a set temperature or the like, but is not limited to this example. The control amount y is measured by a measuring instrument such as a sensor (not shown). In the above example, the control amount y is measured by a thermometer.

  The control device 1 finally controls the control amount y so as to become the target value r. The control device 1 determines the value of the manipulated variable u and inputs it to the controlled plant 2 in order to make the controlled variable y follow the target value r.

  The control device 1 includes an operation amount update unit 10, a timer 21, a measurement unit 22, a difference unit 23, and the like.

  The timer 21 generates a predetermined cycle Tc, and operates the operation amount update unit 10 and the measurement unit 22 every fixed cycle Tc.

Measuring unit 22, every the period Tc, measuring the current operation amount u and the current controlled variable y according to the control object plant 2. Then, the measured current control amount y is output to the subtractor 23 as the illustrated control amount y ₀ , and the measured current operation amount u is output to the operation amount update unit 10 as the illustrated operation amount u 0.

The above differentiator 23 and enter any desired value r (set by the user value, etc.), a control amount y ₀ and the target differential current value e _0, which is the difference between the target value r, calculated as follows To do.

e ₀ = r−y ₀
Then, the generated target deviation current value e ₀ is input to the operation amount update unit 10.

Note that the configuration itself for generating such a target deviation current value e ₀ is an existing configuration.

The operation amount update unit 10 includes a terminal response correction unit 11, an operation change amount calculation unit 12, and an adder 13. The target deviation current value e ₀ is input to the terminal response correction unit 11. The manipulated variable u0 is one input of the adder 13.

The end response correction unit 11 receives the input target deviation current value e ₀ , a preset plant response model, “current and past operation change amount {du (t)} t” (until the current time) The corrected target deviation e * is calculated using the time series data {du (t)} t) of the past operation change amount. The corrected target deviation e * is input to the operation change amount calculation unit 12.

The operation change amount calculation unit 12 calculates the next operation change amount du based on the input correction target deviation e *. Then, the next operation change amount du is set as the other input of the adder 13. Accordingly, the adder 13 adds the operation change amount du to the current operation amount u0, thereby generating the next operation amount u (correction operation amount u _s ). Then, the corrected operation amount u _s (next operation amount u) is input to the control target plant 2.

  The operation change amount calculation unit 12 and the adder 13 may be regarded as constituting an operation amount calculation unit (not shown) that determines a new operation amount based on the corrected target deviation e *. .

  Here, as shown in the figure, the end response correction unit 11 inputs the operation change amount du generated and output by the operation change amount calculation unit 12, and accumulates the operation change amount du as time series data. This is the “current and past operation change amount {du (t)} t”.

  In addition, you may consider that the difference machine 23 and the operation amount update part 10 comprise the operation amount calculation part which determines the said operation amount integrally.

  The terminal response correction unit 11 holds a plant response model in advance. A specific example of this plant response model is data (function S (t)) shown in FIG. 5 described later.

  Here, in this method, the step response (response to the unit step input) of the control target plant 2 is measured in advance, and this measured data is stored in advance as a function S (t) shown in FIG. Further, the convergence value when the step response converges is defined as a termination gain S (∞) shown in FIG. The function S (t) and the terminal gain S (∞) are used when calculating the corrected target deviation e *. Details will be described later. Note that the step response is not limited to unit step input, but may be obtained by appropriate conversion from responses to operation inputs of other shapes such as impulse input and lamp input.

The end response correction unit 11 is based on the past operation based on the previously stored plant response model, the “current and past operation change amount {du (t)} t”, the target deviation current value e _{0, and the} like. The end response (that is, the residual of the target deviation in the sufficient future) is calculated as the corrected target deviation e *. Alternatively, the corrected target deviation e * is defined as the difference between the predicted value of the convergence value of the control amount y according to the past operation amount u (its change amount du) up to the present and the target value r. May be.

The end response correction unit 11 may be regarded as having processing functions such as an operation change amount storage unit (not shown) and a correction target deviation calculation unit. In the case of this example, for example, the operation change amount storage unit (not shown) accumulates the operation change amount du and forms time series data. The correction target deviation calculation unit (not shown) includes, for example, a plant response model registered in advance, the target deviation current value e _0, and the time series data “{du (t)} t of the operation change amount. Based on the above, a corrected target deviation e * is calculated.

  In addition, instead of the time-series data “{du (t)} t” of the operation change amount, a storage unit (an intermediate calculation value storage shown in FIG. 3) that stores intermediate calculation values in the correction target deviation calculation process described later. Part) may be used as a substitute for accumulating the time series data “{du (t)} t” itself of the operation change amount.

  A specific example of the process of calculating the corrected target deviation e * will be described later. The corrected target deviation e * will be described with reference to FIG.

  Here, the control device 1 includes an arithmetic processor such as a CPU / MPU (not shown) and a storage device such as a memory. Furthermore, an input / output interface (not shown) for inputting the operation amount u to the control target plant 2 and acquiring the control amount y is also provided.

