JPS6014362B2 - Variable sampling period control method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a sampling control device for a process, and more particularly to a sampling control device suitable for accurately controlling when the performance characteristics of a controlled process change depending on the operating state.

When a controlled process is directly controlled by a digital computer (hereinafter abbreviated as DDC), a sample value control method is often adopted.

That is, the input and output signals of the computer used as a control device are temporally discontinuous sampling value signals. In conventional DDC systems, the sampling period is short enough to ensure a good control response, and the sampler is controlled to open and close at a fixed period, input to a computer, and the manipulated variable calculated by the computer is given to the controlled object. It is taken.

However, in this method, the sampling period is fixed, so in some cases it may be made shorter than necessary, and the sampler operates at the sampling period. For example, this applies to steady response. Furthermore, as a method of controlling a process whose dynamic characteristics change depending on the operating state, a method has been proposed in which the gain of the control system is changed according to the dynamic characteristics of the process.

However, in this case as well, the control period is kept constant. The control period is defined by the smallest time constant among the time constants determined from the operating characteristics that vary depending on various operating conditions of the process. Therefore, as in the case described above, there is a drawback that the control algorithm is executed with an unnecessarily small control cycle even when the time constant of the process is large. On the other hand, the following three types of control methods using variable sampling periods have been proposed as methods for solving the drawbacks of the above-mentioned conventional techniques.

The first method is a variable sampling period, in which the sampling period is shortened when the rate of change of the error signal is large, and the sampling period is lengthened when the rate of change of the signal is small, such as in a steady state.

However, this method applies only to controllers that perform proportional operation with a gain of 1, and is not applicable to commonly used controllers that perform proportional, integral, or differential operations, or those that perform other complex control calculations. I can't. The second method is to estimate the current rate of change in the manipulated variable from the sum of the past rates of change in the manipulated variable, and when this estimated value is large, the sampling period is shortened. This is a variable sampling period that increases the sampling period.

In this method, the sampling period should originally be variable depending on the characteristics of the process, but it is replaced by the amount of change in the manipulated variable, so even if the characteristics of the process remain unchanged, it is superimposed on the change in the target value and the controlled variable. The drawback is that the sampling period changes due to noise. The third method proposes a method of determining the sampling period based on the angular frequency of the closed-loop transfer function for a sample value control system as shown in Fig. 1, but in an actual computer control system, the method shown in Fig. 2 is proposed. As shown in the figure, there is also a sampler 15 on the input side to the control system.
is provided. In Figures 1 and 2, 9 is a target value signal, 10 is an adder, 11 is a sample and hold circuit,
12 is a process to be controlled, 13 is a feedback compensation circuit, i4 and 15 are samplers, 16 is a feedback compensation circuit, and 18 is a control signal. The third method is to find the closed loop transfer function in the control system shown in Figure 1,
The sampling period is determined from the reciprocal of the angular frequency at which the closed-loop gain is, for example, 0.01 or less, and the sampling period is automatically changed in accordance with changes in the dynamic characteristics of the controlled process 12. However, if a similar control method is applied to the control system shown in FIG. 2, it will only make the calculations even more complicated, which is not necessarily a good idea. The purpose of the present invention is to eliminate the above-mentioned drawbacks of the prior art,
The objective is to determine the optimal sampling period according to the operating state of the controlled process.

A feature of the present invention is that the process to be controlled is approximated by a first-order lag characteristic, and the change in time constant corresponding to the operating state is calculated and stored offline as a function of the control amount of the process. The purpose is to select the corresponding time constant and determine the optimal sampling period.

Another feature of the present invention is that, when the sampling period for a certain time constant is not determined in a one-to-one correspondence, means is provided for calculating the sampling period corresponding to the control amount from the similarity of the characteristics.

A specific embodiment of the present invention shown in FIG. 3 will be explained below.

FIG. 3 consists of a first control system 1, a second control system 2, and a third control system 3, and controls a controlled object 7. In FIG.

The first control system 1 receives a plurality of control amount signals 8 as input signals,
Estimate the process equivalent time constant.

This has means for performing an off-line dynamic characteristic analysis of the controlled process in advance and storing the time constant of the controlled process with respect to the controlled variable. The dynamic characteristics of the controlled process are grasped as a time constant when the controlled process is approximated by, for example, a first-order lag transfer function, and stored as a time constant for the controlled variable. That is, by storing the time constant as a function of the controlled variable, it is possible to estimate the time constant for any controlled variable. As described above, the first control system uses the control amount signal 8 as an input signal and outputs the signal 4 according to the estimated time constant. The second control system 2 uses the estimated time constant signal 4 as an input signal and outputs a signal 5 corresponding to the optimum sampling period lj.

That is, the optimal sampling period is determined as a function of the estimated equivalent time constant of the process. Equivalent time constant Tm of the process
The optimal sampling period Δtm (constant value) for (constant value) is calculated offline in advance and stored in the storage means of the second control system. If so, the control period Δt in that case is calculated using the equation '1' using the similarity. △ (
Temple x △tm] '1' Here, [ ] is a Gauss symbol.

