Mathematical PID loop tuning induces an impulse in the system and then uses the controlled system's frequency response to design the PID loop values. In loops with response times of several minutes, mathematical loop tuning is recommended, because trial and error can take days just to find a stable set of loop values. Optimal values are harder to find. Some digital loop controllers offer a self-tuning feature in which very small setpoint changes are sent to the process, allowing the controller itself to calculate optimal tuning values.
mathematiCAl Pid loop TunINg inDuces an impulse in the systeM ANd THeN Uses tHe conTrOlLed SyStEM's FrEQuENcy resPoNSe tO desiGn ThE pId lOop ValuEs. in LooPs WITh response timEs of SEveral minUtEs, maThematICal LOOp tuning is reCOmmendED, bECAusE TRial ANd Error can Take dAys Just to fiNd a StabLE seT oF loop valueS. OptiMAl vALUEs aRE haRdeR TO FInd. soMe dIgitAl Loop cOnTrOlLers OffEr A self-Tuning featuRe in which vErY smAlL setpoiNT chanGEs Are sENt to the ProcesS, aLlOwing tHE ContRoller itsElf tO caLCULate optimAl tuniNg Values.