  A predetermined application program is stored in the storage device (not shown) in advance. When the arithmetic processor executes the application program, for example, various processing functions (the terminal response correction unit 11, the operation change amount calculation unit 12, and the like) of the operation amount update unit 10 are realized. Furthermore, the operations of the measurement unit 22 and the subtractor 23 may be realized by software, but the present invention is not limited to this example, and a dedicated circuit or the like may be used.

  FIG. 2 is a diagram for explaining the operation of the termination response correction unit 11.

  Specific examples are shown on the upper side and the lower side in the figure in the terminal response correction unit 11 of FIG. On the lower side, a specific example of time-series data of the operation change amount du and the operation amount u corresponding to the operation change amount du is shown.

  In FIG. 2, the time t shown in the figure is the present, the left side of the figure is the past and the right side of the figure is the future. Thus, in the illustrated example, the current and future operation change amounts du are all “0” (the operation amount u does not change). On the other hand, in the past, as shown in the figure, the operation change amount du is not “0”, and the operation amount u has changed. An example of the control amount y corresponding to such a past operation change amount {du (t)} t (change in the operation amount u) is shown on the upper side of the figure. In the figure, the past operation change amount {du (t)} t is, for example, illustrated du (t−Tc), du (t−2Tc), du (t−3Tc), and the like.

In this example, first, a y ₀ of the current controlled variable y is shown. Here, it is predicted that the control amount y continues to change as shown in the figure by the past operation change amount {du (t)} t and eventually converges to “y _n + y ₀ ” shown in the figure. The The change in the control amount y is caused by the past operation change amount {du (t)} t (as described above, the current and future operation change amounts {du (t)} t are all '0'. So). Further, the y ₀ will mean the current values of the controlled variable y in such a change. Then, by changing only the amount of y _n further illustrated from now it will eventually converge to _{"y n +} y 0". Incidentally, the y _n is referred to as "end response correction value".

As described above, a change in the operation amount u is not immediately reflected in the control amount y, and there is a time lag. Since the current value of the street controlled variable y above are y ₀ shown, the difference between the target value r becomes target deviation current value e ₀ shown. As described above, the target deviation current value e ₀ is obtained by the adder 13.

Then, it is predicted that it will converge to “y _n + y ₀ ” as it is (when there is no change in the control amount y), and the target value r will not be reached. As shown in the figure, the difference between the target value r and the convergence value “y _n + y ₀ ” is the corrected target deviation e *. In other words, the correction target deviation e * means that the predicted value “y _n + y ₀ ” that is finally reached due to the change in the past operation amount up to the present time is still the target value r. It is a gap (difference) between them. Therefore, the manipulated variable u may be further changed so as to fill this gap. The predicted value “y _n + y ₀ ” can also be said to be a predicted value of the convergence value of the control amount y according to the past change in the manipulated variable up to the present time.

Here, conventionally, as an example, the next operation amount u (operation change amount du) is determined based on the target deviation current value e ₀ . That is, the operation change amount du corresponding to the current gap amount (target deviation current value e ₀ ) is obtained. However, as described above, the current state is still changing, and eventually becomes “y _n + y ₀ ”, so this value e ₀ is too large as the gap amount. This is the cause of the overshoot. On the other hand, in this method, overshoot can be suppressed by using the correction target deviation e *. Further, by using the corrected target deviation e *, it is possible to guarantee the convergence of the control amount y to the target value r.

The operation change amount calculation unit 12 itself may have an existing configuration. The difference is that, conventionally, the operation change amount du is determined based on the target deviation current value e ₀ , but in this method, the operation change amount du is determined based on the corrected target deviation e *.

Obtaining the corrected target deviation e * means obtaining the gap amount until the target value r is finally reached by predicting the influence of the past operation change on the control amount y by the plant response model. . The operation of the operation change amount calculation unit 12 means that an operation change amount to be added is determined according to the gap amount e *.

  The conventional PID control and model predictive control do not have such a predictive function (a function for obtaining the corrected target deviation e *). In other words, conventionally, there is no function for calculating the target deviation obtained by correcting the terminal response as described above.

  In this method, the correction target deviation is obtained by prediction, and the operation change amount du is configured to be a simple calculation for the correction target deviation, so that advanced optimization calculation like conventional model predictive control is not required, It can also be implemented easily.

  Hereinafter, an example of the operation of the termination response correction unit 11 will be described with reference to FIGS. 3, 4, 5, and 6.

First, as shown in FIG. 3, the case of the example, determine the termination response correction value y _n shown in FIG. 2. Thereby, the correction target deviation e * will be asked by the difference between the target deviation current value e ₀ and the termination response correction value _{y n (e * = e 0} -y n).

