Control systems, pid, and high-order transfer functions

[baggepinnen]

@romain-chiap

First question: how can I simplify this transfer function?

minreal(Gin) simplifies the transfer function.

@romain-chiap

Gout = (P*Gin) / (s+P*Gin)

Don’t do this, use the function feedback(P*Gin) = P*Gin/(1+P*Gin) instead. Is the s in the denominator deliberate or a typo?

@romain-chiap

and I obtain the following warning.

Yes, it’s generally better to convert your systems to statespace representation using the function ss. Do this is soon as possible. See Performance considerations · ControlSystems.jl for some details as to why.

@romain-chiap

it tells me System is improper, a state-space representation is impossible. Any mathematical explanation cue?

likely due to the non-minimal realization.

Try

Gin=tf([1.7664, 8.8576, 5.120000000000001, 0],[0.00046575, 0.022725, 0.32, 2.8432, 8.8576, 5.120000000000001, 0])
Gin = ss(Gin)
Ginr = minreal(Gin, 1e-8)
Gout = feedback(P*Gin)