Week 09
Discretizing Continuous Systems
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
A continuous model must be converted to discrete state matrices with an explicit sampling period and hold assumption before digital control. Under a zero-order hold, continuous poles map as z=e^(sT), and a large T can hide fast modes and transients.
Concept map
- Sampling period
- Zero-order hold
- Discrete state matrix
- Pole mapping
Technical anchor
Use Ad=e^(AT) and Bd=∫[0,T]e^(Aτ)B dτ. Map representative damping and natural-frequency locations from the s-plane into the z-plane.
How I review it
Compare discrete poles and step responses for several T choices, and separately quantify the difference between a simple Euler approximation and exact zero-order-hold discretization.
Connection to the full course
Unit 9 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.