Detailed formulas

Explanation of formula variables

Meaning of the variables in the following formulas:

Variable	Meaning
	Present sample time
	System deviation
	System deviation value from the previous sampling step
FEED_FWD	Disturbance variable
Y	Current output (halt mode) or YMAN (manual mode)
YD	D component
	Value of the D-component from the previous sampling step
YI	I component
	Value of the I component from the previous sampling step
YP	P component

System deviation

The system deviation will be determined as follows:

Manipulated variable

The manipulated variable consists of various terms which are dependent on the operating mode:

After summation of the components manipulated variable limiting takes place, so that:

Overview of the calculation of the control components

Following this an overview on the different calculations of the control components in relation to the elements trig_err can be found:

Controller type	Controller components
PI controller (ERR ≤ trig_err)	YP and YD for manual, halt and automatic modes YI for automatic operating mode YI for manual and halt operating mode
PD controller (ERR> trig_err )	YP and YI for manual, halt and automatic modes YD for automatic mode YD for manual and halt operating mode

PI controller: YP and YD for all operating mode

YP and YD for manual, halt, automatic and cascade modes are located as follows:

PI controller: I component for automatic mode

YI for automatic mode is determined as follows (ti > 0):

The I component is formed according to the trapezoid rule.

PI controller: I component YI for manual and halt modes

YI for manual and halt are located as follows

PD controller: YP and YI for all modes

YP and YI for manual, halt, and automatic modes are determined as follows

PD controller: D component for automatic mode

YD for automatic mode is determined as follows:

PD controller: D component for manual and halt operating mode

YD for manual, halt and automatic modes is determined as follows: