JPS6266302A - Determining method for pid parameter - Google Patents

Abstract

PURPOSE:To perform optimum control without losing the continuity of the control by interposing a nonlinear element in front of a proportional arithmetic part and connecting an integral arithmetic part in parallel to it, and generating a limit cycle in said state. CONSTITUTION:A controller 10 performs general PID (proportional plus integral plus derivative) control in normal operation, but determines an optimum PID parameter at need while carrying on the operation and then returns to the normal operation with the obtained optimum parameter. Namely, the controller 10 enters a tuning state by receiving an external command for turning or detecting an abnormal controlled variable autonomously. In the tuning state, the nonlinear element 16 is interposed in front of the proportional arithmetic part 11 and the integral arithmetic part 12 is connected in parallel to it. The nonlinear element 16 places a process in a self-oscillation state (limit cycle) and observes it so as to know the characteristics of the process prior tuning.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a method for determining PID parameters for achieving optimal control of a controlled object (process) in a feedback control system.

[Conventional technology]

In the feedback control system, a proportional integral derivative (PID) calculation is performed on the deviation (e) between the set value (mp) and the controlled variable (pv) fed back from the process, and the result is used as the manipulated variable - in the process. given to.

In order to perform optimal control, the PI for PIDID calculation is
It is assumed that the D parameter is set to an optimal value.

Adjustment of PID parameters has conventionally been performed manually, and the step response method and limit sensitivity method are well known. However, in both cases, it takes a long time to measure the characteristics, and the quantity control for this characteristic measurement is stopped, and the pvt at that time:
cannot be the desired value.

On the other hand, methods have long been proposed in which a controller has nonlinear characteristics and a limit cycle is caused in the process. In these methods, the configuration of the controller is as shown in Fig. 3 during tuning, and nonlinear element 2 is controlled by discontinuous control operation (two-position control is typical, so the following explanation will be limited to that). It is intended to be introduced into the signal path in a similar manner. Once a limit cycle occurred as shown in FIG. 4, it was easy to determine the characteristics and optimal parameters of process 1 from the waveform. In addition, in the figure, (a) shows the manipulated variable, and (b) shows the deviation.

[The problem that the invention attempts to solve]

However, in this case, if the value M at the two positions of nonlinear element 1 is too large, the range of fluctuation in the manipulated variable due to it is too large;
- It is unsuitable except in cases where very fast response is not required, such as in temperature control systems.

On the other hand, the limit cycle is the equilibrium point (sp”
Since m) at pv is used as the operating reference point, if M is set small, the limit cycle may not occur when a disturbance occurs in the process or when sp changes significantly. Moreover, it remains in a place far away from the pvl'isp at that time, which is undesirable.

In the end, this conventional method lacked practicality.

[Means for solving problems]

In the present invention, a nonlinear element is inserted before the proportional calculation part, and an integral calculation part is connected in parallel to the nonlinear element, and limit calculation is performed while continuing feedback control of the process.
A cycle is generated, and PID parameters are determined from the observation results.

[Effect]

The ideal limit cycle generation point can be calculated from the limit cycle generation point observed in the above configuration, and the process characteristics and optimal PID parameters can be determined from there.

〔Example〕

FIG. 1 is a block diagram showing an embodiment of the present invention. FIG. 1(a) shows the configuration of the controller in a normal operating state, and FIG. 1(b) shows the configuration at the time of tuning, that is, when determining PID parameters. It shows.

In the normal operating state, the controller 10 outputs to the process 1 the proportional calculation unit 11, the integral calculation unit 12, the differential calculation unit 13, and the operation amount m obtained by adding the calculation results of each calculation unit. 114, and a human power section 15 that calculates the deviation e between the control amount pv fed back from the process 1 and the set value sp and supplies it to each of the above-mentioned calculation sections.

Here, the manipulated variable m is generally determined by equation (1).

K, Ti, and Td are proportional gain, integration time, and
In the differential time, these are called PII) parameters. The first term on the right side is the output of the proportional action, the second term is the integral action, and the third term is the output of the differential action. Depending on the nature of the process and the purpose of control, the differential term may be eliminated (pr control), or the proportional/differential term may be made to act only on pv (
Although various modifications of IPD control) are possible, such control operations are collectively referred to as PID control.