The termination response correction value _{y n} is a termination response prediction _{y nA,} based on the free response prediction _{y nB,} is determined. That is, it is obtained by y _n = y _nA −y _nB (difference between y _nA and y _nB ).

The end response prediction y _nA (t) is a sufficiently predicted value of the control amount y based on the past operation change amount du.

The free response prediction y _nB (t) is a predicted value of the control amount y based on the past operation change amount du. This is the current time t
y _nB (t−Δt), y _nB (t), y _nB (t + Δt), y _nB (t + 2Δt),..., y _nB (T)
Thus, it is predicted as a time series. Among these, the current free response prediction is y _nB (t) at time t. In addition, although said (DELTA) t is said Tc, for example, it is not restricted to this example. Here, T represents the end time of the previous prediction section or prediction horizon (see, for example, Non-Patent Document 2) that has been advanced from time t to t + Δt, t + 2Δt. Therefore, it can be said that T is not a constant value but a value that gradually slides in the future in conjunction with the current time t.

The terminal response prediction _ynA and the free response prediction _ynB are updated each time a new operation change amount du (t) is added.

The difference between the end response prediction y _nA (t) and the free response prediction y _nB (t) is calculated as the end response correction value y _n (t). That is, y _n (t) = y _nA (t) −y _nB (t).

Here, FIG. 4 also shows specific examples of the terminal response predicted value y _nA (t) and the free response predicted value y _nB (t). FIG. 4 further shows y _nA (t) and y _nB (t) based on FIG. In the following description, the current controlled variable y is assumed to be a y ₀ shown.

As shown in the drawing, y ₀ itself, which is the current value of the control amount y, is a result of being influenced by the past operation amount u (operation change amount du), and in the illustrated example, the control amount y at a past time is shown. now it has become a y ₀ changed from _1. If the manipulated variable u does not change as it is, it is predicted that the controlled variable y will continue to change as shown in the figure and converge to “y _n (t) + y ₀ ” in the future. Here, it is assumed that the current time is the time t shown in the figure.

As shown in the figure, the terminal response predicted value y _nA (t) is a difference between the convergence value “y _n (t) + y ₀ ” and the y ₁ . That is, the control amount y is by way of illustration of the operation amount u, eventually through the current value _{y 0} from _{y 1} converges to _{"y n (t) + y} 0". The terminal response predicted value y _nA (t) may be regarded as corresponding to the amount of change (“y _n (t) + y ₀ ” −y ₁ ).

Also, now is the middle of the change in the controlled variable y, the value has a y ₀ shown. It may be assumed that the amount of change (y ₀ −y ₁ ) from y ₁ to the current value corresponds to the free response predicted value y _nB (t).

Then, as shown in the figure, the difference between the terminal response predicted value y _nA (t) and the free response predicted value y _nB (t) is the above y _n (t).

When the end response correction value y _n (t) is obtained as described above, the difference between the target deviation current value e ₀ (t) and the end response correction value y _n (t) is obtained as follows. Then, the corrected target deviation e * (t) is calculated.

e * (t) = e ₀ (t) -y _n (t)
In the multi-input / output system, as in the conventional model predictive control technique, the related signals such as the control amount y, the target value r, the target deviation e, the operation change amount du, and the operation amount u are regarded as vectors and are described above. It goes without saying that the corrected target deviation e * (t) can be calculated in the same manner as the calculation method of this example. At this time, the calculation from the corrected target deviation e * to the operation change amount du may be a multiplication of a constant gain matrix.

  In addition, when a disturbance signal affecting the control system can be observed, a disturbance model may be added to the corrected target deviation e * to further correct the influence of the observed disturbance signal.

  In the above, FIG. 3 was demonstrated.

Hereinafter, with reference to FIG. 5 and FIG. 6, a specific example of a method for calculating the termination response prediction _ynA and the free response prediction _ynB will be described.

For calculating these _ynA and _ynB , as described above, a plant response model created and stored in advance is used.

  FIG. 5 shows a specific example of the plant response model.

  A function S (t) shown in FIG. 5 is a specific example of the plant response model.

  This function S (t) is the plant step response (response to unit step input; sometimes referred to as indicial response). The function S (t) can be obtained by measuring an actual measurement value using the control target plant 2 in advance. That is, a unit step input is performed on the control target plant 2, and the output (control amount y) of the control target plant 2 is measured. The output data (time-series data of the controlled variable y; indicating temporal change) of the controlled plant 2 is a function S (t) shown in FIG.

  Here, the convergence value when the step response converges is defined as a termination gain S (∞). For example, the last value of the measured value (time series data) is used as the termination gain S (∞).

For example, the termination response correction unit 11 calculates the termination response prediction y _nA (t) and the free response prediction y _nB (t) shown in FIG. 6 using the function S (t) and the termination gain S (∞). Thus, the predicted values y _nA (t) and y _nB (t) are calculated.

