in Fig. \[fig:sindyLib\].

![Building and evaluation of the library[]{data-label="fig:sindyLib"}](bibGrafikSVG){width="\linewidth"}

Practical evaluation and results {#sec:practicalEvaluation}
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In order to evaluate the presented concept, we used different model parameters and differing data quality to identify a simple system. Our aim was to determine under which conditions the proposed identification procedure succeeds in finding a suited model, which parameters influence model quality, and where the limitations lay. The influence of the size of the library is studied in the first experiment by varying the degree of polynomials used. The robustness to sample rate and measurement noise are further aspects under test.

Example: Hysteresis-controlled tank system
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The level of the basin in Fig. \[fig:Wassertank\] is controlled to a certain height by a *two-point controller* with an upper set point $h_{max}$ and a lower set point $h_{min}$. A leak causes a constant drain $Q_{out} \in \mathbb{R} < 0$, which neglects the influence of the current water level. The controller with control signal $u(t)$ turns the pump on whenever $h_{min}$ is reached, resulting in a steady inflow $Q_{in} \in \mathbb{R} > 0$. The pump is turned off when the level raises over $h_{max}$.

\[tank\_model\]

The length of the supply pipe $l_P$ can be used to 