Feedback linearization

The idea behind the scheme design by global linearization is to find an appropriate return, the linearized a nonlinear system and thus simplifies control. In most cases this is the output returned, so the method is also known as linearization by output feedback.

Nonlinear control systems in state space representation:

.. .

Can be prepared by a feedback

Be linearized. If the state feedback

Elected as governor, is the linearized controlled system

.. .

.

The controlled system is asymptotically stable if all eigenvalues ​​of the system matrix have negative real part.

Example: Van der Pol system

A Van der Pol system is described by the following differential equation:

After rewriting the canonical Steuerbarkeitsnormalform with, and we obtain

.

In order to

And

And thus the return

.

The linearized state space representation is thus

.

The associated homogeneous linear differential equation is

.

• Control Theory