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

Chapter 1:

! 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)|