Logix5000 Controllers General Instructions - SLAC Confluence

Special Instructions (FBC, DDT, DTR, PID) 509The PID equation used in the PID instruction is a positional formequation with the option of using either independent gains ordependent gains. When using independent gains, the proportional,integral, and derivative gains only affect their specific proportional,integral, or derivative terms respectively. When using dependentgains, the proportional gain is replaced with a controller gain whichaffects all three terms. You can use either form of equation to performthe same type of control. The two equation types are merely providedto let you use the equation type with which you are most familiar.Gains Option Derivative Of EquationDependent gains(ISA standard)error (E)CV=t1K CE ----dE+∫Edt + T d------ + BIASdtT i0process variable (PV)E = SP - PVCV =t1K CE + ----∫Edt∠T dPVd---------- + BIASdtT i0E = PV - SPCV =t1K CE ----dPV+∫Edt + T d---------- + BIASdtT i0Independent gainserror (E)process variable (PV)E = SP - PVtdECV = K PE+ K i ∫Edt + K d------ + BIASdtt0CV = K PE+ K i ∫Edt∠K dPVd---------- + BIASdt0E = PV - SPtdPVCV = K PE+ K i ∫Edt + K d---------- + BIASdt0Publication 1756-RM003I-EN-P - January 2007