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Laboratory Manual: ME 80: System Dynamics and Controls John Webster, Susan Zheng, and William Messner

ME 94 Project—Fall 2014

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Table of Contents 2 - Table of Contents / Arduino Resources

3 - How to use this manual

4 - Lab 1: Introduction to Arduino and control systems

10 - Lab 2: System control with a photoresistor

15 - Lab 3: System control using a motor with quadrature

encoder

22 - Lab 4: System Identification from step response

26 - Lab 5: Time domain frequency response of motor system

A note on available Arduino resources: The Arduino is an open source pla orm with many sample code op ons posted on the Arduino playground site:

h p://playground.arduino.cc/

The code in these labs has been adapted from various examples on this site. Some labs have links to specific topics for more informa on.

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How to use this manual:

Each Lab exercise in this manual is comprised of three parts:

1. Pre‐lab and setup: Before the lab, assemble the circuit using the diagram provided. For some of

the labs, there will be test or calibra on code to ensure the circuit is connected properly and the

Arduino is gathering data.

2. In Lab: Read and understand the included code, which is bordered in blue. There are comments

highligh ng important sec ons. Use this code to gather data, which can be cut and pasted into an

Excel spreadsheet.

3. Post‐Lab: Modify or write new code to change the func on of the circuit or controller. Some labs

include data analysis .

To ini ally set up your Arduino and breadboard, use the

adhesive to tape the breadboard in place, and carefully

snap the Arduino into the clips. Be gentle with this, as the

boards can snap easily during this step.

To connect the Ardunio to your computer,

connect the serial cable as shown. The

computer can only provide limited current,

so connect the 9V using the provide cable.

The power LED should light green.

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Lab 1: Introduction to Arduino and control systems

Before Class

1. Download the appropriate Arduino so ware for your OS from www.arduino.cc/en/Main/So ware

2. Assemble the circuit shown in Fig.1 below.

3. Read the breakdown of the code for Part 1. Most Arduino programs follow this structure.

4. Enter the code on the following page into the Arduino window to make your LED flash on and off every second.

Materials

The Arduino microcontroller is a powerful way to use your computer to control

devices in the real world. This lab will introduce you to the basics of se ng up

and using the Arduino to control a simple set of flashing LEDs.

Arduino board, breadboard, and USB cable

6 red LEDs

6 330 Ω resistors (informa on on resistor color‐coding can be found here: resistor chart )

1 10K Ω resistor

1 push bu on switch

Assorted jumper cables

Figure 1: Setup for 1 blinking LED. Note that LEDs have a posi ve and nega ve

side and must be oriented correctly to func on. For this circuit, the posi ve wire

should be connected to pin 2. Use a 330 Ω resistor in this circuit.

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//Blinking LED

//This code will cause 1 LED mounted on pin 2 to flash on and off every second

int LEDpin=2;

void setup()

pinMode(LEDpin, OUTPUT);

Comment sign (//) allows for titles and explanations,

Light grey text indicates a comment

Creates an integer variable and assigns a value to it

Breakdown of Code for Part 1

Semicolon follows every command like the period at the end of a sentence

In this case, LEDpin is assigned the value 2

Assigns functions to pins on the Arduino board

Sets pin 2 (LEDpin) to output mode

Brackets indicate beginning and end of void xxxx () commands

void loop()

digitalWrite(LEDpin,HIGH);

delay(1000);

digitalWrite(LEDpin,LOW);

delay(1000);

Creates a repeating loop

Turns LEDpin (2) on to High (5 Volts)

Waits 1 second (1000 milliseconds)

Turns off LEDpin

Waits another second

Bracket indicates end of void loop () command

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//Blinking LED

//This code will cause 1 LED mounted on pin 2 to flash on and off every second

int LEDpin=2;

void setup() pinMode(LEDpin, OUTPUT);

void loop() digitalWrite(LEDpin,HIGH);

delay(1000);

digitalWrite(LEDpin,LOW);

delay(1000);

Copyable code for Part 1

In Lab

1. Expand the circuit to the 6 LED and switch configura on shown

in Fig. 2

2. Using the example code from Part 1, write your own code us‐

ing the same format to make the LEDs flash in sequence.

3. Using the code for Part 2, use the bu on to create a simple

counter.

Figure 2: Setup for part 2. The 10K Ω resistor connects the

push bu on switch to ground.

