add zip recipe to makefile

Makefile

@@ -20,6 +20,11 @@ $(SUBMISSION_FILENAME): .PHONY $(OUT_DIR)
 	$(TEX) $(SRC_DIR)/submission.md -o $(OUT_DIR)/$@ $(TEX_FLAGS)
 	mv mermaid-filter.err $(OUT_DIR)
 
+zip: .PHONY $(OUT_DIR)
+	rm -rf $(OUT_DIR)/lab_2_submission_akbar_alvi_rahman_20386125.zip
+	zip -j $(OUT_DIR)/lab_2_submission_akbar_alvi_rahman_20386125 $(OUT_DIR)/*.pdf
+	zip -r $(OUT_DIR)/lab_2_submission_akbar_alvi_rahman_20386125 images csv src/lab_2
+
 $(OUT_DIR):
 	mkdir -p $(OUT_DIR)
 

src/lab_2/LeibRampStepper.c

@@ -0,0 +1,204 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <windows.h>
+#include <math.h>
+
+/* Only needed in Windows program to maintain compatibility with Arduino version of C/C++ */
+#define bool BOOL
+#define true 1
+#define false 0
+const bool FWDS = true;
+const bool BWDS = false;
+
+const long ticksPerSec = 1000; // ms on PC
+// on Arduino it is 1E6 for micros (for s/w) or 1.6E7 for 62.5 ns ticks (for h/w)
+
+/* Function prototypes: */
+/* PC only, don't need function prototypes on Arduino as they get added within compilation process */
+void moveOneStep();
+void computeNewSpeed();
+long computeStepsToGo();
+void goToPosition(long newPosition);
+void printLoop();
+long millis(void);
+
+/* Note: we are using global variables ONLY to preserve compatibility with the Arduino program structure.
+   They should not normally be used in C or C++ programs as they make for a poor software design. */
+/* Global variables relating to stepper motor position counting etc. */
+long stepsToGo;             /* Number of steps left to make in present movement */
+long targetPosition;        /* Intended destination of motor for given movement */
+volatile long currentPosition = 0;   /* Position in steps of motor relative to startup position */
+float maxSpeed;            /* Maximum speed in present movement (not nec. max permitted) */
+bool direction;             /* Direction of present movement: FWDS or BWDS */
+
+/* Global variables used in simplistic and Leib Ramp algorithms */
+volatile float p;   /* Step interval in clock ticks or microseconds */
+float p1, ps;       /* Minimum and maximum step periods */
+float deltaP;      /* You'll be able to get rid of this later */
+float R;           /* Multiplying constant used in Eiderman's algorithm */
+
+/* Global variable used for noting previous time of a step in timed loop and for calculating speed and accel */
+long prevStepTime=0;
+long millisAtStart;
+float prevSpeed=0.0;
+
+/* Define permissible parameters for motor */
+// For testing on PC only, not for use in Arduino program: try movements in order of 50-100 steps
+float accelSteps=20; /* leave this as a variable as we may over-write it */
+const float minSpeed = 1.0;
+const float maxPermissSpeed = 20.0;
+const float maxAccel = 10.0;
+
+int main()
+{
+    unsigned long currentMillis = millis();
+    prevStepTime = 0;
+    long positionToMoveTo;
+    while(true)
+    {
+        printf("Enter position to move to in profile (or 999 to terminate)\n");
+        scanf("%ld", &positionToMoveTo);
+        if (positionToMoveTo==999) break;
+        printf("        Time (s),  Speed (steps/s), Accel (steps/s^2),  Posit'n (steps), Step time (ticks)\n");
+
+        goToPosition(positionToMoveTo);
+
+        /* -------------------------------------------------------------- */
+        /* Start of pre-computation code - only executed once per profile */
+        // STEP 1																 
+        // Define number of steps in acceleration phase using Equation (3)
+        accelSteps = (long)(( maxPermissSpeed * maxPermissSpeed - minSpeed * minSpeed) / ( 2.0 * (float)maxAccel)); // Equation 4 but need to consider initial speed
+        stepsToGo = computeStepsToGo();
+        maxSpeed = maxPermissSpeed;
+        if (2 * accelSteps > stepsToGo)
+        {
+            // STEP 2 
+			      // Define maximum speed in profile and number of steps in acceleration phase 
+            // Use Equations (4) and (5)
+            maxSpeed = sqrt(minSpeed * minSpeed + stepsToGo * maxAccel); // Modified version of eq. 5
+            accelSteps = (long)(stepsToGo / 2);
+        }
+
+        // STEPS 3 and 5														  
+        // Calculate initial value of and p1 and R    Set p = p1
+        p1 = (float)ticksPerSec / sqrt( minSpeed * minSpeed + 2 * maxAccel); // Eq 17 incorporating initial velocity
+        p = p1;
+        R = (float) maxAccel / ((float)ticksPerSec * (float)ticksPerSec); // Eq 19
+        ps = ((float)ticksPerSec) / maxSpeed; // STEP 4 Eq 7 in paper
+
+        /* End of pre-computation code                                    */
+        /* -------------------------------------------------------------- */
+        millisAtStart = millis(); /* Needed only to tabulate speed vs. time */
+
+        /* Timed loop for stepping, and associated coding */
+        while(stepsToGo > 0)
+        {
+            currentMillis = millis();
+            if (currentMillis - prevStepTime >= p)
+            {
+               moveOneStep();
+               prevStepTime = currentMillis;
+               computeNewSpeed();
+            }
+        }
+    }
+    return 0;
+}
+
+/* Only needed for compatibility with Arduino program because millis() is not a native Windows API function */
+long millis(void)
+{
+    return GetTickCount();
+}
+
+/* Move a single step.  */
+void moveOneStep()
+{
+  if (p != 0) /* p=0 is code for "don't make steps" */
+  {
+    // Print to screen instead of making a step
+    if (direction == FWDS)
+    {
+      currentPosition++;
+    }
+    else
+    {
+      currentPosition--;
+    }
+    
+    /* Instead of actually making step, print out parameters for current step */
+    float speed = (float)(ticksPerSec)/p;
+    float accel = (float)(ticksPerSec)*(speed-prevSpeed)/p;
+    printf("%16.3f, %16.3f,  %16.3f, %16ld, %16.3f\n", 0.001*(millis()-millisAtStart), speed, accel, currentPosition, p);
+    prevSpeed = speed;
+  }
+}
+
+/* Calcuate new value of step interval p based on constants defined in loop() */
+void computeNewSpeed()
+{
+    float q;
+    float m;
+    stepsToGo = computeStepsToGo();
+
+    /* ----------------------------------------------------------------- */
+    /* Start of on-the-fly step calculation code, executed once per step */
+    if (stepsToGo == 0)  //  STEP 6a
+    {
+        p = 0; // Not actually a zero step interval, used to switch stepping off
+        return;
+    }
+    else if (stepsToGo >= accelSteps && (long)p > (long)ps) // Speeding up
+    {
+        m = -R;  // Equation (9)
+    }
+    else if (stepsToGo <= accelSteps)  // Slowing down
+    {
+        m = R;  // Equation 10
+    }
+    else  //  Running at constant speed
+    {
+        m = 0;  // Equation (11)
+    }
+    /* else p is unchanged: running at constant speed */
+
+    /* Update to step interval based on Eiderman's algorithm, using temporary variables */
+    // STEP 6b, c and d using Equations (12) and (13)
+    q = m * p * p; // this is a part of optional enhancement
+    p = p * ( 1 + q + 1.5 * q * q); // this is an enhanced approximation -equation [22]
+    /* Need to ensure rounding error does not cause drift outside acceptable interval range:
+      replace p with relevant bound if it strays outside */
+    if (p > p1)
+    {
+        p = p1;
+    }
+    /* End of on-the-fly step calculation code */
+    /* ----------------------------------------------------------------- */
+}
+
+/* Work out how far the stepper motor still needs to move */
+long computeStepsToGo()
+{
+    if (direction == FWDS)
+    {
+        return targetPosition - currentPosition;
+    }
+    else
+    {
+        return currentPosition - targetPosition;
+    }
+}
+
+/* Set the target position and determine direction of intended movement */
+void goToPosition(long newPosition)
+{
+    targetPosition = newPosition;
+    if (targetPosition - currentPosition > 0)
+    {
+        direction = FWDS;
+    }
+    else
+    {
+        direction = BWDS;
+    }
+}

