IEVref: | 351-47-41 | ID: | |

Language: | en | Status: 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: ${I}_{\text{IAE}}={\displaystyle \underset{0}{\overset{\infty}{\int}}\left|e\left(t\right)\right|}\cdot \text{d}t$ Criterion of Integral Absolute Error ${I}_{\text{ISE}}={\displaystyle \underset{0}{\overset{\infty}{\int}}{e}^{2}\left(t\right)}\cdot \text{d}t$ Criterion of Integral Squared Error ${I}_{\text{ITAE}}={\displaystyle \underset{0}{\overset{\infty}{\int}}t\cdot \left|e\left(t\right)\right|}\cdot \text{d}t$ Criterion of Integral of Time multiplied Absolute value of Error Therein Note 3 to entry: This entry was numbered 351-26-35 in IEC 60050-351:2006. | ||

Publication date: | 2013-11 | ||

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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:

${I}_{\text{IAE}}={\displaystyle \underset{0}{\overset{\infty}{\int}}\left|e\left(t\right)\right|}\cdot \text{d}t$ Criterion of Integral Absolute Error

${I}_{\text{ISE}}={\displaystyle \underset{0}{\overset{\infty}{\int}}{e}^{2}\left(t\right)}\cdot \text{d}t$ Criterion of Integral Squared Error

${I}_{\text{ITAE}}={\displaystyle \underset{0}{\overset{\infty}{\int}}t\cdot \left|e\left(t\right)\right|}\cdot \text{d}t$ 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.