Here, the control cycle is Tc, and the number of data of the operation change amount du in the model section (a fixed period used for processing; that is, a fixed period from the present to the past) is A. Note that the Tc may be regarded as having one aspect of the sampling period of the data of the operation change amount du. Further, the current target deviation value is e ₀ (t), and the time series data of the operation change amount in the past predetermined period up to the present time is {du (t)} t.

The terminal response predicted value y _nA (t) is a terminal response (predicted value of the convergence value of the controlled variable y; predicted value of the sufficiently controlled value y in the future) according to the past operation, and the terminal gain S (∞ ) Etc. and is calculated by the following formula (1). (K = 0.1.2 ...)

自由応答予測値y_ｎＢ(t)は、過去の操作量ｕ（操作変化量ｄｕ）に応じた制御量yの変動量の推定値であり、特に過去から現在までの変動量の推定値であり、上記関数Ｓ（ｔ）等を用いて下記の（２）式により計算する。

The free response predicted value y _nB (t) is an estimated value of the fluctuation amount of the control amount y according to the past operation amount u (operation change amount du), and is particularly an estimated value of the fluctuation amount from the past to the present. Using the function S (t) and the like, the calculation is performed by the following equation (2).

尚、上記（１）式、（２）式における“ｄｕ（ｔ−ｋＴｃ）”の具体例を、図２の下側に示している。これは、上記過去の操作変化量{du(t)}tの具体例と見做してもよい。また、この例では、例えば、Ａ＝３となっている。

A specific example of “du (t−kTc)” in the above equations (1) and (2) is shown on the lower side of FIG. This may be regarded as a specific example of the past operation change amount {du (t)} t. In this example, for example, A = 3.

The end response correction value y _n (t) is calculated by the following equation (3) using the calculated end response predicted value y _nA (t) and the free response predicted value y _nB (t).

補正目標偏差e*(t)は、上記目標偏差現在値ｅ_０(t)と、上記算出した終端応答補正値y_ｎ(t)を用いて、下記の（４）式により算出する。

The corrected target deviation e * (t) is calculated by the following equation (4) using the target deviation current value e ₀ (t) and the calculated end response correction value y _n (t).

以上の処理により、終端応答補正部１１によって、補正目標偏差e*(t)を得る。

Through the above processing, the corrected target deviation e * (t) is obtained by the terminal response correction unit 11.

  However, the processing described above is an example of processing for obtaining the corrected target deviation e * (t), and is not limited to this example. For example, as described above, instead of the time series data “{du (t)} t” of the operation change amount, an intermediate calculation value in the correction target deviation calculation process is stored in the intermediate calculation value storage unit in FIG. You may make it memorize | store. Hereinafter, such a modification will be described. Therefore, in the case of the above example, the intermediate calculation value storage unit of FIG. 3 is not necessary.

In the case of the above example, the end response predicted value and the free response predicted value are calculated using the formula for calculating the end response predicted value y _nA (t) and the formula for calculating the free response predicted value y _nB (t) as needed. In the case of the modified example, the following method is used.

That is, in the case of the modified example, the calculation result of the terminal response predicted value y _nA (t) and the free response predicted value y _nB (t) calculated before the current time t, not the time series data of the operation change amount, Calculation is performed using the (current) operation change amount at that time.

と計算し、この算出結果を、終端応答予測値ｙ_ｎＡ（ｔ+ Tc）としてもよい。尚、更に、この終端応答予測値ｙ_ｎＡ（ｔ+ Tc）を上記図３の中間計算値記憶部に記憶して、その後、記憶された終端応答予測値ｙ_ｎＡ（ｔ+ Tc）を用いて終端応答予測値ｙ_ｎＡ（ｔ+ ２Tc）を算出するようにしてもよい。これは、自由応答予測値についても同様である。Specifically, since the terminal response predicted value y _nA (t) is a predicted value in the sufficiently future of the control amount y based on the past operation change amount du, in the above example, as shown in FIG. In the next time t + Tc after the elapse of the control cycle Tc from time t, the operation change amount du (t + Tc) at time t + Tc and the end response predicted value _ynA (at time t) t)

It is good also considering this calculation result as the end response predicted value y _nA (t + Tc). Further, this terminal response predicted value y _nA (t + Tc) is stored in the intermediate calculation value storage unit of FIG. 3, and thereafter, the stored terminal response predicted value y _nA (t + Tc) is used. The terminal response predicted value y _nA (t + 2Tc) may be calculated. The same applies to the free response predicted value.

