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

Table 2

Transfer functions and fitness values of worst and average cases of 3rd order PSO optimized DIs.

TFs of worst cases of 3rd order DIs along with their fitness function values (F.V.)		TFs of average cases of 3rd order DIs along with their fitness function values (F.V.)
Transfer function	F.V.	Transfer function	F.V.
𝐻1(𝑧)=0.142394𝑧^3+0.428511𝑧^2−0.306611𝑧+0.217758𝑧^3−0.903135𝑧^2−0.674295𝑧+0.568774	0.666364	𝐻1(𝑧)=−0.65685𝑧^3−0.806245𝑧^2−0.820988𝑧−0.19093𝑧^3+0.100534𝑧^2−0.473273𝑧−0.550301	0.548217
𝐻2(𝑧)=−0.738721𝑧^3−0.425561𝑧^2−0.787252𝑧+0.588187𝑧^3−0.0845531𝑧^2−0.714103𝑧−0.24424	2.38383	𝐻2(𝑧)=−0.171166𝑧^3+0.795027𝑧^2+0.339133𝑧+0.481229𝑧^3−0.740329𝑧^2−0.0821587𝑧−0.130453	0.651617
𝐻3(𝑧)=0.524852𝑧^3+0.958813𝑧^2+0.585323𝑧+0.779817𝑧^3−0.462779𝑧^2−0.380859𝑧−0.247247	3.91385	𝐻3(𝑧)=0.522989𝑧^3+0.163603𝑧^2−0.0262705𝑧+0.483852𝑧^3−0.979861𝑧^2−0.140418𝑧+0.0831846	0.673745
𝐻4(𝑧)=0.979099𝑧^3−0.852921𝑧^2+0.960434𝑧+0.875076𝑧^3−0.827092𝑧^2−0.246012𝑧+0.135716	4.06169	𝐻4(𝑧)=0.225804𝑧^3+0.780081𝑧^2+0.758662𝑧−0.0994224𝑧^3−0.237348𝑧^2−0.575985𝑧−0.13299	0.713815
𝐻5(𝑧)=0.0594656𝑧^3+0.700018𝑧^2+0.346537𝑧+0.314347𝑧^3−0.791867𝑧^2−0.573836𝑏𝑧+0.410591	4.68934	𝐻5(𝑧)=0.123855𝑧^3+0.491766𝑧^2+0.727444𝑧+0.568523𝑧^3−0.319642𝑧^2−0.287981𝑧−0.331056	0.976067