In general:
A system with input variables u 1 (t ) ... u p (t ) and output variables v 1 (t ) ... v q (t ), which has a certain transfer function, is called a transfer element (EDIN 19 226 Part 2) (Figure U 8).
A transfer element has the property that the input variables are independent variables and the output variables are variables of the relationship.
The unique allocation in a specific case is generally implicitly stated by a set of relationships (e.g. differential equations) and can be determined through measurements, system analyses, laws of nature, amongst others (according to DIN 19 229).
A differentiation is made between
- a linear transfer element, which has a linear relationships between the input and output signal and
- a non-linear transfer element, in which the relationship between the input and output signal matches any function, as does the relationship between
- a time-invariant and
- time-variant transfer element.
Basic transfer elements:
Here a distinction is made between three basic elements, namely
- P-element with proportional behaviour. The output signal follows directly proportionally to the input signal without delay or other dynamic effects (Figure U 9 a);
- I-element with integrating behaviour. The output signal follows the integral of the input signal over time without other dynamic effects (b).
- D-element with differentiating behaviour. The output signal is proportional to the time derivative of the input signal (c);
There are also elements with time delay. In fluid technology, these are normally:
- PT1-elements, i.e. P-elements with a 1st order time delay, in which the output responds with a time delay with an exponential function (Figure U 10 a) and
- PT2-elements, i.e. P-elements with a 2nd order time delay. At lower damping, they tend to overshoot (typical for hydraulic cylinders with mass (b).
There are also three combinations:
- PI element: created through the parallel structure of a P-element and an I-element (Figure U 11 a);
- PD-element: created through the parallel structure of a P-element and D-element; sudden increase in subsequent P-behaviour, particularly for slow controlled subsections (b);
- PID-element: Combination of P, I and D-behaviour; used in difficult controlled subsections (c).
Figure U 8: Illustration of a transfer element
Figure U 9: Basic transfer elements
Figure U 10: Transfer elements with time delay
Figure U 11: Combined transfer elements