The third control system 3 is a control algorithm execution control system, and in the case of velocity type proportional or integral control, the manipulated variable 6 is determined by the {2} formula.

△P(t)=K, xe(t)+KP{e(t)−e(t
-△t)}/△t~ ■ko) to △P(t)
: Control output (operated amount) at time t KI: Integral control gain KP: Proportional control gain e(t): Control deviation at time t (:R(t)-A(t)) R(t): Control output at time t Target value A(t): Actual value at time t The basic matters of the present invention have been described, but examples of control characteristics when the present invention is applied in comparison with the conventional technology are shown in Figs. 4 to 6. show.

FIG. 4 shows the case of a conventional constant sampling period.

Figure a shows a case where the target value changes over time to. FIG. 5B shows an example where the time constant TP of the controlled process is relatively large with respect to the sampling period T (TP>>T). That is, the optimal sampling period Tminl for the minimum time constant of the process is equal to the sampling period T=Tm
The control characteristics are shown as in. It can be seen that both the manipulated variable and the controlled variable have large fluctuations. In the same figure, c is the process time constant T
The figure shows fluctuations in the manipulated variable and controlled variable when P is relatively small (TP>T).

The sampling period is T=Tmjn as in the case of b in the same figure.
It is. In this case, the controllability is good as is clear from the characteristics shown in Figure 4 c, but if control is performed with a constant sampling period, the sampling period is the same in both cases b and c of Figure 4, so the time constant TP of the process It can be seen that when is large, controllability is significantly reduced. FIG. 5 shows the second control method using the variable sampling period in the prior art described above.
This is an example of the method described above.

Figure a shows the change in the target value, and Figure b shows the control characteristics corresponding to the sampling timing at that time. In this case, the variable sampling period control estimates the current rate of change in the manipulated variable from the sum of the past rates of change in the manipulated variable, shortens the sampling period when the estimated value is large, and increases the sampling period when the estimated value is small. Because it is a method, Ji-anka. When the target value changes, the sampling period is gradually changed based on the sum of the change rates of the manipulated variables. These changes in the sampling period will be clear from FIG. When the time constant TP of the process is relatively large, both the manipulated variable and the controlled variable have large fluctuations. Similarly, c in the figure is a case where the process time constant TP is relatively small.

As is clear from Figures b and c, although the time constant of the process fluctuates depending on the operating state, control is controlled because the sampling period is changed by focusing on the rate of change of the manipulated variable. In terms of characteristics, good results are not necessarily obtained.
In particular, the control characteristics are poor when the time constant of the process is large, as in the case of FIG. FIG. 6 shows an example of control characteristics when the present invention is applied.

Figure a shows the change in the target value, and Figure b shows the change in the manipulated variable and control amount corresponding to the sampling period at this time. Compared to FIGS. 4 and 5, there is a characteristic in the change in sampling period. This is the case when the time constant TP of the controlled process is relatively large, and the case c in the figure is the case where TP is small.

That is, since the sampling period is changed depending on the magnitude of the time constant TP of the controlled process, it can be seen that the control characteristics are significantly improved compared to the cases shown in FIGS. 4 and 5. When TP is large, increase the sampling period,
Since the sampling period is shortened when TP is small, it is possible to follow the target value with the minimum number of operations required. As is clear from the above, the effect of the present invention is that the sampling period is made variable according to the time constant of the process, so the control algorithm is always executed at the optimal control period (sampling period), so the minimum necessary operation is required. The reason is that it is possible to follow changes in the target value by the number of times. Further, according to the present invention, in order to make the sampling period variable according to the dynamic characteristics of the plant, the proportional gain TP and integral gain K of the proportional-integral adjustment function in the computer can be considered as fixed values. Arithmetic processing within a computer can be significantly simplified.

This will be explained below. First, the controlled object (first
Consider the case where the characteristic in FIG. 12) is a first-order lag and is described as in equation (A-1).

etc.2F-main A(t)+reed P(t)
…”(A-1) Here, A(t): Process state quantity at time t P(t): Control output (operated amount) at time t K: Process gain T: Process time constant This is the control period △ Convert * to the sample value system of t,
A(i)=e "F A(i-1) ten (1-e "")
KP(i-1).・．． ．．・．． (A-2).

However, i and i-1 each mean a value at the current sampling time. On the other hand, when the control algorithm (formula ■) of the velocity type proportional/integral adjustment function is converted to a sample value system, P(i
〉-P(i-1)=K, (R(i)-A(i))+KP
{(R(i)-A(i))-(R(i-1)-A(i-
1))} ...It is expressed as (A-3).

(If we organize A-3 with respect to P i , P(i)
=-(K, 10KP)A(i)+KPA(i-1)10P(
i-1) ten (K, ten KP) R (i) - KPR (i-1)
...(A-4).

Substituting equation (A-2) into this and rearranging, P(i)=
{1e 了 “K, 10 (1-e-了 1) KP}A(
i-1) 10{,-(・-e4)(K, 10KP)K}P(
i-1) ten (K, ten KP) R (i) - KPR (i-1)
...(A-5).

