vault backup: 2025-02-05 14:38:06

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--- a/Observability~20250203-063556.md
+++ b/Observability~20250203-063556.md
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+Xdd = Ax + Bu
+
+Y = Cx + Du
+
+  
+  
+
+A and B decide if it is controllable
+
+C and D decide if it is observable
+
+# Controlability
+
+- System can be uncontrollable linearly, but controllable non-linearly
+  
+
+  
+
+## Linear Systems
+
+1. Compute Controllability Matrix C = [B AB … A^(n-1)B]
+2. If rank( C) = n <==> controllable
+3. Singular value decomposition (SVD) tells us about:it orders singular vectors to show most controllable to least controllable states
+
+  
+
+- If system is controllable then:
+    
+    - Arbitrary eigenvalue (pole) placementu = -Kx <==> xd = (A-BK)x
+    - Reachibility (get to any state in R^n)R_t = R_n
+
+Definitions
+
+- Reachable set R_t: all vectors in Rn that can be reached zome where sys is controllable
+- Controllability Matrix: C = [B AB … A^(n-1)B]This matrix is equivalent to an impulse response in dicrete time: basically matrix says wether the control input reaches all the states eventually.
+- Controllability Gramian:W_t = 
+    
+    - ![冖 DDzYm ](Exported%20image%2020231126171851-0.png)
+- Stabilizibility: all unstable directions (eigenvectors) are controllable.
+    
+    - Unstable and lightly damped directions should be controllable!
--- a/System/Learning~20250203-063559.md
+++ b/System/Learning~20250203-063559.md
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+[https://apmonitor.com/pdc/](https://apmonitor.com/pdc/)
+
+[https://apmonitor.com/pdc/index.php/Main/ModelSimulation](https://apmonitor.com/pdc/index.php/Main/ModelSimulation)
+
+[https://ch.mathworks.com/de/videos/tech-talks/controls.html](https://ch.mathworks.com/de/videos/tech-talks/controls.html)
+
+  
+
+  
+
+Good overview of drone control
+
+[A_review_on_drones_controlled_in_real-time.pdf](https://onedrive.live.com/embed?resid=D05036151E62BA13%213756&filename=A_review_on_drones_controlled_in_real-time.pdf&authkey=!AEvlrbu_TdPVjBw)
--- a/.stversions/OneNote/OSD/Control
+++ b/.stversions/OneNote/OSD/Control
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+- Eye()
+- Zeros()
+- Ones()
+- Eig()
+- Step()
+- Ss()
+- Ctrb() --> contrability matrix [B AB … A^(n-1)B]
+- Rank() --> rank
+- Place() --> pole placement
+- Svd(, 'econ')
--- a/System/Modelling~20250203-093639.md
+++ b/System/Modelling~20250203-093639.md
@@ -0,0 +1,10 @@
+![[eth-984-02 (1).pdf]]
+
+  
+  
+  
+  
+  
+  
+
+![[Husnic_ZelimirPhD_test.pdf]]
--- a/.stversions/OneNote/OSD/Control
+++ b/.stversions/OneNote/OSD/Control
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+==A====utomatic Control Of Aircraft & Missile ( Blakelock)==
+
+  
+> From <[https://archive.org/details/AutomaticControlOfAircraftMissileBlakelock/page/n79/mode/2up](https://archive.org/details/AutomaticControlOfAircraftMissileBlakelock/page/n79/mode/2up)>
--- a/System/Planning~20250203-063544.md
+++ b/System/Planning~20250203-063544.md
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+# Overview
+
+1. Make a model of our drone that is very simple
+2. Analyse the basic behaviour
+3. Define weaknesses and see wether it all works
+4. Iterate and include higher dynamics
+5. Iterate and include noise and material decay
+
+  
+
+As a quick intro and inspiration watch this:
+
+[https://www.youtube.com/watch?v=A7wHSr6GRnc&ab_channel=MATLAB](https://www.youtube.com/watch?v=A7wHSr6GRnc&ab_channel=MATLAB)
--- a/System/Resources~20250203-063558.md
+++ b/System/Resources~20250203-063558.md
@@ -0,0 +1,16 @@
+[https://ethz.ch/content/dam/ethz/special-interest/mavt/dynamic-systems-n-control/idsc-dam/Lectures/Control-Systems-2/Exercises/python-control.pdf](https://ethz.ch/content/dam/ethz/special-interest/mavt/dynamic-systems-n-control/idsc-dam/Lectures/Control-Systems-2/Exercises/python-control.pdf)
+
+  
+  
+
+# Books
+
+- Dynamical Systems with Applications using Python
+  
+
+  
+  
+
+Websites
+
+- [https://www.eigensteve.com/](https://www.eigensteve.com/)