src/lab_2/LeibRampStepper/LeibRampStepper.ino

@@ -0,0 +1,286 @@
+/* Stepper motor demonstration program written by Arthur Jones,
+   4 November 2018.  Implements a simplistic and ineffective ramping 
+   algorithm but provides framework for implementation of LeibRamp 
+   algorithm described by Aryeh Eiderman, http://hwml.com/LeibRamp.pdf
+
+   Makes use of background work and some aspects of code developed
+   by Choaran Wang, 2017-18. This in turn incorporates some ideas
+   used in the AccelStepper library:
+   https://www.airspayce.com/mikem/arduino/AccelStepper/
+
+   Serial input aspects are based closely upon:
+   http://forum.arduino.cc/index.php?topic=396450
+   Example 4 - Receive a number as text and convert it to an int
+   Modified to read a long */
+
+const int stepPin = 13;
+const int dirPin = 9;
+const bool FWDS = true;
+const bool BWDS = false;
+
+const long ticksPerSec = 1000000; // microseconds in this case
+
+
+/* Define permissible parameters for motor */
+// For testing by watching LED: try movements in order of 100 steps
+//float accelSteps=20; /* leave this as a variable as we may over-write it */
+//const float minSpeed = 2.0;
+//const float maxPermissSpeed = 20.0;
+//const float maxAccel = 10.0;
+//const long stepLengthMus = 10000;
+// For lab testing with real motor: try movements in the order of 3000 steps
+ float accelSteps=1000; /* leave this as a variable as we may over-write it */
+ const float minSpeed=10.0;
+ const float maxPermissSpeed=100000000.0;
+ const float maxAccel=500.0;
+ const long stepLengthMus=100;
+
+/* Intervals in milliseconds for user-defined timed loops */
+const long printInterval = 1000;
+
+/* Global variables used for loop timing */
+unsigned long prevMillisPrint = 0;        /* stores last time values were printed */
+
+/* Global variables used in serial input */
+enum {numChars = 32};
+char receivedChars[numChars];    /* an array to store the received data */
+long dataNumber = 0;             /* Value read from serial monitor input */
+boolean newData = false;
+
+/* Global variables relating to stepper motor position counting etc. */
+long stepsToGo;             /* Number of steps left to make in present movement */
+long targetPosition;        /* Intended destination of motor for given movement */
+volatile long currentPosition = 0;   /* Position in steps of motor relative to startup position */
+double maxSpeed;            /* Maximum speed in present movement (not nec. max permitted) */
+bool direction;             /* Direction of present movement: FWDS or BWDS */
+
+volatile float p;   /* Step interval in clock ticks or microseconds */
+float p1, ps;       /* Minimum and maximum step periods */
+double deltaP;      /* You'll be able to get rid of this later */
+double R;           /* Multiplying constant used in Eiderman's algorithm */
+
+/* Global variable used for noting previous time of a step in timed loop */
+long prevStepTime;
+
+void setup()
+{
+    long stepsToGo = 0;
+    currentPosition = 0;
+    goToPosition(dataNumber);
+    pinMode(stepPin, OUTPUT);
+    pinMode(dirPin, OUTPUT);
+    Serial.begin(9600);
+    Serial.println("Enter target position in number of steps and hit return");
+  
+    prevStepTime = micros();
+}
+
+void loop()
+{
+    unsigned long currentMillis = millis();
+    unsigned long currentMicros;
+    recvWithEndMarker();
+    stepsToGo = computeStepsToGo();
+    if (convertNewNumber())
+    {
+        Serial.print("Converted number: datanumber is: ");
+        Serial.println(dataNumber);
+        // Only get to this stage if there was new data to convert
+        if (stepsToGo <= 0)
+        {
+            // Only get to this stage if not busy, otherwise will have thrown away input
+            goToPosition(dataNumber);
+            Serial.print("Got target position: ");
+            Serial.println(targetPosition);
+      
+      
+            /* Define number of steps in acceleration phase using Equation (3) */
+            accelSteps = long(( maxPermissSpeed * maxPermissSpeed) / ( 2.0 * (double)maxAccel)); // Equation 4 but need to consider initial speed
+            stepsToGo = computeStepsToGo();
+            maxSpeed = maxPermissSpeed;
+            
+            if (2 * accelSteps > stepsToGo)
+            {
+               // Define maximum speed in profile and number of steps in acceleration phase 
+                maxSpeed = sqrt(minSpeed * minSpeed + stepsToGo * maxAccel); // Modified version of eq. 5
+                accelSteps = (long)(stepsToGo / 2);
+            }
+            ps = ((double)ticksPerSec) / maxSpeed; // Eq 7
+      
+            p1 = (double)ticksPerSec / sqrt( minSpeed * minSpeed + 2 * maxAccel); // Eq 17 but need initial velocity
+            p = p1;
+            R = (double) maxAccel / ((double)ticksPerSec * (double)ticksPerSec); // Eq 19
+        }
+    }
+  
+    /* Timed loop for stepping */
+    currentMicros = micros();
+    if (currentMicros - prevStepTime >= p)
+    {
+        moveOneStep();
+        prevStepTime = currentMicros;
+        computeNewSpeed();
+    }
+  
+    /* Timed loop for printing */
+    if (currentMillis - prevMillisPrint >= printInterval)
+    {
+        // save the last time you printed output
+        prevMillisPrint = currentMillis;
+        printLoop();
+    }
+}
+
+/* Move a single step, holding pulse high for delayMicroSeconds */
+void moveOneStep()
+{
+    if (p != 0) /* p=0 is code for "don't make steps" */
+    {
+        digitalWrite(stepPin, HIGH);
+        if (direction == FWDS)
+        {
+            /* Is something missing here? */
+            digitalWrite(dirPin, HIGH);
+            currentPosition++;
+        }
+        else
+        {
+            /* Is something missing here? */
+            digitalWrite(dirPin, LOW);
+            currentPosition--;
+        }
+        delayMicroseconds(stepLengthMus);
+        digitalWrite(stepPin, LOW);
+    }
+}
+
+/* Calcuate new value of step interval p based on constants defined in loop() */
+void computeNewSpeed()
+{
+    double q;
+    double m;
+    stepsToGo = computeStepsToGo();
+
+    /* ----------------------------------------------------------------- */
+    /* Start of on-the-fly step calculation code, executed once per step */
+    if (stepsToGo == 0)
+    {
+        p = 0; // Not actually a zero step interval, used to switch stepping off
+        return;
+    }
+    else if (stepsToGo > accelSteps && (long)p > long(ps))  //Speeding up
+    {
+        m = -R;  // definition following equation 20
+    }
+    else if (stepsToGo <= accelSteps)   //  Slowing down
+    {
+       m = R;
+    }
+    else   //  Running at constant speed
+    {
+       m = 0;
+    }
+  
+    /* Update to step interval based on Eiderman's algorithm, using temporary variables */
+    q = m * p * p; // this is a part of optional enhancement
+    p = p * ( 1 + q + 1.5 * q * q); // this is an enhanced approximation -equation [22]
+    /* Need to ensure rounding error does not cause drift outside acceptable interval range: 
+       replace p with relevant bound if it strays outside */
+    if (p < ps)
+    {
+        p = ps;
+    }
+    if (p > p1)
+    {
+        p = p1;
+    }
+    /* End of on-the-fly step calculation code */
+    /* ----------------------------------------------------------------- */
+}
+
+/* Work out how far the stepper motor still needs to move */
+long computeStepsToGo()
+{
+    if (direction == FWDS)
+    {
+        return targetPosition - currentPosition;
+    }
+    else
+    {
+        return currentPosition - targetPosition;
+    }
+}
+
+/* Set the target position and determine direction of intended movement */
+void goToPosition(long newPosition)
+{
+    targetPosition = newPosition;
+    if (targetPosition - currentPosition > 0)
+    {
+        direction = FWDS;
+    }
+    else
+    {
+       direction = BWDS;
+    }
+}
+
+/* Receive data from serial port finishing with "newline" character.
+   Based on http://forum.arduino.cc/index.php?topic=396450 Example 4 */
+void recvWithEndMarker()
+{
+    static byte ndx = 0;
+    char endMarker = '\n';
+    char rc;
+  
+    if (Serial.available() > 0) 
+    {
+        rc = Serial.read();
+    
+        if (rc != endMarker) 
+        {
+            receivedChars[ndx] = rc;
+            ndx++;
+            if (ndx >= numChars) 
+            {
+               ndx = numChars - 1;
+            }
+        }
+        else 
+        {
+            receivedChars[ndx] = '\0'; // terminate the string
+            ndx = 0;
+            newData = true;
+        }
+    }
+}
+
+bool convertNewNumber()
+/* Converts character string to long integer only if there are new
+       data to convert, otherwise returns false */
+{
+    if (newData) 
+    {
+        dataNumber = 0.0;             
+        dataNumber = atol(receivedChars);   
+        newData = false;
+        Serial.println(dataNumber);
+        return true;
+    }
+    else
+    {
+        return false;
+    }
+}
+
+/* Print current position of stepper using timed loop */
+void printLoop()
+{
+    /* Sample all counters one after the other to avoid delay-related offsets */
+    Serial.print("Current position = ");
+    Serial.print(currentPosition);
+    Serial.print("\r\n");
+    Serial.print("p = ");
+    Serial.print(p);
+    Serial.print("\r\n");
+}