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Code for Part 2:

const int Button = 11;

int buttonPushCounter = 0;

int buttonState = 0;

int lastButtonState = 0;

void setup()

pinMode(Button, INPUT);

pinMode(2, OUTPUT);

pinMode(3, OUTPUT);

pinMode(4, OUTPUT);

pinMode(5, OUTPUT);

pinMode(6, OUTPUT);

pinMode(7, OUTPUT);

Serial.begin(9600);

void loop()

delay(100);

buttonState = digitalRead(Button);

Creates integer variables

Sets up board outputs

Initiates serial communication, click

icon to view

Checks if the button is pressed

Code con nued on next page

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if (buttonState != lastButtonState)

if (buttonState == HIGH)

buttonPushCounter++;

Serial.println("on");

Serial.print("number of button pushes:");

Serial.println(buttonPushCounter);

else

Serial.println("off");

lastButtonState = buttonState;

if (buttonPushCounter == 1)

digitalWrite(2, HIGH);







If the button state has changed, a button press is registered

The number of button presses is output to the serial monitor (println is equivalent to hitting Enter on the monitor)

A series of IF statements turns on one more LED for every button press


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if (buttonPushCounter > 6)

buttonPushCounter = 0;

digitalWrite(2, LOW);






Post Lab

1. Draw the system block diagram of each varia on

of the circuit

2. Are any of these systems feedback loop systems?

3. Using the code for part 3, use the bu on circuit

to create a binary counter. Hint: (use if

statements for each of the LEDs and the %

command to determine remainders.

For example, the first LED lights on odd numbers, so

the code would be

if (buttonPushCounter %2 ==1)


else digitalWrite(2, LOW);

After 6 presses, the counter resets to 0, and all the LEDs are turned off

Summary of Deliverables:

1. Block diagram of the 2 LED systems

2. Arduino code for a Binary Counter

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Lab 2: System identification and control with a photoresistor

Before Class

1. Assemble the circuit shown in Fig. 1below, and place it in the kit box.

2. Using the instruc ons for Part 1 on the next page, write code to calibrate the LED and photoresistor setup.

3. Using the output from the serial monitor, plot a graph of LED output vs. photoresistor input in Excel.

Materials

The photoresistor adds a sensor component to control the brightness of the LEDs as a

closed loop system. This lab will implement two controllers: Propor onal and

Propor onal‐Integral, and compare their effec veness.

3 yellow LEDs (higher energy than red ones)

3 330 Ω resistors

1 10 KΩ resistor

1 photoresistor

Arduino and breadboard

Jumper cables and alligator clips as appropriate

Fig. 1. Circuit for Lab 2.

‐Note that the 330 Ω

resistors are for the

LEDS and the 10KΩ is

for the photoresistor.

‐Remember that LEDs

must be oriented

with short end to

ground

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Part 1: Calibra ng the photoresistor

With the Arduino and breadboard inside the kit box (to limit external light), implement the fol‐

lowing code to calibrate the photoresistor. Using the output from the serial monitor, plot the

resistor value vs. the output value by copying the serial values into Excel. Use values up to the

END OF READINGS message. Record the resistor value with output 0, the maximum resistor val‐

ue, and at what brightness it is reached.

//LAB 2 Part 1

int value=0;

int brightness = 0;

void setup ()

pinMode(A0, INPUT);

pinMode(3, OUTPUT);

Serial.begin(9600);

Serial.print("Value");

Serial.println(" Brightness");

void loop ()

analogWrite(3,brightness);

delay(100);

value=analogRead(A0);

Serial.print(value);

Serial.print(" ");

Serial.println(brightness);

delay(100);

brightness = brightness+1;

if (brightness >255)

Serial.println("END OF READINGS");

NOTE: The brightness is being changed using a

Pulse Width Modula on (PWM) signal. This

signal can vary from 0 (on 0%) of the me to

255 (always on). A PWM signal rapidly turns

the LED (or motor or anything else) on and off

to make it dimmer (or move more slowly).

Because the maximum PWM output is 255, the program will output an END OF READINGS message

Every time the code completes 1 loop, the brightness output increases by 1


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//LAB TWO STEP RESPONSE:

int SensorValue;

double currentMillis;

double previousMillis = 0;

long interval = 10;

void setup()

pinMode(A0, INPUT);

pinMode(3, OUTPUT);

Serial.begin(9600);

Serial.print(" ");

Serial.print(" ");

Serial.println("Time");

Serial.print(" Sensor Value");

void loop()


currentMillis = millis();

if (currentMillis - previousMillis > interval)

previousMillis = currentMillis;

SensorValue = analogRead(A0);

Serial.print(currentMillis/1000);

Serial.print(" ");

Serial.println(SensorValue);

Creates a 32 bit (10 digit) integer

This code uses the milils() function instead of a delay() function. millis() records the number of milliseconds since the program started running for more accurate timing. With an interval value of 10, the code prints a new sensor value every 10 milliseconds.

