JPS5998203A - Optimizing control method - Google Patents

Optimizing control method

Info

Publication number
JPS5998203A
JPS5998203A JP20724782A JP20724782A JPS5998203A JP S5998203 A JPS5998203 A JP S5998203A JP 20724782 A JP20724782 A JP 20724782A JP 20724782 A JP20724782 A JP 20724782A JP S5998203 A JPS5998203 A JP S5998203A
Authority
JP
Japan
Prior art keywords
attained
answer
solution
value
convergence
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
JP20724782A
Other languages
Japanese (ja)
Inventor
Masahiro Nakajima
中島　雅博
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Toshiba Corp
Original Assignee
Toshiba Corp
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Toshiba Corp filed Critical Toshiba Corp
Priority to JP20724782A priority Critical patent/JPS5998203A/en
Publication of JPS5998203A publication Critical patent/JPS5998203A/en
Pending legal-status Critical Current

Links

Classifications

    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators

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  • Engineering & Computer Science (AREA)
  • Health & Medical Sciences (AREA)
  • Artificial Intelligence (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Evolutionary Computation (AREA)
  • Medical Informatics (AREA)
  • Software Systems (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Feedback Control In General (AREA)

Abstract

PURPOSE:To make an optimal control possible by preparing plural error values to be convergence discriminating references and attaining the best answer within the range of the largest permitted error value to perform the control if the convergence precision to an exact answer is not attained in a prescribed time. CONSTITUTION:Two error groups, namely, an error value group (epsilon1) for exact answer and an error value group (epsilon2) in an allowable maximum range are prepared. An initial value is substituted to a controlled system converted to a mathematical model, and ths initial value is used to perform the convergence calculation once. The calculated value attained as the result is evaluated by the error value group epsilon1 with discrimination objects such as a target functional expression and a constraint expression. If the exact answer is attained, the calculation is terminated normally; but if it is not attained, the operation is advanced to the next block. In case that the exact answer is not attained, it is discriminated whether the attained value is better than the value attained in the preceding convergence calculation or not, and the current answer is preserved if it is better than the preceding answer, but it is not preserved if the preceding answer is better.

Description

【発明の詳細な説明】 〔発明の技術分野〕 本発明は、電子計算機を用いて製造工程等の制御を行う
計算制御における最適化制御方法に関する。DETAILED DESCRIPTION OF THE INVENTION [Technical Field of the Invention] The present invention relates to an optimization control method in computational control for controlling manufacturing processes and the like using an electronic computer.

〔発明の技術的背景〕[Technical background of the invention]

最適化制御においては、数学モデル化した制御対象の操
作変数を最適に決定する最適化問題が生ずる。このため
目的する状態を評価しつる関数として変数ベクトルＸの
スカラ関数 ｆ（ｘ）＝　ｆ（ｘｌ　ｅ　”２＋　”””＋　”ｎ）
である目的関数の値を最大または最小にするベクトルＸ
の値を求めるいわゆる数理計画問題を解く必要がある。In optimization control, an optimization problem arises in which the manipulated variables of a mathematically modeled controlled object are optimally determined. Therefore, the scalar function f(x) = f(xl e "2+ """+ "n) of the variable vector
Vector X that maximizes or minimizes the value of the objective function
It is necessary to solve a so-called mathematical programming problem to find the value of .

このようなベク、トル又は。Such vector, tor or.

等式制約式：　ｈｌ（Ｘ）−〇　（１−ｌ、２・・・・
・・ｐ）不等式制約式ｇ１（Ｘ）≦（ｊ＝’＋２＋・・
・・・・ｑ）のもとでｎ次元実数空間を有する列ベクト
ルとして求められる。Equality constraint: hl(X)-〇 (1-l, 2...
・・p) Inequality constraint expression g1(X)≦(j=′+2+・・
...q) is obtained as a column vector having an n-dimensional real number space.

ところで上述の関数ｆ（・）、ｈｘ（・）、ｇｌ（・）
のうちの一つでも非線形でない場合には上記最適化問題
は非線形最適化問題となり、この解法は非線形計画法と
よばれている。By the way, the above functions f(・), hx(・), gl(・)
If even one of them is nonlinear, the above optimization problem becomes a nonlinear optimization problem, and this solution method is called nonlinear programming.

この非線形計画法は解析的に解を求めることが一般に不
可能であって、電子計算機によって計算をくり返し行い
誤差を減少させていき、所定の誤差範囲に収ったかどう
か、また各制約式の不満足度がある誤差範囲に収ったか
どうかなどの複数個の収束判定用の誤差値によって収束
計算を終了させ解を求めるのが普通である。In this nonlinear programming method, it is generally impossible to find a solution analytically, and the calculations are repeated using an electronic computer to reduce the error. Usually, the convergence calculation is terminated and a solution is found using a plurality of error values for determining convergence, such as whether the degree falls within a certain error range.

このようにして求められた解は計算制御における操作変
数として用いられろ。The solution obtained in this way can be used as a manipulated variable in calculation control.

