Assume that we have a LQG controller and our state space model is known. Now we are implementing an integral action into the LQG controller, so it would be a LQGI controller.
The LQGI controller are very similar to a PID controller, due to the proportional, integral and derivative actions. But the LQGI has one thing that the PID doesn't have - observer. In this case, the observer has a kalman filter.
So my question is: Is it possible to "split" the LQGI controller, into several PID controllers, with an observer?
Let's say we are having a MDOF system for 3 hanging masses with dampers and springs. That would be 3 PID and 3 observers, if we convert the LQGI controller into PID's?
The reason why I'm asking this question is because I want to build a LQGI with only analog electrical components. Matrix algebra is not easy in analog electrica components, but creating a PID with analog electrical components is super easy!