JPS62119601A

JPS62119601A - Method of adjusting automatically control constant of pid controller

Info

Publication number: JPS62119601A
Application number: JP26015585A
Authority: JP
Inventors: Masataka Iwasaki; 昌隆岩崎; Shiro Hozumi; 穂積　史郎; Hozumi Yamada; 山田　穂積; Koji Ebisu; 戎　晃司
Original assignee: Matsushita Seiko Co Ltd; Matsushita Electric Industrial Co Ltd
Current assignee: Panasonic Ecology Systems Co Ltd; Panasonic Holdings Corp
Priority date: 1985-11-20
Filing date: 1985-11-20
Publication date: 1987-05-30

Abstract

PURPOSE:To adjust automatically the control constant of a PID controller without intervention of the manual operation of the operator by using function approximation in response to a step response waveform of a process. CONSTITUTION:A new coordinate axes t', y' taking an inflection point of a step response waveform using a step response output as y-axis and time as t-axis as an origin are provided, a process gain K is given to approximate the step response waveform as a linear lag system on the (t'-y') axes, the approximation equation obtained by the approximation is subjected to coordinate conversion into (t-y) axes to estimate a linear lag time constant T and a dead time L thereby deciding the optimum value of a proportional gain Kp, an integration time Ti and a differentiation time Td being control constants of a PID controller. The step response of the process is an S-shaped curve and the step response of the process is approximated by (dead time system) + (linear lag system), and the (t'-y') axes taking the inflection point of the step response as the origin are provided resulting that the step response of the process on the (t'-y') axes is considered to be the step response of the linear lag system.

Description

【発明の詳細な説明】産業上の利用分野本発明は、ＰＩＥ）制御における制御定数である比例ゲ
イン（Ｋｐ）、積分時間（Ｔｉ）、微分時間（Ｔｄ）の
最適値を自動調整するＰＩＤ調節器の制御定数自動調整
方法に関するものである。DETAILED DESCRIPTION OF THE INVENTION Field of Industrial Application The present invention is a PID control system that automatically adjusts the optimal values of control constants such as proportional gain (Kp), integral time (Ti), and derivative time (Td) in PIE control. The present invention relates to a method for automatically adjusting control constants of a device.

従来の技術従来、ＰＩＤ調節器の制御定数は操作者の手によって試
行錯誤的”に決定されていた。一方、制御理論の方面か
ら、制御対象に最適な制御定数を算出する方法としては
、　　Ｚｉｅｇｌｅｒ−Ｎｉｃｈｏｌｇ　（ジークラ・
ニコルス）の方法、北森の方法など数多くの方法が提案
されている。Conventional technology Conventionally, the control constants of PID regulators have been determined by the operator through trial and error.On the other hand, from the perspective of control theory, a method for calculating optimal control constants for a controlled object is the Ziegler method. -Nicholg
Many methods have been proposed, such as the method of Nichols) and the method of Kitamori.

発明が解決しようとする問題点しかしながら、前記のような方法は、試行錯誤的方法で
は、パラメータの決定に多くの手間と時間を必要とした
。また制御理論の方面からのパラメータ決定法では演算
式が複雑であったり、計算３　ベー／量が膨大である等、実用化には問題があった。本発明は
、この問題点をｊＷ決し、操作者の手をわずられせる必
要が々く１　しかも筒中な演算を行々うだけでよいＰＩ
Ｄ調節器の制御定数自動調整方法を提供するものである
。Problems to be Solved by the Invention However, the above method requires a lot of effort and time to determine the parameters using a trial and error method. In addition, parameter determination methods based on control theory have problems in practical application, such as complicated calculation formulas and enormous amounts of calculations. The present invention solves this problem and eliminates the need for the operator's intervention.
This invention provides a method for automatically adjusting control constants of a D regulator.

問題点を解決するだめの手段この目的を達成するために、本発明のＰＩＤ調節器の制
御定数自動調整方法は、プロセスのステップ応答波形に
対して、関数近似という方法を用いる。Means for Solving the Problems In order to achieve this object, the method for automatically adjusting control constants for a PID controller of the present invention uses a method of function approximation for the step response waveform of the process.

