Digital systems
System description

Let us consider a system, consisting of a cylindrical tank, without any outlet, only with a spillover at the top. It is supplied by a water pipe from a source (e.g. water conduit), drawing a constant flux, independent neither on time or tank level. The incoming flux cannot be adjusted, only fully opened or closed.

After opening the input pipe (step change of control variable from zero to a constant value), the water level in the tank will continuously grow, i.e. the growth velocity is constant, independent on time nor current level. The level is determined by flux and bottom plate surface. This behavior continues, until the level reaches the spillover. After that, all superfluous water flows over and the level settles at a constant value (assuming, that all overflowing water is properly drained away). The system thus contains a nonlinearity, consisting in the level limitation (saturation).