Dear friends
Thank you in advance for your help and collaboration. Here in my lab we are working on a photosynthetic plant and we have a non-linear subactuated bilinear model (attached image with the model). The u(t) (dilution rate), the two output variables are x1(biomass) and x3 (volume), alpha1,2 are positive constants and a1,2 are constants. E(t) is a bounded disturbance.
In this type of systems it is necessary to obtain a system in its canonical form (chain of integrators), to be able to propose a Sliding Mode array control?
How would you implement a sliding mode system in this type of systems?
Thank you in advance, if you are also interested in collaborating with the multidisciplinary working group, write to me at [email protected]
Kind regards
Hi Dr. Abraham Efraim Rodriguez-Mata,
I'm unfamiliar with the photosynthesis process in plants. But assuming that volume x3 can never be negative, then x1 seems stabilizable if you can ensure that the dilution rate satisfies the following condition:
u > (max{μ} − min{Σ})·x3
Due to the polarity of u(t) in the x1-dot and x3-dot equations, if x1 decreases, then x3 increases and vice versa. However, if x3-dot = − u(t), then both x1 and x3 are stabilizable with:
u = K·sign(x3)
where
K > max{μ} − min{Σ}
See the stream plot.
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