src/lab_2/LeibRampStepperMac.c

@@ -0,0 +1,203 @@
+// Leib Ramp Stepper program with millis function adapted for MacOS
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <time.h>
+
+
+/* Only needed in Windows program to maintain compatibility with Arduino version of C/C++ */
+typedef enum { false, true } bool; 
+#define true 1
+#define false 0
+const bool FWDS = true;
+const bool BWDS = false;
+
+const long ticksPerSec = 1000; // ms on PC
+// on Arduino it is 1E6 for micros (for s/w) or 1.6E7 for 62.5 ns ticks (for h/w)
+
+/* Function prototypes: */
+/* PC only, don't need function prototypes on Arduino as they get added within compilation process */
+void moveOneStep();
+void computeNewSpeed();
+long computeStepsToGo();
+void goToPosition(long newPosition);
+void printLoop();
+long millis(void);
+
+/* Note: we are using global variables ONLY to preserve compatibility with the Arduino program structure.
+   They should not normally be used in C or C++ programs as they make for a poor software design. */
+/* Global variables relating to stepper motor position counting etc. */
+long stepsToGo;             /* Number of steps left to make in present movement */
+long targetPosition;        /* Intended destination of motor for given movement */
+volatile long currentPosition = 0;   /* Position in steps of motor relative to startup position */
+float maxSpeed;            /* Maximum speed in present movement (not nec. max permitted) */
+bool direction;             /* Direction of present movement: FWDS or BWDS */
+
+/* Global variables used in simplistic and Leib Ramp algorithms */
+volatile float p;   /* Step interval in clock ticks or microseconds */
+float p1, ps;       /* Minimum and maximum step periods */
+float deltaP;      /* You'll be able to get rid of this later */
+float R;           /* Multiplying constant used in Eiderman's algorithm */
+
+/* Global variable used for noting previous time of a step in timed loop and for calculating speed and accel */
+long prevStepTime=0;
+long millisAtStart;
+float prevSpeed=0.0;
+
+/* Define permissible parameters for motor */
+// For testing on PC only, not for use in Arduino program: try movements in order of 50-100 steps
+float accelSteps=20; /* leave this as a variable as we may over-write it */
+const float minSpeed = 1.0;
+const float maxPermissSpeed = 20.0;
+const float maxAccel = 10.0;
+
+int main(int argc, char *argv[1])
+{
+    unsigned long currentMillis = millis();
+    prevStepTime = 0;
+    long positionToMoveTo;
+    sscanf(argv[1], "%ld", &positionToMoveTo);
+    printf("        Time (s),  Speed (steps/s), Accel (steps/s^2),  Posit'n (steps), Step time (ticks)\n");
+
+    goToPosition(positionToMoveTo);
+
+    /* -------------------------------------------------------------- */
+    /* Start of pre-computation code - only executed once per profile */
+    // STEP 1																 
+    // Define number of steps in acceleration phase using Equation (3)
+    accelSteps = (long)(( maxPermissSpeed * maxPermissSpeed - minSpeed * minSpeed) / ( 2.0 * (float)maxAccel)); // Equation 4 but need to consider initial speed
+    stepsToGo = computeStepsToGo();
+    maxSpeed = maxPermissSpeed;
+    if (2 * accelSteps > stepsToGo)
+    {
+        // STEP 2 
+    		      // Define maximum speed in profile and number of steps in acceleration phase 
+        // Use Equations (4) and (5)
+        maxSpeed = sqrt(minSpeed * minSpeed + stepsToGo * maxAccel); // Modified version of eq. 5
+        accelSteps = (long)(stepsToGo / 2);
+    }
+
+    // STEPS 3 and 5														  
+    // Calculate initial value of and p1 and R    Set p = p1
+    p1 = (float)ticksPerSec / sqrt( minSpeed * minSpeed + 2 * maxAccel); // Eq 17 incorporating initial velocity
+    p = p1;
+    R = (float) maxAccel / ((float)ticksPerSec * (float)ticksPerSec); // Eq 19
+    ps = ((float)ticksPerSec) / maxSpeed; // STEP 4 Eq 7 in paper
+
+    /* End of pre-computation code                                    */
+    /* -------------------------------------------------------------- */
+    millisAtStart = millis(); /* Needed only to tabulate speed vs. time */
+
+    /* Timed loop for stepping, and associated coding */
+    while(stepsToGo > 0)
+    {
+        currentMillis = millis();
+        if (currentMillis - prevStepTime >= p)
+        {
+           moveOneStep();
+           prevStepTime = currentMillis;
+           computeNewSpeed();
+        }
+    }
+    return 0;
+}
+
+/* Only needed for compatibility with Arduino program because millis() is not a native MacOS function */
+long millis(void)
+{
+    struct timespec _t; 
+    clock_gettime(CLOCK_REALTIME, &_t); 
+    return _t.tv_sec*1000 + lround(_t.tv_nsec/1e6); 
+}
+
+/* Move a single step.  */
+void moveOneStep()
+{
+  if (p != 0) /* p=0 is code for "don't make steps" */
+  {
+    // Print to screen instead of making a step
+    if (direction == FWDS)
+    {
+      currentPosition++;
+    }
+    else
+    {
+      currentPosition--;
+    }
+    
+    /* Instead of actually making step, print out parameters for current step */
+    float speed = (float)(ticksPerSec)/p;
+    float accel = (float)(ticksPerSec)*(speed-prevSpeed)/p;
+    printf("%16.3f, %16.3f,  %16.3f, %16ld, %16.3f\n", 0.001*(millis()-millisAtStart), speed, accel, currentPosition, p);
+    prevSpeed = speed;
+  }
+}
+
+/* Calcuate new value of step interval p based on constants defined in loop() */
+void computeNewSpeed()
+{
+    float q;
+    float m;
+    stepsToGo = computeStepsToGo();
+
+    /* ----------------------------------------------------------------- */
+    /* Start of on-the-fly step calculation code, executed once per step */
+    if (stepsToGo == 0)  //  STEP 6a
+    {
+        p = 0; // Not actually a zero step interval, used to switch stepping off
+        return;
+    }
+    else if (stepsToGo >= accelSteps && (long)p > (long)ps) // Speeding up
+    {
+        m = -R;  // Equation (9)
+    }
+    else if (stepsToGo <= accelSteps)  // Slowing down
+    {
+        m = R;  // Equation 10
+    }
+    else  //  Running at constant speed
+    {
+        m = 0;  // Equation (11)
+    }
+    /* else p is unchanged: running at constant speed */
+
+    /* Update to step interval based on Eiderman's algorithm, using temporary variables */
+    // STEP 6b, c and d using Equations (12) and (13)
+    q = m * p * p; // this is a part of optional enhancement
+    p = p * ( 1 + q + 1.5 * q * q); // this is an enhanced approximation -equation [22]
+    /* Need to ensure rounding error does not cause drift outside acceptable interval range:
+      replace p with relevant bound if it strays outside */
+    if (p > p1)
+    {
+        p = p1;
+    }
+    /* End of on-the-fly step calculation code */
+    /* ----------------------------------------------------------------- */
+}
+
+/* Work out how far the stepper motor still needs to move */
+long computeStepsToGo()
+{
+    if (direction == FWDS)
+    {
+        return targetPosition - currentPosition;
+    }
+    else
+    {
+        return currentPosition - targetPosition;
+    }
+}
+
+/* Set the target position and determine direction of intended movement */
+void goToPosition(long newPosition)
+{
+    targetPosition = newPosition;
+    if (targetPosition - currentPosition > 0)
+    {
+        direction = FWDS;
+    }
+    else
+    {
+        direction = BWDS;
+    }
+}

