Hi, I wonder if there is any straightforward way to model a system consisting of a first-order-plus-delay plant T(s) = K.exp(-delay.s)/(tau.s + 1) and a PI controller using components from ModelingToolkitStandardLibrary. I built a system with first-order plant T(s) = K/(tau.s + 1) and a PI controll…

[image] VPBML: model a system consisting of a first-order-plus-delay plant T(s) = K.exp(-delay.s)/(tau.s + 1) and a PI controller Thanks. Is there any way I can model a system consisting of a first-order-plus-delay plant T(s) = K.exp(-delay.s)/(tau.s + 1) and a PI controller in ModelingToolki…

Yes, you can program a component that implements the Padé approximant - Wikipedia … See also: RATIONAL APPROXIMATION OF TIME DELAY Custom Components · ModelingToolkitStandardLibrary.jl Documentation for ModelingToolkitStandardLibrary.jl. Sometimes it is ea…

I’m not sure if there is an interface to the delay solvers exposed from MTK. Since you are this far talking about a linear system and a linear controller you could model and simulate this using ControlSystems.jl . Unfortunately, ControlSystems cannot model both time delays and static nonlinearities a…

[image] baggepinnen: non-minimum phase zeros they introduce. Does this approximation introduces a non-minimum phase zero? \frac{1}{1+sT} or this one? \frac{6-2sT}{6 + 4sT + (sT)²} See: https://ris.utwente.nl/ws/portalfiles/portal/134422804/Some_remarks_on_Pade-approximations.pdf

Thanks for the answer and suggestion. I took a quick look and ControlSystems.jl seems to be a better choice. Do you know if we can simulate the behavior of the above system (FOPD plant with PI controller) with the presence of output noise somehow?

If your system is linear, use ControlSystems.jl, otherwise ModelingToolkit… You can also derive a linearized model from ModelingToolkit and then use that in ControlSystems…

Yes you can, but this has to be done in discrete time. You need to Discretize the plant model using the function c2d Compute the closed-loop transfer function from output noise n to plant output z, this is given by (assuming measured output y = z + n) G_n = \dfrac{-PC}{1 + PC} which can be compu…

Here’s something to get you started using ControlSystemsBase, Plots τ = 1 # Delay time Ts = 0.1 # Sampling time P = tf(1, [1, 1]) * delay(τ) Pd = c2d(P, Ts) # Discretized plant using ZoH discretization with sample time Ts C = pid(1, 1; Ts) # A very well-tuned PI controller Gn = feedback(Pd*C)…

The latter yes – it has a NMP zero at 3/T.

Model a first-order-plus-delay system in ModelingToolkit

Specific Domains Modelling & Simulations

baggepinnen February 4, 2024, 10:39am 2

Unfortunately there is currently no delay component in the standard library

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Model a first-order-plus-delay system in ModelingToolkit

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