PID
This document provides an in-depth look at PID (Proportional-Integral-Derivative) control algorithms, detailing their structure, purpose, and mathematical formulations. The PID algorithm is defined as F(s)=P*(1+1/(Ti*s)+Td*s) with output uk computed from past errors. Key parameters including proportional gain (P), integral time constant (Ti), and derivative time constant (Td) are outlined along with register management for error terms. The text also delves into different types of PID strategies, classifications, and modifications, presenting essential insights for control system design and implementation.
PID
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Presentation Transcript
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