Part 2: Iden fying the system step

response

A number of factors in a system can be

iden fied by observing the system response to

a step input.

1. Enter the code provided and use the serial

monitor to plot the output vs. me in Excel

2. Using the methods described in Lecture 9,

iden fy the system parameters. Is this a 1st

or 2nd order system?

In Lab

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int brightness = 0;

float Kp = 0.1;

int outputValueint = 0;

int error=0;

int refValue = 800;

int SensorvValue;

float Output;

double Time;

void setup ()

pinMode(A0, INPUT);

pinMode(3, OUTPUT);

Serial.begin(9600);

Serial.print("Time");

Serial.print(" SensorValue");

Serial.print(" LEDbrightness");

Serial.println(" Error");

void loop ()

analogWrite(3,brightness);

delay(100);

int SensorValue = analogRead(A0);

error = refValue - SensorValue;

Time = millis();

Serial.print(Time);

Serial.print(" ");

Serial.print(SensorValue);

Serial.print(" ");

Serial.print(brightness);

Serial.print(" ");

Serial.println(error);

Output = Kp*error;

brightness = (int) Output;

if (brightness == 256)

brightness = 255;

if (brightness > 255)

brightness = 255;

if(brightness < 0)

brightness = 0;

Part 3: Propor onal Control

1. Using the code provided, implement a propor‐

onal controller on the system and plot the re‐

sponse vs. me in Excel.

2. Is there s ll error a er the system has been

running for a while? What is the value?

Your reference value should be below the saturation value identified in Part 1

If the system is not arriving at a steady state, reduce the Kp value.

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Post lab: Propor onal + Integral control

Using the above block diagram and the code provided for

Part 2, write code to add integral control to your propor on‐

al controller. The shell code is provided below:

Loop:

Write output to LED

Read sensor value

Error = Reference — sensor value

error_integral = Error + error_integral

Output = Kp *error + Ki* error_integral

Plot your output value in Excel and compare to propor onal

control. Is this controller faster? What is the difference in

steady state errors?


1. Calibra on plot with photoresistor values at PWM of 0,

photoresistor satura on value, and PWM output where this

occurs.

2. System response plot of Propor onal controller and steady

state error value

3. PI controller response plot and steady state error value.

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Lab 3: System control using a motor with a quadrature encoder

Before Class

Materials

This lab will implement the same Propor onal and Propor onal‐Integral controllers

used in Lab 2 on a motor with a mounted encoder to control the motor speed.

1 Pololu 9.7:1 Gearmotor with 48 CPR Encoder

1 H bridge integrated circuit

Wires and jumper cables as necessary

Arduino and Breadboard

Fig. 1: Circuit for Lab 3

1. Assemble the circuit as show below, using the diagrams on the fol‐

lowing page to assist in connec ng the H‐bridge

2. Write code using the shell provided to power up the motor and en‐

sure it is working correctly

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Part 1: The H‐bridge

The H‐bridge integrated circuit contains two pairs of transistors which change the polarity of an

input voltage, allowing the direc on of the motor to be changed using code instead of physically

modifying the circuit. It also provides the maximum voltage and amperage to the motor while

using a digital PWM (see Lab 2, page 8 for an explana on) input to specify the speed.

Figure 2: Diagram H Bridge transistors

Figure 3: The H‐bridge chip. Note the indent marking

the top of the chip. Make sure this indent is poin ng

towards the top of the breadboard in your circuit.

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Figure 4: Wiring diagram for the H‐bridge. To

build the circuit in Figure 1 connect the pins as

follows:

H‐bridge pin Connects to

1 Arduino pin 9

2 Arduino pin 7

3 Motor Lead 1

4,13 GND

5,12 GND

6 Motor Lead 2

7 Arduino pin 6

8 Arduino Vin

16 +5V

To connect to the motor:

Color Func on

Red Motor Lead

Black Motor Lead

Green encoder GND

Blue +5V

Yellow encoder A output (Arduino pin 2)

White encoder B output (Arduino pin4)

To connect to the Arduino:

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Part 1: Tes ng the motor

To ensure the motor is working correctly, write

code to turn the motor on using the H‐Bridge.

Shell code is provided below:

1. void setup()

—Set pins 6, 7, and 9 to OUTPUT

—Digital write pin 6 to HIGH and pin 7 to LOW —Digital write pin 9 to HIGH

2. void loop() — leave this empty, this code just runs the motor con nuously.

Part 2: Implemen ng Propor onal Control

1. Use the following code to implement a propor‐

onal controller for the speed of the motor.

This code uses an Interrupt to read the encoder

while rapidly switching back and forth to calculate

and output the velocity and run the controller.

