Digital systems
System characteristics

If the influx is interrupted (pipe closed), the level stops rising and settle at the reached point. After reopening the pipe, the filling will continue the same way.

The level is proportional to filled volume, which is an integral of flux value at the input over time. The system has an integral character; it can be called as a first order integrator with saturation. In control engineering, such system is often called as a system with first order astatism. It means that with constant input value (flux), the output (level) will not settle at any value – there is no steady state value, the system is astatic. This is true, while operating in linear operation range, before tank overflow.

On the other hand, the static system will always have a certain output value, where the system settles, if driven by constant input variable.

Notice: The term "static system" is a slightly ambiguous in the context of control engineering. The first meaning stands for a system without intrinsic dynamics, whose output immediately (without delay) reacts to the input variable changes. The other meaning stands for a dynamical system, where the output settles at a constant value after step change of input variable – such system is a contraposition to astatic system.

Fig. 8.3: Hydraulic system with integration behavior

The term "static system" is in control technology somewhat confusing because it is used in two senses. The first corresponds to the system without its own dynamics, the output immediately (without delay) responds to changes in input variables. In the second sense, corresponds to dynamic systems, for which the step change of the input variable output also stabilizes at a constant value, but only in the aftermath of transient - so named system is the antithesis of the term astatic system.