Optimization of Integer Order Integrators for Deriving Improved Models of Their Fractional Counterparts

Table 6

Comparisons of RME values of the proposed half integrators based on optimized DIs with the existing models.

𝜔  (𝜋 rad)	Proposed half integrators based on 2nd order PSO optimized DI			Proposed half integrators based on 3rd order PSO optimized DI		Gupta-Madhu-Jain half integrator	Krishna half; integrator
	𝐻2nd-fo-2(𝑧)	𝐻2nd-fo-4(𝑧)	𝐻2nd-fo-6(𝑧)	𝐻3rd-fo-3(𝑧)	𝐻3rd-fo-6(𝑧)
0.25	−15.79	−24.55	−43.25	−15.79	−29.26	−35.53	−17.42
0.5	−17.52	−38.74	−55.85	−17.52	−38.97	−53.62	−28.31
0.75	−25.82	−41.56	−85.14	−25.81	−42.61	−53.65	−35.56
1.0	−58.3	−58.3	−55.44	−64.01	−74.75	−45.26	−42.05
1.25	−31.25	−57.34	−53.48	−31.13	−50.67	−38.93	−37.13
1.75	−28.94	−81.15	−75.32	−29.82	−58.25	−33.59	−40.57
2.0	−32.62	−75.83	−55.54	−32.62	−73.25	−34.88	−46.46
2.25	−41.43	−57.13	−48.99	−41.15	−58.93	−43.69	−55.28
2.75	−32.99	−59.6	−59.6	−36.33	−46.94	−32.6	−29.8
3.0	−29.56	−56.03	−47.75	−28.27	−46.74	−33.74	−24.3