src/lab_2/PIDClosedLoop/PIDClosedLoop.ino

@@ -0,0 +1,247 @@
+
+/* Example of driving servomotor using PID closed loop control */
+
+#include <SPI.h>     /* Needed to communicate with LS7366R (Counter Click) */
+#include <PID_v1.h>
+
+/* Serial input aspects are based closely upon: 
+   http://forum.arduino.cc/index.php?topic=396450
+   Example 4 - Receive a number as text and convert it to an int
+   Modified to read a float */
+
+/* LS7366R aspects very loosely based on concepts used in controlling
+   the Robogaia 3-axis encoder shield though implementation is very different
+   https://www.robogaia.com/3-axis-encoder-conter-arduino-shield.html */
+
+/* Pins used for L298 driver */
+const int enA = 13;      /* PWM output, also visible as LED */
+const int in1 = 8;       /* H bridge selection input 1 */
+const int in2 = 9;       /* H bridge selection input 2 */
+const float minPercent = -100.0;
+const float maxPercent = 100.0;
+
+/* Used to to initiate SPI communication to LS7366R chip (Counter click) */
+const int chipSelectPin = 10;
+
+/* Size of buffer used to store received characters */
+enum {numChars = 32};
+
+/* Intervals in milliseconds for user-defined timed loops */
+const int printInterval = 1000;           
+const int controlInterval = 20;
+
+/* Global variables used in serial input */ 
+char receivedChars[numChars];   // an array to store the received data
+float dataNumber = 0;             
+boolean newData = false;
+
+/* Global variables used for motor control and encoder reading */
+double percentSpeed = 0;
+double encoderPosnMeasured = 0; 
+double positionSetPoint = 0; 
+
+/* PID */
+double Kp = 0.1;
+double Ki = 0.1;
+double Kd = 0.05;
+
+PID myPID(&encoderPosnMeasured, &percentSpeed, &positionSetPoint, Kp, Ki, Kd, DIRECT);
+
+/* Global variables used for loop timing */
+unsigned long prevMillisPrint = 0;        /* stores last time values were printed */
+unsigned long prevMillisControl = 0;
+
+/* Overlapping regions of memory used to convert four bytes to a long integer */
+union fourBytesToLong
+{
+  long result;
+  unsigned char bytes [4];
+};
+
+void setup() 
+{
+  Serial.begin(9600);
+  Serial.print("Kp"); Serial.print(Kp);
+  Serial.print("Ki"); Serial.print(Ki);
+  Serial.print("Kd"); Serial.println(Kd);
+  Serial.println("Enter desired motor position: ");
+  
+  /* Set up and initialise pin used for selecting LS7366R counter: hi=inactive */
+  pinMode(chipSelectPin, OUTPUT);   
+  digitalWrite(chipSelectPin, HIGH);
+
+  SetUpLS7366RCounter();
+
+  delay(100);
+
+  /* Configure control pins for L298 H bridge */
+  pinMode(enA, OUTPUT);
+  pinMode(in1, OUTPUT);
+  pinMode(in2, OUTPUT);
+
+  /* Set initial rotation direction */
+  digitalWrite(in1, LOW);
+  digitalWrite(in2, HIGH);
+
+  delay(100);
+  positionSetPoint = 0;
+  encoderPosnMeasured=readEncoderCountFromLS7366R();
+  myPID.SetOutputLimits(-100,100);
+  myPID.SetMode(AUTOMATIC);
+}
+
+void loop() 
+{
+  unsigned long currentMillis = millis();
+
+  // Call control loop at frequency controInterval
+  if (currentMillis - prevMillisControl >= controlInterval) {
+    // save the last time the control loop was called
+    prevMillisControl = currentMillis;
+    controlLoop();
+  }
+
+  // Call print loop at frequency of printInterval
+  if (currentMillis - prevMillisPrint >= printInterval) {
+    // save the last time you printed output
+    prevMillisPrint = currentMillis;
+    printLoop();
+  }
+  
+  recvWithEndMarker();// Update value read from serial line
+  // If a valid number has been read this is set to the current required position
+  if(convertNewNumber()){
+     positionSetPoint=dataNumber;
+  }
+}
+
+void controlLoop()
+{
+   // Get the current position from the encoder
+  encoderPosnMeasured=readEncoderCountFromLS7366R();  // Get current motor position
+  myPID.Compute();          // Use the PID library to compute new value for motor input
+  driveMotorPercent(percentSpeed);    // Send value to motor
+}
+
+
+void driveMotorPercent(double percentSpeed)
+/* Output PWM and H bridge signals based on positive or negative duty cycle % */
+{
+      percentSpeed = constrain(percentSpeed, -100, 100);
+      int regVal = map(percentSpeed, -100, 100, -255, 255);
+      analogWrite(enA, (int)abs(regVal));   // Write value to speed control pin
+      digitalWrite(in1, regVal>0);          // Set the value of direction control pins to true or false
+      digitalWrite(in2, !(regVal>0));
+}
+
+void printLoop()
+/* Print count and control information */
+{  
+   double error;
+   Serial.print("Actual position: ");
+   Serial.print(encoderPosnMeasured);
+   Serial.print("\t");
+   Serial.print("Desired position: ");
+   Serial.print(positionSetPoint);
+   Serial.print("\t");
+   error = positionSetPoint - encoderPosnMeasured; 
+   Serial.print("Error: ");
+   Serial.print(error); 
+   Serial.print("\t");
+   //   Serial.print(percentSpeed);
+   Serial.print("\r\n");
+}
+
+ 
+long readEncoderCountFromLS7366R()
+/* Reads the LS7366R chip to obtain up/down count from encoder.  Reads four
+   bytes separately then concverts them to a long integer using a union */
+{
+    fourBytesToLong converter; /* Union of four bytes and a long integer */
+    
+    digitalWrite(chipSelectPin,LOW); /* Make LS7366R active */
+    
+    SPI.transfer(0x60); // Request count
+    converter.bytes[3] = SPI.transfer(0x00); /* Read highest order byte */
+    converter.bytes[2] = SPI.transfer(0x00); 
+    converter.bytes[1] = SPI.transfer(0x00); 
+    converter.bytes[0] = SPI.transfer(0x00); /* Read lowest order byte */
+    
+    digitalWrite(chipSelectPin,HIGH); /* Make LS7366R inactive */
+   
+    return converter.result;
+}
+
+void SetUpLS7366RCounter(void)
+/* Initialises LS7366R hardware counter on Counter Click board to read quadrature signals */
+{
+    /* Control registers in LS7366R - see LS7366R datasheet for this and subsequent control words */
+    unsigned char IR = 0x00, MRD0=0x00;
+    
+    // SPI initialization
+    SPI.begin();
+    //SPI.setClockDivider(SPI_CLOCK_DIV16);      // SPI at 1Mhz (on 16Mhz clock)
+    delay(10);
+
+   /* Configure as free-running 4x quadrature counter */
+   digitalWrite(chipSelectPin,LOW); /* Select chip and initialise transfer */
+   /* Instruction register IR */
+   IR |= 0x80;   /* Write to register (B7=1, B6=0) */
+   IR |= 0x08;   /* Select register MDR0: B5=0, B4=0, B3=1 */
+   SPI.transfer(IR); /* Write to instruction register */ 
+   /* Mode register 0 */
+   MRD0 |= 0x03;    /* 4x quadrature count: B0=1, B1=1 */
+   /* B2=B3=0: free running.  B4=B5=0: disable index. */
+   /* B6=0: asynchronous index.  B7: Filter division factor = 1. */
+   SPI.transfer(MRD0);
+   digitalWrite(chipSelectPin,HIGH); 
+
+   /* Clear the counter i.e. set it to zero */
+   IR = 0x00; /* Clear the instructino register IR */
+   digitalWrite(chipSelectPin,LOW); /* Select chip and initialise transfer */
+   IR |= 0x20; /* Select CNTR: B5=1,B4=0,B3=0; CLR register: B7=0,B6=0 */
+   SPI.transfer(IR); /* Write to instruction register */ 
+   digitalWrite(chipSelectPin,HIGH); 
+}
+
+void recvWithEndMarker() 
+/* Receive data from serial port finishing with "newline" character. 
+   Based on http://forum.arduino.cc/index.php?topic=396450 Example 4 */
+{
+    static byte ndx = 0;
+    char endMarker = '\n';
+    char rc;
+    
+    if (Serial.available() > 0) {     // If data is available read value from serial monitor
+        rc = Serial.read();
+
+        if (rc != endMarker) {        // Store character in buffer if not end marker
+            receivedChars[ndx] = rc;
+            ndx++;
+            if (ndx >= numChars) {
+                ndx = numChars - 1;
+            }
+        }
+        else {      // Add end of string character and change flag to indicate new data is available
+            receivedChars[ndx] = '\0'; // terminate the string
+            ndx = 0;
+            newData = true;
+        }
+    }
+}
+
+bool convertNewNumber() 
+/* Converts character string to floating point number only if there are new
+       data to convert, otherwise returns false */
+{
+    if (newData) {
+        dataNumber = 0.0;             
+        dataNumber = atof(receivedChars);   
+        newData = false;
+        return true;
+    }
+    else
+    {
+       return false;
+    }
+}

