Obsidian/4 Qualifying Exam/3 Notes/Feedback Control Theory.md

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# Chapter 1:
![[Pasted image 20241012132644.png]]
Notable signals:
- r - reference or command input
- e - tracking error
- u - control signal, controller output
- d - plant distrurbance
- y - plant output
- n - sensor
# Chapter 2 - Norms
>[!note] Signal Norms
>1-Norm
> $$||u||_1 = \int_{-\infty}^{\infty} |u(t)|dt$$
> 2-Norm
> $$||u||_2 = \left(\int_{-\infty}^{\infty} u(t)^2 dt \right)^{1/2}$$
> $\infty$-Norm
> $$||u||_\infty = \text{sup}_t |u(t)|$$