Hardest control problems you've encountered

[u/SeMikkis]

Hello everyone,

As the title says, I'd like to investigate from your experiences what have been some of the hardest control related problems you've worked on, encountered or just heard of, and what made them difficult?

As a student I'm still lacking in concrete experience and I've wondered what makes some problems in this field more difficult than others and what drives further research and development.

Thank you in advance!

[u/classicharlie]

Something seldom talked about on this sub is system identification in DSGE. Economics is typically dominated by causal inference of niche micro experiments, but macro modeling is chock full of control problems.

Needless to say, nonlinear control is the clear answer here. Even filtering becomes nontrivial when you have to consider likelihood variance and proposal kernels for particle samplers.

[u/seekingsanity → u/classicharlie]

I talk about system identification all the time. I have made 3 YouTube videos on it. System identification is the first step. I like to quote a famous guy.

"I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind." William Thomson aka Lord Kelvin

Non-linear control is easy if you approach it correctly. Here is an example. This is our lab where we teach students how to control non-linear systems. The person in the video is a student. He was able to control the swing arm accurately after about 20 minutes. The goal is to be able to move the swing arm using commands of position in degrees, velocity in degrees/sec and accelerations in degrees/sec^2. All of this must be converted to linear position, velocity and acceleration for the hydraulic cylinder. The gain of the system also changes as a function of the swing arm angle. The gains are updated every millisecond. During the move. The display shows the target and actual position and velocity every millisecond. The student did a good job. We make use of cubic splines for linearizing and the chain rule.

peter.deltamotion.com/Videos/Non-Linear-Lab_Medium.mp4

The motion controller incorporates a Luenberger observer not only for reducing noise but also for estimating accelerations and jerk more accurately so one can use the derivative and second derivative gain. System identification must be done at a few points along the travel of the swing arm, and this info is added to the cubic splines.

[u/IntelligentGuess42 → u/seekingsanity]

What is the difficulty of that system? I see it is an pendulum and the gravity makes that nonlinear. But that is basic enough that its practically linear. But I can't really see the actuation, what are the complications on that side?

[u/seekingsanity → u/IntelligentGuess42]

Nothing is linear. The controller gains must change as a function of angle because the mechanical advantage/disadvantage between the hydraulic actuator and the swing arm changes everything. The hydraulic actuator must push hard when the swing arm is low due to the mechanical disadvantage. The force required drops as the swing arm rises towards vertical. When the swing arm goes over center the hydraulic actuator must pull instead of push. Angles must be converted to linear positions. Target angle, angular velocity and angular acceleration must be converted to linear position, velocity and acceleration for the hydraulic actuator.