Technical Document. Minimum Step on Servo. Tuyen Hoang

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1 Servo Motor for the Dagu - Hoang 1 California State University, Long Beach Department of Electrical Engineering Technical Document Minimum Step on Servo Tuyen Hoang

2 Servo Motor for the Dagu - Hoang 2 Table of Contents ABSTRACT... 3 INTRODUCTION OF THE SERVO... Error! Bookmark not defined. CONNECTION TO THE ARDUINO... 3 CENTERING THE SERVO... 5 CENTERING THE SERVO: CODE... 5 TESTING THE SERVO: CODE... 6 TEST SWEEP... 6 TEST SWEEP: CODE... 7 RAW EXPERIMENTAL RESULTS... 8 RESULTS OF THE MEASUREMENTS... 9 DIFFERENCE OF 8-BIT AND 16-BIT RESOLUTION INTRODUCTION TO THE FAST PWM AND PHASE-CORRECT PWM MODE THEORETICAL 127 POSSIBLE POSITIONS FOR THE 8-BIT RESOLUTION THEORETICAL 127 POSSIBLE POSITIONS FOR THE 8-BIT RESOLUTION:CODE CONCLUSION REFERENCES... 14

3 Servo Motor for the Dagu - Hoang 3 Abstract The purpose of this document is to elaborate on how to find the minimum step size for the Dagu and which of the resolutions was more preferable to use - the 8-bit or the 16-bit one. A servo is connected to an Arduino and lets the user control the angles of the servo using scripts that can be modified. This document discusses the test that were done to find the minimum step size possible for the servo and the reasoning why the 16-bit resolution is more preferable for controlling the servo. Introduction of the Servo A servo is a small motor, and includes a potentiometer that can be modified for different applications, a gearbox, an integrated circuit (could be an amplifier), and an output shaft bearing. Servos are used in many applications, including radio controlled vehicles, helicopters, robots, etc. Servos are either geared for torque, or for speed, having to sacrifice one or another. A servo has usually three wires connected to it, usually red, yellow, and black. The red one is for power (usually supplies 5 to 6 volts), the black one is for ground, and the yellow one is the control input line. The colors of the wire may vary. There are digital and analog servos. The difference between these two is how a signal is processed by a receiver. An analog servo receives a signal at 30Hz. A digital servo receives a signal that updates the servo motor position 300 times a second, ten times more than of an analog servo. Digital servos send a pulse that can be controlled and are usually more accurate than analog servos.

4 Servo Motor for the Dagu - Hoang 4 Connection to the Arduino In order to find the step size of the servo, first the servo was connected to the Arduino, using the GND, +5V, and PIN9 for control, which is the pulse signal, and is controlled by pulse width modulation (PWM). PIN9 was used because this pin enables the PWM functions with a 16-bit resolution, which is discussed later. The control wire can also be connected to PIN11 or other pins for an 8-bit resolution, depending on the application. Figure 1 shows the connections from the servo to the pins on the Arduino. Pin Layout for a 16-bit resolution Figure 1: Pin Layout for a 16-bit resolution (Azega 2012)

5 Servo Motor for the Dagu - Hoang 5 Centering the servo To test the servo, the code for centering the servo is used to determine the exact center of the Dagu. Following this, the code was included in a new script called Testing the Servo. This script was used to also test the servo, but additionally gives the user the ability to determine the minimum and maximum points and to modify the step size. A different, more efficient (or accurate) script Test Sweep is discussed later, used in order to find the minimum step size possible and is tested using a laser in order to find the angle of the step size. After that, the 8-bit and 16-bit resolutions are compared, and it is determined which one is more preferable to use on the Dagu. Centering the servo: Code #include <Servo.h> Servo servo1; // initiate servo object "servo1" const int center = 1500; void setup() servo1.attach(9,1100,1900); // attaches the servo on pin 9 (servo 1) servo1.writemicroseconds(center); //center the servo delay(2000); servo1.detach(); void loop() The value 1100 was used to set the starting position and 1900 was determined to be the ending position was used to set the center. Either PIN9 or PIN10 can be used here, as both pins are controlled by Timer1.

