Routh Arrays

So, this week, we learned about Routh arrays. It's evidently a theorem about the sign changes of the real part of the roots of a polynomial based on the coefficients. I knew a few of these from my undergrad and graduate math days, but didn't think they were very important. I kind-of knew there would be some interest in the roots of polynomials, but didn't know exactly how it would come into play.

There's a MATLAB function someone evidently wrote to compute Routh arrays https://www.mathworks.com/matlabcentral/fileexchange/58-routh-m. It's super-useful. I got my homework done this week in ~30-45 minutes using it, which I think that might have take 4 hours or more computing all the Routh arrays by hand.

I always knew there was more to Brandon Routh than met the eye, and now I found out what it is. I was always very sorry he never got to reprise his role as The Man of Steel, and was very happy to see he was cast in the Arroverse "Crisis on Infinite Earths" story arc. More "Arne Saknussemm" notes on my way to the center of the control engineering universe.

Control Engineering Degree Ahoy!

So, this Fall 2019 semester, I matriculated at UW-Platteville as a distance education MS student in their Control Engineering program. I am taking Engineering 7310 Control Engineering I. It's simply fascinating. Chapter 2 of the book should be entitled, "Everything You Wanted to Know About Transfer Functions (but Were Afraid to Ask)" - it's simply fascinating.

It appears that in according-to-Hoyle control engineering, one has ODEs on manifolds, but simply takes a coordinate patch about a point of interest, pulls back the vector field along the coordinate patch, takes the Jacobian matrix of the vector field at the point of interest and evaluates it, then finds the transfer function for that linear system of ODEs with constant coefficients via a Laplace transform. [I peeked ahead in Bullo and Lewis, and this appears to be exactly what they do (at least in certain places). This simultaneously took the wind out of my sails and gave me hope as to what can be done in the real world.] It appears there are even ways to approximate a higher-order than second-order system by the transfer function of a second-order system, so mass-spring-dashpot systems/RLC circuits are completely general by some points-of-view.

I really think control engineering is my calling. This is all just fascinating. Next semester, we go over state-space representations of control systems, which is where manifold topology evidently comes into the picture. I really wish I had know about this in my undergrad. Of course, then I likely wouldn't have a Ph.D. in manifold topology; there's always a trade-off.

But, I think I'm on the right path now. We'll see if we can get it to pay actual dividend in terms of an increased salary in the future.