JPH01240903A

JPH01240903A - Method for deciding weight of evaluation function

Info

Publication number: JPH01240903A
Application number: JP6720688A
Authority: JP
Inventors: Koichi Takahashi; 孝一高橋
Original assignee: Fuji Electric Co Ltd
Current assignee: Fuji Electric Co Ltd
Priority date: 1988-03-23
Filing date: 1988-03-23
Publication date: 1989-09-26

Abstract

PURPOSE:To reduce a time required for the decision of weight by selecting the weight of an evaluation function so that the value of each matrix element equivalent to PI control can be set at almost the same value as a solution found according to the method of the PI control out of the optimum regulator solutions as rough weight at the time of deriving the optimum regulator solution after the designation of the weight. CONSTITUTION:In the selection of the 'weight' of the evaluation function at the time of deciding an integral type optimum regulator 'solution', the rough 'weight' is selected so as to be set a value equal to the solution found by the PI control without performing the response calculation of a state variable after deriving the 'solution', and after that, the 'weight' of the evaluation function is decided by a on-going system. In such a way, the selective criterion of the 'weight' of the evaluation function at the time of deciding the optimum regulator 'solution' can be offered, and the reduction of the response calculation time of the state variable at the time of selecting the 'weight' of the evaluation function can be realized.

Description

【発明の詳細な説明】〔産業上の利用分野〕この発明は、現代制御理論の分野に属するものであり、
成る評価関数を設定し、評価関数の直が最小となるよう
な状態フィードバックを施すという最適制御において、
評価関数の重みを決定する重み決定方法に関するもので
おる。[Detailed Description of the Invention] [Field of Industrial Application] This invention belongs to the field of modern control theory.
In optimal control, the evaluation function is set and state feedback is applied so that the directivity of the evaluation function is minimized.
This paper relates to a weight determination method for determining the weight of an evaluation function.

更に詳しくは、この発明は、評価関数の１重み”選択手
法を用いて１重み”指定後の積分型最適レギュレータ１
解”導出段階において概略の′重み“選択手法を提供す
ることにより、評価関数の１重み”決定時の状態変数の
応答計算時間を削減する手法に関する。More specifically, the present invention provides an integral optimal regulator 1 after specifying 1 weight of the evaluation function using a 1 weight selection method.
The present invention relates to a method for reducing the response calculation time of a state variable when determining one weight of an evaluation function by providing a method for selecting an approximate weight at the solution derivation stage.

[Conventional technology]

この種の重み決定方法としては、評価関数の“重み”を
指定し積分型最適レギュレータ１解”導出後に、状態変
数の応答計算を行ないその応答より評価関数の１重み”
を決定するという手法がとられていた。This type of weight determination method specifies the "weight" of the evaluation function, derives one solution of the integral type optimal regulator, calculates the response of the state variable, and uses the response to calculate the one weight of the evaluation function.
A method was used to determine.

[Problem to be solved by the invention]

しかし、との手法では評価関数の１重み”指定変更のた
びに、応答計算まで行なう必要が１評価関数の“重み”
決定に時間を要するという欠点が６りた。However, in this method, it is necessary to calculate the response every time the designation of one weight of the evaluation function is changed.
The disadvantage was that it took time to make a decision.

この発明は、上記欠点を除去し、積分型最適レギュレー
タ１解”決定に際しての評価関数の重み決定において、
重み決定に要する時間を削減すると、とのできる重み決
定方法を提供することを目的とする。This invention eliminates the above-mentioned drawbacks, and in determining the weight of the evaluation function when determining the integral type optimal regulator 1 solution.
It is an object of the present invention to provide a weight determination method that can reduce the time required for weight determination.

[Means to solve the problem]

この発明では、積分型最適レギュレータとＰＩ制闘との
等価性に着目した。This invention focuses on the equivalence between the integral type optimal regulator and PI control.

[Effect]

積分型最適レギュレータ６解”決定時の評価関数の１重
み”選択に２いて、１解”導出後の状態変数の応答計算
を行なわず、概略の１重み”をＰ工制御によシ求めた解
と同じになるように選択した後に、従来方式により評価
関数の１重み”を決定する。これによ）応答計算時間の
削減を図ることができる。Integral type optimal regulator 6 solution ``1 weight of evaluation function at the time of determination'' was selected, and 1 solution ``1 weight approximately without calculating the response of the state variable after derivation'' was determined by P engineering control. After selecting it so that it is the same as the solution, the conventional method is used to determine the "1 weight" of the evaluation function.This makes it possible to reduce the response calculation time.

〔Example〕

一般に、連続系における制御対象の状態方程式は次の様
に表現される。但し以下に記される諸量は状態ベクトル
でおる。Generally, the state equation of a controlled object in a continuous system is expressed as follows. However, the quantities described below are state vectors.

文−ＡＸ＋ＢＵ　　　　　　　　・・・・・・（１）上
式を離散直系の積分型最適レギュレータで設計する場合
（但し、式（１）は可制御・可観測でおる。）次の様に
表現される。Sentence - AX + BU ...... (1) When the above equation is designed using a discrete direct system integral type optimal regulator (however, equation (1) is controllable and observable), it is expressed as follows. .