上記（５）式（ｍ＝1,2,….）のように計算し、この計算結果からm=1として、自由応答予測値ｙ_ｎＢ（ｔ+Tc）を得てもよい。Similarly, in the case of the above example, the free response predicted value y _nB (t) is the control amount y based on the past operation change amount du, and the current time is t.
y _nB (t−Δt), y _nB (t), y _nB (t + Δt), y _nB (t + 2Δt),..., y _nB (T)
Thus, it is predicted as a time series. On the other hand, in the modified example, at the next time t + Tc after the elapse of the control cycle Tc from time t, the operation change amount du (t + Tc) at time t + Tc and the free response prediction at the time t value
y _nB (t−Δt | t), y _nB (t | t), y _nB (t + Δt | t), y _nB (t + 2Δt | t), ..., y _nB (T | t)
(Where the symbol | t indicates a prediction at time t)

It is also possible to calculate as in the above equation (5) (m = 1, 2,...), And obtain a free response predicted value y _nB (t + Tc) with m = 1 from this calculation result.

上記（６）式（ｍ＝1,2,….）のようにも計算できる。Here, y _nB (t + mTc | t + Tc) (m = 1, 2,...) Is a predicted free response value at time t + Tc,
y _nB (t + mTc | t) (m = 1, 2,...) is a free response prediction value at time t.

It can also be calculated as in the above equation (6) (m = 1, 2,...).

On the other hand, using the intermediate calculation value stored in the intermediate calculation value storage unit and the (current) operation change amount, the terminal response predicted value y _nA (t) and the free response predicted value y _nB (t) are obtained. In the calculation method of the above formula (5) to be calculated, the calculation amount can be reduced and executed at a higher speed than the calculation method of the above formula (6) in which a large number of product-sum operations are performed each time.

Therefore, if the current time is t + Tc, the terminal response predicted value y _nA (t) and the free response predicted value y _nB (t + mTc | t) (m = 1, 2,... Is stored (accumulated) in the intermediate calculation value storage unit shown in FIG. 3 as an intermediate calculation value in the correction target deviation calculation process, the time series data “{ Without storing (accumulating) du (t)} t ”, it is possible to calculate the end response predicted value y _nA (t + Tc) and the free response predicted value y _nB (t + Tc) at the current time t + Tc. it can.

After calculating the end response predicted value y _nA (t) and the free response predicted value y _nB (t) by the above processing, thereafter, as in the above example, for example, a calculation formula of the end response correction value shown in FIG. The corrected target deviation e * (t) may be calculated using the target deviation calculation formula.

  As described above, the operation change amount calculation unit 12 calculates the next operation change amount du (t) using the corrected target deviation e * (t).

  The operation change amount calculation unit 12 stores data (or formulas) for the calculation process in advance, and an example thereof is shown in FIG.

  FIG. 7 shows a specific example of data stored in advance by the operation change amount calculation unit 12.

  As shown in the figure, this data indicates the relationship between the corrected target deviation e * and the operation change amount du. This is represented by a linear function (du = a · e * + b (a is a slope, b is a y-intercept), and b = 0 in the illustrated example) in the illustrated example. Therefore, the illustrated data may be held, or a linear function may be held.

  The operation change amount calculation unit 12 uses the illustrated data or the linear function or the like to calculate the operation change amount du (t) corresponding to the correction target deviation e * (t) obtained by the end response correction unit 11. Ask.

  In the illustrated example, an upper limit value du_max and a lower limit value du_min of the operation change amount du are further included. Accordingly, the operation change amount calculation unit 12 outputs the upper limit value du_max when the operation change amount du (t) calculated using, for example, the linear function exceeds the upper limit value du_max, and falls below the lower limit value du_min. Outputs the lower limit du_min.

  In addition, the illustrated data and linear functions are arbitrarily determined in advance by, for example, a developer and are stored in the operation change amount calculation unit 12.

  FIG. 8 shows a specific example of the plant response model.

  In this example as well, the function S (t), which is the step response (indicial response) of the plant, is shown as an example of the plant response model, as in FIG.

  The example of FIG. 8 also shows a reverse response in the initial stage, like the example of FIG. 5, and shows a response (control amount y) that converges to a constant value after once overshooting. The convergence value, that is, the termination gain S (∞) is “10” in the illustrated example.

  FIG. 9 shows a specific example of data stored in advance by the operation change amount calculation unit 12.

  This example also shows the relationship between the corrected target deviation e * and the operation change amount du in the form of a linear function (du = a · e * + b), as in the example shown in FIG. In the illustrated specific example, the inclination a = 0.085 and the y-intercept b = 0. Further, as in FIG. 7, an upper limit value du_max and a lower limit value du_min of the operation change amount du are also set. In the illustrated example, the upper limit value du_max = 5 and the lower limit value du_min = −5.

  As described above, the operation change amount calculation unit 12 itself may be the same as the conventional one. Therefore, the data shown in FIG.

  FIGS. 10A and 11A show simulation results of target value responses (changes in target value r and control amount y) when the data shown in FIG. 9 is used. FIG. 10A shows the case of this method (for example, the configuration of FIG. 1), and FIG. 11A shows the conventional case for comparison. The conventional example is integral control, and this method is also based on integral control.

  10 (a) and 11 (a) show the control amount y when the target value r is changed stepwise as shown.

