Table 3 Statistical performance of different algorithms.

SFOA-based exp-PID (proposed)

1.5879E − 03

1.7332E − 03

1.6378E − 03

3.4804E − 05

FLA-based exp-PID

1.7589E − 03

2.0011E − 03

1.8664E − 03

5.6876E − 05

GCRA-based exp-PID

1.9638E − 03

2.1595E − 03

2.0427E − 03

5.2099E − 05

MSA-based exp-PID

1.6791E − 03

1.8378E − 03

1.7560E − 03

3.6183E − 05

DO-based exp-PID

2.0734E − 03

2.2335E − 03

2.1472E − 03

4.1672E − 05