6 Servo Motor for the Dagu - Hoang 6 Testing the servo: Code #include <Servo.h> Servo servo1; // intantiate servo object "servo1" const int center = 1500; void setup() servo1.attach(10,1100,1900); // attaches the servo on pin 10 to servo1.writemicroseconds(center); delay(2000); void loop() for(int pos = 1100; pos < 1900; pos += 2) servo1.writemicroseconds(pos); delay(15); // waits 15ms for the servo to reach the position for(int pos = 1900; pos > 1100; pos -= 2) servo1.writemicroseconds(pos); delay(15); // waits 15ms for the servo to reach the position delay(2000); Test Sweep The script Test Sweep, which was discussed earlier in this document, was modified to change the minimum and maximum angle of the Dagu (only limited by its physical frame, hindering it to move further up or down). The angle, stored in pos could be changed to determine the angle. For this experiment, the angle was made arbitrarily small in order to find the minimum step size that the servo was able to produce.

7 Servo Motor for the Dagu - Hoang 7 Test Sweep: Code #include <Servo.h> Servo myservo; int pos = 0; // create servo object )to control a servo // variable to store the servo position void setup() myservo.attach(10); // attach the servo to pin 10 (16-bit to the servo object void loop() myservo.write(75); delay(2000); for(pos = 0; pos < 90; pos += 1) // center the servo // wait 2s before starting the loop // go from 0 degrees to 90 degrees // in steps of 1 degree myservo.write(pos); delay(100); // tell servo to go to position in variable 'pos' // wait 100ms for the servo to reach the position for(pos = 90; pos>=0; pos-=1) // go from 90 degrees to 0 degrees myservo.write(pos); delay(100); // tell servo to go to position in variable 'pos' // wait 100ms for the servo to reach the position

8 Servo Motor for the Dagu - Hoang 8 Raw Experimental Results 1 step 30cm Distance 150cm Distance Distance/Angle (for 16-bit) 0.41cm cm 0.73 Distance/Angle (for 8-bit) 1.25cm cm 2.14 Table 1 10 steps 30cm Distance 150cm Distance Distance/Angle (for 16-bit) 4.05cm 7.69 => 7.69/10= cm 7.28 => 7.28/10=0.728 Distance/Angle (for 8-bit) 12.42cm => 22.49/10= cm => 20.43/10=2.043 Table 2 30 steps 30cm Distance 150cm Distance Distance/Angle (for 16-bit) 12.0cm => 21.82/30= cm => 21.07/30=0.702 Distance/Angle (for 8-bit) 49.1cm => 58.58/30= cm => 57.21/30=1.907 Table 3 For the 8-bit resolution, when measuring 30 steps for both 30cm and 150cm distance, the results were undesirable. The numbers did not come out as expected and was due to the instability and jittering of the servo. This was a problem when using the 8-bit resolution.

9 Servo Motor for the Dagu - Hoang 9 Results of the Measurements To measure the step size, a laser, which was mounted to the Dagu, was used to point to the wall. One step upwards was applied and the laser was pointed at a straight angle to the wall. The change in distance on the wall was measured using a piece of tape; one tape to mark the position of the initial step and another one to mark the final position of the step. In order to so, the delay value between each step had to be high enough to see each step separately, e.g. 10 seconds when it was necessary to measure the step. The initial step was determined to be 1.9cm, at a distance of 150cm from the end of the laser to the wall. The angle was calculated to be Another test was done at a distance of 30 cm from the end of the laser to the wall; this step was determined to be 0.4cm which corresponds to an angle of Another test, where 10 steps instead of a single step was run for accuracy: it yielded more accurate results. The results can be found on page 8. Figure 2 shows the graphical representation of one step measured at a 150cm distance using a 16-bit resolution. Graphical Representation of the Experiment for the 16-bit resolution Figure 2: Graphical representation of the Experiment for the 16-bit resolution

