PID Purpose Algorithm: F(s)=P*(1+1/(Ti*s)+Td*s) uk=uk1+Q0*ek+Q1*ek1+Q2*ek2 Q0=P*(1+T/Ti+Td/T) Q1=-P*(1+2*Td/T) Q2=P*Td/T

PID - continued Inputs : ek Outputs : uk Registers : uk1, ek1, ek2 Parameters: P, Ti, Td, T Test Remarks

PID - continued P = 2 Ti = 5 Td = 0 T = 2

PID - continued P = 2 Ti = maximum Td = 3 T = 2

PID algorithms classification Programmable controller - PID algorithm modification PID modification - many auxiliary parameters Differences: algorithm type, parameters names, integral/derivative part implementation etc.

PID classification - continued Standard controller parameter names P - proportional gain PB - Proportionality band [%] Ti - integral time constant [time unit] Td - derivative time constant [tiem unit]

PID classification - continued Three types of PID algorithm Ideal PID algorithm ISA Ideal parallel Interactive algorithm

PID classification - continued Proportional part of PID  GAIN vs. PB  PID, I.PD, PID A, PID B...  Deviation units - e.u. or %?  P, PB, Pp and Pi transformation

PID classification - continued Integral part of PID  Ti, Tip, Tii, I, reset, repeats  PID, I.PD, PID A, PID B...  Deviation units - e.u. or %?  Ti, Tip, Tii transformation

PID classification - continued Derivative part of PID  Td, D, Tdp, Tdi, Rate  PID, I.PD, PI.D, PID A, PID B...  Deviation units - e.u. or %?  Td, Tdp, Tdi transformation  Filtering

Auxiliary data of PID algorithm Control action limits  OUTPUTmin/max, wind up effect Control action trend limits Set Point Limits  SPmin/max, prevent operator mistakes Set Point Ramping  batch control, set point programming Deviation Gap  non linear control action, +hysteresis