pH variations with light
Now we need a transfer function that giving a light input delivers and output such as the one observed. To that purpose we can observe that the response (pH variation) behaves like a first order system with a lagging time.
We work on the frequency plane (using Laplace transforms). Thus, transfer function of a first order system with a lagging time is such as:
Using the transfer function of the system we can get the response such as:
y(t) = pH - pH
0
y(s)= L [y(t)] where L[] function is Laplace transform
y(s) = G(s)·u(s)
With the experimental data we have obtained the parameters values:
And with them we can adjust almost perfectly the experimental upwards dynamics:
We assume that the dynamics downwards should have the same underlying physics, so parameters should remain the same, we obtain a theoretical simulation and tallies real data:
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