mmme2046 notes on control 2 lecture

uni/mmme/2046_dynamics_and_control/control.md

@@ -3,9 +3,18 @@ author: Akbar Rahman
 date: \today
 title: MMME2046 // Control
 tags: [ mmme2046, uon, uni, control ]
-uuid: 
+uuid: 73e04dd2-ee4c-4952-a9b7-7df3930d2d2d
+lecture_slides: ./lecture_slides/Control 2 2022.pdf
 ---
 
+# Lecture Slides Corrections
+
+## p26
+
+First line should be
+
+$$C(s) = \frac{5}{s(s+5)} = \frac 1s \frac{1}{1+0.2s}$$
+
 # System and Block Diagrams
 
 # Laplace Transform
@@ -48,3 +57,39 @@ Taking the inverse gives:
 
 $$X_0 = 1 - e^{-at}$$
 
+# Non-Linearity
+
+Sometimes, components of a system will not reduce to a simple linear relationship.
+When this is the case superposition and Laplace transforms do not apply/are not valid.
+
+Reasons for this include:
+
+- saturation
+
+  ![](./images/vimscrot-2023-02-06T16:10:06,638264779+00:00.png)
+
+- backlash 
+
+  ![](./images/vimscrot-2023-02-06T16:10:23,750576923+00:00.png)
+
+- clearance 
+
+  ![](./images/vimscrot-2023-02-06T16:10:39,624151288+00:00.png)
+
+- coulomb friction 
+
+  ![](./images/vimscrot-2023-02-06T16:10:55,163385436+00:00.png)
+
+- material non-linearity
+
+  ![](./images/vimscrot-2023-02-06T16:11:17,999306580+00:00.png)
+
+- flow through an orifice  (choked flow)
+
+  ![](./images/vimscrot-2023-02-06T16:11:34,160399051+00:00.png)
+
+## Linearisation
+
+System behaviour is approximated to a linear relationship near the "nominal" operating point:
+
+![](./images/vimscrot-2023-02-06T16:13:20,353784072+00:00.png)