CODEWITHSUNDEEP
approximationpid-controller
Adi
Adi

Reputation: 1

approximation to make a fractional PID

I have to design a fractional order PID controller using the IMC method for my project and I need to find an approximation for (s − ψ) ^α,something similar to:

>THE FOLLOWING LINES ARE FROM THE ATTACHED IMAGE

 s^α ∼= e^α(s−1)

 (s − ψ)^α ∼= e^(α(s−1)−αψ)

 (s − ψ)^α ∼= (s^α)\*(e^−αψ)   

   Can anyone give me a different approximation 

     \[IMC method for fractional order PID\](https://i.sstatic.net/wDUpQ.png) 

   We tried looking into Chebyshev approximation and we couldn't find anything. We just need a different    approximation and the rest of the method would be the same as in the attached image.

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Views: 25

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