diff --git a/uni/mmme/2046_dynamics_and_control/control.md b/uni/mmme/2046_dynamics_and_control/control.md index 294773c..57f1041 100644 --- a/uni/mmme/2046_dynamics_and_control/control.md +++ b/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) diff --git a/uni/mmme/2046_dynamics_and_control/hydraulic_position_control_system.md b/uni/mmme/2046_dynamics_and_control/hydraulic_position_control_system.md new file mode 100755 index 0000000..7457790 --- /dev/null +++ b/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) + diff --git a/uni/mmme/2046_dynamics_and_control/images/vimscrot-2023-02-06T16:10:06,638264779+00:00.png b/uni/mmme/2046_dynamics_and_control/images/vimscrot-2023-02-06T16:10:06,638264779+00:00.png new file mode 100644 index 0000000..f22dde8 Binary files /dev/null and b/uni/mmme/2046_dynamics_and_control/images/vimscrot-2023-02-06T16:10:06,638264779+00:00.png differ diff --git a/uni/mmme/2046_dynamics_and_control/images/vimscrot-2023-02-06T16:10:23,750576923+00:00.png b/uni/mmme/2046_dynamics_and_control/images/vimscrot-2023-02-06T16:10:23,750576923+00:00.png new file mode 100644 index 0000000..0372ea1 Binary files /dev/null and b/uni/mmme/2046_dynamics_and_control/images/vimscrot-2023-02-06T16:10:23,750576923+00:00.png differ diff --git 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+![](./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