Increasing observer bandwidth may transmit more measurement noise into the inferred velocity and feedback force. This is a deterministic Luenberger observer, not a covariance-optimized Kalman filter. Noise is a seeded uniform offset held for 20 ms; the underlying position measurement is continuous in this teaching model.
Make one fair comparison
Pin speed ratio 1 with 0.01 m bounded position noise. Change only the ratio to 5. Inspect estimated velocity and applied force after the startup. Keep the same seed and noise amplitude.
Before moving a setting, write which signal you expect to change and why. A faster-looking curve alone does not explain the mechanism. Keep the initial state and all other settings visible in the pinned run.
Fast estimation is a tradeoff
For the ideal unsaturated observer-based loop, the combined eigenvalues are those of A−BK and A−LC. This separation principle makes design manageable. It does not say that transient peaks, saturation or noise are harmless. With measurement noise n, error dynamics include −Ln; large observer gains can magnify its effect on velocity estimates and the resulting control force.
First compare recovery with no noise and a deliberately wrong initial estimate. Then reset that initial mismatch and compare observer speed using the same seeded noise. This separates two effects that a single busy plot can hide. Kalman filtering introduces statistical process and measurement assumptions to choose correction gains; choosing a fast Luenberger observer is not the same procedure.
What to change next
If the fast observer removes initial error but produces larger force fluctuations, separate startup requirements from steady noise tolerance. Try a moderate observer bandwidth first. A Kalman model can later formalize noise assumptions, but it will still need validation against the actual sensor and plant.
Increasing observer bandwidth may transmit more measurement noise into the inferred velocity and feedback force. This is a deterministic Luenberger observer, not a covariance-optimized Kalman filter. Noise is a seeded uniform offset held for 20 ms; the underlying position measurement is continuous in this teaching model.
CHECK YOUR UNDERSTANDING: If the observer trusts each noisy position reading more strongly, what happens to the control effort?
Increasing observer bandwidth may transmit more measurement noise into the inferred velocity and feedback force. This is a deterministic Luenberger observer, not a covariance-optimized Kalman filter. Noise is a seeded uniform offset held for 20 ms; the underlying position measurement is continuous in this teaching model.