[patrick5415]

Your whole argument is based around “if you have good model...”. This where most all control theory falls on its face. Getting a good is hard. For lqr that model better be mostly linear.

Oh, you system model isn’t first order? Now you need an estimator/Kalman filter. Or more sensors. That’s just more complexity for questionable benifit, which is why lqr is beloved by academics [0]. For anything that would be adaquetly controlled with pid, stick with that. After about 2 hours fiddling with the knobs, it’ll be close enough.

This whole idea of optimality is based on bad intuition. Which states do you care about? Why? Is that more valuable than control effort? Why? Who is doing the economic analysis to determine what ultimately costs us more money? In the end, this thing are tuned just like pid: you stop when the step response looks nice. Besides all that, for a lot of systems, and in particular flexible structures with a lot of states, “penalizing state excursions” isn’t really useful intuition to begin with for almost all state space represtations. You are better off with a pid and notch filter.

[0] I decided to complete my PhD in controls so could make statements like that with at least marginal credibility.