ITAE

The ITAE criterion (engl .: i ntegral of t ime-multiplied a m pletely value of e rror) is a criterion from the control technology , which has a characteristic value for the quality of control returns.

In order to assess the quality of the control behavior, especially complex safety-relevant regulations, standards are mostly used. The L ¹ norm , the L ² norm (energy content) and the maximum norm (maximum of the entire function) are common. The average power is also widespread, especially with periodic signals such as the . These are in various dependencies that often help in assessing a process. The present procedure is based on the L ¹ standard. ${\displaystyle ||G||_{\infty }:=\sup \left|G(j\omega )\right|}$ ${\displaystyle pow}$ ${\displaystyle \sin }$

The ITAE criterion is calculated using the following integral:

${\displaystyle I=\int _{0}^{\infty }|e|\cdot t\cdot \mathrm {d} t}$

With as a control deviation and as a time. The smaller the value , the better the regulation. ${\displaystyle e}$ ${\displaystyle t}$ ${\displaystyle I}$

Since the resulting area would have an infinitely large value if the system deviation remained , the integral is often formed over the difference : ${\displaystyle e(\infty )}$ ${\displaystyle \left[e(t)-e(\infty )\right]}$

${\displaystyle Q_{\mathrm {ITAE} }=\int _{0}^{\infty }|e(t)-e(\infty )|\cdot t\cdot \mathrm {d} t}$

This characteristic value can be used to determine the quality of the regulation in the context of the time delay through the regulation process itself. The faster the control commands are implemented, the smaller the characteristic value. The so-called rule area is multiplied by the time variable. In this way, the control quality is not only determined by the initial part of the step response, but the small amplitudes over time are taken into greater account.

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1. ^ Manfred Reuter, Serge Zacher: Control engineering for engineers , Vieweg Verlag, 11th edition (2004), ISBN 3-528-05004-7