More informa on here: interrupts

2. Plot the Motor Speed vs. Time and observe the

steady state error.

To ensure the H‐bridge is func oning properly, set 6 to LOW and 7 to HIGH and see that the motor turns the other direc on.

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#define encoder0PinA 2 #define encoder0PinB 4 volatile long encoder0Pos=0; long newposition; long oldposition = 0; double newtime; double oldtime = 0; double vel; int refSpeed = 200; int error = 0; float Output; float kp = 0.2; void setup() pinMode(9, OUTPUT); pinMode(7, OUTPUT); pinMode(6, OUTPUT); digitalWrite(7, LOW); digitalWrite(6, HIGH); digitalWrite(9, HIGH); pinMode(encoder0PinA, INPUT); digitalWrite(encoder0PinA, HIGH); pinMode(encoder0PinB, INPUT); digitalWrite(encoder0PinB, HIGH); attachInterrupt(0, doEncoder, RISING); Serial.begin (9600); Serial.println(" "); Serial.println(" "); Serial.print("Time"); Serial.print(" Motor Speed"); Serial.print(" Output"); Serial.println(" Error");

Code for Part 2

Calls doEncoder function as an Interrupt

If speed is output as negative (or a number greater than 1,000, switch the HIGH and LOW values on pins 6 and 7 to change motor direction with the H-bridge


Adjust Kp if system is not stabilizing or is responding slowly.

The volatile keyword lets the pro-gram know the value will change with the Interrupt, so it will not remain the same every loop

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void loop()

newposition = encoder0Pos;

newtime = (.000001*micros());

vel = abs((newposition-oldposition)/(newtime-oldtime));

error = refSpeed - vel;

Output = kp*error;

analogWrite(9,Output);

if(Output == 256)

Output = 255;

if(Output > 255)

Output = 255;

if(Output < 0)

Output = 0;

Serial.print (newtime);

Serial.print (" ");

Serial.print(vel);

Serial.print (" ");

Serial.print(Output);

Serial.print (" ");

Serial.println(error);

oldposition = newposition;

oldtime = newtime;

delay(50);

Reads current runtime in microseconds and converts to seconds

Calculates rotational speed in counts/sec by dividing difference in encoder position and dividing by the elapsed time in seconds

Proportional controller section (same as in Lab 2)


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void doEncoder()

if (digitalRead(encoder0PinA) == digitalRead(encoder0PinB))

encoder0Pos++;

else

encoder0Pos--;

The doEncoder function is run every time the encoder value changes in the Interrupt

Post lab: Propor onal + Integral control

Using the above block diagram and the code provided for

Part 2, write code to add integral control to your propor on‐

al controller. The shell code is provided below:

Loop:

Write output to Motor

Read encoder value

Error = Reference — sensor value

error_integral = Error + error_integral

Output = Kp *error + Ki* error_integral

Plot your output value in Excel and compare to propor onal

control. Is this controller faster? What is the difference in

steady state errors?


1. Plot of Motor Speed vs. Time for Propor onal and PI

controllers

2. Steady state error values

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Lab 4: System Identification from Step Response

Before Class

Materials

This lab will use the same motor with encoder to determine the system proper es and

transfer func on from the motor response to a step input—in this case from a low to

high speed.






1. Assemble the circuit as show below. It is the same circuit as Lab 3, just with a bu on connec ng

one of the motor leads to the 5V output on the Arduino.

2. Using the code you wrote in Lab 3, Part 1, test that the bu on is working correctly by uploading

the code and pressing the bu on. The motor should speed up. If it shuts off, connect the jumper

from the switch to the opposite motor lead and test again.

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Part 1: System Parameters from Step Response

#define encoder0PinA 2

#define encoder0PinB 4

volatile long encoder0Pos = 0;

int newposition;

int oldposition = 0;

double newtime;

double oldtime = 0;

double vel;

const int numReadings = 11;

int readings[numReadings];

int index = 0;

int total = 0;

int average = 0;

The Pololu encoder does not read steady state speeds very accurately, as small varia ons in

ming intervals can cause large varia ons in motor output speed. To limit this effect, this

code employs a smoothing algorithm to calculate a floa ng average motor speed (based off

of 11 samples). This allows for smoother measurements while s ll maintaining enough res‐

olu on to observe the step response.