ｆｌｌＪｍ対、ｔ　　Ｘ（ｋ＋１）−Ａ’Ｘ（ｋ）＋Ｂ
’Ｕ（ｋ）　　　−・−・−（２）出力信号　Ｙ（ｋ）
−ＣＸａｃ）　　　　　　　　　＝・・（３）誤差信号
　ｅ　（ｙ、、＞　＝　ＹＣｋ）　−Ｒｃｋ）　　　　
　　　””　（４）〔Ｒ（ｋ）；設定置〕但しＡ’（ｔ）−、Ｌ−”　Ｉ：　Ｓ　ｌ　−Ａ　）Ｂ’Ｃ
ｔ）−ｆ　Ａ’（τ）Ｂｄτ ここで、ｊＸ（ｋ＋１）＝Ｘ（ｋ＋１）−ＸＱｃ）　　　　　　
　　　　　・・・・・−（５ンΔυ（ｋ）−υ（ｋ）−
υ（ｓｃ−１）・・”　Ｃ６）とおくと、次の様に離散
値形状態方程式が得られる。fllJm pair, t X(k+1)-A'X(k)+B
'U(k) −・−・−(2) Output signal Y(k)
-CXac) =... (3) Error signal e (y,, > = YCk) -Rck)
"" (4) [R(k); Setting position] However, A'(t)-, L-" I: S l -A ) B'C
t)-f A'(τ)Bdτ Here, jX(k+1)=X(k+1)-XQc)
・・・・・・−(5nΔυ(k)−υ(k)−
υ(sc-1)...'' C6), the discrete value form equation of state is obtained as follows.

・・・・・・（７）Ｘ（ｋ＋１）−φｘＱｃ）＋ｒΔυ□ｃ）　　　　　　
＝”　（８）式（８）に対して評価関数を次の様に定義
する。・・・・・・(7) X(k+1)−φxQc)+rΔυ□c)
=” (8) The evaluation function for equation (8) is defined as follows.

式（９）の評価関数のもとて状態方程式（８）の最適レ
ギュレータ１解”は、次の様になる。Based on the evaluation function of equation (9), the "optimal regulator 1 solution" of state equation (8) is as follows.

＝　ｆ　ＡＸｃｋ＞＋にｅ（ｋ）　　”　（１０）ここ
でＦ−−［Ｒ＋ｚ　Ｐｚ）ｚ　Ｐφ　　　　−・−・（１
１）ただし、Ｐは離散値形リカツチ方程式％式％（１２）を解くことで求められる。= f AXck>+ to e(k) ” (10) Here, F−−[R+z Pz)z Pφ −・−・(1
1) However, P can be found by solving the discrete-valued Rikkatchi equation % formula % (12).

式（１０）は、次の様にυ（ｋ）について求めることが
できる。Equation (10) can be obtained for υ(k) as follows.

・・・・・・（１５）ＵＱＣ）＝　ｆ　ＸＱｃ）＋　Ｋ　、Ｘ、　ｅ　（１）
式（１３）と制御対象を表わす式（２）と組み合わせる
と、レギュレータ（最適制御系）は図の様になる。...... (15) UQC) = f XQc) + K, X, e (1)
When formula (13) is combined with formula (2) representing the controlled object, the regulator (optimal control system) becomes as shown in the figure.

図において、１は離散値系制御対象を表わし、２Ａ、２
Ｂはそれぞれ最適レギュレータ解を示す。In the figure, 1 represents a discrete value controlled object, 2A, 2
B indicates the optimal regulator solution, respectively.

ここでＰＩ制御と比較した場合、式（１３）の第１項は
比例ゲイン、第２項は積分時間に相当する。Here, when compared with PI control, the first term in equation (13) corresponds to a proportional gain, and the second term corresponds to an integral time.

式（１５）は、次の様な各行列素で表わされ、ここでｆ
１１〜ｆｔｍ、に１．〜ｋｔｍの最適レギュレ−夕解の
うち従来のＰＩ制御に相当する各行列要素の直が、ＰＩ
制御の方法に従って求めた解とほぼ同じ肱となる様に、
式（９）の評価関数の１重み”Ｑ、Ｈの指定を行なえば
、概略の”重み”選択が可能となる。したがって、最適
レギュレータ解導出段階で、と僚価基準の１重み”選択
基準の手法を取９入れれば、状態変数の応答計算の削減
が図れる。Equation (15) is expressed by each matrix element as follows, where f
11~ftm, 1. ~ktm's optimal regulation - The directivity of each matrix element corresponding to conventional PI control among the solutions is PI
So that the solution is almost the same as the one obtained according to the control method,
By specifying the 1 weight Q and H of the evaluation function in Equation (9), it becomes possible to roughly select the ``weight''. Therefore, in the optimal regulator solution derivation stage, the selection criteria By adopting the method 9, it is possible to reduce the number of state variable response calculations.

〔Effect of the invention〕

この発明によれば、最適レギュレータ１解”決定時の評
価関数の“重み”の選択基準が提供されることになシ、
評価関数の１重み”選択時の状態変数の応答計算時間の
削減が図れる。According to the present invention, criteria for selecting the "weight" of the evaluation function when determining the "optimal regulator 1 solution" is provided.
It is possible to reduce the response calculation time of the state variable when selecting "1 weight" of the evaluation function.

[Brief explanation of the drawing]

図は本発明の適用対象とするレギュレータを示すブロッ
ク図である。符号の説明１・・・・・・離散直系制御対象、２Ａ、２Ｂ・・・・
・・最適レギュレータ解The figure is a block diagram showing a regulator to which the present invention is applied. Explanation of symbols 1...Discrete direct control objects, 2A, 2B...
・Optimal regulator solution

Claims

[Claims] 1) In determining the weight of the evaluation function when determining the integral type optimal regulator solution, at the stage of deriving the optimal regulator solution after specifying the weight, the approximate weight is set to PI control among the optimal regulator solutions. A method for determining the weight of an evaluation function, characterized in that the weight of the evaluation function is selected so that the value of each corresponding matrix element becomes approximately the same value as the solution obtained according to the PI control method.