Table 6 Qualitative comparison of reduced model performance parameters.

Proposed model

\(\frac{{10.784{s^2} - 7.7438s+7.5338 \times {{10}^{ - 13}}}}{{5.457{s^3}+16.5184{s^2}+30.6793s+22.2031}}\)

1.5106e-14

5.9454

12.1124

4.4382

0.1630

0.9255

BTM PSO [39]

\(\frac{{1.074{s^2} - 0.3678s+0.001127}}{{{s^3}+1.227{s^2}+5.454s+0.4189}}\)

0.0023

35.3890

13.1658

13.9193

1.1835

0.5120

BTM MM [35]

\(\frac{{ - 1.185{s^2} - 0.01565s+1.63 \times {{10}^{ - 14}}}}{{{s^3}+1.227{s^2}+5.454s+0.4189}}\)

5.9064e-14

10.7890

9.4334

13.8070

5.3746

0.6104

RAM FDM [38]

\(\frac{{ - 0.04292{s^2} - 5.725 \times {{10}^{ - 4}}s+5.96 \times {{10}^{ - 16}}}}{{{s^3}+0.7511{s^2}+0.1878s+0.01532}}\)

6.1391e-12

35.2297

20.0942

10.4908

1.9847

0.0014

DPR CSF [48]

\(\frac{{ - 0.1221{s^2} - 0.001664s+1.732 \times {{10}^{ - 15}}}}{{{s^3}+1.47{s^2}+0.4766s+0.04452}}\)

4.2437e-12

30.5728

14.7212

9.3351

1.8383

0.0054

RA DT [49]

\(\frac{{ - 5.561 \times {{10}^8}{s^2} - 7.418 \times {{10}^6}s+3.245 \times {{10}^{ - 10}}}}{{(8.9083{s^3}+7.0977{s^2}+2.259s+0.1985) \times {{10}^9}}}\)

0

31.9332

17.8236

9.6095

1.8658

0.0028

BTM [50]

\(\frac{{1.276{s^2} - 1.045s+0.1127}}{{{s^3}+1.227{s^2}+5.454s+0.4189}}\)

0.2599

46.6217

22.2921

35.2833

5.5604

0.7749

DM FDM [51]

\(\frac{{ - 4.862 \times {{10}^8}{s^2} - 7.418 \times {{10}^6}s+7.722 \times {{10}^{ - 6}}}}{{(0.5895{s^3}+3.865{s^2}+5.615s+1.985) \times {{10}^8}}}\)

6.7057e-14

7.8734

16.2519

20.4098

11.7772

5.4834

TMM FDM [52]

\(\frac{{ - 0.08432{s^2} - 0.001193s}}{{{s^3}+0.6417{s^2}+0.2538s+0.03194}}\)

0

18.5030

15.8887

9.2253

1.7016

0.0069

SEM SRAM [53]

\(\frac{{ - 4.648 \times {{10}^5}{s^2} - 6200s+6.454 \times {{10}^{ - 9}}}}{{(13.13{s^3}+8.152{s^2}+2.033s+0.1659) \times {{10}^6}}}\)

5.5849e-12

34.3205

21.1364

10.7207

2.0160

0.0012