It’s been a slow week.
I need to complete the discussion that started with the latest control theory post. Much of that is still just math (stage III), not yet a lecture (stage IV), so I could have my work cut out for me. (There, now I’m covered if I don’t get a post out this Monday!)
I sort of figured out why a negative phase margin implies instability – that was one of two open questions at the end of the latest control theory post… more precisely, I can see it but I don’t actually understand it. The easiest way to see it is to look at a Nyquist plot… if the phase margin is negative, we must have an encirclement of the point (-1,0)… and that implies instability. But I don’t understand Nyquist plots. Still, I know how to see why the properties of phase margins are not symmetric about -180°.
My very next controls example has turned out to be effectively intractable for a Manipulate command: the animation is too slow to be useful. I’m looking for other ways to phrase the solution.
(The inverse Laplace Transform is out-and-out huge for this example… can I somehow get to a numerical solution faster? Would a direct solution of the differential equation be faster? Should I just go for a set of still images? Or will a root-locus animation work? We’ll see. But that’s not for this Monday.)
You may have noticed the comments about a spectrophotometer… I know what I’m going to try, when I get a little time. My guess – from reading Wikipedia! – is that the illuminant is actually equal-intensity, and the numbers I was given are a reflectance spectrum. If so, I have all I need to compute XYZ. If I get out a red color, I’ll find it plausible; if I don’t, I’ll send the questioner to the manufacturer.
Oh, at some point I will need to work out the color parameters for my new monitor.
I wanted to add one comment to last week’s mention of the founding of National Geographic to discuss a huge storm. One of the first issues interested people faced 125 years ago was to realize that there had actually been one huge storm. We take that for granted today.
A friend send me a link to a NY Times article about MOOCs – massive open online courses. As you might expect, I found it especially interesting reading because I’m taking my second MOOC (Computational Investing, from Geordia Tech, thru Coursera). My first was an introduction to the R statistical package. And there’s a fascinating one scheduled in January on Image Processing. (Let me put it this way: I’ve owned the primary text for that course for a few years… and I’ve just ordered the second and third. The fourth is $400, and I’m not going there.)
And that’s all I have this morning. Now let me see what math my alter ego the kid wants to do for a while, before my grownup picks up control theory.