Week 04
Controllability
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
Controllability asks whether an input can move the state to any desired point in finite time. Rank loss in the controllability matrix shrinks the reachable subspace, and actuator placement changes B and therefore the result.
Concept map
- Controllability matrix
- Rank test
- Reachable states
- Actuator placement
Technical anchor
For an n-state model, form Cc=[B AB ... A^(n-1)B] and test rank(Cc)=n. Compare candidate actuator locations by replacing B and inspecting rank and the smallest singular value.
How I review it
Do not stop at rank; identify weakly controllable state directions and mark the physical mode that receives little actuator authority.
Connection to the full course
Unit 4 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.