## PID tuning

When process identification has been done and control law choosen, PID controller actions are set according to the following tables, given for various PID equations:

- stable with proportional response,
- unstable with integral response.

Stable process, proportional response Process: Gs static gain = ΔS/ΔE (S output, E input), τ pure lag, θ first order time constant. Controller: G _{C} gain (=100/PB, proportional band), Ti integral constant (s), Td derivative constant (s) |
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Mode Action |
P |
PI serie |
PI parallel |
PID serie |
PID parallel |
PID mixed |

G_{C} |
(0.8×θ)/(Gs×τ) | (0.8×θ)/(Gs×τ) | (0.8×θ)/(Gs×τ) | (0.85×θ)/(Gs×τ) | (0.4+θ/τ)/(1.2×Gs) | (0.4+θ/τ)/(1.2×Gs) |

Ti | maxi | θ | (Gs×τ)/0.8 | θ | (Gs×τ)/0.75 | θ+0.4×τ |

Td | 0 | 0 | 0 | 0.4×τ | (0.35×θ)/Gs | (θ×τ)/(2.5×θ+τ) |

Unstable process, integral response Process: K static gain = (ΔS/Δt)/ΔE (S output, E input), τ pure lag. |
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Mode Action |
P |
PI serie |
PI parallel |
PID serie |
PID parallel |
PID mixed |

G_{C} |
0.8/(K×τ) | 0.8/(K×τ) | 0.8/(K×τ) | 0.85/(K×τ) | 0.9/(K×τ) | 0.9/(K×τ) |

Ti | maxi | 5×τ | (K×τ^{2})/0.15 |
4.8×τ | (K×τ^{2})/0.15 |
5.2×τ |

Td | 0 | 0 | 0 | 0.4×τ | 0.35/K | 0.4×τ |