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

Table 1

Transfer functions and fitness values of worst and average cases of 2nd order PSO optimized DIs.

TFs of worst cases of 2nd order DIs along with their fitness function values (F.V.)		TFs of average cases of 2nd order DIs along with their fitness function values (F.V.)
Transfer function	F.V.	Transfer function	F.V.
𝐻1(𝑧)=0.373324𝑧^2+0.427523𝑧+0.397575𝑧^2−0.042561𝑧−0.999916	0.643052	𝐻1(𝑧)=0.22896𝑧^2−0.825829𝑧−0.502494𝑧^2−0.776284𝑧−0.181729	0.382107
𝐻2(𝑧)=−0.929251𝑧^2+0.381076𝑧−0.75834𝑧^2−0.725805𝑧−0.306558	3.90016	𝐻2(𝑧)=−0.336478𝑧^2−0.82224𝑧+0.101197𝑧^2−0.818946𝑧−0.147828	0.407093
𝐻3(𝑧)=0.541699𝑧^2+0.241831𝑧+0.506633𝑧^2−0.0552516𝑧−1	4.73234	𝐻3(𝑧)=0.0849835𝑧^2+0.752164𝑧+0.756218𝑧^2−0.167219𝑧−0.882869	0.50102
𝐻4(𝑧)=−0.354583𝑧^2−0.833923𝑧−0.813869𝑧^2−0.0637125𝑧−1	5.89578	𝐻4(𝑧)=−0.39729𝑧^2−0.795585𝑧−0.130415𝑧^2−0.722962𝑧−0.318656	0.618717
𝐻5(𝑧)=0.353852𝑧^2+0.203374𝑧+0.466221𝑧^2−0.0406162𝑧−1	18.799	𝐻5(𝑧)=0.284382𝑧^2+0.949776𝑧+0.363676𝑧^2−0.401952𝑧−0.648204	0.737534