Detailed Formulas

Variable Definition

Definition of the variables in the following formulas:

Variable	Definition
dt	time difference between the present cycle and the previous cycle
Xd	current internally formed system deviation
Xd(new)	system deviation value from the current sampling step
Xd(old)	system deviation value from the previous sampling step
Z	disturbance
AP	bumpless transfer (only in P, D or PD controllers)
kp	proportional rate
tn	reset time
tv	derivative action time
t1	delay time constant
X(new)	value of process variable from the current sampling step
X(old)	value of process variable from the previous sampling step
Y	manipulated variable
YP	P-component (only when input status bit 9 = 1)
YI	I-component (only when input status bit 10 = 1)
YD	D-component (only when input status bit 11 = 1)

Manipulated Variable

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

Y = YP+YI+YD+AP+Z

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

Yau ≤ Y ≤ Yao

P Component YP for all Operating Modes

YP for manual, halt, automatic and cascade mode is determined as follows:

For input status bit 9 (proportional component) = 1 the following applies:

YP = kp · xd

For input status bit 9 (proportional component) = 0 the following applies:

YP = 0

I Component YI for Automatic and Cascade Mode

YI for automatic and cascade mode is determined as follows:

For input status bit 10 (integral component) = 1 the following applies:

For input status bit 10 (integral component) = 0 the following applies:

YI = 0

The I component is formed according to the trapezoid rule.

I Component YI for Manual and Halt Mode:

YI for manual and halt mode is determined as follows:

For input status bit 10 (integral component) = 1 the following applies:

YI = Y - YP - Z

For input status bit 10 (integral component) = 0 the following applies:

YI = 0

D Component YD for Automatic and Cascade Mode

YD for automatic and cascade mode is determined as follows:

For input status bit 11 (derivative component) = 1 and input status bit 12 (Derivative component on x/xd) = 0 the following applies:

For input status bit 11 (derivative component) = 1 and input status bit 12 (Derivative component on x/xd) = 1 the following applies:

For input status bit 11 (derivative component) = 0 the following applies:

YD = 0

D component YD for manual and halt mode

YD for manual and halt modes is determined as follows:

YD = 0