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7.4 PID Algorithm Selection (PIDISA or PIDIND) and Gain
Calculations
The PID function supports both the Independent Term (PID_IND) and ISA standard (PID_ISA) forms of
the PID algorithm. The Independent Term form takes its name from the fact that the coefficients for
the proportional, integral and derivative terms act independently. The ISA algorithm is named for the
Instrument Society of America (now the International Society for Measurement and Control), which
standardized and promoted it.
The two algorithms differ in how words 6 through 8 of the reference array are used and in how the
PID output (CV) is calculated.
The Independent term PID (PID_IND) algorithm calculates the output as:
PID Output = Kp * Error + Ki * Error * dt + Kd * Derivative + CV Bias
where Kp is the proportional gain, Ki is the integral rate, Kd is the derivative time, and dt is the time
interval since the last solution.
The ISA (PID_ISA) algorithm has different coefficients for the terms:
PID Output = Kc * (Error + Error * dt/Ti + Td * Derivative) + CV Bias
where Kc is the controller gain, Ti is the Integral time and Td is the Derivative time. The advantage of
PID_ISA is that adjusting Kc changes the contribution for the integral and derivative terms as well as
the proportional term, which can simplify loop tuning.
If you have the PID_ISA Kc, Ti and Td values, use the following equations to convert them to use as
PID_IND parameters:
Kp = Kc, Ki = Kc/Ti, and Kd = Kc * Td
The following diagram shows how the PID_IND algorithm works:
Error Term
Sign
SP
+/-
Dead
Band
-/+
Deriv Action
PV
Δ
Value
Δ
Time
The ISA Algorithm (PID_ISA) is similar except that its Kc gain coefficient is applied after the three
terms are summed, so that the integral gain is Kc / Ti and the derivative gain is Kc * Td.
Bits 0, 1 and 2 in the Config Word set the Error sign, Output Polarity and Derivative Action,
respectively.
GFK-2950C
CV
Proportional Term =
Bias
Kp * Error
Integral Term =
Previous Integ. Term +
Δ
Ki * Error *
Time
Derivative Term =
Δ
Value
Kd *
Δ
Time
Figure 16: PID_IND Diagram
February 2018
Chapter 7. PID Built-In Function Block
Slew
Upper / Lower
+
Limit
Polarity
Clamp
355
CV
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