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D-4 • E2 RX/BX/CX I&O Manual 026-1614 Rev 4 5-JAN-2013
sate for error.
To reduce this lag time, Derivative Mode is used.
Derivative Mode constantly analyzes the rate of change of
the error, makes a prediction about what the future error
will be, and makes an adjustment to the output in an
attempt to reduce the rate of change in the error.
In layman’s terms, Derivative Mode causes PID con-
trol to “overshoot” the amount of output percentage to
compensate for the slow reaction times of the P and I
Modes. As a result, Derivative Mode slows the rate error
change down to a level the P and I Modes can handle.
The “D” Mode Calculation
To determine the “D” Mode adjustment for each
update, PID performs the following calculation:
“D” mode adjustment = K
d
* (E – (2E
-1
/t
-1
)+(E
-2
/t
-2
))
K
d
= derivative gain
E = current error
E
-1
=error from the previous update
t
-1
=the amount of time elapsed since the previous exe-
cution
E
-2
=error from the update before the previous update
t
-2
=the amount of time elapsed between 2 executions
ago and the previous execution
The factors E
-1
/t
-1
and
E
-2
/t
-2
are the rates of change
of the error (in units per minute). The rate of change for
the previous error (E
-1
) weighs twice as much in the
Derivative Mode calculation as the 2
nd
previous error (E
-
2
), since E
-1
is closer to the current rate of change than E
-2
.
The derivative gain K
d
is a multiplier that changes the
total size of the Derivative Mode adjustment. If Derivative
Mode is causing PID control to react too quickly or too
slowly, the derivative gain may be adjusted to correct the
problem. Higher values of K
d
result in quicker reactions;
lower values result in slower reactions.
How Condenser Control and
HVAC PID Differs From The
Others
The RMCC approaches condenser control and HVAC
control from a different angle than other PID-controlled
systems such as Pressure Control and Case Control. PID
control for Pressure Control and Case Control seeks to
maintain a constant equality between the input and the set
-
point. Specifically, in Pressure Control, the RMCC tries to
keep the suction pressure or temperature equal to the suc
-
tion setpoint, and in Case Control, the RMCC tries to keep
the case temperature equal to the temperature setpoint.
Condenser Control and HVAC Control seek only to
keep pressure or temperature values
below or above their
setpoints. Thus, the system is only concerned when the
input value is on the wrong side of the setpoint (e.g., above
the setpoint in Condenser Control and Cooling Control, or
below the setpoint in Heating Control). Any value on the
other side of the setpoint is considered an acceptable value
for the purposes of controlling, and therefore the output
will be at or near 0%.
Condenser PID and HVAC Cooling Control only react
to pressure or temperature levels that climb above the set
-
point. Likewise, in HVAC Heating Control, the tempera-
ture level must be below the heating setpoint in order to
begin heating. The 0-100% output percentage is then
determined based on the distance between the input and
setpoint, and the rate of change.
Output at Setpoint
Mathematically, the only difference between PID for
Condenser and HVAC Control and PID for other systems
is the Output at Setpoint value.
The Output at Setpoint value is simply the percentage
the output will be when the input value is stabilized at the
setpoint. In other words, when the PID input equals the
PID setpoint, the PID output percentage will be fixed at
the Output at Setpoint value.
Output at Setpoint is the value that determines where
the throttling range is placed. As mentioned in “Throttling
Range” on page 1, the Throttling Range is the range of
input values across which Proportional Mode will gradu
-
ally move the output percentage from 0% to 100%
(excluding effects by the Integral and Derivative Modes).
The Output at Setpoint value basically tells the RMCC
where to place the Throttling Range in relation to the set
-
point (this is explained in further detail below).
Output at Setpoint for Non-Condenser/
HVAC PID
For all non-condenser and non-HVAC PID control, the
Output at Setpoint is fixed at 50% (except for Analog Out
-
put Modules, which may be programmed with any value
from 0-100%). As mentioned before, this means that PID
control will constantly strive to achieve a stable system
where the input is equal to the setpoint and the output is
50%.
The throttling range in a PID Control application with
a 50% Output at Setpoint is placed in such a way as to put
the setpoint right in the middle of the throttling range, as
shown in
Figure D-3.