first draft of submission

src/submission.md

@@ -1,9 +1,8 @@
 ---
 author: Akbar Rahman (20386125)
 date: \today
-title: Change Me
-tags: [ change_me ]
-uuid: Change Me
+title: MMME3085---Lab 2 Coursework
+tags: [ mmme, mmme3086 ]
 documentclass: article
 geometry:
     - margin=1in
@@ -15,4 +14,146 @@ geometry:
 \tableofcontents
 \newpage
 
-# Header
+# Question 1
+
+As you increase the proportional gain, you increase the responsiveness of the motor to error,
+but it is easy to go too high and cause the motor to oscillate around the target position.
+This is because the motor current is set proportional to the error.
+This means that if the motor is spinning too quickly, the proportional control will not slow
+down the motor in time to avoid overshoot.
+Additionally, if the target position is set too close to the motor, the proportional control
+maybe not push enough current to motor to actually get it spinning in some cases.
+
+# Question 2
+
+When derivative control is added at low levels (0.02) it reduces the oscillations.
+This is because derivative control only considers the rate of change of of the error
+and therefore tries to bring the rate of change to zero.
+
+# Question 3
+
+There are two if statements in the loop function as the controller will work best and be able to respond
+to changes faster if the control functions are run more frequently.
+The faster the better.
+However, the Arduino does not really need to print to serial every time as it is only used to ensure
+the Arduino is running properly.
+
+If `prevMillisControl` and `prevMillisPrint` was replaced with just one variable, the `printLoop` function
+would never run as the variable would have been updated to equal `currentMillis` before the print loop's
+if statement will check its condition.
+
+# Question 4
+
+First the library is `include`d on line 4:
+
+```c
+#include <PID_V1.h>
+```
+
+Then a PID object is created using the `myPID` function on line 48.
+This object holds all the properties of the PID controller including values of $K_p$, $K_i$, and $K_d$,
+as well as a pointers to variables with the current motor position, speed, and set point.
+
+```c
+PID myPID(&encoderPosnMeasured, &percentSpeed, &positionSetPoint, Kp, Ki, Kd, DIRECT);
+```
+
+Some initialisation is run in `setup` on lines 89 and 90:
+
+```c
+  myPID.SetOutputLimits(-100,100);
+  myPID.SetMode(AUTOMATIC);
+```
+
+Then the main control loop starts.
+The `loop` function runs the `controlLoop` function every 20 milliseconds (as defined by
+`controlInterval`) on line 101.
+The `controlLoop` function retrieves the current motor position and stores it in the variable
+that the PID controller has a pointer to.
+`myPID.Compute()` is then called to recompute the motor speed required to get to the set point
+and this is stored in the `percentSpeed` variable as the controller has a pointer to it.
+This new speed is passed to the `driveMotorPercent` function to update the motor's speed.
+
+# Question 5
+
+The mathematically complex operations in `loop()` as it is run infrequently.
+This is because it is inside an if statement with condition `convertNewNumber()`, which
+returns `false` if there is no new data to convert (i.e. if there has not been any serial input
+since the last loop).
+Essentially, the complex operations only run once per serial input, meaning it is run very infrequently
+compared to how many times the loop runs.
+
+# Question 6
+
+Complex operations in `computeNewSpeed()` have been avoided because this function runs very frequently
+(on the order of microseconds).
+Therefore it is important that the function does not consume too many processor cycles,
+else the Arduino will be able to do little else.
+
+# Question 7
+
+If the stepper motor is run too quickly, steps will be skipped and it will not accelerate or
+accelerate slowly.
+It also makes a different noise to normal operation.
+
+This is because the pole pairs of the motor will be activated too soon if attempting to spin
+the motor too fast.
+If they are activated too soon, they will not have the desired effect of speeding up the rotation
+of the shaft, as the magnets of the motor will not be aligned as needed.
+
+This is also why the steppers use a ramp function, so that the shaft has time accelerate to the
+desired speed without skipping steps.
+
+# Question 8
+
+```{ .matplotlib caption="A plot of velocity and acceleration for SimplisticRampStepper" dpi=150 }
+import numpy as np
+import matplotlib.pyplot as plt
+
+TIME = 'Time_s'
+SPEED = 'Speed_stepss'
+ACCEL = 'Accel_stepss2'
+POS = 'Positn_steps'
+STEP = 'Step_time_ticks'
+
+data = np.genfromtxt("csv/SimplisticRampStepper_out_50.csv",
+                 delimiter=",", names=True, dtype=float)
+
+fig, ax1 = plt.subplots()
+ax2 = ax1.twinx()
+
+ax1.plot(data[TIME], data[SPEED], label='Speed [steps/s]', color='tab:blue')
+ax2.plot(data[TIME], data[ACCEL], label='Acceleration [steps/s^2]', color='tab:red')
+ax1.set_ylabel('Speed [steps/s]')
+ax2.set_ylabel('Acceleration [steps/s^2]')
+
+ax1.set_xlabel("Time [s]")
+
+fig.tight_layout()
+```
+
+```{ .matplotlib caption="A plot of velocity and acceleration for LeibRampStepper" dpi=150 }
+import numpy as np
+import matplotlib.pyplot as plt
+
+TIME = 'Time_s'
+SPEED = 'Speed_stepss'
+ACCEL = 'Accel_stepss2'
+POS = 'Positn_steps'
+STEP = 'Step_time_ticks'
+
+data = np.genfromtxt("csv/LeibRampStepper_out_50.csv",
+                 delimiter=",", names=True, dtype=float)
+
+fig, ax1 = plt.subplots()
+ax2 = ax1.twinx()
+
+ax1.plot(data[TIME], data[SPEED], label='Speed [steps/s]', color='tab:blue')
+ax2.plot(data[TIME], data[ACCEL], label='Acceleration [steps/s^2]', color='tab:red')
+ax1.set_ylabel('Speed [steps/s]')
+ax2.set_ylabel('Acceleration [steps/s^2]')
+
+ax1.set_xlabel("Time [s]")
+
+fig.tight_layout()
+```