Zustandsrückführung

Zustandsrückführung, often translated as state feedback, is a control system design technique where the control input to a system is determined by a linear combination of the system's state variables. This means that instead of relying solely on the output of the system, the controller has direct access to and utilizes information about all the internal states of the system to generate its control signal.

The fundamental idea behind state feedback is to manipulate the system's poles, which dictate the system's dynamic behavior (e.g., stability, speed of response, damping). By choosing appropriate feedback gains, the designer can place these poles at desired locations in the complex plane, thereby achieving specific performance characteristics for the closed-loop system. The general form of a state feedback control law is u = -Kx, where u is the control input, x is the state vector, and K is the state feedback gain matrix.

State feedback controllers are powerful because they can often achieve arbitrary pole placement for controllable systems, meaning that any set of desired pole locations can be attained by selecting the appropriate K matrix. This allows for significant flexibility in shaping the system's response. However, state feedback requires that all state variables are measurable or observable. If not all states are directly measurable, an observer (state estimator) can be used to estimate the unmeasured states, and then state feedback can be implemented using these estimated states. This combined approach is known as observer-based state feedback or the separation principle. Zustandsrückführung is a core concept in modern control theory and is widely applied in various engineering disciplines.