In this way, the controller 10 performs general PID control during normal operation, but if necessary, determines optimal PID parameters while continuing operation, and then returns to normal operation using the obtained optimal parameters. Next, a method for determining the PID parameters will be explained in detail.

The controller 10 enters the tuning state by receiving a tuning command from the outside or by autonomously detecting an abnormality in PV. In the tuning state,
As shown in FIG. 1(b), a nonlinear element 16 is inserted before the proportional calculation section 11, and an integral calculation section 12 is connected in parallel thereto. That is, KI Tl
is left as is, and the differential operation is erased by setting Td=Q.

Although the nonlinear element 16 is not necessarily limited to this, here, one having two-position nonlinear characteristics similar to the nonlinear element 2 in FIG. 3 is used. This nonlinear element is used to cause self-oscillation (limit cycle) in the process and observe it in order to know the characteristics of the process as a prerequisite for tuning.

By the way, the limit cycle (hereinafter referred to as ideal limit cycle) that occurs in the fc configuration shown in FIG.
The generation point of is 1/N determined from the transfer function a of the process shown in (a), (jω) and the descriptive function N(X, ω) of the nonlinear element shown in (b) in Fig. 5. (X, ω) (indicated by a 0 mark in the figure). This intersection is Gp(jω)
This is very effective in finding the optimum PID parameter. This is the amplitude X obtained from the observation of this ideal limit cycle as shown in Figure 4.

This is because the conventional limit sensitivity KO and the vibration period 'rco' at that time can be found from the following equation from and the period TCQ.

K,=4M/πXo・・・・・・・・・・・・・・・
・(2) T e O' ” 7co...
(3) However, from the actual process,
In other words, as mentioned above, it is practically difficult to obtain these data directly while continuing process control.

Therefore, in the present invention, a limit cycle is generated in the configuration shown in FIG. 1(b), and the limit cycle generation point at that time (this is indicated by a circle in FIG. 2).

Note that 0) in the figure is the process transfer function Gp(jω),
(b) Controller 1 when Ti is set to an appropriate value
From the data of the Nyquist diagram of 1/N obtained from the descriptive function N(X, ω) of 0, find the data of the ideal limit cycle generation point (indicated by ■ in Figure 2). This is how it was done. This will be explained next.

First, the transfer function Gp(,)(
s is Laplace operator) focuses on the movement from the equilibrium point,
It is approximated as shown in equation (4).

0p(s)=@”/T8 ・・・・・・−・−(4
) L: Delay time T: Response slope On the other hand, the generated limit cycle is approximated by a sine wave,
It is expressed by equation (5).

・=X−ωt ・・・・・・・・・・・・・・・・・・
(5) Since the descriptive function of the nonlinear element having two-position nonlinear characteristics as shown in FIG. 1(b) is 4M/πX, the output m of the proportional calculation unit 11 and the output m of the integral calculation unit 12 The output m and the manipulated variable m are each expressed by the following equations.

m, = half gtnωt (6) m =
m, +m, ・・・・・・・・・・・・・・・
(8) Vibration component of control amount pv. Then, (4)
, (8) Formula % Formula % (9) Here, the deviation is -1. Therefore, (5), (9)
From the formula, the angular frequency ω is given by ω=2π/T c and the period 'r
The above can be calculated by converting to e, but of course the process flow,
T itself is an unknown quantity.

Next, if we also eliminate the integral action in Figure 1(b) (that is, Ts = oo), then the limit cycle at that time is the ideal limit cycle, and el = Xos
tnω. t・・・・・・・・・・・・・・・・・・
When I period is Tco (-2π/ω0), Too=4L
・・・・・・・・・・・・・・・・・・ （e
It can be seen that it is.

Here, instead of finding the process glue, T itself, XI)
, Te, (2) one-wheel type and (to), a
1! From the formula, X0=αX ・・・・・・・・・・・・・・・・・・
・・aηT,. = αTc ・・・・・・・・・
・・・・・・・・・ @ Easily X as a groan. ,'rco
can be found. However, in the process of deriving the αη~Kan formula, an approximation of tan'θ=θ (θ is a sufficiently small arbitrary angle) is performed.

