Separation theorem

This article deals with the separation theorem in control theory. For the separation theorem on perfect capital markets , see Fisher's separation theorem . For the separation theorem in the context of portfolio theory , see Tobin separation .

The separation theorem is a fundamental theorem for the design of state controllers with observers . It says that the eigenvalues ​​of a state control without an observer are not shifted if the state variables are reconstructed by an observer. The poles of the observer are added to the poles of the state control loop without an observer.

This means that the controller can initially be designed without taking the necessary observer into account. This is then added in a second design step.

Furthermore, it can be shown that the guide behavior is determined only by the poles of the control, while the interference behavior of the poles of the control and it is determined the observer.

Individual proof

1. ↑ Otto Föllinger: Control engineering, introduction to the methods and their application . 8th edition. Hüthig Verlag, Heidelberg 1994, ISBN 3-7785-2336-8 . Section 13.7.6 / (13.200)