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

Table 4

Example  2 controllers.

Controller	Normalized transfer function
𝑃𝐼	𝑅0𝑛(𝑠)=6.4875𝑠+37.7482𝑠
𝑃𝐼^𝛼	𝑅2𝑛(𝑠)=18.9095𝑠^0.5+1.7512𝑠^0.5
𝐼𝐼^𝛽	𝑅3𝑛(𝑠)=25.9015𝑠^0.5−13.9576𝑠
𝐼^𝛼𝐷^1−𝛼	𝑅4𝑛(𝑠)=22.4055𝑠+0.43864𝑠^0.5