This approximation is sufficiently effective if the system shown in FIG. 1(b) is stable.

From the above explanation, it has become clear that ideal limit cycle data can be obtained by calculation from the limit cycle observed data X, Tc in the configuration shown in FIG. 1(b).

X obtained in this way. +TCO (2), (3)
Substitute correctly into the equation 2) Add the proportional gain K to the equation),
K(!=4KM/πX.=4KM/παX...
...to) TCO'=Teo-αTc...song...concave...Qυ as K(+ and Tco
Find I. In order to obtain the optimum PID parameter from this, a well-known method such as the Ziegler-Nichols method shown in the following table may be used.

Alternatively, it is also easy to use equations (15) and (16) to find L and T, which indicate the characteristics of the process.

Note that if the descriptive function of the controller 10 in the configuration of FIG. 1(b) is represented by N, then FIG. 2 shows the Nyquist curve of 1/N when TI is an appropriate value. However, in general, when the amplitude locus, that is, (b) in the figure, passes through the frequency locus, that is, (a) in the figure, from the inside to the outside as X increases, the limit φ is stable.

By the way, in the control system shown in FIG. 1, even during tuning, the controller 10 still operates to cancel the deviation e, that is, maintain a closed loop control system using feedback.

In this state, for example, if a disturbance occurs in the process from where the integral calculation unit 12 is connected,
Even when the value of M is small due to a large change in Sp and it becomes impossible to follow the nonlinear element 16 alone, the integral calculation section 12 works effectively to adjust the nonlinear element 16.
By changing the origin of the vibration itself, the deviation e
It is possible to cancel the In other words, nonlinear element 1
By making M of 4 small, it is possible to ensure fast response in normal tuning conditions.

From the amplitude
After simply determining the D parameter, the operation returns to the normal operation shown in FIG. 1(a) using the obtained PID parameter.

In addition, the proportional, integral, and differential calculation parts, nonlinear elements,
Input/output section, switching control means between normal operation state and tuning state, limits generated in the process during tuning) - cycle waveform observation means, X from observation results
There are no particular limitations on the specific configuration of the means for determining and Te, calculating Ke+TcO', and further calculating the new PID parameter from KclTco'. That is, these may be realized by individual components, or the above-mentioned functional means may be realized by using a microcomputer and chronologically executing a program stored in a memory in advance.

In connection with this, the algorithm for determining X and Tc from waveform observation and the relational expression that connects K e + TCO' to the optimal PID parameter are not particularly limited.
The use of the Ziegler e-Nicholas method mentioned above is just one example.

〔Effect of the invention〕

As explained above, according to the present invention, by inserting a nonlinear element before the proportional calculation unit and generating a limit cycle with the integral calculation unit connected in parallel to these elements, the optimal calculation is performed based on the observation results. PID parameters can be easily determined, feedback control of the process can be effectively maintained during the process, and optimal control can be continued by updating PID parameters as appropriate without breaking control continuity.

[Brief explanation of drawings]

FIG. 1 is a block diagram showing an embodiment of the present invention, FIG. 2 is a Nyquist diagram showing the characteristics of the control system shown in FIG. 1, FIG. 3 is a block diagram showing a conventional example, and FIG. FIG. 5 is a Nyquist diagram showing the characteristics of the control system shown in FIG. 3. 1... Process, 10 e... Controller, 11
...Proportional calculation section, 12..... Integral calculation section, 13.
...Differential operation section, 16...Nonlinear element.

Claims (1)

[Claims] In a PID controller that performs PID control on the deviation between the set value and the controlled variable fed back from the process, and outputs the obtained manipulated variable to the process, a nonlinear element is inserted before the differential calculation section, and a nonlinear element is inserted in parallel with these elements. While continuing process control with an integral calculation unit connected to the process, limit cycles occurring in the process are observed to determine the process characteristics, and from the results, the optimal PID parameters to be used for subsequent process control are determined. A method for determining PID parameters characterized by: