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PID

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

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PID

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  1. 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

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

  3. PID - continued • P = 2 • Ti = 5 • Td = 0 • T = 2

  4. PID - continued • P = 2 • Ti = maximum • Td = 3 • T = 2

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

  6. 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]

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

  8. 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

  9. 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

  10. 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

  11. 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

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