I took time off from work this week… I got some of my Xmas shopping done… asked several control theory questions of my own in comments – just to start singling them out – and answered a couple of them, too….
I also read through an old (1965) book of mine, Coughanowr & Koppel’s “Process Systems Analysis and Control”. It’s a pleasant book, with a lot of small bite-size chapters But it is old: it includes 3 chapters on setting up analog computers for simulating control problems! On the other hand, it also includes an introduction to nonlinear dynamical systems. But what I like is the compact chapters. In fact, I was thinking that the book would be very nicely implemented as a blog, one chapter per post. (No, I’m not going to do that. It isn’t mine to do with.)
You might guess from the fact that no technical post went out last Monday that I’m still struggling with the completion of my Example 1 in control theory. Certainly not not the best choice I’ve ever made for a first example… but that’s part of the problem: one of the issues Carstens raises can’t very well apply to every control problem, but I don’t see what restricts it to a smaller field of applicability. Oh, everything would have been fine if I had ignored Carstens’ use of a rate generator to correct this issue – crossover frequency very close to corner frequency – in his first real control problem, but thought I was looking at an isolated correction to a schoolboy solution. As it is, I am probably going to have to say, I really have serious questions about the applicability of Carstens’ analysis, and I’ll just have to keep my eyes open for more real-world information.
(Ultimately, I chose that example because I wanted to illustrate that the standard textbook solution wasn’t a real-world solution. I’m just shocked and confused by how much territory this particular example seems to cover.)
But then I took it easy for two days, reading fiction. Oh, Tuesday night I hit the local supermarket and bought a box of 10 twinkies… I didn’t wait for yesterday’s announcement that Hostess was going out of business. It would be far-fetched wishful thinking to hope that given the run yesterday on Twinkies and Wonder Bread, maybe they won’t need to close. In any case, that box of twinkies should provide a nice taste-memory for a decade or so. I don’t want twinkles at all often, but I couldn’t stand the prospect of never having another one – now I can. (A friend joked that the twinkies themselves might have lasted a decade, but I think that’s a terrible thing to say.)
I’ve been looking at something called the Capital Asset Pricing Model… the presentation in the MOOC I’m taking (that’s a massive open online course, specifically computational investing) wasn’t as clear as I would have liked. Actually, no presentation has been as clear as I would have liked – which is shocking since one of my sources is a math book! I wasn’t surprised that my two books entitled “Investments” just slid over a rather strange equation, but it shocked me that the math book did, too. I’m thinking I should write this up, especially since it’s a nice follow-up to one of my regression posts.
Oh, I had said that I ordered a couple of books for an image processing course coming in January… they arrived… they both look daunting and fascinating. (Almost all mathematics does, to me.) In particular, Sapiro’s “Geometric Partial Differential Equations and Image Analysis”. Chapter 2 is “Geometric Curve and Surface Evolution”… chapter 4 begins by explaining how the typical image smoothing operation of radial Gaussian filtering can be described by a differential equation [namely the heat equation]….
But so far what I’ve picked out was a comment from the historical introduction. “… the field [PDEs in image processing] really took off thanks to the independent works of Koenderinck and….
Why did that leap out at me? Because Koenderink is the author of “Color for the Sciences”, an iconoclastic book that I started looking at but put down because it was taking a strange approach. I’ll move it up a bit on my (rather large) list of things to do.
Oh, speaking of MOOCs, there’s another interesting class coming late in January: Control of Mobile Robots. Considering that Carstens’ troubling solution was for a robotic cart, I’m going to have to take the course….