vault backup: 2024-10-12 13:36:04

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
+> $$||u||_\infty = \text{sup}_t |u(t)|$$
+