src/lab_2/ProportionalClosedLoop/ProportionalClosedLoop.ino

@@ -0,0 +1,235 @@
+
+/* Example of driving servomotor using simple proportional closed loop control */
+
+#include <SPI.h>     /* Needed to communicate with LS7366R (Counter Click) */
+
+/* Serial input aspects are based closely upon: 
+   http://forum.arduino.cc/index.php?topic=396450
+   Example 4 - Receive a number as text and convert it to an int
+   Modified to read a float */
+
+/* LS7366R aspects very loosely based on concepts used in controlling
+   the Robogaia 3-axis encoder shield though implementation is very different
+   https://www.robogaia.com/3-axis-encoder-conter-arduino-shield.html */
+
+/* Pins used for L298 driver */
+const int enA = 13;      /* PWM output, also visible as LED */
+const int in1 = 8;       /* H bridge selection input 1 */
+const int in2 = 9;       /* H bridge selection input 2 */
+const float minPercent = -100.0;
+const float maxPercent = 100.0;
+
+/* Used to to initiate SPI communication to LS7366R chip (Counter click) */
+const int chipSelectPin = 10;
+
+/* Size of buffer used to store received characters */
+enum {numChars = 32};
+
+/* Intervals in milliseconds for user-defined timed loops */
+const int printInterval = 1000;           
+const int controlInterval = 20;
+
+/* Global variables used in serial input */ 
+char receivedChars[numChars];   // an array to store the received data
+float dataNumber = 0;             // new for this version
+boolean newData = false;
+
+/* Global variable used for motor control */
+double percentDutyCycle;
+
+long encoderPosnMeasured = 0; 
+double positionSetPoint = 0;  
+
+/* Proportional gain constant */
+double Kp = 0.1;
+
+/* Global variables used for loop timing */
+unsigned long prevMillisPrint = 0;        /* stores last time values were printed */
+unsigned long prevMillisControl = 0;      /* Stores last time control loop executed */
+
+/* Overlapping regions of memory used to convert four bytes to a long integer */
+union fourBytesToLong
+{
+  long result;
+  unsigned char bytes [4];
+};
+
+void setup() 
+{
+    Serial.begin(9600);
+    Serial.println("Enter desired motor position: ");
+    
+    /* Set up and initialise pin used for selecting LS7366R counter: hi=inactive */
+    pinMode(chipSelectPin, OUTPUT);   
+    digitalWrite(chipSelectPin, HIGH);
+  
+    SetUpLS7366RCounter();
+  
+    delay(100);
+  
+    /* Configure control pins for L298 H bridge */
+    pinMode(enA, OUTPUT);
+    pinMode(in1, OUTPUT);
+    pinMode(in2, OUTPUT);
+  
+    /* Set initial rotation direction */
+    digitalWrite(in1, LOW);
+    digitalWrite(in2, HIGH);
+}
+
+void loop() 
+{
+    unsigned long currentMillis = millis();
+    
+    // Call control loop at frequency controInterval
+    if (currentMillis - prevMillisControl >= controlInterval) 
+    {
+      // Save the current time for comparison the next time the loop is called
+      prevMillisControl = currentMillis;
+      controlLoop();
+    }
+    
+    // Call print loop at frequency of printInterval
+    if (currentMillis - prevMillisPrint >= printInterval) 
+    {
+      // Save the current time for comparison the next time the loop is called
+      prevMillisPrint = currentMillis;
+      printLoop();
+    }
+    
+    recvWithEndMarker();  // Update value read from serial line
+    // If a valid number has been read this is set to the current required position
+    if(convertNewNumber())
+    {
+       positionSetPoint = dataNumber;
+    }
+}
+
+void controlLoop()
+{
+    double error;
+    // Get the current position from the encoder
+    encoderPosnMeasured = readEncoderCountFromLS7366R();
+    // Calculate the difference in position from the required position
+    error = positionSetPoint - (double)encoderPosnMeasured;
+    // Multiply by the gain
+    percentDutyCycle = error * Kp;
+    driveMotorPercent(percentDutyCycle);
+}
+
+/* Output PWM and H bridge signals based on positive or negative duty cycle % */
+void driveMotorPercent(double percentDutyCycle)
+{
+      // constrain the duty cycle to a value between -100 and 100 then map to +-255
+      percentDutyCycle = constrain(percentDutyCycle, -100, 100);
+      int regVal = map(percentDutyCycle, -100, 100, -255, 255);
+      analogWrite(enA, (int)abs(regVal));     // Write value to speed control pin
+      digitalWrite(in1, regVal>0);            // Set the value of direction control pins to true or false
+      digitalWrite(in2, !(regVal>0));
+}
+
+/* Print count and control information */
+void printLoop()
+  {  Serial.print("Actual position: ");
+     Serial.print(encoderPosnMeasured);
+     Serial.print("\t");
+     Serial.print("Desired position: ");
+     Serial.print(positionSetPoint);
+     Serial.print("\t");
+     Serial.print("Error: ");
+     Serial.print(positionSetPoint - (double)encoderPosnMeasured);
+     Serial.print("\r\n");
+}
+
+/* Reads the LS7366R chip to obtain up/down count from encoder.  Reads four
+   bytes separately then concverts them to a long integer using a union */
+long readEncoderCountFromLS7366R()
+{
+    fourBytesToLong converter; /* Union of four bytes and a long integer */
+    
+    digitalWrite(chipSelectPin,LOW); /* Make LS7366R active */
+    
+    SPI.transfer(0x60); // Request count
+    converter.bytes[3] = SPI.transfer(0x00); /* Read highest order byte */
+    converter.bytes[2] = SPI.transfer(0x00); 
+    converter.bytes[1] = SPI.transfer(0x00); 
+    converter.bytes[0] = SPI.transfer(0x00); /* Read lowest order byte */
+    
+    digitalWrite(chipSelectPin,HIGH); /* Make LS7366R inactive */
+   
+    return converter.result;
+}
+
+/* Initialises LS7366R hardware counter on Counter Click board to read quadrature signals */
+void SetUpLS7366RCounter(void)
+{
+    /* Control registers in LS7366R - see LS7366R datasheet for this and subsequent control words */
+    unsigned char IR = 0x00, MRD0=0x00;
+    
+    // SPI initialization
+    SPI.begin();
+    //SPI.setClockDivider(SPI_CLOCK_DIV16);      // SPI at 1Mhz (on 16Mhz clock)
+    delay(10);
+
+   /* Configure as free-running 4x quadrature counter */
+   digitalWrite(chipSelectPin,LOW); /* Select chip and initialise transfer */
+   /* Instruction register IR */
+   IR |= 0x80;   /* Write to register (B7=1, B6=0) */
+   IR |= 0x08;   /* Select register MDR0: B5=0, B4=0, B3=1 */
+   SPI.transfer(IR); /* Write to instruction register */ 
+   /* Mode register 0 */
+   MRD0 |= 0x03;    /* 4x quadrature count: B0=1, B1=1 */
+   /* B2=B3=0: free running.  B4=B5=0: disable index. */
+   /* B6=0: asynchronous index.  B7: Filter division factor = 1. */
+   SPI.transfer(MRD0);
+   digitalWrite(chipSelectPin,HIGH); 
+
+   /* Clear the counter i.e. set it to zero */
+   IR = 0x00; /* Clear the instructino register IR */
+   digitalWrite(chipSelectPin,LOW); /* Select chip and initialise transfer */
+   IR |= 0x20; /* Select CNTR: B5=1,B4=0,B3=0; CLR register: B7=0,B6=0 */
+   SPI.transfer(IR); /* Write to instruction register */ 
+   digitalWrite(chipSelectPin,HIGH); 
+}
+
+/* Receive data from serial port finishing with "newline" character. 
+   Based on http://forum.arduino.cc/index.php?topic=396450 Example 4 */
+void recvWithEndMarker() 
+{
+    static byte ndx = 0;
+    char endMarker = '\n';
+    char rc;
+    
+    if (Serial.available() > 0) {   // If data is available read value from serial monitor
+        rc = Serial.read();
+
+        if (rc != endMarker) {      // Store character in buffer if not end marker
+            receivedChars[ndx] = rc;
+            ndx++;
+            if (ndx >= numChars) {
+                ndx = numChars - 1;
+            }
+        }
+        else {    // Add end of string character and change flag to indicate new data is available
+            receivedChars[ndx] = '\0'; // terminate the string
+            ndx = 0;
+            newData = true;
+        }
+    }
+}
+
+bool convertNewNumber() 
+/* Converts character string to floating point number only if there are new
+       data to convert, otherwise returns false */
+{
+    if (newData) {
+        dataNumber = 0.0;             
+        dataNumber = atof(receivedChars);   
+        newData = false;
+        return true;
+    }
+    else
+    {
+       return false;
+    }
+}

src/lab_2/SimpleControlNoFeedback/SimpleControlNoFeedback.ino

@@ -0,0 +1,208 @@
+/* Example of driving servomotor and reading encoder signals */
+
+#include <SPI.h>     /* Needed to communicate with LS7366R (Counter Click) */
+
+/* Serial input aspects are based closely upon: 
+   http://forum.arduino.cc/index.php?topic=396450
+   Example 4 - Receive a number as text and convert it to an int
+   Modified to read a float */
+
+/* LS7366R aspects very loosely based on concepts used in controlling
+   the Robogaia 3-axis encoder shield though implementation is very different
+   https://www.robogaia.com/3-axis-encoder-conter-arduino-shield.html */
+
+/* Pins used for L298 DC Motor driver */
+#define enA 13      /* PWM output, also visible as LED */
+#define in1 8       /* H bridge selection input 1 */
+#define in2 9       /* H bridge selection input 2 */
+#define minPercent -100.0
+#define maxPercent 100.0
+
+/* Used to to initiate SPI communication to LS7366R chip (Counter click) */
+#define chipSelectPin 10
+
+/* Size of buffer used to store received characters */
+#define numChars 32
+
+/* Intervals in milliseconds for user-defined timed loops */
+#define printInterval 1000           
+
+/* Global variables used in serial input */ 
+char receivedChars[numChars];   // an array to store the received data
+float dataNumber = 0;             
+boolean newData = false;
+
+/* Global variable used for motor control */
+double percentSpeed;
+
+/* Global variables used for loop timing */
+unsigned long prevMillisPrint = 0;        /* stores last time values were printed */
+
+/* Overlapping regions of memory used to convert four bytes to a long integer */
+union fourBytesToLong
+{
+  long result;
+  unsigned char bytes [4];
+};
+
+void setup() 
+{
+  Serial.begin(9600);
+  Serial.println("Enter PWM duty cycle as a percentage (positive for forward, negative for reverse");
+  
+  /* Set up and initialise pin used for selecting LS7366R counter: hi=inactive */
+  pinMode(chipSelectPin, OUTPUT);   
+  digitalWrite(chipSelectPin, HIGH);
+
+  SetUpLS7366RCounter();
+
+  delay(100);
+  
+  /* Configure control pins for L298 H bridge */
+  pinMode(enA, OUTPUT);
+  pinMode(in1, OUTPUT);
+  pinMode(in2, OUTPUT);
+
+  /* Set initial rotation direction */
+  digitalWrite(in1, LOW);
+  digitalWrite(in2, HIGH);
+
+}
+
+void loop() 
+{
+  unsigned long currentMillis = millis();
+
+  // Print out value to serial monitor at interval specified by printInterval variable
+  if (currentMillis - prevMillisPrint >= printInterval) {
+    // save the last time you printed output
+    prevMillisPrint = currentMillis;
+    printLoop();
+  }
+
+  // Check if new data has been input via serial monitor
+  recvWithEndMarker();
+  if(convertNewNumber())  // Update value read from serial line
+  {
+     percentSpeed=dataNumber;
+     driveMotorPercent(percentSpeed);  // Send new speed value to motor driver
+  }
+}
+
+void driveMotorPercent(double percentSpeed)
+/* Output PWM and H bridge signals based on positive or negative duty cycle % */
+{
+      percentSpeed = constrain(percentSpeed, -100, 100);   // Value must be in range -100 to +100
+      int regVal = map(percentSpeed, -100, 100, -255, 255);   // Scale value to range -255 to +255
+      analogWrite(enA, (int)abs(regVal));     // Write value to speed control pin
+      digitalWrite(in1, regVal>0);            // Set the value of direction control pins to true or false
+      digitalWrite(in2, !(regVal>0));         // depending on whether speed is positive or negative
+}
+
+void printLoop()
+/* Print count and control information */
+{
+   /* Sample counter chip and output position and requested speed */
+   long encoderCountFromLS7366R = readEncoderCountFromLS7366R();
+   
+   Serial.print("Count from LS7366R = ");
+   Serial.print(encoderCountFromLS7366R); 
+   Serial.print(" Percent speed = ");
+   Serial.print(percentSpeed);
+   Serial.print("\r\n");
+}
+ 
+long readEncoderCountFromLS7366R()
+/* Reads the LS7366R chip to obtain up/down count from encoder.  Reads four
+   bytes separately then concverts them to a long integer using a union */
+{
+    fourBytesToLong converter; /* Union of four bytes and a long integer */
+    
+    digitalWrite(chipSelectPin,LOW); /* Make LS7366R active */
+    
+    SPI.transfer(0x60); // Request count
+    converter.bytes[3] = SPI.transfer(0x00); /* Read highest order byte */
+    converter.bytes[2] = SPI.transfer(0x00); 
+    converter.bytes[1] = SPI.transfer(0x00); 
+    converter.bytes[0] = SPI.transfer(0x00); /* Read lowest order byte */
+    
+    digitalWrite(chipSelectPin,HIGH); /* Make LS7366R inactive */
+   
+    return converter.result;
+}
+
+
+void SetUpLS7366RCounter(void)
+/* Initialiseds LS7366R hardware counter on Counter Click board to read quadrature signals */
+{
+    /* Control registers in LS7366R - see LS7366R datasheet for this and subsequent control words */
+    unsigned char IR = 0x00, MRD0=0x00;
+    
+    // SPI initialization
+    SPI.begin();
+    //SPI.setClockDivider(SPI_CLOCK_DIV16);      // SPI at 1Mhz (on 16Mhz clock)
+    delay(10);
+
+   /* Configure as free-running 4x quadrature counter */
+   digitalWrite(chipSelectPin,LOW); /* Select chip and initialise transfer */
+   /* Instruction register IR */
+   IR |= 0x80;   /* Write to register (B7=1, B6=0) */
+   IR |= 0x08;   /* Select register MDR0: B5=0, B4=0, B3=1 */
+   SPI.transfer(IR); /* Write to instruction register */ 
+   /* Mode register 0 */
+   MRD0 |= 0x03;    /* 4x quadrature count: B0=1, B1=1 */
+   /* B2=B3=0: free running.  B4=B5=0: disable index. */
+   /* B6=0: asynchronous index.  B7: Filter division factor = 1. */
+   SPI.transfer(MRD0);
+   digitalWrite(chipSelectPin,HIGH); 
+
+   /* Clear the counter i.e. set it to zero */
+   IR = 0x00; /* Clear the instructino register IR */
+   digitalWrite(chipSelectPin,LOW); /* Select chip and initialise transfer */
+   IR |= 0x20; /* Select CNTR: B5=1,B4=0,B3=0; CLR register: B7=0,B6=0 */
+   SPI.transfer(IR); /* Write to instruction register */ 
+   digitalWrite(chipSelectPin,HIGH); 
+   
+}
+
+void recvWithEndMarker() 
+/* Receive data from serial port finishing with "newline" character. 
+   Based on http://forum.arduino.cc/index.php?topic=396450 Example 4 */
+{
+    static byte ndx = 0;
+    char endMarker = '\n';
+    char rc;
+    
+    if (Serial.available() > 0) {  // If data is available read value from serial monitor
+        rc = Serial.read();
+
+        if (rc != endMarker) {   // Store character in buffer if not end marker
+            receivedChars[ndx] = rc;
+            ndx++;
+            if (ndx >= numChars) {
+                ndx = numChars - 1;
+            }
+        }
+        else {  // Add end of string character and change flag to indicate new data is available
+            receivedChars[ndx] = '\0'; // terminate the string
+            ndx = 0;
+            newData = true;
+        }
+    }
+}
+
+bool convertNewNumber() 
+/* Converts character string to floating point number only if there are new
+       data to convert, otherwise returns false */
+{
+    if (newData) {
+        dataNumber = 0.0;             
+        dataNumber = atof(receivedChars);   
+        newData = false;
+        return true;
+    }
+    else
+    {
+       return false;
+    }
+}

