102
PID Equation Formats
The controller supports two different forms of the PID equation as specified by the Gain Form setting. The two
forms require different units for entry of the PID tuning parameters.
Standard
The standard form is more commonly used in industry because its time-based settings for the integral and deriva-
tive coefficients are more meaningful. This form is selected by default.
Parameter
Description
Units
K
p
Gain
unitless
T
i
Integral Time
seconds or seconds/repeat
T
d
Derivative Gain
seconds
Output (%) = K
p
e(t) +
f
e(t)dt + T
d
de(t)
dt
1
T
i
Parameter
Description
Units
e(t)
Current Error
% of full scale
dt
Delta Time Between Readings
seconds
de(t)
Difference Between Current Error & Previous Error
% of full scale
Parallel
The parallel form allows the user to enter all parameters as Gains. In all cases, larger gain values result in faster
output response. This form is used in the WebMaster controller and is used internally by the Control Module.
Parameter
Description
Units
K
p
Proportional Gain
unitless
K
i
Integral Gain
1/ seconds
K
d
Derivative Gain
seconds
Output (%) = K
p
e(t) + K
i
f
e(t)dt + K
d
de(t)
dt
Integral Value Management
To determine the integral component of the PID calculation, the controller software must maintain a running total
of the accumulated area under the error curve (Current Integral). The sign of the value added to the accumulated
Current Integral during each cycle may be positive or negative based on the current Direction setting as well as the
relative values of the current process reading and the set point.
Override Control
The Current Integral accumulates when the output is set to Auto mode. If the controller is switched to Off mode,
the value no longer accumulates, but it is not cleared. Therefore, PID control will resume where it left off if the
controller is switched from Off back to Auto. Similarly, accumulation of the Control Integral will be suspended if
the output is interlocked and resume after the lock-out is removed.
Bumpless Transfer
When the output is switched from Hand to Auto mode, the controller calculates a value for the Current Integral
using the current error to generate the same output percent as the Hand Output setting. This calculation does not
use the Derivative tuning setting to minimize errors from momentary fluctuations in the input signal. This feature
ensures a smooth transition from manual to automatic control with minimal overshoot or undershoot as long as the
user sets the Hand Output percentage close to the value that the process is expected to require for optimal control
in Auto mode.
