Table 10 Optimum gains of proposed and other controllers.
Controllers − algorithms | Parameters | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
KPS | KIS | KDS | \(\lambda\) S | \(\mu\) S | KPC | KIC | KDC | \(\lambda\) C | \(\mu\) C | Hbup | Hbdown | |
PI-HAALO | 30 | 8.299 | 0 | 1 | 0 | 20 | 0.8517 | 0 | 1 | 0 | 0 | 0 |
PID-PSO12 | 8.2724 | 19.1082 | 0.5159 | 1 | 1 | 16.8093 | 8.2129 | 0.3467 | 1 | 1 | 2.8493 | − 3.9185 |
PID-PPSO12 | 20 | 19.9364 | 1.0257 | 1 | 1 | 18.9230 | 0.4408 | 0 | 1 | 1 | 11.0747 | − 18.1291 |
PID-ALO12 | 4.8662 | 1.0845 | 0.0577 | 1 | 1 | 4.3679 | 0.0351 | 9.4898 | 1 | 1 | 0.2482 | − 9.1854 |
PID-RIME | 17.501 | 5.69854 | 874e−7 | 1 | 1 | 9.03235 | 0.0979 | 0.256 | 1 | 1 | 0 | 0 |
PID-GEO | 20 | 3.199 | 0 | 1 | 1 | 1.5845 | 5.36412 | 9.6521 | 1 | 1 | 1.2907 | 0 |
PID-GA12 | 4.5341 | 10.4119 | 0.0773 | 1 | 1 | 10.5768 | 13.9666 | 15.9050 | 1 | 1 | 8.1984 | − 15.8896 |
FOPID-HAALO | 11.0214 | 8.0854 | 18.7841 | 0.9924 | 3448e−13 | 11.7069 | 7.7887 | 15.5277 | 0.82317 | 0.0071 | 3.2514 | − 1.0254 |
FOPID-PSO12 | 3.0006 | 12.2041 | 1.0619 | 0.9351 | 0.3260 | 3.3328 | 14.0403 | 1.3530 | 0.3080 | 0.0719 | 20 | − 17.7777 |
FOPID-PPSO12 | 0.3659 | 11.3479 | 2.0341 | 0.5613 | 0.3577 | 8.4507 | 14.4807 | 1.0683 | 0.7041 | 0.0177 | 6.5840 |  − 8.0318 |
FOPID-ALO12 | 2.2623 | 8.0692 | 1.7222 | 0.7845 | 0.3448 | 13.7069 | 17.7887 | 18.5277 | 0.2317 | 5.0788e−5 | 12.3755 | − 0.7385 |
FOPID-RIME | 2.0145 | 12.2543 | 10.5412 | 0.94125 | 0.00147 | 15.15 | 0.6455 | 1.0365 | 0.5412 | 0.00014 | 1.23 | − 0.145 |
FOPID-GEO | 1.02145 | 16.9854 | 3.78412 | 0.9924 | 0.3448 | 18.7069 | 5.7887 | 10.257 | 0.3234 | 75e−7 | 18.3755 | − 0.7385 |
FOPID-GA12 | 1.5312 | 12.7514 | 1.9267 | 0.9283 | 0.3410 | 13.0542 | 19.0341 | 0.6248 | 0.3180 | 0.0737 | 4.3712 | − 12.1320 |