Chapter 7. PID Built-In Function BlockGFK-2950C February 2018 3557.4 PID Algorithm Selection (PIDISA or PIDIND) and GainCalculationsThe PID function supports both the Independent Term (PID_IND) and ISA standard (PID_ISA) forms ofthe PID algorithm. The Independent Term form takes its name from the fact that the coefficients forthe proportional, integral and derivative terms act independently. The ISA algorithm is named for theInstrument Society of America (now the International Society for Measurement and Control), whichstandardized and promoted it.The two algorithms differ in how words 6 through 8 of the reference array are used and in how thePID 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 Biaswhere Kp is the proportional gain, Ki is the integral rate, Kd is the derivative time, and dt is the timeinterval 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 Biaswhere Kc is the controller gain, Ti is the Integral time and Td is the Derivative time. The advantage ofPID_ISA is that adjusting Kc changes the contribution for the integral and derivative terms as well asthe 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 asPID_IND parameters:Kp = Kc, Ki = Kc/Ti, and Kd = Kc * TdThe following diagram shows how the PID_IND algorithm works:Ki * Error * ΔTimeIntegral Term =Proportional Term =Kp * ErrorDeadBandCVBiasSlewLimit ClampUpper / Lower Polarity CVSPPVError TermSignDeriv Action+/-Δ ValueΔ TimeDerivative Term =Δ TimeKd * Δ Value-/++Previous Integ. Term +Figure 16: PID_IND DiagramThe ISA Algorithm (PID_ISA) is similar except that its Kc gain coefficient is applied after the threeterms 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.
