I know we've had threads on dynamical systems and control systems/theory before in the past so let's have another one
I need feedback/input from actual, practiced control engineers. All of the control systems books I've read (Nise and Ogata, mostly*) have been well and swell teaching me the academic fundamentals on control theory.But, I have a job as a New Grad control systems+signal processing engineer. My boss isn't paying me to develop cute little analog computers of LTI systems using op-amps, caps, and resistorsnone of these textbooks nor the resources I find online talk about how to design control systems from a numerical/iterative standpoint, that would be appropriate for numerical methods in software (note: yes, I can program). It's always either a focus on frequency-domain, pure analog stuff while avoiding ewww ICKY state-space methods, or naive, LTI state-space implementations where I can at best assume the authors maybe might have (if I'm lucky) thought about naive "integrate + increment" basic-bitch euler method implementations, as if the euler method doesn't explode to infinity 99% of the time if you look at it the wrong waymy question is, how/where can I learn to implement practical control systems, which involve using numerical analysis and iterative methods, with a focus on numerical/digital software implementations, for systems that might be linear or non-linear, and might-be-time-invariant-but-almost-certainly-are-time-varying? *I've just recently bought pretty much the entire Dover catalog on control systems, but all of the texts seem to have much the same issue
>>16165011You are the expert here, but shouldn't the analog versions all have some convertible form to transform an integral into an infinite sum that translates to the digital version? Like isn't this what you are looking for?More generally however, depending on how far down the control systems totem pole you are, solutions are numerically evaluated via plug and chug. 1. Try some coefficients in a given control loop2. Evaluate system behavior3. Adjust the numbers / change control loopThere might be something more in the lofty realms of aerospace, but if you need a damn GREAT model if you are expecting to control it from theory alone. I suppose you could jam the above algorithm into a somewhat generalized self-tuning loop, depending on operating parameters.
>>16165011I like Brogan's modern control theory. They have a decent amount of focus for linearization based control (which is about as good as you'll get in a lot of these circumstances). Another option could be something like model predictive control or robust control theory (which actively tune the model over time to try and make it be a better approximation of the time-varying system).If you want to get really general, Sontag's Mathematical Control Theory has a decent amount of coverage on the mathematical process of stability design. Khalil also has a pretty good book on non-linear control at a grad level.In general, numerical analysis probably will play less of a role than you are thinking in a practical controller. It may play a role in terms of using RK4 for some stabilization point estimate or something, but in general the best practice for control theory is KISS. If you can achieve stability with a simple adaptive LQG controller, you do it. Most tractable systems are pretty well approximated by time-varying quadratic dynamics, and you can much more tractably solve problems if your blocks are a good approximation than if they are a result of some sophisticated but unstable and sensitive numerical solution method.
>>16165029I'm going to take a look at those books, thanks for the recsI suppose a lot of my confusion comes from inexperience. They want me to implement these control systems, and I have a good theoretical understanding, but I haven't seen very many practical software-controlling-hardware control systems in the wild. I also don't have any senior control engineers at my company to ask, so I'm left in the dark; I don't have a good idea of what's reasonable or not.So, using my "intuition" and theoretical experience, and knowing that the controllers are implemented in nested loops among nested loops, I assumed that more advanced/proper software control systems would use more advanced numerical solving techniques like RK4 (since they're essentially numerically solving diffeqs with input and feedback from actual, physical systems)>>16165019>You are the expert hereI wish lol, I'm trying to get there>shouldn't the analog versions all have some convertible form to transform an integral into an infinite sum that translates to the digital versionYes, but that gives me the differential equation/difference equation for the system. What I'm concerned about, is after we have those equations/models, what is the standard way to then numerically integrate that differential/difference equation over time while including the feedback and state information we receive as our system evolves over timeI really want to try adaptive control but I have to get this basic stuff squared away in my head first
>>16165068From Nise do you remember the Fundamental Theorem of Control Engineering?Beyond a certain point you reach a trade-off where you only get more optimal performance by making the system more sensitive. There are robust control techniques which use adaptivity to achieve more reliable stability (generally at the cost of optimality and complexity), but in general you want to keep the system as simple as you can reasonably manage. Don't add things that are "adaptive" and picky and prone to breaking unless you really really need them. If it can adapt to be improved with good data, it certainly can be adapted to be less stable with bad data. You don't know that you'll always have good data. If you need it for stability (e.g., stochastic robust methods for triple integrators) then do it. Don't make it more complicated than it actually needs to be if a simpler controller will do the job well.
>>16165011Definitely not an expert, but you could just look at the documentation of existing software i.e. https://www.mathworks.com/help/overview/control-systems.html and it will usually explain what kind of numerical methods they implement, or at least give useful references.
>>16165094Sorry, I didn't mean to imply I wanted to apply adaptive control to everything I do, just that I was excited to learn about how to actually implement it. KISS has been burned into my brain >>16165099I've taken a quick glance at finding white papers and open-source projects that have control systems, but never got too far. I think this is the next best thing I can try while I get my footing.
>>16165130You don't need to apologize. I just used to see this a lot with my undergrads. If you haven't already taken a look at a digital controls textbook see if you can get your hands on a pdf of Nagle's digital control system analysis and design (or a cheap used copy, definitely don't go spend $200 for it full price if you can avoid it).Digital control books tend to be closer to what you'd be looking for in terms of implementation. A digital control setup like in Nagle's book can actually be implemented in code with a for loop instead of requiring complicated simulation systems like Matlab/simulink to make it work out.
What's the best introductory textbook on control theory?
>>16166310What's your level of math and what's your general background? The standard recommendation if you have taken a signals and systems class is Nise's Control Systems Engineering.If you have a fairly strong math background and can skip straight to grad level stuff Brogan's Modern Control Theory is great for state space oriented control and Astrom's Feedback Systems has great coverage of PID and frequency domain control. Some people also really like Chen's Linear System Theory and Design but I'm not a huge fan personally.
I'm about to start a PhD related to control systems but the only thing I know about control is two undergrad classes, one on state space and one on classical. Wat do.
>>16166501What will your PhD be focusing on?At any rate, really start learning about dynamical systems theory. Strogatz's Nonlinear Dynamics is a good starting point
>>16166621My advisor seems to be pretty open about different topics but the lab in general is about AI and algorithms with some neuroscience.I've had that book sitting on my shelf for years without reading the whole thing lol. I've gotten through some chapters and while it is fascinating I feel IQgapped sometimes. If I read it casually then I can grasp the basic concepts fine enough but actually doing the derivations and math takes me forever.
>>16166636I've recommended it a bunch in class already, but Brogan's modern control theory is a great linear systems introduction to the grad side of control and should give you a decent foundation to approach non-linear control if you need it.Personally I liked Khalil's non-linear systems more than Strogatz. But that's just like my opinion man.
on a similar topic, i read somewhere that older books on ODE focused on quantitative theory but lately there’s been a shift of focus towards qualitative theory because most ODE can’t be solved so it’s best to know what a solution might look like instead of knowing how to express it in closed form. any recommendations on both kinds of books?
