Table 3 Optimized controller parameters and ST and JITAE results of Test-system-2
Algorithm | ISFS: PID [1] | DSA: FOPID [23] | DSA: FOPI–FOPD [23] | CGO: FOPID–FOPI |
|---|---|---|---|---|
Controller parameters | \({K}_{P}=0.3898\) | \({K}_{P}=2.5578\) | \({K}_{P1}=2.3181\) | \({K}_{P1}= 2.3126\) |
\({K}_{I}=1.0113\) | \({K}_{I}=2.9999\) | \({K}_{P2}=2.9999\) | \({K}_{P2}=1.6944\) | |
\({K}_{D}= 0.7695\) | \({K}_{D}=0.7937\) | \({K}_{I}=2.9879\) | \({K}_{I1}=2.9913\) | |
\(\lambda =1.0020\) | \({K}_{D}=0.4391\) | \({K}_{I2}=2.6311\) | ||
\(\mu =1.2510\) | \(\lambda =1.0000\) | \({K}_{D}=0.6339\) | ||
\(\mu =1.4642\) | \({\lambda }_{1}=1e{-}8\) | |||
\({\lambda }_{2}=1.0000\) | ||||
\(\mu =1.5000\) | ||||
ST (s) (2% band) | ||||
\(\Delta {F}_{1}\) | 6.25 | 2.34 | 1.22 | 1.708 |
\(\Delta {F}_{2}\) | \(6.48\) | 3.63 | 2.25 | 1.95 |
\(\Delta {P}_{tie}\) | \(4.40\) | 2.33 | 1.05 | 0.84 |
\({J}_{ITAE}\) | n/a | 0.0121 | 0.0034 | 0.0028 |