Conventionally, the terminal response correction unit 11 does not exist, and the correction target deviation e * is not generated. For example, the target deviation current value e ₀ (t) is used. For this reason, as shown in FIG. 11A, the control amount y (t) follows the step target value r (t) but has a large overshoot amount.

On the other hand, in the case of this method, as shown in FIG. 10 (a), the amount of overshoot is greatly suppressed and the control response can be improved as compared with the case of the prior art shown in FIG. 11 (a). I understand that. As shown in FIG. 10B, the corrected target deviation e * (t) is a signal having a smaller amplitude than the target deviation current value e ₀ (t) by correcting the end response. Because.

For comparison, the target deviation current value e ₀ (t) in the case of the prior art is shown in FIG. As shown in the figure, the target deviation current value e ₀ (t) also varies more greatly than the present method shown in FIG. This is because the fluctuation of the control amount y (t) is large.

In this example, as shown in FIG. 10D, the end response predicted value y _nA (t), the free response predicted value y _nB (t), and the end response correction value y _n (t) are calculated. Then, by correcting the target deviation current value e ₀ (t) shown in FIG. 10B based on the calculated end response correction value y _n (t), the corrected target deviation e * ( t) is required.

  Further, in this example, since the operation change amount calculation unit 12 generates the operation change amount du (t) using the corrected target deviation e * (t) shown in FIG. 10B, the operation change amount du (t) is shown in FIG. As described above, the fluctuation of the operation amount u (t) is small. For comparison, FIG. 11C shows an operation change amount du (t) and an operation amount u (t) in the case of the prior art. As apparent from a comparison between FIG. 10C and FIG. 11C, in the case of this method, the fluctuation of the operation amount u (t) can be reduced as compared with the conventional technique.

  According to the above-described present invention, the following effects can be obtained.

  In the present invention, a plant response model is used to predict a target deviation residual (corrected target deviation e * (t)) sufficiently in accordance with the past operation change amount du, and based on this predicted residual. Determine the amount of change in operation. That is, the minimum necessary change is added to the operation amount while considering the influence of the past operation. For this reason, overshoot can be suppressed. Such highly accurate and highly stable control based on the prediction of the end response of the plant can be realized with a simple configuration (relatively small memory and CPU resources).

  Or, compared with the conventional MPC control method, it is not necessary to repeat optimization calculations such as a quadratic programming problem for each control cycle, and predictive control can be realized at extremely high speed and low cost.

  As described above, according to the present invention, it can be said that overshoot suppression can be accurately realized with a simple configuration (with a relatively small calculation load).

  In addition, control loops that have already been installed can be easily updated with less man-hours such as adding a terminal response prediction part, and temperature controllers, PLCs (Programmable Logic Controllers) and DCS (DCS) It has the effect of being able to be easily implemented on hardware with limited computing resources such as Distributed Control System) and embedded control devices.

  Hereinafter, with reference to FIG. 12 to FIG. 14, the difference between the control device of this example and the conventionally known internal model control will be described.

  First, with reference to FIGS. 12 and 13, the operation of the control device of this example will be described using a transfer function.

Here, the actual plant transfer function is P * (s), the plant model is P (s), the controller is K (s), the plant steady gain is P (0), the controlled variable is y (t), and the operation The amount is u (t), the target value is r (t), the correction target deviation is e * (t), the end response prediction is _ynA (t), and the control amount is predicted only by the past operation change amount. If y _nB (t), the configuration of the control device of this example can be approximately expressed by a transfer function block as shown in FIG.

  Here, the controller K (s) shown in FIG. 12 may be considered to correspond to, for example, “operation change amount calculator 12 + adder 13” in FIG.

In FIG. 12, the corrected target deviation e * is input to the controller K (s), and a new manipulated variable u (t) is generated and output. The manipulated variable u (t) is input to the actual plant transfer function P * (s), the plant model P (s), and the steady gain P (0). The output of the actual plant transfer function P * (s) is the controlled variable y (t), the output of the plant model P (s) is the free response prediction y _nB (t), and the output of the steady gain P (0) is the above It may be assumed that the end response prediction y _nA (t).

The difference between the control amount y (t) and the free response prediction y _nB (t) is added to the termination response prediction y _nA (t) as a feedback signal. The difference between the addition result and the target value r (t) is input to the controller K (s) as the new corrected target deviation e *.

のように、積分器で近似することができる。尚、ｋ_Ｉは、積分ゲインである。Here, since the controller K (s) is an operation of adding the operation change amount every time,

It can be approximated by an integrator as follows. Incidentally, _{k I} is an integral gain.

  The operation of the control device of this example will be described in more detail with reference to FIG.