Part 1: Code


Sets number of values in each calculated average

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void setup()

pinMode(9, OUTPUT);

pinMode(6, OUTPUT);

pinMode(7, OUTPUT);

Serial.begin(9600);

Serial.println(" ");



Serial.println(" Motor Speed");

attachInterrupt(0, doEncoderA, CHANGE);

attachInterrupt(1, doEncoderB, CHANGE);




for (int thisReading = 0; thisReading < numReadings; thisReading++)

readings[thisReading] = 0;

void loop()

newtime=(.000001*micros());

if ((newtime-oldtime)>.00001)

newposition=encoder0Pos;

vel=abs((newposition-oldposition)/(newtime-oldtime));

total= total - readings[index];

readings[index] = vel;

total= total + readings[index];

index = index + 1;

if (index >= numReadings)

index = 0;

average = total / numReadings;

Serial.print(newtime);

Serial.print(" ");

Serial.println(average);

oldposition=newposition;

oldtime=newtime;

Attaches interrupts both A and B encoders for higher resolution

Measures average speed from the measured motor speeds and number of readings


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void doEncoderB() if(digitalRead(encoder0PinA) == digitalRead(encoder0PinB)) encoder0Pos++; else encoder0Pos--; void doEncoderA() if(digitalRead(encoder0PinA) == digitalRead(encoder0PinB)) encoder0Pos--; else encoder0Pos++;

Recording Data:

1. To start, upload the code and open the serial monitor. The motor should spin slowly and the

velocity output should be roughly constant (make sure autoscroll is turned on).

2. Push the bu on, and the motor will spin faster, as the values on the serial monitor increase to

a second steady state value.

3. Once the steady state value is reached, turn off autoscroll, and copy the me and motor speed

data into excel and plot.

Data Analysis:

1. Using the methods described in Lecture 9 and the 7‐fold Way, fit a transfer

func on to the data, and use MATLAB to generate the Bode plot.

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Lab 5: Time domain frequency response of the motor system

Before Class

Materials

This lab will compare the transfer func on generated in

lab 4 with an actual sinusoidal input to the motor.






1. Assemble the circuit as show below — This is the same circuit as labs 3

and 4, but the bu on switch from lab 4 will not be used.

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//Lab 5 frequency response

#define encoder0PinA 2

#define encoder0PinB 4

volatile long encoder0Pos=0;

long newposition;

long oldposition = 0;

double newtime;

double oldtime = 0;

long interval = 20;

long vel;

long Output;

int ledPin = 10;

float sinVal;

int ledVal;

const int numReadings = 10;

int readings[numReadings];

int index = 0;

int total = 0;

int average = 0;

In Lab

Use the code provided to input a sinusoidal waveform into the motor and record the response.

Copy and paste the data into Excel to plot the Output and Motor Speed vs. Time. This data will be

compared with the transfer func on derived in Lab 4.

Code for Lab 5:


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void setup()

pinMode(9, OUTPUT);

pinMode(7, OUTPUT);

pinMode(6, OUTPUT);




pinMode(encoder0PinA, INPUT);

digitalWrite(encoder0PinA, HIGH);

pinMode(encoder0PinB, INPUT);

digitalWrite(encoder0PinB, HIGH);

attachInterrupt(0, doEncoder, RISING);

Serial.begin (9600);




Serial.print(" ");

Serial.print("Output");

Serial.print(" ");

Serial.println("MotorSpeed");

for (int thisReading = 0; thisReading < numReadings; thisReading++)

readings[thisReading] = 0;


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void loop()

for (int x=0; x<360; x++)

sinVal = (sin(radians(x)));

Output = int(sinVal*70+185);

delay(10);

analogWrite(9, Output);

newtime = (.000001*micros());

newposition = encoder0Pos;

vel = abs((newposition-oldposition)/(newtime-oldtime));

total= total - readings[index];

readings[index] = vel;

total= total + readings[index];

index = index + 1;

if (index >= numReadings)

index = 0;

average = total / numReadings;

Serial.print(newtime);

Serial.print(" ");

Serial.print(Output);

Serial.print(" ");

Serial.println(average);

if (newtime - oldtime > interval)

oldposition = newposition;

oldtime = newtime;

This For loop is the heart of this lab exercise. It outputs a sine wave varying from 115 (the approximate output where the motor will spin) and 255 (maximum motor speed)

NOTE: if your motor is stopping at any point while the code is running, shift the sine wave up by adding a constant to the

sinVal*70+185 and subtracting half of that value from 70

This exercise also incorporates the smoothing algorithm to reduce timing errors


30

void doEncoder()

if (digitalRead(encoder0PinA) == digitalRead(encoder0PinB))

encoder0Pos++;

else

encoder0Pos--;

Post Lab

A er plo ng the data in Excel, use the graphical method in Lecture 9 to

plot the data as a point on the Bode Plot of the transfer func on obtained in

Lab 4. How close is this point to the actual curve?

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