Detailed formulas
Original instructions
About us
Explanation of formula variables
Meaning of the variables in the formulas:
Variable
Meaning
is the time differential between the current cycle and the previous cycle
System deviation (SP - PV)
System deviation value from the current sampling step
System deviation value from the previous sampling step
FEED_FWD
Disturbance variable
Value of controlled variable from the current sampling step
Value of controlled variable from the previous sampling step
Y
current output (halt mode) or YMAN (manual mode)
YD
D component
YI
I component
YP
P component
Manipulated variable
The manipulated variable is composed of various terms:
After summation of the components manipulated variable limiting takes place, so that:
System deviation
The system deviation will be determined as follows:
ERR = SP - PV, if reverse = 0
ERR = PV - SP, if reverse = 1
Overview of the calculation of the control components
Following this an overview on the different calculations of the control components in relation to the gains kp, ki and kd can be found:
P component YP for all operating modes
YP for manual, halt and automatic modes is determined as follows:
I component YI for automatic mode
YI for automatic mode is determined as follows:
For ki > 0 the following applies:
For ki = 0 the following applies:
The I component is formed according to the trapezoid rule.
I component YI for manual and halt modes
YI for manual, halt and automatic modes is determined as follows:
For ki > 0 the following applies:
For ki = 0 the following applies:
D component YD for automatic mode
YD for automatic mode and cascade is determined as follows:
For kd > 0 and d_on_pv = 0 the following applies:
For kd > 1 and d_on_pv = 0 the following applies:
For kd = 0 the following applies:
D component YD for manual and halt modes
YD for manual, halt and automatic modes is determined as follows: