Week 05
Observability
I use the saved simulation video as a starting point to revisit state-space control, observers, and digital control.
What I connect in this unit
Observability determines whether output history and known inputs can distinguish the initial state. Rank deficiency creates hidden modes whose internal states produce identical outputs, and sensor selection changes this through C.
Concept map
- Observability matrix
- Rank test
- Hidden modes
- Sensor selection
Technical anchor
For an n-state model, stack Oc=[C; CA; ...; CA^(n-1)] and test rank(Oc)=n. Change C for each sensor candidate and inspect which eigenvector is nearly orthogonal to the measurement.
How I review it
Compare output curves from two initial states differing in one component, then consider separately whether a small distinction remains usable in measurement noise.
Connection to the full course
Unit 5 of 12. This study sequence connects the system flow visible in the video with standard control topics; it is not a claim about lecture weeks.