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How to use a discretized controller with NDSolve?

• To: mathgroup at smc.vnet.net
• Subject: [mg105007] How to use a discretized controller with NDSolve?
• From: Joe Hays <hays.joe at gmail.com>
• Date: Tue, 17 Nov 2009 05:16:40 -0500 (EST)

Hello all,

I thought I'd check to see if there is a better way to perform a
calculation. I've been using NDSolve to determine the response of a system
of nonlinear differential equations representing a controlled double
pendulum. So, each pendulum has an associated input, say U[i].

The dynamics are discribed by continuous ODEs, however, my controller is
discrete, meaning, every 'dt' seconds new updates are sent to each U[i].
Assuming I know what the desired list of U[i] updates are before hand...
I've used the Piecewise[] function to create piecewise continuous functions
representing each U[i] to inject into the double pendulum system of ODEs.

This is not the way I would do this in other languages but given my somewhat
primitive skills in Mathematica... this is what I came up with. My solutions
appear to be correct so my question is motivated more to improve my
Mathematica skills.

Any thoughts or points are welcome.

Thx.

Joe