Chapter 7. PID Built-In Function Block356 PACSystems* RX7i, RX3i and RSTi-EP CPU Programmer's Reference Manual GFK-2950C7.4.1 Derivative TermThe Derivative Term is Kd (word 7 of the reference array) multiplied by the time rate of change of theError term in the interval since the last PID solution.Derivative = Kd * Δerror / dt = Kd * (Error – previous Error) / dtwheredt = Current controller time – controller time at previous PID solution.Two bits in the Config Word (word 13 of the reference array) affect the calculation of Δerror: ErrorTerm Mode and Derivative Action. For additional information about the operation of these bits, referto Config Word above.7.4.2 Error Term ModeThe sign of the Error term is determined by the value of a mode bit in the reference array for the PIDfunction.In reverse acting mode, the change in the error term is:Δerror = (Error – previous Error) = ΔSP – ΔPVwhereΔPV = (PV – previous PV), and ΔSP = (SP – previous SP).However, in direct acting mode, the error term is (PV – SP), the sign of the change in the error term isreversed:Δerror = (Error – previous Error) = = ΔPV – ΔSP.7.4.3 Derivative Action on PV BitBy default, the change in the error term depends on changes in both SP and PV. If SP is constant,ΔSP = 0, and SP has no effect on the derivative term. When SP changes, however, it can cause largetransient swings in the derivative term and hence the output. Loop stability can be improved byeliminating the effect of SP changes on the derivative term.To calculate the Derivative based only on the change in PV, set bit 2 of the Config Word to 1. Thismodifies the equations above by assuming SP is constant (ΔSP = 0).7.4.4 Combined Operation of Error Term and Derivative Action ModesBit 0 of Config Word Bit 2 of Config Word Error Term ValueValue Error Term Mode Value Derivative Action0 Reverse Acting (default) 0 ΔSP included ΔSP –ΔPV1 Direct Acting 0 ΔSP included ΔPV –ΔSP0 Reverse Acting (default) 1 ΔSP ignored –ΔPV1 Direct Acting 1 ΔSP ignored ΔPV