In this formula, (K, 10KP)R(i)-KPR(i-1)
The term is considered to be a forced disturbance term for this system, so
If this term is set to almost zero and ignored, the characteristic equation of the system itself can be expressed as a general equation from (A-2) and (A-5) as follows.

×(i)=■・×(i-1)...(A-6) Here,
, (i) = A (i) X2 (i) = P (i) =
Hakama) 4t. =e ChiF, no, 2 ni (1-e raw) K -4t Thing: -e 了K, 10 (1-e cow) KP Thing ni 1-(1-e4) (K, 10 KP) K Therefore , the characteristic equation of the system is given by the characteristic root Z and the determinant (ZO-■)=○ using the unit matrix 0=l and 9l.

...---(A-7>..Z-(of,.22 of 10)Z
＋の、．． (A-8).

The characteristics of the entire system depend on the plate Z of formula (A-8). Here, if we set Z=0 as a condition that the system does not become a secondary oscillation system, and give Z=B (0<8<1) as a condition that the system becomes stable, the Fumono-Bokumono Yumi also becomes a child.・・・--A-9).
Two equations of 10/22 are obtained.

Solving this, the proportional/integral gain of the proportional/integral adjustment function is KP= 1...(A-10)K,
= 1-8K (1-e-half).

This formula (A-10) represents the following.

In other words, for a controlled object whose process time constant and gain are given by T and K, the proportional/integral gain is expressed as (A-1
0), the system will always have stable characteristics if it is changed according to the equation. Input sample data for each part,
In a computer that outputs intermittently to a process, (A-
10) KP, KI and control deviation input e(t
), the calculation according to the formula {2- is executed.

The problem in this case is that in many processes, the process time constant T in equation (A-10) is variable depending on the operating state of the process, and it takes a lot of processing time and memory capacity to calculate the raw term e. will be required. Specifically, the optimal value is obtained by performing Taylor expansion or Maclaurin expansion using software processing inside the computer, but as the number of terms in the expansion increases, the accuracy increases, so it is repeated until the specified accuracy is achieved while increasing the number of terms as appropriate. There is a need. For a small computer for process control, performing this processing for each sampling is a considerable burden, and it is difficult to avoid using a large capacity computer or slowing down the processing speed. The above example shows the case where the process is first-order delayed, but
Generally, it is more complicated, and the number of e-raw terms in the (A-lo) equation is also larger. Also, when using predictive control or adaptive control, the number of terms in e-``'' increases.

By the way, in the case of the present invention, the sampling period Δt is determined according to the process time constant T as shown in the equation '1}.In this equation, brush=band, which is constant.

As a result, equation (A-10) can be expressed as equation (A-11). KP= 1 (A-11)
4tK(e-'F-1) K,= 1-3 K(1-e-4) This formula is, ``The proportional/integral gain KP, K, is independent of the process time constant T, and is dependent on the process gain K. This means that it is sufficient to set it so that it is inversely proportional.

In other words, the effect of the present invention is that by changing the control period Δt using the formula [1}, KP, K, 4te・end at the time of calculation,
This means that e-raw calculations can be omitted.

Further, although the present invention has great effects when implemented alone, it can also be implemented in combination with the second variable sampling period control described in the prior art.

This is particularly effective when considering control in the steady state region shown in FIG. 6c. In other words, when the change in the manipulated variable is small, T
The period is larger than the sampling period determined by P,
When a change in the manipulated variable is detected, the control algorithm is executed at a sampling period determined from TP, as already described in the present invention. Such control has the effect of reducing the number of operations in the steady state region of FIG. 6c. Further, a variable sampling period control method in which the sampling period is set to be larger than the sampling period determined by the present invention when the control amount deviation is below a certain fixed value, and the sampling period is set to be the sampling period determined by the present invention when the controlled amount deviation exceeds the certain value. However, the same effects as the present invention can be obtained.

BRIEF DESCRIPTION OF THE DRAWINGS Fig. 1 is an explanatory diagram of the prior art, Fig. 2 is a general control system of a DDC, Fig. 3 is a block diagram illustrating an embodiment of the present invention, and Figs. FIG. 5 shows an example of control characteristics when the prior art is implemented, and FIG. 6 shows an example of control characteristics when the present invention is implemented.

Explanation of symbols, 1...First control system, 2...
...Second control system, 3...Third control system, 4.
... Process time constant, 5 ... Control period signal, 6 ... Manipulated amount, 7 ... Controlled process, 8
...Process control amount.

Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6

Claims (1)

[Scope of Claims] 1. In a system in which a process to be controlled is directly controlled by a digital computer, a first device that stores changes in a time constant corresponding to the operating state of the process as a function of a controlled variable;
and a second storage means storing an optimum sampling period determined from the time constant, the first storage means determining a time constant corresponding to the control amount during the operation, A variable sampling period control method, characterized in that an optimum sampling period corresponding to a time constant is determined from the second storage means, and the controlled process is controlled using the determined sampling period. 2. The variable sampling period control method as set forth in claim 1, characterized in that when the control amount deviation is below a certain value, control is performed at a sampling period larger than the sampling period determined from the second storage means. .