〔背景技術の問題点〕[Problems with background technology]

ところが、このような非線形最適化問題は環境条件にと
もなう入力値によっては必ずしも解は求まらず、収束計
算が永久に終了しないことがある。However, in such a nonlinear optimization problem, a solution may not always be found depending on input values associated with environmental conditions, and convergence calculation may not be completed forever.

これを防止するため収束計算の時間を一定時間に制限し
、その一定時間に収束しない場合には解が存在しないも
のとして計算を打切り、計算エラーとして扱うことが行
われている。To prevent this, the time for convergence calculation is limited to a fixed time, and if the solution does not converge within the fixed time, the calculation is aborted as if no solution exists and treated as a calculation error.

しかし、収束計算の結果値を計算制御に使用している場
合には解が存在しないことは制御において支障を来たす
ことになり避けるべきである。However, when the result value of convergence calculation is used for calculation control, the absence of a solution will cause problems in control and should be avoided.

このため、計算エラーを生ずる確率を極力低減させるた
め最初から収束判定用の誤差値を大きく設定しておくこ
とも行われるが、この方法では厳密解が存在する場合に
おいても誤差を伴った解しか得られないことになり、制
御の最適性を損うという問題点がある。For this reason, in order to reduce the probability of calculation errors as much as possible, the error value for convergence judgment is set large from the beginning, but with this method, even if an exact solution exists, only a solution with an error exists. Therefore, there is a problem in that the optimality of control is impaired.

〔発明の目的〕[Purpose of the invention]

そこで、本発明は最適化問題において解が存在しないと
いう事態を極力さけしかもできるだけ厳密な解を得ると
いう相反する要求を満足させるような収束計算によって
制御を行う最適化制御方法を提供することを目的とする
。SUMMARY OF THE INVENTION Therefore, an object of the present invention is to provide an optimization control method that performs control using convergence calculations that satisfies the conflicting demands of avoiding the situation where no solution exists in an optimization problem as much as possible and obtaining a solution that is as exact as possible. shall be.

〔発明の概要〕[Summary of the invention]

上記目的を達成するため１本発明にかかる最適化制御方
法においては収束判定基準となる誤差値を複数準備し１
通常は最も小さい誤差値を使用して厳密解を求め、一定
時間内に厳密解までの収束精度に達しないときは許容可
能なよシ大きな誤差値の範囲内でできるだけ良好な解を
求め、これらにより得られた解を用いて制御を行うよう
にしており、解の不存在を極力避けるとともにできるだ
け厳密な解を求めて制御を行うことを可能にするもので
ある。In order to achieve the above object, 1. In the optimization control method according to the present invention, a plurality of error values are prepared as convergence judgment criteria.
Normally, the smallest error value is used to find the exact solution, and if the convergence accuracy to the exact solution cannot be reached within a certain period of time, a solution as good as possible is found within an allowable larger error value. The control is performed using the solution obtained by the method, and it is possible to avoid the non-existence of a solution as much as possible and to perform control by finding the exact solution as possible.

〔発明の実施例〕[Embodiments of the invention]

以下、フローチャートにしたがって本発明の主要部をな
す解を求める方法の一実施例を詳細に説明する。Hereinafter, one embodiment of the method for finding a solution, which is the main part of the present invention, will be described in detail according to a flowchart.

本実施例では厳密暦月の誤差値群である　（＝　ｄおよ
び許容できる最大限の範囲の誤差値群である（ε２）の
一つの誤差値を準備しているものとする。In this embodiment, it is assumed that one error value (=d), which is a group of error values for a strict calendar month, and one error value (ε2), which is a group of error values in the maximum allowable range, are prepared.

まず最初に数学モデル化された制御対象に対して初期値
を代入する（プロ、り１０）。次にこれらの初期値を用
いて収束計算を１回だけ実行する（ブロック２０）。そ
の結果得られた計算値は目的関数式、制約式等の判定対
象式を用いて誤差値群ε１によって評価され、厳密解が
得られたときは計算は正常終了し、得られないときは次
のブロックへ進む（ブロック３０）、厳密解が得られな
いときＫは得られた値が前回の収束計算で得られた値よ
りも良好な解であるかどうかが判断され（ブロック侵）
、もし今回の解の方が良好ならばその解を保存しくブロ
ックＳＯ）　、前回の解の方が良好ならば今回の解の保
存は行わずに次のブロックへ進む。First, initial values are assigned to the mathematically modeled control object (Pro 10). Next, a convergence calculation is performed only once using these initial values (block 20). The calculated value obtained as a result is evaluated by the error value group ε1 using the target function expression, constraint expression, etc. If an exact solution is obtained, the calculation ends normally, and if not, the next step is (block 30), if an exact solution cannot be obtained, K determines whether the obtained value is a better solution than the value obtained in the previous convergence calculation (block violation).
, If the current solution is better, save that solution (block SO), If the previous solution is better, proceed to the next block without saving the current solution.

