Vorwärtslinearisation

Vorwärtslinearisation is a technique used in control theory and signal processing to approximate a nonlinear system with a linear one. The core idea is to linearize the system around a specific operating point. This operating point can be an equilibrium point, a desired trajectory, or any other relevant state. By considering small deviations from this operating point, the nonlinear behavior of the system can be approximated by a linear differential equation or transfer function.

The process typically involves expanding the nonlinear function representing the system's dynamics using a Taylor series expansion. The higher-order terms, which represent the nonlinearities, are then neglected, assuming that the deviations from the operating point are small. This simplification results in a linear model that is easier to analyze and design controllers for using established linear control techniques.

Vorwärtslinearisation is particularly useful when designing controllers for systems that exhibit strong nonlinear characteristics. It allows for the application of well-developed linear control design methods, such as PID control or pole placement, which would be difficult or impossible to apply directly to the original nonlinear system. However, it's important to note that the accuracy of the linearized model is dependent on the size of the deviations from the operating point. If the system operates far from the chosen point, the linear approximation may become inaccurate, leading to degraded performance or even instability. Therefore, careful selection of the operating point and consideration of the system's operating range are crucial for successful application of vorwärtslinearisation.