src/lab_2/SimplisticRampStepper.c

@@ -0,0 +1,178 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <windows.h>
+#include <math.h>
+
+/* Only needed in Windows program to maintain compatibility with Arduino version of C/C++ */
+#define bool BOOL
+#define true 1
+#define false 0
+const bool FWDS = true;
+const bool BWDS = false;
+
+const long ticksPerSec = 1000; // ms on PC
+// on Arduino it is 1E6 for micros (for s/w) or 1.6E7 for 62.5 ns ticks (for h/w)
+
+void moveOneStep();
+void computeNewSpeed();
+long computeStepsToGo();
+void goToPosition(long newPosition);
+long millis(void);
+
+/* Note: we are using global variables ONLY to preserve compatibility with the Arduino program structure.
+   They should not normally be used in C or C++ programs as they make for a poor software design. */
+/* Global variables relating to stepper motor position counting etc. */
+long stepsToGo;             /* Number of steps left to make in present movement */
+long targetPosition;        /* Intended destination of motor for given movement */
+volatile long currentPosition = 0;   /* Position in steps of motor relative to startup position */
+float maxSpeed;            /* Maximum speed in present movement (not nec. max permitted) */
+bool direction;             /* Direction of present movement: FWDS or BWDS */
+
+/* Global variables used in simplistic and Leib Ramp algorithms */
+volatile float p;   /* Step interval in clock ticks or microseconds */
+float ps;       /* Maximum step periods */
+float deltaP;      /* You'll be able to get rid of this later */
+
+/* Global variable used for noting previous time of a step in timed loop and for calculating speed and accel */
+long prevStepTime=0;
+long millisAtStart;
+float prevSpeed=0.0;
+
+/* Define permissible parameters for motor */
+// For testing on PC only, not for use in Arduino program: try movements in order of 50-100 steps
+float accelSteps=20; /* leave this as a variable as we may over-write it */
+const float minSpeed = 1.0;  // in steps/s
+const float maxPermissSpeed = 20.0;   // in steps/s
+const float maxAccel = 10.0;     // in steps/s^2
+
+int main()
+{
+    unsigned long currentMillis = millis();
+    prevStepTime = 0;
+    long positionToMoveTo;
+    while(true)
+    {
+        printf("Enter position to move to in profile (or 999 to terminate)\n");
+        scanf("%ld", &positionToMoveTo);
+        if (positionToMoveTo==999) break;
+        printf("        Time (s),  Speed (steps/s), Accel (steps/s^2),  Posit'n (steps), Step time (ticks)\n");
+
+        goToPosition(positionToMoveTo);
+
+        /* -------------------------------------------------------------- */
+        /* Start of pre-computation code - only executed once per profile */
+        
+        float maxInterval = ((float)ticksPerSec) / minSpeed;
+        ps = ((float)ticksPerSec) / maxPermissSpeed;
+        deltaP = (maxInterval - ps) / accelSteps;
+        stepsToGo = computeStepsToGo();
+        maxSpeed = maxPermissSpeed;
+        if (2 * accelSteps > stepsToGo)
+        {
+            accelSteps = (long)(stepsToGo / 2);
+        }
+
+        p = maxInterval;
+        
+        ps = ((float)ticksPerSec) / maxSpeed;
+        /* End of pre-computation code                                    */
+        /* -------------------------------------------------------------- */
+        millisAtStart = millis(); /* Needed only to tabulate speed vs. time */
+
+        /* Timed loop for stepping */
+        while(stepsToGo > 0)
+        {
+            currentMillis = millis();
+            if (currentMillis - prevStepTime >= p)
+            {
+               moveOneStep();
+               prevStepTime = currentMillis;
+               computeNewSpeed();
+            }
+        }
+    }
+    return 0;
+}
+
+long millis(void)
+/* Only needed for compatibility with Arduino program because millis() is not a native Windows API function */
+{
+    return GetTickCount();
+}
+
+void moveOneStep()
+/* Move a single step.  If this were running on the Arduino we would holding pulse high for delayMicroSeconds */
+{
+  if (p != 0) /* p=0 is code for "don't make steps" */
+  {
+    // Print to screen instead of making a step
+    if (direction == FWDS)
+    {
+      currentPosition++;
+    }
+    else
+    {
+      currentPosition--;
+    }
+    
+    /* Instead of actually making step, print out parameters for current step */
+    float speed = (float)(ticksPerSec)/p;
+    float accel = (float)(ticksPerSec)*(speed-prevSpeed)/p;
+    printf("%16.3f, %16.3f,  %16.3f, %16ld, %16.3f\n", 0.001*(millis()-millisAtStart), speed, accel, currentPosition, p);
+    prevSpeed = speed;
+  }
+}
+
+/* Calcuate new value of step interval p based on constants defined in timed loop */
+void computeNewSpeed()
+{
+  stepsToGo = computeStepsToGo();
+
+  /* Start of on-the-fly step calculation code, executed once per step */
+  if (stepsToGo == 0)
+  {
+    p = 0; // Not actually a zero step interval, used to switch stepping off
+    return;
+  }
+  else if (stepsToGo >= accelSteps && (long)p > (long)ps) // Changed to make ramps even length
+  /* Speeding up */
+  {
+    p -= deltaP;
+  }
+  else if (stepsToGo <= accelSteps)
+  /* Slowing down */
+  {
+    p += deltaP;
+  }
+  /* else p is unchanged: running at constant speed */
+
+  /* End of on-the-fly step calculation code */
+}
+
+/* Work out how far the stepper motor still needs to move */
+long computeStepsToGo()
+{
+  if (direction == FWDS)
+  {
+    return targetPosition - currentPosition;
+  }
+  else
+  {
+    return currentPosition - targetPosition;
+  }
+}
+
+/* Set the target position and determine direction of intended movement */
+void goToPosition(long newPosition)
+{
+  targetPosition = newPosition;
+  if (targetPosition - currentPosition > 0)
+  {
+    direction = FWDS;
+  }
+  else
+  {
+    direction = BWDS;
+  }
+}
+

