Symmetrical optimum

The symmetrical optimum is a design method of control engineering for single-variable systems with only real poles.

A prerequisite for the applicability of the method is that the time constants of the control loop in a group of large and a group of small time constants may be divided so that each large time constant much greater than the sum of the small time constant of its own:

large time constants ${\displaystyle T_{\nu },\nu =1\ldots n}$

small time constants ${\displaystyle \tau _{\mu },\mu =1\ldots m}$

${\displaystyle T_{1}\ldots T_{n}\gg \sum _{\mu =1}^{m}\tau _{\mu }=\tau _{\Sigma }}$

When designing the controller according to the symmetrical optimum, the crossover frequency of the open control loop should be in the middle between and . ${\displaystyle \textstyle {\frac {1}{\tau _{\Sigma }}}}$ ${\displaystyle \textstyle max\left({\frac {1}{T_{\nu }}}\right)}$

Another optimization method in control technology is the optimum amount .

literature

• Otto Föllinger : Control engineering, Hüthig, ISBN 3-7785-2336-8