Happenings – 2012 Nov 24

This week marks the real beginning of the holiday season here in the U.S. Many people get Thursday and Friday off – and Friday may be a bigger shopping day than the day after Xmas.

I worked on Control Theory Example 1 some more. I’m just going to have to compute the phase margin in the general case, I think. But if I struggle with it, I may switch to writing up the Capital Asset Pricing Model (CAPM) – I think I have the post pretty well laid out in my head.

I did re-work the computation of XYZ tristimulus values for the data in this comment, using a D50 illuminant instead of equal intensity; the result is still a red color on my monitor, as I would hope… since the data was for a Pantone red of some kind.

As for that imaging course starting in January, I actually owned two of the 5 books listed, not just one… and having ordered and received two more, I’m well set.

And the 8-week course I’m taking now, computational investing? It’s moving quite a bit slower than the professor had hoped. The syllabus called for 8 quizzes and 5 homework assignments. Well, the second homework assignment will be graded as quiz 3 – oops, quiz 4 – due Friday Nov 30, i.e. toward the end of week 5. If nothing else, I’ve gotten to run Python… and learned the CAPM.

Control Theory: Example 1 part 2

review: K = 1

Let us resume Example 1. We started with the following transfer function, for which I arbitrarily assumed K = 1 and that the given factor of 100 was part of the plant G. There are two poles at -4, and 0.

… which had the following open loop Bode plot

Happenings – 2012 Nov 17

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.

Happenings – 2012 Nov 10

It’s been a slow week.

Mathematically….

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.

Control Theory – Example 1 P-only control

Introduction

Everyone under the sun seems to have their own way of organizing control theory. I may very well end up – I hope I end up – with a few different conceptual approaches for myself. But to begin with, I’m going to just start with examples, so that I’ve got a lot of material to try organizing. If you’re new to control theory, my beginning may seem rather chaotic. Sorry.

It is also my intention to stay with classical control theory for quite a while… I’ll move to state space after I’m comfortable with SISO – single input, single output – and the pre-state-space methodologies.

This first example does one positive thing: it illustrates the effect of proportional control.

It also does a few things that are not quite positive: that is, it raises a few questions. I’m more than a little glad it’s not perfectly straight-forward. Let me not keep secrets:

• Carstens’ first real design problem, later in the book, suggests that this solution is not an acceptable real-world design.
• Tuning rules such as Ziegler-Nichols, which require that the system be brought to the edge of instability, cannot be applied.
• Minimizing the obvious measures of error do not agree with his solution – although his looks pretty standard to me.

My point is not that his solution is incorrect, but that it’s sort of incomplete. It’s a student exercise. Let me rephrase that: I’m delighted to know if the solution to an exercise really is a real-world solution, regardless of whether it is or is not… just so I know which.

Let me start by grabbing a drawing from an earlier post.

Happenings – 2012 Nov 3

Where to start? I have a few topics, but none cry out “I’m the lead story!”

Well, there was Sandy….

I have an electronic collection of the first hundred years of National Geographic. Unfortunately, it can’t be read by any of my current computers. (It’s all images of pages, but they wrapped them all in software which I can’t get running any more.)

But when I got them, I looked at the initial issues. The specific impetus for founding National Geographic and publishing things… was a major storm in about 1886. Think about what they didn’t have: a satellite picture of the whole thing. What they could try to collect was reports scattered in time and space, ranging from residents in the American midwest to ship captains in the Atlantic ocean. Like Sandy, the storm lasted several days, but accumulating and sifting thru the data took months, if not a year. And National Geographic’s first few issues tried to assemble and assess all that, to get a picture of just how far-reaching the storm had been. As I recall, it was bigger than they originally thought, and that was big enough to arouse their interest in the first place.

The blog….

The post on arithmetic functions set off a record-breaking week: 2254 hits. Two weeks before was only the first time I had broken 2000 hits. To top it off, October shattered the previous monthly total, with 8750 hits, the first ever over 8000. Thanks to all of you who are reading me.

The course on computational investing….