src/lab_2/SimplisticRampStepper/SimplisticRampStepper.ino

@@ -0,0 +1,349 @@
+/* Stepper motor demonstration program written by Arthur Jones,
+   4 November 2018.  Implements a simplistic and ineffective ramping 
+   algorithm but provides framework for implementation of LeibRamp 
+   algorithm described by Aryeh Eiderman, http://hwml.com/LeibRamp.pdf
+
+   Makes use of background work and some aspects of code developed
+   by Choaran Wang, 2017-18. This in turn incorporates some ideas
+   used in the AccelStepper library:
+   https://www.airspayce.com/mikem/arduino/AccelStepper/
+
+   Serial input aspects are based closely upon:
+   http://forum.arduino.cc/index.php?topic=396450
+   Example 4 - Receive a number as text and convert it to an int
+   Modified to read a long */
+
+// #define USEINTERRUPTS
+const int stepPin = 13;
+const int dirPin = 9;
+const bool FWDS = true;
+const bool BWDS = false;
+#ifdef USEINTERRUPTS
+const long ticksPerSec = 16000000; // Clock speed of Arduino
+#else
+const long ticksPerSec = 1000000; // microseconds in this case
+#endif
+
+
+/* Define permissible parameters for motor */
+// For testing by watching LED: try movements in order of 100 steps
+//float accelSteps=20; /* leave this as a variable as we may over-write it */
+//const float minSpeed = 2.0;
+//const float maxPermissSpeed = 20.0;
+//const float maxAccel = 10.0;
+//const long stepLengthMus = 10000;
+
+// For lab testing with real motor: try movements in the order of 3000 steps
+  float accelSteps=1000; /* leave this as a variable as we may over-write it */
+  const float minSpeed=10.0;
+  const float maxPermissSpeed=1000.0;
+  const float maxAccel=500.0;
+  const long stepLengthMus=100;
+
+/* Intervals in milliseconds for user-defined timed loops */
+const long printInterval = 1000;
+
+/* Global variables used for loop timing */
+unsigned long prevMillisPrint = 0;        /* stores last time values were printed */
+
+/* Global variables used in serial input */
+enum {numChars = 32};
+char receivedChars[numChars];    /* an array to store the received data */
+long dataNumber = 0;             /* Value read from serial monitor input */
+boolean newData = false;
+
+/* Global variables relating to stepper motor position counting etc. */
+long stepsToGo;             /* Number of steps left to make in present movement */
+long targetPosition;        /* Intended destination of motor for given movement */
+volatile long currentPosition = 0;   /* Position in steps of motor relative to startup position */
+double maxSpeed;            /* Maximum speed in present movement (not nec. max permitted) */
+bool direction;             /* Direction of present movement: FWDS or BWDS */
+
+volatile float p;   /* Step interval in clock ticks or microseconds */
+float p1, ps;       /* Minimum and maximum step periods */
+double deltaP;      /* You'll be able to get rid of this later */
+double R;           /* Multiplying constant used in Eiderman's algorithm */
+
+/* Global variable used for noting previous time of a step in timed loop */
+long prevStepTime;
+
+void setup()
+{
+  long stepsToGo = 0;
+  currentPosition = 0;
+  goToPosition(dataNumber);
+  pinMode(stepPin, OUTPUT);
+  pinMode(dirPin, OUTPUT);
+  Serial.begin(9600);
+  Serial.println("Enter target position in number of steps and hit return");
+
+// If USEINTERRUPTS is defined at the start of the program this section will be used
+#ifdef USEINTERRUPTS
+  cli();
+  TCCR1A = 0; // No output compare
+  TCCR1B = 0;
+  TCCR1B |= (1 << WGM12); //CTC mode
+  OCR1A = 0; // Set to zero for the present time: catch this to switch interrupt off
+  TCCR1B |= (1 << CS12);  // 256 prescaler: overwritten in ISR
+  TIMSK1 |= (1 << OCIE1A); //enable timer compare interrupt
+  sei();
+#else  //
+  // Use built-in Arduino function micros() to get the time in microseconds since the program started running.
+  // Documentation: https://www.arduino.cc/reference/en/language/functions/time/micros/
+  prevStepTime = micros();   // This is a built-in Arduino function.
+#endif
+}
+
+void loop()
+{
+  unsigned long currentMillis = millis();
+  unsigned long currentMicros;
+  recvWithEndMarker();
+  stepsToGo = computeStepsToGo();
+  if (convertNewNumber())
+  {
+    /* Only get to this stage if there was new data to convert */
+    if (stepsToGo <= 0)
+    {
+      /* Only get to this stage if not busy, otherwise will have thrown away input */
+      goToPosition(dataNumber);
+
+      /* Delete these and replace with Leib Ramp formulae */
+      double maxInterval = ((double)ticksPerSec) / minSpeed;
+      ps = ((double)ticksPerSec) / maxPermissSpeed;
+      deltaP = (maxInterval - ps) / accelSteps;
+      /* End of section requiring redefinitions */
+
+      stepsToGo = computeStepsToGo();
+      maxSpeed = maxPermissSpeed;
+      if (2 * accelSteps > stepsToGo)
+      {
+        /* Definiiton of S where ther is no constant speed period - check it is still applicable */
+        accelSteps = (long)(stepsToGo / 2);
+        /* Need to redefine maxSpeed here as we never fully accelerate */ 
+      }
+
+      /* Will need to over-write these with correct initial value of p and p1, along with R */
+      p = maxInterval;
+      p1 = (double)ticksPerSec/minSpeed;
+      /* End of section requiring redefinitions */
+
+      ps = ((double)ticksPerSec) / maxSpeed; /* Eq 7 in paper: this is OK */
+
+#ifdef USEINTERRUPTS
+      if (p != 0)
+      {
+        // Re-enable interrupts if non-zero steps
+        TIMSK1 |= (1 << OCIE1A);
+      }
+#endif
+    }
+  }
+#ifndef USEINTERRUPTS
+
+  /* Timed loop for stepping, and associated coding */
+  currentMicros = micros();
+  if (currentMicros - prevStepTime >= p)
+  {
+    moveOneStep();
+    prevStepTime = currentMicros;
+    computeNewSpeed();
+  }
+#endif
+  /* Timed loop for printing */
+  if (currentMillis - prevMillisPrint >= printInterval)
+  {
+    /* Save the last time output was printed */
+    prevMillisPrint = currentMillis;
+    printLoop();
+  }
+}
+
+void moveOneStep()
+/* Move a single step, holding pulse high for delayMicroSeconds */
+{
+  if (p != 0) /* p=0 is code for "don't make steps" */
+  {
+    digitalWrite(stepPin, HIGH);
+    if (direction == FWDS)
+    {
+      /* Is something missing here? */
+      currentPosition++;
+    }
+    else
+    {
+      /* Is something missing here? */
+      currentPosition--;
+    }
+    delayMicroseconds(stepLengthMus);
+    digitalWrite(stepPin, LOW);
+  }
+}
+
+void computeNewSpeed()
+/* Calcuate new value of step interval p based on constants defined in loop() */
+{
+  /* You may need to declare some temporary variables for this function... */
+  stepsToGo = computeStepsToGo();
+
+  if (stepsToGo == 0)
+  {
+    p = 0; // Not actually a zero step interval, used to switch stepping off
+    return;
+  }
+  else if (stepsToGo > accelSteps && (long)p > long(ps))
+  /* Speeding up */
+  {
+    /* Delete this simplistic change to p and replace with something else */
+    p -= deltaP;
+  }
+  else if (stepsToGo <= accelSteps)
+  /* Slowing down */
+  {
+    /* Delete this simplistic change to p and replace with something else */
+    p += deltaP;
+  }
+  else
+  /* Running at constant speed */
+  {
+    /* For simpplistic approach, p=p so do nothing to it.  
+       But you will need to put something here for Leib ramp ... */
+  }
+  /* Update to step interval based on Leib ramp algorithm, using temporary variables */
+
+  /* Need to ensure rounding error does not cause drift outside acceptable interval range: 
+     replace p with relevant bound if it strays outside - so need to write some code here */
+
+  
+}
+
+long computeStepsToGo()
+/* Work out how far the stepper motor still needs to move */
+{
+  if (direction == FWDS)
+  {
+    return targetPosition - currentPosition;
+  }
+  else
+  {
+    return currentPosition - targetPosition;
+  }
+}
+
+void goToPosition(long newPosition)
+/* Set the target position and determine direction of intended movement */
+{
+  targetPosition = newPosition;
+  if (targetPosition - currentPosition > 0)
+  {
+    direction = FWDS;
+  }
+  else
+  {
+    direction = BWDS;
+  }
+}
+
+void recvWithEndMarker()
+/* Receive data from serial port finishing with "newline" character.
+   Based on http://forum.arduino.cc/index.php?topic=396450 Example 4 */
+{
+  static byte ndx = 0;
+  char endMarker = '\n';
+  char rc;
+
+  if (Serial.available() > 0) 
+  {
+    rc = Serial.read();
+
+    if (rc != endMarker) 
+    {
+      receivedChars[ndx] = rc;
+      ndx++;
+      if (ndx >= numChars) 
+      {
+        ndx = numChars - 1;
+      }
+    }
+    else 
+    {
+      receivedChars[ndx] = '\0'; // terminate the string
+      ndx = 0;
+      newData = true;
+    }
+  }
+}
+
+bool convertNewNumber()
+/* Converts character string to long integer only if there are new
+       data to convert, otherwise returns false */
+{
+  if (newData) 
+  {
+    dataNumber = 0.0;             // new for this version
+    dataNumber = atol(receivedChars);   // new for this version
+    newData = false;
+    return true;
+  }
+  else
+  {
+    return false;
+  }
+}
+
+void printLoop()
+/* Print current position of stepper using timed loop */
+{
+  /* Sample all counters one after the other to avoid delay-related offsets */
+  Serial.print("Current position = ");
+  Serial.print(currentPosition);
+  Serial.print("\r\n");
+}
+
+#ifdef USEINTERRUPTS
+ISR(TIMER1_COMPA_vect)
+/* Interrupt service routine which essentially just calls moveOneStep and computeNewSpeed.
+   However, it also changes the prescale value on-the-fly so that the full range of possible
+   step rates can be exploited, from around 0.25 Hz upwards, limited by step pulse width. */
+{
+  if (p == 0)
+  {
+    // Disable interrupt to avoid endless calling of interrupt if not needed
+    TIMSK1 &= !(1 << OCIE1A);
+  }
+  moveOneStep();
+
+  /* Adapt prescaler to keep OCR1A as large as possible within acceptable range */
+  if (p < 65536)
+  {
+    // Prescaler 1
+    OCR1A = (long)p - 1;
+    TCCR1B = (TCCR1B & 0xF8) | 0x01;
+  }
+  else if (p < 524288)
+  {
+    // Prescaler 8
+    OCR1A = ((long)p >> 3) - 1;
+    TCCR1B = (TCCR1B & 0xF8) | 0x02;
+  }
+  else if (p < 4194304)
+  {
+    // Prescaler 64
+    OCR1A = ((long)p >> 6) - 1;
+    TCCR1B = (TCCR1B & 0xF8) | 0x03;
+  }
+  else if (p < 16777216)
+  {
+    // Prescaler 256
+    OCR1A = ((long)p >> 8) - 1;
+    TCCR1B = (TCCR1B & 0xF8) | 0x04;
+  }
+  else
+  {
+    // Prescaler 1024
+    OCR1A = ((long)p >> 10) - 1;
+    TCCR1B = (TCCR1B & 0xF8) | 0x05;
+  }
+  computeNewSpeed();
+}
+#endif

