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)

uni/mmme/2046_dynamics_and_control/hydraulic_position_control_system.md

@@ -0,0 +1,25 @@
+---
+author: Akbar Rahman
+date: \today
+title: MMME2046 // Hydraulic Position Control System
+tags: []
+uuid: 0007f41b-73e0-4e3f-987b-42cde198dbcf
+lecture_slides: ./lecture_slides/Control 2 2022.pdf
+---
+
+This system allows for a great amplification of force, whilst still allowing for manual override in
+the case of power failure.
+It can also be adapted to angular displacements using a rack and pinion.
+
+![](./images/vimscrot-2023-02-06T16:20:17,316986199+00:00.png)
+
+1. Operator changes setting ($x_i$), Piston ($x_o$) is fulcrum
+2. Spool valve lets fluid into cylinder
+
+   ![](./images/vimscrot-2023-02-06T16:25:06,170856014+00:00.png)
+
+3. $x_i$ becomes fulcrum and piston moves until valve closes
+
+
+   ![](./images/vimscrot-2023-02-06T16:26:16,876441767+00:00.png)
+

uni/mmme/2046_dynamics_and_control/stability.md

@@ -0,0 +1,43 @@
+---
+author: Akbar Rahman
+date: \today
+title: MMME2046 // Stability
+tags: []
+uuid: 2b0062f7-cc8a-4e52-8e12-1eb731e056af
+lecture_slides: ./lecture_slides/Control 2 2022.pdf
+---
+
+# Introduction to Transient and Steady-State Responses
+
+![](./images/vimscrot-2023-02-06T17:03:18,594676084+00:00.png)
+
+A stable system settles.
+An unstable system has increasing amplitude in its fluctuations.
+
+The steady-state error is how accurate a system will be once settled.
+
+If we subject control systems to standard input we can compare and tune their performance.
+
+Consider three inputs:
+
+i. step input
+ii. ramp input (linear change with time)
+iii. harmonic input (considered in vibration)
+
+These inputs are useful because they
+
+- are easily to apply in practice
+- approximate to operating conditions in control systems
+
+
+![](./images/vimscrot-2023-02-06T17:10:11,891784480+00:00.png)
+
+# Practical Measurement of Transient Response
+
+![](./images/vimscrot-2023-02-06T17:10:48,755879402+00:00.png)
+
+a. maximum overshoot
+b. number of oscillations
+c. rise time
+d. settling time
+e. steady state error