Table 1 Ziegler-Nichols rule
Type of controller | \({{\varvec{K}}}_{{\varvec{p}}\boldsymbol{ }}={\varvec{K}}\) | \({{\varvec{T}}}_{{\varvec{i}}}\) | \({{\varvec{T}}}_{{\varvec{d}}}\) | \({{\varvec{K}}}_{{\varvec{i}}\boldsymbol{ }}={\boldsymbol{ }{\varvec{K}}}_{{\varvec{p}}\boldsymbol{ }}/{{\varvec{T}}}_{{\varvec{i}}}\) | \({{\varvec{K}}}_{{\varvec{d}}\boldsymbol{ }}={{{\varvec{K}}}_{{\varvec{p}}}{\varvec{T}}}_{{\varvec{d}}}\) |
|---|---|---|---|---|---|
P-control | \(0.5{K}_{c}\) | \(\infty\) | \(0\) | \(0\) | \(0\) |
PI control | \(0.45{K}_{c}\) | \({T}_{c }/1.2\) | \(0\) | \(0.54{K}_{c}/{T}_{c}\) | \(0\) |
PD control | \(0.8{K}_{c}\) | \(\infty\) | \({T}_{c }/8\) | \(0\) | \(0.1{{K}_{c}T}_{c}\) |
PID control (classical) | \(0.6{K}_{c}\) | \({T}_{c }/2\) | \({T}_{c }/8\) | \(1.2{K}_{c}/{T}_{c}\) | \(0.075{{K}_{c}T}_{c}\) |
Pessen integration | \(0.7{K}_{c}\) | \({2T}_{c }/5\) | \({3T}_{c }/20\) | \(1.75{K}_{c}/{T}_{c}\) | \(0.105{{K}_{c}T}_{c}\) |
Control with some overshoot | \({K}_{c }/3\) | \({T}_{c }/2\) | \({T}_{c }/3\) | \(\left(2/3\right){K}_{c}/{T}_{c}\) | \(\left(1/9\right){{K}_{c}T}_{c}\) |
Control with no overshoot | \(0.2{K}_{c}\) | \({T}_{c }/1.2\) | \({T}_{c }/3\) | \(\left(2/5\right){K}_{c}/{T}_{c}\) | \(\left(1/15\right){{K}_{c}T}_{c}\) |