second order equation implementation if controllogix

I simply integrated twice
y(t)=2*a *exp(b*t)/b + y`(0)*t+ y(0)
Simple. I don't see a problem.

For the chart please down load RMCTools and look at the on-line
http://deltamotion.com/support/webh...Components/Curve_Tool/Curve_Tool_Overview.htm
http://deltamotion.com/products/software/rmctools.php
https://www.bing.com/images/search?q=curve+tool+rmctools&qpvt=curve+tool+RMCTools&FORM=IGRE
The curve tools can approximate any function that has one argument.
This is simple. If you can enter your data into an Excel spreadsheet you can then copy and paste the table into RMCTools

If a and b are not constant then an interactive approach is required.
 

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