と計算され、目標値r(t)から制御量y(t)への入出力特性は、P(s)F(s)で計算される。Assume that the actual plant transfer function P * (s) and the plant model P (s) match. At this time, since y (t) = y _nB (t) is established, the feedback signal becomes zero. Here, the local loop formed by the controller K (s) and the plant steady gain P (0) is defined as a transfer function F (s) representing the input / output characteristics from the target value r (t) to the manipulated variable u (t). In summary, the transfer function F (s) is

The input / output characteristics from the target value r (t) to the controlled variable y (t) are calculated as P (s) F (s).

となるため、閉ループの定常ゲインが１となり、最終的な目標値追従が定常状態で達成されることが分かる。これより、本手法では、オーバーシュートの抑制だけでなく目標値追従を達成することができることが分かる。Here, if we take the 0 limit of P (s) F (s),

Therefore, it can be seen that the steady-state gain of the closed loop is 1, and the final target value tracking is achieved in a steady state. From this, it can be seen that this method can achieve not only overshoot suppression but also target value tracking.

  On the other hand, FIG. 14 shows a conventionally known internal model control method (for example, see pages 88 to 93 of Non-Patent Document 3).

  In the example shown in FIG. 14, the plant model P (s) is arranged in parallel with the actual plant transfer function P * (s), the target deviation is calculated for the difference between the outputs, and the controller Q ( A feedback signal is generated via s).

The input to the controller Q (s) corresponds to the target deviation current value e ₀ (t). The controller Q (s) generates and outputs an operation amount u (t) corresponding to the target deviation current value e ₀ (t). This manipulated variable u (t) is input to the actual plant transfer function P * (s) and the plant model P (s). The output of the actual plant transfer function P * (s) is the controlled variable y (t), and the output of the plant model P (s) is y _M (t) shown. The difference between y _M (t) and the controlled variable y (t) is fed back. That is, the difference between the target value r (t) and the feedback value is input to the controller Q (s) as the target deviation current value e ₀ (t).

  It is known that the controller Q (s) is designed from the inverse of the minimum phase element of the actual plant transfer function, that is, the inverse model of the plant excluding unstable elements. In addition, only when the actual plant transfer function can be expressed in a simple manner such as a first-order lag system, a second-order lag system, and an integral system, it is equivalent to the internal model control by appropriately converting the block diagram of the internal model control. A design method for converting to PID control and deriving PID parameters is known.

  As described above, the purpose of internal model control is to realize a good follow-up to the target value of the controlled variable by including the plant model in the control loop and further including a partial inverse model of the plant. It is a control method.

The approximate operation of the control device of this example shown in FIGS. 12 to 13 is similar to that of FIG. 14, but there is a clear difference if they are compared as shown. If the control block of the conventionally known internal model control shown in FIG. 14 is compared with the control block of the control device of this example shown in FIG. 12, the difference between them is clear. That is, it can be seen that the control block of the present method in FIG. 12 is different from the internal model controller Q (s) in FIG. 14 in that it has y _nA (t) that is the termination response prediction.

  In other words, according to the block diagram approximated by the transfer function expression, the control device of this example theoretically adds the above-mentioned terminal response prediction function for the purpose of suppressing overshoot in addition to the internal model control function. May be considered equivalent.

  However, the control device of this example does not need to use an inverse model of the actual plant transfer function as in the conventionally known internal model control, and can be realized more easily.

  In addition, as described above, since the step response model having an arbitrary waveform can be used in the control device of this example, unlike the PID control based on the internal model control, the reverse response, the dead time, and other third-order or higher order. It can be easily applied to an actual plant containing higher-order components.

  The plant response model is not limited to the step response, and may be, for example, an impulse response model, a transfer function model, a state space model, or the like.

Further, the terminal response predicted value y _nA corresponds to the amount of change from the past value (y ₁ ) to the convergence value (y _n + y ₀ ) of the control amount y according to the past change in the manipulated variable up to the present. I can also say.

Moreover, it is said that the free response predicted value _ynB corresponds to the amount of change from the past value (y ₁ ) to the current value (y ₀ ) of the control amount y according to the past change in the manipulated variable up to the present. You can also.

  The plant response model is not limited to the example of the impulse response model, and may be, for example, a transfer function model or a state space model.

  Finally, FIG. 15 shows a process flowchart of the control device 1.

  Here, FIG. 15A shows a processing flowchart of the operation amount update unit 10 in particular.

  Here, as shown in FIG. 15B, for example, the control device 1 includes an arithmetic processor 31 such as a CPU / MPU, a storage device 32 such as a memory, and the like. A predetermined application program is stored in the storage device 32 in advance. When the arithmetic processor 31 executes this application program, the various processing functions of the control device 1 (particularly, the operation amount update unit 10) are realized as described above, and the processing of the flowchart of FIG. Realized.

  Hereinafter, the process of the flowchart shown in FIG. 15A will be described.

  This process is executed at regular intervals (here, executed every cycle Tc).