作用この方法によって、（むだ時間系）＋（−次遅れ系）近
似したプロセスの一次おくれ時定数（Ｔ）。Effect: By this method, the first-order lag time constant (T) of the process approximated (dead time system) + (-order lag system).

むだ時間ＣＸＪ）が数値計算によって求められ・ＰＩＤ
調節器の制御定数である比例ゲイン（Ｋｐ）、積分時間
（Ｔｉ）、微分時間（Ｔｄ）の最適値が簡単な算術式に
よって求める事ができる。Dead time CXJ) is determined by numerical calculation and PID
Optimal values of the proportional gain (Kp), integral time (Ti), and differential time (Td), which are control constants of the regulator, can be determined by simple arithmetic expressions.

実施例以下本発明の実施例について図面を参照にしながら説明
する。EXAMPLES Hereinafter, examples of the present invention will be described with reference to the drawings.

第１図は、プロセスのステップ応答を示す図でアリ、プ
ロセスのステップ応答はＳ字形の曲線となっている。こ
のプロセスのステップ応答を（むだ時間系）＋（−次遅
れ系）で近似するために、第２図に示すようにステップ
応答の変曲点を原点とするｔ　−ｙ軸を設ける。ｔ　−
ｙ軸上では、プロセスのステップ応答は、−次遅れ系の
ステップ応答と考えることができる。FIG. 1 is a diagram showing the step response of the process, and the step response of the process is an S-shaped curve. In order to approximate the step response of this process as (dead time system) + (-order lag system), a t-y axis whose origin is the inflection point of the step response is provided as shown in FIG. t-
On the y-axis, the step response of the process can be considered as a step response of a -order lag system.

一次遅れ系の伝達関数はＴ、−次遅れ時定数　Ｋ：プロセスゲインと表わされる
。The transfer function of the first-order lag system is expressed as T, -th order lag time constant, and K: process gain.

（１）式の単位ステップ応答は、初期値を０とすると α となる。If the initial value is 0, the unit step response of equation (1) is α becomes.

今、プロセスゲイン（Ｋ）の値をこちらが与えるとする
と（２）式は。Now, assuming that we give the value of process gain (K), equation (2) is as follows.

６　ペーノｙ（ｔ）＝Ｋ　（１−ｅ　　　　）　　　　　　　　　
　　・・・・・・（３）となる。6 Peno y(t)=K (1-e)
......(3).

今、サンプリング時間１＝１．．１２・・・・・・ｔｎ
のときの応答を’ｌ　＋　＋　７２・・・・・・ｙｎと
したときの観測データを（ｔｉ＋’１１）ｌ＝１．２・
・・・・・ｎとし、この観測データをｔ−ｙ軸上で表現
したものを（１土。Now, sampling time 1=1. ．． 12...tn
When the response is 'l + + 72...yn, the observed data is (ti+'11)l=1.2・
....n, and this observation data expressed on the t-y axis is (1 Sat.

ｙｌ）、ｔｉ＞Ｏ、ｘ＜ｎ　とする。またプロセスケイ
ン（Ｋ）をｔ　−ｙ軸上で表現したものをｋとする。yl), ti>O, and x<n. Further, let k be the process key (K) expressed on the t-y axis.

問題は観測データ（’ｉｔ”Ｉｉ）’−１，２・・・・
・・ｎ。The problem is observational data ('it'Ii)'-1, 2...
・・n.

１１〉０．Ｋ＜ｎおよびＫから未知数αを最適に推定す
ることである。11〉0. The objective is to optimally estimate the unknown α from K<n and K.

（３）式を変形してＹ（ｔ）　　　　　　−ａｔ □−１−−ｅ　　　　　　　　　　　・・・・・・（４
）さらに両辺の自然対数をとってＹ　（ｔ）　＝αｔ　　　　　　　　　　　　・川・・
（６）６ベーゾとなり、−次式となる。Transforming equation (3), Y(t) −at □−1−−e ・・・・・・(4
) Furthermore, taking the natural logarithm of both sides, we get Y (t) = αt ・River...
(6) It becomes 6 beso, and becomes the following formula.

したがって、観測データ（τ１４１）ｉ＝１．２・・・
・・・ｎ　ｌ　ｔｌ、＞Ｏ、Ｋ＜ｎおよびＫから未知数
αを最適に推定するという問題は、観測データム定するという問題に置き換えることができる。Therefore, observation data (τ141) i=1.2...
... n l tl, >O, K<n, and the problem of optimally estimating the unknown α from K can be replaced with the problem of determining the observation datum.

