From 1cc63c4309753981143f9aaf8eae13be7956f144 Mon Sep 17 00:00:00 2001 From: Dane Sabo Date: Tue, 15 Oct 2024 17:01:01 -0400 Subject: [PATCH] vault backup: 2024-10-15 17:01:01 --- 4 Qualifying Exam/3 Notes/Feedback Control Theory.md | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/4 Qualifying Exam/3 Notes/Feedback Control Theory.md b/4 Qualifying Exam/3 Notes/Feedback Control Theory.md index efddcf68..06c3db35 100644 --- a/4 Qualifying Exam/3 Notes/Feedback Control Theory.md +++ b/4 Qualifying Exam/3 Notes/Feedback Control Theory.md @@ -83,4 +83,6 @@ $$ \left[\matrix{e \\u}\right] = -\left[\matrix{PS & S \\ T & CS}\right] \left[\ > If $||\Delta||_\infty <1$: > $$ \left| \frac{\tilde P (j\omega)}{P(j\omega)} - 1 \right| \leq | W_2(j\omega) | \text{ , } \forall \omega$$ -$|W_2(j\omega)|$ is the uncertainty profile. This inequality describes a disk in teh complex plane: at each frequency the point P~/P lies in the disk with center 1, radius |W_2|. \ No newline at end of file +$|W_2(j\omega)|$ is the uncertainty profile. This inequality describes a disk in teh complex plane: at each frequency the point P~/P lies in the disk with center 1, radius |W_2|. + +W_2 is basically a transfer function that will always be greater in magnitude than that P~/P -1