From 90ef0bf0ae599832d9f27c03b9df078bb4a73f24 Mon Sep 17 00:00:00 2001 From: Dane Sabo Date: Mon, 14 Oct 2024 15:01:08 -0400 Subject: [PATCH] vault backup: 2024-10-14 15:01:08 --- .../3 Notes/Feedback Control Theory.md | 14 +++++++++++--- 4 Qualifying Exam/3 Notes/Robust Control.md | 2 +- Pasted image 20241014145054.png | Bin 0 -> 70809 bytes 3 files changed, 12 insertions(+), 4 deletions(-) create mode 100644 Pasted image 20241014145054.png diff --git a/4 Qualifying Exam/3 Notes/Feedback Control Theory.md b/4 Qualifying Exam/3 Notes/Feedback Control Theory.md index 8274f418..50d1b296 100644 --- a/4 Qualifying Exam/3 Notes/Feedback Control Theory.md +++ b/4 Qualifying Exam/3 Notes/Feedback Control Theory.md @@ -1,4 +1,5 @@ -# Chapter 1: +All info from [[doyleFeedbackControlTheory2009]] +# Chapter 1 - Introduction ![[Pasted image 20241012132644.png]] Notable signals: - r - reference or command input @@ -34,7 +35,14 @@ Notable signals: >> $$ ||\hat G||_2 = \left(\frac{1}{2\pi} \int_{-\infty}^\infty |\hat G(j\omega)|^2d\omega \right) ^{1/2} = \left( \int_{\infty}^\infty |G(t)|^2 dt \right)^{1/2}$$ ![[Pasted image 20241012135404.png]] +# Chapter 3 - Basic Feedback Loop +![[Pasted image 20241014145054.png]] +P, C, and F are system transfer functions. For a system to be **well-posed**, they cannot all be strictly proper. P is almost always strictly proper while the others aren't. +Something interesting - If $\frac{1}{1+PCF}$ is proper, then this suggests that the system output goes to zero when $j\omega\rightarrow \infty$. This isn't true in reality, because real systems will behave in a not linear way at high frequencies. - - +>[!tip] Nine System Transfer Functions +>$$\left(\matrix{x_1 \\ x_2 \\ x_3}\right) = \frac{1}{1+PCF} \left[\matrix{1 & -PF & -F \\ C & 1 & -CF \\ PC & P & 1}\right] \left(\matrix{r \\ d \\ n}\right) $$ +>**Notable Properties**: +>- All 9 transfer functions are strictly proper if 1+PCF is not strictly proper. +>- If all 9 transfer functions are stable, then the system is **internally stable** diff --git a/4 Qualifying Exam/3 Notes/Robust Control.md b/4 Qualifying Exam/3 Notes/Robust Control.md index 7be1c9b2..92445bd3 100644 --- a/4 Qualifying Exam/3 Notes/Robust Control.md +++ b/4 Qualifying Exam/3 Notes/Robust Control.md @@ -1,6 +1,6 @@ # History ## Where did Robust Control come from? -After the beginnings of modern control and the development of optimal control, John Doyle released a paper in 1978 titled [Guaranteed Margins for LQG regulators](doyleGuaranteedMarginsLQG1978a). This is a less than one page paper that basically gave birth to the robust control field, with a three word abstract: "There are none." I'm working out the kinks in this one ([[Basic Feedback Control]]), but essentially the gaussian part of the LQG is what destroys the guaranteed part of the phase and gain margins. The additional estimator involved can really screw with things. +After the beginnings of modern control and the development of optimal control, John Doyle released a paper in 1978 titled [Guaranteed Margins for LQG regulators](doyleGuaranteedMarginsLQG1978a). This is a less than one page paper that basically gave birth to the robust control field, with a three word abstract: "There are none." I'm working out the kinks in this one ([[Feedback Control Theory]]), but essentially the gaussian part of the LQG is what destroys the guaranteed part of the phase and gain margins. The additional estimator involved can really screw with things. 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