αの推定値αｅとすると、最小二乗法により、αｅは次
のように推定される。Assuming that the estimated value of α is αe, αe is estimated as follows using the least squares method.

ｔ　−ｙ軸上で一αｅｔｙ＝Ｋ（１−ｅ）　　　　　　　・・・・・−（８）と
推定されたステップ応答をｔ−ｙ軸上の原点がｔ、ｙ軸
上で（ｔｌ、ｙ、）と表わされるとして（８）式をｔ　
−ｙ軸上で表現すると、ｙ＝ム−Ｂｅ−ａｅｔ　　　　　　　　・・・・・・（
９）７へ／但し　Ａ＝に＋７．　　　　　　　・・・・・・（１０
）Ｂ−ｘ　＋　ｅａｅ　＋　ｉ　＋　　　　　川・・（
１１）となる。The step response estimated as 1αet y=K(1-e)...-(8) on the t-y axis is expressed as follows: the origin on the t-y axis is t, and the origin on the y-axis is (tl, y , ), equation (8) is expressed as t
- Expressed on the y-axis, y=Mu-Be-aet ・・・・・・(
9) To 7/ However, A=+7.・・・・・・(10
)B-x + eae + i + river...(
11).

（９）式の示すグラフは第３図のようになりむだ時間の
推定値Ｌｅは＋７＝Ｏとなる時刻として求まシ、Ｌｅ−□　　　　　　　・川・・（１２）αｅまた、−次おくれ時定数の推定値Ｔｏは次のように々る
。The graph shown by equation (9) is as shown in Figure 3, and the estimated value Le of the dead time is found as the time when +7=O. The estimated value To of the constant is as follows.

’ｌ’ｅｌ＝−・・印・（１３） αｅ以上のことより前記Ｔ、ＬがそれぞれＴｅ　、Ｌｅと推
定されてたので前記ＰＩＤ調節計の制御定数Ｋｐ、Ｔｉ
、Ｔｄは、ジーグラ・ニコルスの方法によれば表１のよ
うに決定される。'l'el=-...mark (13) αe From the above, since the above T and L were estimated to be Te and Le, respectively, the control constants Kp and Ti of the PID controller
, Td are determined according to the Ziegler-Nichols method as shown in Table 1.

表１発明の効果以上のように本発明は、プロセスのステップ応答観測デ
ータを与えることによって操作者の手をわずられせるこ
となしにＰＩＤ調節器の制御定数を自動調整することが
でき、その効果は犬なるものがある。Table 1 Effects of the Invention As described above, the present invention can automatically adjust the control constant of a PID regulator without requiring the operator's intervention by providing step response observation data of the process. The effect is like a dog.

[Brief explanation of drawings]

第１図は本発明のＰＩＤ調節器の制御定数自動調整方法
説明のだめのプロセスのステップ応答ヲ示すグラフ、第
２図はｔ　−ｙ軸の選定を示すグラフ、第３図はむだ時
間の推定を示すグラフである。Fig. 1 is a graph showing the step response of the process for explaining the automatic control constant adjustment method of the PID controller of the present invention, Fig. 2 is a graph showing the selection of the t-y axis, and Fig. 3 is the graph showing the estimation of the dead time. This is a graph showing.

Claims

[Claims]

Regarding the process to be controlled as a controlled system consisting of a first-order lag system and a dead time system, the first-order lag time constant (T
) and the dead time (L), and from the T and L, the proportional gain (Kp), which is the control constant of the PID controller, and the integral time (T
i) A control constant automatic adjustment method for a PID controller that determines the optimal value of the differential time (Td), in which the origin is the inflection point of a step response waveform with the step response output as the y-axis and time as the t-axis. A new coordinate axis @t@-@y@ axis is provided, a process gain (K) is provided, and the step response waveform is changed to the @t
The linear lag time constant (T) and dead time (L) are estimated by approximating a linear lag system on the @-@y@ axis and converting the coordinates of the approximation formula obtained by the above approximation to the ty axis. , the proportional gain (Kp) which is the control constant of the PID regulator
, an integral time (Ti), and a differential time (Td).