Fractional-Order 𝑃𝐼 Control of First Order Plants with Guaranteed Time Specifications

Table 3

Example  1 controllers.

Controller	Normalized transfer function
𝑃𝐼	𝑅0𝑛(𝑠)=3.4636𝑠+8.2888𝑠
𝑃𝐼^𝛼	𝑅2𝑛(𝑠)=1.3545𝑠^0.5+9.7104𝑠^0.5
𝐼𝐼^𝛽	𝑅3𝑛(𝑠)=9.7104𝑠^0.5−5.3232𝑠
𝐼^𝛼𝐷^1−𝛼	𝑅4𝑛(𝑠)=7.8117𝑠+0.4831𝑠^0.5