Table 7 Summary of the dynamics of the different controllers and their PID gains

Controller dynamics

Controller

No controller

Manual

ZN-RL

QPSO-LQR

Overshoot (Hz)

0.7437

0.2962

0.3485

0.04521

Steady-state error (Hz)

0.4794

0.0001267

0.0007038

0.00007

Duration of steady-state analysis (s)

10

10

10

10

Controller gains

PID gains

Values

\({K}_{p}\)

-

2.0121

2.244

79.0763

\({K}_{i}\)

-

0.9989

2.3194

282.0301

\({K}_{d}\)

-

1.0117

0.5428

43.7655