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:

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

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

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