I am trying to apply Laplace transformation to my cost model in order to use a PI controller in the future. If I understood correctly I have to transform my time-domain functions to the frequency-domain (or S domain). My proportional gain is given by the time-domain function as:
Lrelative = λcurrent / λminimal
where, λ = is the throughput of my system, and L is the parameter used to get an equilibrium among all λ. I use the function above to change the parameter L. The table below exemplifies the function with data.
How do I convert this function to the frequency domain or take the Laplace transform of this equation? What are the steps? Could you please explain in a stepwise?
I guess I have to use the Laplace transform $\frac{1}{a} \times x(t)$, because it is similar to my function. But how do I transform my time-domain function to a frequency-domain function?
Thanks