What? If you have a good model of your system then you can (relatively easily) turn it into an optimization problem and use a LQR to choose gains for you. It’s true, this method still gives you knobs you might have to tune (Q and R), but these are easily conceptualized because they slide the cost of state excursions and control effort along a Pareto boundary. That means that you can get optimal PID gains just by saying how much you penalize a state excursion vs. how much you penalize control effort (e.g. distance from your reference point v.s. fuel use, or something like that.)
It’s also certainly true that a LQR won’t help you if you have no a priori knowledge of your system, but for many of the mechanisms we need to control this isn’t a problem.
It’s also certainly true that a LQR won’t help you if you have no a priori knowledge of your system, but for many of the mechanisms we need to control this isn’t a problem.