Table 2 Parameters of PID controllers
Parameter | PSO | WCA | HBA | AOS | COA |
|---|---|---|---|---|---|
\({\text{K}}_{\text{P}1}\) | −1.5710 | −2.5854 | −3.0000 | −3.0000 | −3.0000 |
\({\text{K}}_{\text{d}1}\) | −2.9629 | −0.6201 | −3.0000 | −3.0000 | −2.8049 |
\({\text{K}}_{\text{i}1}\) | −2.5130 | −2.7656 | −3.0000 | −3.0000 | −2.9959 |
\({\text{K}}_{\text{P}2}\) | −1.2623 | −1.6248 | −3.0000 | −3.0000 | −0.4804 |
\({\text{K}}_{\text{d}2}\) | −2.0399 | −1.3508 | −3.0000 | −3.0000 | −2.7286 |
\({\text{K}}_{\text{i}2}\) | −0.8412 | −0.6896 | −0.4000 | −0.5696 | −0.53057 |
\({\text{K}}_{\text{P}3}\) | −2.8177 | −0.8436 | −3.0000 | −3.0000 | −2.3027 |
\({\text{K}}_{\text{d}3}\) | −1.0046 | −0.9239 | −3.0000 | −1.8042 | −0.4000 |
\({\text{K}}_{\text{i}3}\) | −2.4193 | −2.8433 | −3.0000 | −3.0000 | −2.9397 |
\({{\uptau }}_{\text{W}}\) | 29.7104 | 7.3959 | 30.0000 | 30.0000 | 14.7056 |
\({\text{K}}_{{\upbeta }}\) | 27.1451 | 18.0232 | 41.7032 | 50.0000 | 10.0000 |
\({\text{R}}_{\text{w}\text{t}}\) | 0.1745 | 0.2006 | 0.3000 | 0.1686 | 0.101994 |