complete lab coursework

report.md

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+---
+author: Akbar Rahman (20386125)
+date: \today
+title: MMME3085---Lab 1 Coursework
+tags: [ mmme3085 ]
+uuid: 864e5249-a02c-4896-b274-a0a76789955c
+---
+
+\maketitle
+\newpage
+
+# Questions
+
+## Question 1
+
+- $V_{ref} = 5$ V when converting the ADC-converted value because the ADC in the Arduino can read
+  from 0 V to 5 V, therefore $n_{ADC} = 0$ means the voltage to the pin is 0 V, and $n_{ADC} = 1023$
+  means the voltage to the pin is 5 V
+- This is not the optimum use of the ADC pin as it means the resolution of the voltage measurement
+  is less precise than it could be (roughly a resolution of 5 mV instead of 3 mV)
+- The resolution could be increased by using an op-amp amplification circuit or a 3.3 V to 5 V level
+  converter circuit
+
+\newpage
+
+## Question 2
+
+- 100 % duty cycle PWM is different from all the others as it is not a wave, but just a DC voltage
+- Voltage is not zero in the OFF region because the rotational inertia is still spinning the motor,
+  which creates a back EMF, and that is the voltage being read in the OFF region.
+  Back EMF is proportional to the speed of the motor, which is why the voltage in the off region is
+  higher when the PWM duty cycle, and therefore speed of the motor, is higher.
+
+![PWM waveform at various duty cycles, labelled where the signal is on (green line) and off (red line)](./images/pwm_on_off.png)
+
+\newpage
+
+## Question 3
+
+- The difference between the ON+ and ON- is that the current will go in opposite directions,
+  resulting in the motor spinning in opposite directions
+- The default PWM frequency of pin 13 on the Arduino Mega 2560 is 976.5625 Hz [^1]
+- The audible frequency we hear is a ~1000 Hz square wave, which can be seen by the fact the period of
+  the wave in figure below is roughly 1 millisecond
+
+  ![PWM waveform at 977 Hz](./images/pwm_frequency.jpg)
+
+\newpage
+
+## Question 4
+
+![Oscilloscope trace of quadrature signal in clockwise (positive) direction. The 0 V datum point is marked by the triangles on the left hand side of the screen.](./images/q4+.jpg){ height=2in }
+
+![Oscilloscope trace of quadrature signal in anti-clockwise (negative) direction. The 0 V datum point is marked by the triangles on the left hand side of the screen.](./images/q4-.jpg){ height=2in }
+
+\newpage
+
+
+## Question 5
+
+- Since the internal timer only looks at one edge of one pulse, it cannot be used to determine the
+  direction of the rotation, which is one of the reasons to use a quadrature in the first place
+- Therefore it is a viable alternative if you only care about the speed of rotation and direction
+  is not important to the application
+
+
+## Question 6
+
+- The main shortcoming observed is that the Arduino appeared to freeze/crash when entering a PWM
+  duty cycle above ~20%
+- When this issues occurs, the Arduino is too busy running the function called by interrupts
+  to be able to print to serial, hence appearing to have frozen/crashed
+- This is due to the fact that at higher speeds, the `updateEncoderStateMachine()` function in
+  triggered by the digital pin interrupts (which take higher priority) so frequently that
+  the `loop()` function is not able to run, due to a lack of free CPU cycles, and therefore serial
+  outputs are not printed and inputs not read
+- This effectively makes the counter useless as it cannot be read from as the Arduino is not able
+  to handle any other processing tasks
+- Additionally, there is a good chance that the Arduino is not able to run all the calls to
+  `updateEncoderStateMachine` in real time, and so the value of `count` would be incorrect (of course
+  this does not matter since we do not have the CPU cycles to do anything with `count` anyway)
+
+
+[^1]: `MotorEncoderAAR.ino` defines that pin 13 is used for PWM output. Pin 13 is connected to timer 0 which defaults to 976.5625 Hz (<https://playground.arduino.cc/Main/TimerPWMCheatsheet/>)