Laplace Transform of differential equations

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M Gokul 2016-5-13

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评论： Star Strider 2016-5-21

i have a plant model with seven ODEs (cX)'=f(cX,cS,cP,Tr), (cP)'=f(cX,cS,cP), (cS)'=f(cX,cS,cP,Tr), (cO2)'=f(cX,cO2,Tr), d(Tr)'=f(Tr,Tag), d(Tag)'=f(Tr,Tag) where ' denote 1st order differential w.r.t time how do i convert to laplace domain so as to apply frequency analysis to do control design?

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Star Strider 2016-5-14

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You would probably need at least the Symbolic Math Toolbox. I would need to see your actual functions (time-domain differential equations) to help you put them in a form that the Control systems Toolbox could use. The Symbolic Math Toolbox — at least the MuMath representation of it in the Symbolic Math Toolbox — is not always easy to work with. I have not delved into MuMath, so I have no idea what other capabilities it might have that the Symbolic Math Toolbox does not. My relatively straigtforward applications of it never caused problems.

Your differential equations must be linear and time-invariant with constant coefficients to be transformed into Laplace space to be used in transfer functions. If that is successful, The rest is a matter of coding. To the best of my knowledge, there are no straightforward methodS to transform Symbolic Math Laplace Transforms to the Control Systems Toolbox functions, so you must apply some ingenuity. There may be more efficient ways to do this; I‘ve not searched.