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IEVref:351-47-41ID:
Language:enStatus: Standard
Term: optimal control
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Definition: type of control for which the performance index reaches a largest or smallest value under specified conditions

Note 1 to entry: Performance index is a mathematical expression which characterises the quality of control under given conditions.

Note 2 to entry: The determination of optimal control parameters frequently results from minimising integral criteria which are often called control areas from the geometric interpretation of the integral. The most important ones are:

I IAE = 0 | e( t ) | dt MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadMeadaWgaaWcbaGaaeysaiaabgeacaqGfbaabeaakiabg2da9maapehabaWaaqWaaeaacaWGLbWaaeWaaeaacaWG0baacaGLOaGaayzkaaaacaGLhWUaayjcSdaaleaacaaIWaaabaGaeyOhIukaniabgUIiYdGccqGHflY1caqGKbGaamiDaaaa@4908@ Criterion of Integral Absolute Error

I ISE = 0 e 2 ( t ) dt MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadMeadaWgaaWcbaGaaeysaiaabofacaqGfbaabeaakiabg2da9maapehabaGaamyzamaaCaaaleqabaGaaGOmaaaakmaabmaabaGaamiDaaGaayjkaiaawMcaaaWcbaGaaGimaaqaaiabg6HiLcqdcqGHRiI8aOGaeyyXICTaaeizaiaadshaaaa@46EB@ Criterion of Integral Squared Error

I ITAE = 0 t| e( t ) | dt MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadMeadaWgaaWcbaGaaeysaiaabsfacaqGbbGaaeyraaqabaGccqGH9aqpdaWdXbqaaiaadshacqGHflY1daabdaqaaiaadwgadaqadaqaaiaadshaaiaawIcacaGLPaaaaiaawEa7caGLiWoaaSqaaiaaicdaaeaacqGHEisPa0Gaey4kIipakiabgwSixlaabsgacaWG0baaaa@4D22@ Criterion of Integral of Time multiplied Absolute value of Error

Therein e(t) is the control difference variable as a function of time as answer to an input appropriate to the technological task, for example a response to a stepwise change of the reference variable.

Note 3 to entry: This entry was numbered 351-26-35 in IEC 60050-351:2006.


Publication date:2013-11
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