src/lab_2/SimplisticRampStepperMac.c

@@ -0,0 +1,177 @@
+// Simplistic Ramp Stepper program with millis function adapted for MacOS
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <time.h>
+
+/* Only needed in Windows program to maintain compatibility with Arduino version of C/C++ */
+typedef enum { false, true } bool; 
+#define true 1
+#define false 0
+const bool FWDS = true;
+const bool BWDS = false;
+
+const long ticksPerSec = 1000; // ms on PC
+// on Arduino it is 1E6 for micros (for s/w) or 1.6E7 for 62.5 ns ticks (for h/w)
+
+void moveOneStep();
+void computeNewSpeed();
+long computeStepsToGo();
+void goToPosition(long newPosition);
+long millis(void);
+
+/* Note: we are using global variables ONLY to preserve compatibility with the Arduino program structure.
+   They should not normally be used in C or C++ programs as they make for a poor software design. */
+/* Global variables relating to stepper motor position counting etc. */
+long stepsToGo;             /* Number of steps left to make in present movement */
+long targetPosition;        /* Intended destination of motor for given movement */
+volatile long currentPosition = 0;   /* Position in steps of motor relative to startup position */
+float maxSpeed;            /* Maximum speed in present movement (not nec. max permitted) */
+bool direction;             /* Direction of present movement: FWDS or BWDS */
+
+/* Global variables used in simplistic and Leib Ramp algorithms */
+volatile float p;   /* Step interval in clock ticks or microseconds */
+float ps;       /* Maximum step periods */
+float deltaP;      /* You'll be able to get rid of this later */
+
+/* Global variable used for noting previous time of a step in timed loop and for calculating speed and accel */
+long prevStepTime=0;
+long millisAtStart;
+float prevSpeed=0.0;
+
+/* Define permissible parameters for motor */
+// For testing on PC only, not for use in Arduino program: try movements in order of 50-100 steps
+float accelSteps=20; /* leave this as a variable as we may over-write it */
+const float minSpeed = 1.0;  // in steps/s
+const float maxPermissSpeed = 20.0;   // in steps/s
+const float maxAccel = 10.0;     // in steps/s^2
+
+int main(int argc, char *argv[])
+{
+    unsigned long currentMillis = millis();
+    prevStepTime = 0;
+    long positionToMoveTo;
+    sscanf(argv[1], "%ld", &positionToMoveTo);
+    printf("        Time (s),  Speed (steps/s), Accel (steps/s^2),  Posit'n (steps), Step time (ticks)\n");
+
+    goToPosition(positionToMoveTo);
+
+    /* -------------------------------------------------------------- */
+    /* Start of pre-computation code - only executed once per profile */
+    
+    float maxInterval = ((float)ticksPerSec) / minSpeed;
+    ps = ((float)ticksPerSec) / maxPermissSpeed;
+    deltaP = (maxInterval - ps) / accelSteps;
+    stepsToGo = computeStepsToGo();
+    maxSpeed = maxPermissSpeed;
+    if (2 * accelSteps > stepsToGo)
+    {
+        accelSteps = (long)(stepsToGo / 2);
+    }
+
+    p = maxInterval;
+    
+    ps = ((float)ticksPerSec) / maxSpeed;
+    /* End of pre-computation code                                    */
+    /* -------------------------------------------------------------- */
+    millisAtStart = millis(); /* Needed only to tabulate speed vs. time */
+
+    /* Timed loop for stepping */
+    while(stepsToGo > 0)
+    {
+        currentMillis = millis();
+        if (currentMillis - prevStepTime >= p)
+        {
+           moveOneStep();
+           prevStepTime = currentMillis;
+           computeNewSpeed();
+        }
+    }
+    return 0;
+}
+
+/* Only needed for compatibility with Arduino program because millis() is not a native MacOS function */
+long millis(void)
+{
+    struct timespec _t; 
+    clock_gettime(CLOCK_REALTIME, &_t); 
+    return _t.tv_sec*1000 + lround(_t.tv_nsec/1e6); 
+}
+
+/* Move a single step.  If this were running on the Arduino we would holding pulse high for delayMicroSeconds */
+void moveOneStep()
+{
+  if (p != 0) /* p=0 is code for "don't make steps" */
+  {
+    // Print to screen instead of making a step
+    if (direction == FWDS)
+    {
+      currentPosition++;
+    }
+    else
+    {
+      currentPosition--;
+    }
+    
+    /* Instead of actually making step, print out parameters for current step */
+    float speed = (float)(ticksPerSec)/p;
+    float accel = (float)(ticksPerSec)*(speed-prevSpeed)/p;
+    printf("%16.3f, %16.3f,  %16.3f, %16ld, %16.3f\n", 0.001*(millis()-millisAtStart), speed, accel, currentPosition, p);
+    prevSpeed = speed;
+  }
+}
+
+/* Calcuate new value of step interval p based on constants defined in timed loop */
+void computeNewSpeed()
+{
+  stepsToGo = computeStepsToGo();
+
+  /* Start of on-the-fly step calculation code, executed once per step */
+  if (stepsToGo == 0)
+  {
+    p = 0; // Not actually a zero step interval, used to switch stepping off
+    return;
+  }
+  else if (stepsToGo >= accelSteps && (long)p > (long)ps) // Changed to make ramps even length
+  /* Speeding up */
+  {
+    p -= deltaP;
+  }
+  else if (stepsToGo <= accelSteps)
+  /* Slowing down */
+  {
+    p += deltaP;
+  }
+  /* else p is unchanged: running at constant speed */
+
+  /* End of on-the-fly step calculation code */
+}
+
+/* Work out how far the stepper motor still needs to move */
+long computeStepsToGo()
+{
+  if (direction == FWDS)
+  {
+    return targetPosition - currentPosition;
+  }
+  else
+  {
+    return currentPosition - targetPosition;
+  }
+}
+
+/* Set the target position and determine direction of intended movement */
+void goToPosition(long newPosition)
+{
+  targetPosition = newPosition;
+  if (targetPosition - currentPosition > 0)
+  {
+    direction = FWDS;
+  }
+  else
+  {
+    direction = BWDS;
+  }
+}
+

src/submission.md

@@ -11,8 +11,6 @@ geometry:
 \maketitle
 \thispagestyle{empty}
 \newpage
-\tableofcontents
-\newpage
 
 # Question 1
 
@@ -27,8 +25,11 @@ 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.
+and tries to bring the rate of change to zero.
+This means that adds a *damping* effect to the controller, slowing it down when it's moving,
+and thereby reducing/eliminating overshoot and oscillations.
 
 # Question 3
 
@@ -68,18 +69,23 @@ Some initialisation is run in `setup` on lines 89 and 90:
 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.
 
+\newpage
+
 # 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.
 
@@ -104,9 +110,11 @@ 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.
 
+\newpage
+
 # Question 8
 
-```{ .matplotlib caption="A plot of velocity and acceleration for SimplisticRampStepper" dpi=150 }
+```{ .matplotlib caption="A plot of velocity and acceleration for SimplisticRampStepper" dpi=300 }
 import numpy as np
 import matplotlib.pyplot as plt
 
@@ -122,17 +130,20 @@ data = np.genfromtxt("csv/SimplisticRampStepper_out_50.csv",
 fig, ax1 = plt.subplots()
 ax2 = ax1.twinx()
 
-ax1.plot(data[TIME], data[SPEED], label='Speed [steps/s]', color='tab:blue')
+lines1 = 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')
+lines2 = 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]')
 
+lines = lines1 + lines2
+ax1.legend(lines, [ l.get_label() for l in lines ])
+
 ax1.set_xlabel("Time [s]")
 
 fig.tight_layout()
 ```
 
-```{ .matplotlib caption="A plot of velocity and acceleration for LeibRampStepper" dpi=150 }
+```{ .matplotlib caption="A plot of velocity and acceleration for LeibRampStepper" dpi=300 }
 import numpy as np
 import matplotlib.pyplot as plt
 
@@ -148,11 +159,14 @@ data = np.genfromtxt("csv/LeibRampStepper_out_50.csv",
 fig, ax1 = plt.subplots()
 ax2 = ax1.twinx()
 
-ax1.plot(data[TIME], data[SPEED], label='Speed [steps/s]', color='tab:blue')
+lines1 = 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')
+lines2 = 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]')
 
+lines = lines1 + lines2
+ax1.legend(lines, [ l.get_label() for l in lines ], loc='upper right')
+
 ax1.set_xlabel("Time [s]")
 
 fig.tight_layout()