Eaton easyE4 Manual page 356

6. Function blocks
6.1 Manufacturer function blocks
352
value (Xi) at a specified scan time. The equation used by the device for the proportional
component is as follows:
YP(t) = Kp * [Xs(t) - Xi(t)]
Integral component
The integral component YI is proportional to the sum of the control difference over time.
The equation used by the device for the integral component is as follows:
YI(t) = Kp * Tc / Tn * [Xs(t) - Xi(t)] + YI (t-1)]
K = Proportional gain
p
Tc = Scan time
Tn = Reset time (also known as integration
time).
Xs(t) = Setpoint with scan time t
Xi(t) = Actual value with scan time t
YI(t–-1)= Value of the integral component of
the manipulated variable with scan time t – 1
Differential component
The differential component YD is proportional to the change in the control difference. So
as to avoid step changes or jumps in the manipulated variable caused by the differential
behavior when the setpoint is changed, the change of the actual value (the process vari-
able) is calculated and not the change in the control difference. This is shown by the fol-
lowing equation:
YD(t) = Kp x Tv / Tc x (Xi (t-1) - Xi(t))
K = Proportional gain
p
Tc = Scan time
Tv = Rate time of the control system (also
called the differential time)
Xi(t) = Actual value with scan time t
Xi(t-1) = Actual value with scan time t - 1
In order for a PID controller to work, it must be enabled with DC_EN =1. The PID con-
troller will provide manipulated variable QV as an output variable. If the DC..EN coil is
not active, the entire PID controller will be disabled and reset. The manipulated variable
at the QV output will assume a value of 0. Function block inputs DC_EP, DC_EI, and DC_
ED all need to be active in order for the proportional term, integral term, and derivative
term to be calculated.
Example: If only coils DC...EP and DC...EI are activated, the PID controller operates as
a PI controller.
easyE4 10/19 MN050009 EN www.eaton.com
Kp = Proportional gain
Xs(t) = SETPOINT value at scan time t
Xi(t) = ACTUAL value at scan time t