From adf928200eae70f3acb029179c116d66c50d52b8 Mon Sep 17 00:00:00 2001 From: Dane Sabo Date: Tue, 15 Oct 2024 17:09:14 -0400 Subject: [PATCH] vault backup: 2024-10-15 17:09:14 --- .../3 Notes/Feedback Control Theory.md | 13 ++++++++++++- 1 file changed, 12 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 06c3db35..9bce832a 100644 --- a/4 Qualifying Exam/3 Notes/Feedback Control Theory.md +++ b/4 Qualifying Exam/3 Notes/Feedback Control Theory.md @@ -74,7 +74,7 @@ Generally speaking: 2. Performance specs that involve u result in weights on S $$ \left[\matrix{e \\u}\right] = -\left[\matrix{PS & S \\ T & CS}\right] \left[\matrix{d \\ n}\right] $$ -# Chapter 4 - Plant Uncertainty +# Chapter 4 - Uncertainty and Robustness >[!important] Multiplicative Disk Perturbation >$$\tilde{P} = (1+\Delta W_2)P$$ > - P is a nominal plant transfer function @@ -86,3 +86,14 @@ $$ \left[\matrix{e \\u}\right] = -\left[\matrix{PS & S \\ T & CS}\right] \left[\ $|W_2(j\omega)|$ 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 + +>[!note] Robustness +>A controller $C$ is robust to set of plants $\mathcal{P}$ with respect to a characteristic if this characteristic holds for every plant in $\mathcal{P}$. +>> [!important] Robust Stability +>> A system is robustly stable if it is internally stable for every plant in the set $\mathcal{P}$. +>> + + + + +