Here, for each of the periods Tc, the operation amount update unit 10, and the target deviation current value e _0, the current operation amount u0 is input. Further, as described above, the operation amount update unit 10 holds a past operation change amount (time series data {du (t)} t of past operation change amounts up to the present)). Further, the plant response model (here, the function S (t) of the plant step response and the terminal gain S (∞)) is registered in the manipulated variable update unit 10 in advance.

Thus, the operation amount update unit 10 first calculates the end response predicted value y _nA (t) using the past operation change amount, the end gain S (∞), and the like (step S11). Further, the free response prediction value y _nB (t) is calculated using the past operation change amount, the function S (t), and the like (step S12). Then, the corrected target deviation e * (t) is calculated using the calculated terminal response predicted value y _nA (t), the free response predicted value y _nB (t) and the target deviation current value e ₀ ( Step S13).

  Then, an operation change amount du (t) is calculated based on the calculated corrected target deviation e * (t) (step S14).

  By adding the calculated operation change amount du (t) to the current operation amount u0, the next operation amount u (t) is determined and output to the control target plant 2.

  According to the control device and the like of the present invention, overshoot suppression can be accurately realized with a simple configuration.

Claims (11)

In a control device that outputs an operation amount to a control target device and causes the control amount of the control target device to follow an arbitrary target value,
Target deviation calculation means for obtaining a difference between the control amount and the target value as a target deviation current value;
A corrected target deviation calculating means for calculating a corrected target deviation based on a plant response model that is held in advance, the target deviation current value, and an operation change amount that is a change amount of the operation amount ;
An operation amount calculating means for determining a new operation amount based on the correction target deviation,
The control device characterized in that the correction target deviation is a difference between a predicted value of a convergence value of the control amount according to a change in the operation amount in the past up to the present time and the target value. Further comprising an operation change amount storage means for storing pre Kimisao operation change amount,
2. The control apparatus according to claim 1, wherein the correction target deviation calculation means calculates the correction target deviation based on past operation change amounts accumulated in the operation change amount storage means. Further comprising an intermediate calculation value storage means for storing the intermediate calculation value in the process of calculating the correction target deviation in the correction target deviation calculation means,
2. The control apparatus according to claim 1, wherein the correction target deviation calculation means calculates the correction target deviation based on past intermediate calculation values accumulated in the intermediate calculation value storage means.   The control device according to claim 1, wherein the plant response model is a step response that is measured in advance using the control target device. The plant response model is a function of the step response and a termination gain that is a convergence value of the step response,
The corrected target deviation calculating means obtains a terminal response predicted value using the terminal gain and also calculates a free response predicted value using the function, and a termination that is a difference between the terminal response predicted value and the free response predicted value. 5. The control apparatus according to claim 4, wherein a response correction value is obtained, and a difference between the target deviation current value and the terminal response correction value is set as the correction target deviation. The terminal response predicted value corresponds to a change amount from the past of the control amount according to a change in the past operation amount to the convergence value,
The control device according to claim 5, wherein the predicted free response value corresponds to a change amount from the past to the present of the control amount according to a change in the past operation amount. When the step response function is S (t), the termination gain is S (∞), the number of operation change data from the past to the present is A, and the sampling period of the data is Tc,
The end response predicted value is calculated by the following equation (1):

The predicted free response value is calculated by the following equation (2).

The control device according to claim 6. The plant response model, the control device according to any one of claims 1 to 3, characterized in that the impulse response model or transfer function or state-space model. Data or a formula indicating a correspondence relationship between the correction target deviation and the operation change amount is preset and stored,
The steering Sakuryou calculation means,
An operation change amount calculating means for obtaining an operation change amount corresponding to the correction target deviation calculated by the correction target deviation calculating means using data or an expression indicating the correspondence relationship ;
Adding means for adding the operation change amount obtained by the operation change amount calculating means to the current operation amount, and outputting the added value as the new operation amount;
Control device according to any one of claims 1-8, characterized in that it comprises a. A control device computer that outputs an operation amount to a control target device and causes the control amount of the control target device to follow an arbitrary target value,
Target deviation calculation means for obtaining a difference between the control amount and the target value as a target deviation current value;
Based on the plant response model held in advance, the target deviation current value, and the amount of change in the operation amount, the convergence value of the control amount according to the change in the operation amount in the past up to the present time. A corrected target deviation calculating means for calculating a corrected target deviation which is a difference between a predicted value and the target value;
An operation amount calculating means for determining a new operation amount based on the corrected target deviation;
Program to function as. A plant control method for a control device that outputs an operation amount to a control target device and causes the control amount of the control target device to follow an arbitrary target value,
The difference between the control amount and the target value is obtained as a target deviation current value,
Based on the plant response model held in advance, the target deviation current value, and the amount of change in the operation amount, the convergence value of the control amount according to the change in the operation amount in the past up to the present time. Calculate a corrected target deviation that is the difference between the predicted value and the target value,
A plant control method characterized by determining a new manipulated variable based on the corrected target deviation.

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