{"id":2933,"date":"2010-10-09T17:53:20","date_gmt":"2010-10-09T16:53:20","guid":{"rendered":"http:\/\/www.walkingrandomly.com\/?p=2933"},"modified":"2011-03-10T15:07:10","modified_gmt":"2011-03-10T14:07:10","slug":"mathematica-8-control-theory-sneak-peek","status":"publish","type":"post","link":"https:\/\/walkingrandomly.com\/?p=2933","title":{"rendered":"Mathematica 8 – Control Theory Sneak Peek"},"content":{"rendered":"

\ufeff\ufeff\ufeffLots of people are hitting Walking Randomly looking for info about Mathematica 8 and have had to walk away disappointed….until now!<\/p>\n

I’ve been part of the Mathematica 8 beta program for a while now and in order to access the goodies I had to sign an NDA which can be roughly summed up as ‘The first rule of Mathematica 8 beta is that you don’t talk about Mathematica 8 beta.’<\/p>\n

As of today, however, I am allowed to show you a tiny little bit of it in advance of it being released. Mathematica 8 will include a massive amount of support for control theory<\/a>. Here’s a brief preview<\/p>\n

Let’s start by building a transfer function<\/a> model<\/p>\n

myTF = TransferFunctionModel[1\/(1 + 2 s + 2 s^2 + s^3), s]<\/pre>\n
\"Transfer<\/p>\n
I can find its poles exactly<\/p>\n
TransferFunctionPoles[myTF]\r\n\r\n{{{-1, -(-1)^(1\/3), (-1)^(2\/3)}}}<\/pre>\n
and, of course, numerically<\/p>\n
TransferFunctionPoles[myTF] \/\/N\r\n\r\n{{{-1., -0.5 - 0.866025 I, -0.5 + 0.866025 I}}}<\/pre>\n
Here’s its bode plot<\/p>\n
BodePlot[myTF]<\/pre>\n
\"Bode
\nHere’s its response to a unit step function<\/p>\n
stepresponse = OutputResponse[myTF, UnitStep[t], t]<\/pre>\n
\"Step
\nLet’s plot that response<\/p>\n
Plot[stepresponse, {t, 0, 10}]<\/pre>\n
\"Step
\nFinally, I convert it to a state space model.<\/p>\n
StateSpaceModel[myTF]<\/pre>\n
\"State
\nThat’s the tip of a very big iceberg ;)<\/p>\n
Update:<\/strong> Mathematica 8 has now been released.\u00a0 See https:\/\/www.walkingrandomly.com\/?p=3018<\/a> for more details.<\/p>\n
Other Mathematica 8 previews<\/h3>\n