Let's see, LQR is an optimal control technique for linear systems given a model.
Given a linear plant model and a PID controller, you can compute all the classic control metrics like phase and gain margins, settling time, and even how the controller would perform according to the LQR metric.
That's the theory. All linear. Theoretically it's as appropriate to apply LQR to a nonlinear plant as it is to apply PID.
If you tweak the four LQR matrices (say, for a second-order system), and couple the gain matrix with the output of a linear observer (Luenberger), that combination system should be able to generate any PID controller. It's an over-parameterization, however (which is why I think PID controllers are ubiquitous. Not many parameters). Many settings will produce the same controller.
If anyone knows a reference that discussed PID and LQR like this, I'd love to see it
Given a linear plant model and a PID controller, you can compute all the classic control metrics like phase and gain margins, settling time, and even how the controller would perform according to the LQR metric.
That's the theory. All linear. Theoretically it's as appropriate to apply LQR to a nonlinear plant as it is to apply PID.
If you tweak the four LQR matrices (say, for a second-order system), and couple the gain matrix with the output of a linear observer (Luenberger), that combination system should be able to generate any PID controller. It's an over-parameterization, however (which is why I think PID controllers are ubiquitous. Not many parameters). Many settings will produce the same controller.
If anyone knows a reference that discussed PID and LQR like this, I'd love to see it