このように計算結果の比較を行ってより良い値を保存す
るのは、非線形計画法のうちには計算を続行するとかえ
って解が悪化する場合があるので。The reason why calculation results are compared in this way and the better value is saved is because in nonlinear programming, continuing calculations may actually worsen the solution.

最良の状態の解を求めるためである。また、解の保存は
一般的なメモリに格納することにより行えばよい。This is to find the best solution. Further, the solution may be saved by storing it in a general memory.

次に収束計算開始後の総合計時間が所定の限界時間を超
えたかどうかを例えばカウンタによりチェックしくブロ
ック６０）、超えていない場合にはプロ、りＪの前に戻
って収束計算を再実行し、超えている場合には次のブロ
ックへ進む。収束計算の時間が所定時間を超えている場
合には、許容できる最大限の誤差値群（＝＝１によって
判定対象式を用いて限界許容層であるかどうかが判断さ
れ（ブロック７０）、存在する場合には計算は正常終了
し、存在しない場合は計算エラーとして終了する。Next, check whether the total time after starting the convergence calculation exceeds a predetermined limit time, for example, using a counter (block 60), and if it does not, return to the front of the program and re-execute the convergence calculation. , if it exceeds, proceed to the next block. If the time for convergence calculation exceeds a predetermined time, it is determined whether or not the layer is in the limit tolerance layer using the determination target expression (block 70), using the maximum allowable error value group (==1), and If it does, the calculation ends normally; if it does not exist, the calculation ends as an error.

以トの実飽１例では収束判定基皐となる誤差値は厳密暦
月と最大許容限界用のコＰト頑だけであったが、３穏類
以上として極力精度の良い解を得ることも可能である。In the first example below, the error values used as the basis for convergence judgment were only the exact calendar month and the maximum allowable limit, but it is also possible to obtain a solution with as high accuracy as possible for three or more moderate classes. It is possible.

以上の方法により得られた値は計算制御において使用さ
れ、制御対象を最適な状態に制御することになる。The values obtained by the above method are used in calculation control to control the controlled object in an optimal state.

〔発明の効果〕〔Effect of the invention〕

以上のような本発明にかかる最適化制御方法によれば、
所定時間内に厳密解が得られないときには許容可能な誤
差値の範囲内で求められたできるだけ良好な解を使用す
るようにしているため、解が存在しないという事態を極
力さけることができるとともに、制御に使用する解を許
容範囲での最小誤差を伴ったものにすることができるた
め、最適な制御を可能にするものである。According to the optimization control method according to the present invention as described above,
When an exact solution cannot be obtained within a predetermined time, the best possible solution found within an allowable error value is used, so the situation where no solution exists can be avoided as much as possible. Since the solution used for control can be made with the minimum error within the allowable range, optimal control is possible.

【図面の簡単な説明】[Brief explanation of drawings]

図は本発明の主要部をなす解を求める方法の一実施例を
示すフローチャートである。The figure is a flowchart showing one embodiment of a method for finding a solution, which is the main part of the present invention.

Claims (1)

【特許請求の範囲】 数学モデル化された制御対象に対して目的に合致する解
を計算機を使用して収束計算で求めて制御を行う最適化
制御方法において、 収束判定基準となる誤差値を複数準備し１通常は最も小
さい誤差値を用いて厳密解を求め、所定時間内にこの厳
密解までの収束精度に達しないときには許容可能なより
大きな誤差値の範囲内でできるだけ良好な解を求め、得
られた解を用いて制御を行う最適化制御方法。[Claims] In an optimization control method that performs control by using a computer to obtain a solution that matches a purpose for a mathematically modeled controlled object through convergence calculation, a plurality of error values are set as convergence judgment criteria. Preparation 1 Normally, the smallest error value is used to find an exact solution, and if the convergence accuracy to this exact solution cannot be reached within a predetermined time, find a solution as good as possible within the range of an allowable larger error value. An optimization control method that performs control using the obtained solution.
JP20724782A 1982-11-26 1982-11-26 Optimizing control method Pending JPS5998203A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
JP20724782A JPS5998203A (en) 1982-11-26 1982-11-26 Optimizing control method

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
JP20724782A JPS5998203A (en) 1982-11-26 1982-11-26 Optimizing control method

Publications (1)

Publication Number Publication Date
JPS5998203A true JPS5998203A (en) 1984-06-06

Family

ID=16536643

Family Applications (1)

Application Number Title Priority Date Filing Date
JP20724782A Pending JPS5998203A (en) 1982-11-26 1982-11-26 Optimizing control method

Country Status (1)

Country Link
JP (1) JPS5998203A (en)

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPS63184109A (en) * 1987-01-27 1988-07-29 Mitsubishi Electric Corp Numerical controller
JPS63184107A (en) * 1987-01-27 1988-07-29 Mitsubishi Electric Corp Numerical controller

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPS63184109A (en) * 1987-01-27 1988-07-29 Mitsubishi Electric Corp Numerical controller
JPS63184107A (en) * 1987-01-27 1988-07-29 Mitsubishi Electric Corp Numerical controller

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