Control from estimated state
Does estimated-state feedback recover like full-state LQR after the same kick?
Try it in the current lab
Pin this LQG run, switch to full-state LQR, then compare with the same kick and Q/R.
Compare LQR and LQG with the same Q/R and kick. LQR reads true state, so only LQG responds to sensor noise; watch estimate error, cart position and force.
The lab recalculates after a setting changes. Pin a run before changing one variable; the response and control-effort plots share the same replay time. PID experiments also show the P/I/D terms; estimator experiments show measured and estimated states.
What the system is doing
LQG feeds the Kalman estimate into the LQR gain. It needs both a plant model and uncertainty assumptions; saturation and nonlinear motion break textbook optimality guarantees.
Connect the design method
The observer now closes the loop: its estimated four-state vector enters the same LQR gain. Pin this run and switch to full-state LQR with the same kick and Q/R. Differences reveal the effect of estimation, but saturation and model mismatch still matter.
u = −K x̂