10 Servo Motor for the Dagu - Hoang 10 Difference of 8-bit and 16-bit resolution After determining the step size with a 16-bit resolution, the step size was found using an 8-bit resolution. For this, the Dagu was connected to PIN11 of the Arduino, using Timer0 with an 8- bit resolution with 256 values. As expected, the results were not as good, but for the sake of testing purposes, the measurements for the step size were done for the same distances of 30cm and 150cm. Similar to the measurements of the 16-bit resolution, for both a 30cm and a 150cm distance, the distances and angles for one step, ten steps and thirty steps were found. Achieving a step size of below 1 degree was not attainable for one step, the angle increased to 2.38 for a 30cm distance and 2.14 for a 150cm distance. For ten steps, the angle increased to and 2.043, respectively. This was as expected, and as a result, the Dagu should be always connected to Timer1 to obtain a 16-bit resolution in order to get a smaller and more accurate step size. The timer register was used to configure the prescaler of the timer was not necessary in this case. A big issue of using an 8-bit resolution was that, assuming an active pulse between 1ms and 2ms (the servo sends a pulse every 20ms), the duty cycle comes out to be 5% (1ms/20ms). As a result, connecting the servo to a pin with 8-bits, or 256 values, gave the servo room for only 12 to 13 positions, since 5% of the total 256 values were For a 16-bit timer, 5% means that the servo could move to 3277 different positions, theoretically, which exceeds the physical capabilities of the servo by far (the servo cannot move to 3000 different positions physically), meaning that the servo could make the step size as small as the rotors would allow. Even though the theoretical values assume that there are only 12 to 13 possible positions, the experiment lead to follow that there it is possible to obtain more than 12 or 13 positions with the 8-bit resolution. The reason is explained in the next section.

11 Servo Motor for the Dagu - Hoang 11 Introduction to the Fast PWM and Phase-Correct PWM mode The 8-bit Timer2 (TMR2) is able to operate in four PWM modes. This section focuses on the two modes that are related to this topic: Fast PWM mode and Phase-Correct PWM mode. These two modes provide the user more control over the duty cycle and frequency of the signal. analogwrite() can be used for most applications, however, the user cannot control the frequency. When using the Fast PWM mode, the timer counts from continuously. For this mode, the two different output compare register values can be set independent of each other, each affecting a different output pin (OCnA, OCnB) (Hill 2012). The output is HIGH when the timer is 0, and LOW when the timer equals the output compare register. For the Phase-Correct PWM mode, the timer counts from 0 to 255, similiarly to the fast PWM mode, however it then jumps back to 0. The output is more symmetrical compared to the other modes due to the fact that the output is turned off as the when the value of the timer matches the value of the output compare register when counting from 0 to 255, and turned on, when it matches the value again, when counting from 255 to 0. The output frequency for this mode is about half the value compared to the fast PWM mode. For further information please refer to the Timer with PWM lecture. Theoretical 127 Possible Positions for the 8-bit resolution To achieve more than the 12 or 13 possible positions that the 8-bit resolution provides, a 2ms period is used, instead of a 20ms period like before. Derived from the information of the previous section, TMR2 repeatedly counts up to the value of a certain register. An interrupt is implemented after every cycle. Inside the interrupt, for the duty cycle of 9 cycles out of 10 is set to 0%. On the 10 th cycle, the servo pulse is generated, and ranges from 1ms to 2ms, in other words, from 128 to 255bit, meaning that now there are 127 possible positions for the servo.

12 Servo Motor for the Dagu - Hoang 12 Theoretical 127 Possible Positions for the 8-bit resolution: Code int counter = 0; void setup() nointerrupts(); TCCR2 = 0; TCNT2 = 0; OCR2 = 10; TCCR2A = (1 << CS12); TCCR2B = (1 << CS12); TIMSK2 = (1 << OCIE1A); interrupts(); ISR(TIMER1_OVF_vect) counter++; OCR2 = 0; if(counter = 1) 0CR2 = 10; if (counter = 10) counter = 0; // enable all interrupts // enable output compare register // reset counter void loop() A counter variable is used to keep track of 10 interrupts. TMR2 is configured to overflow an interrupt every 2ms. In the interrupt, the variable counter is incremented to keep track on how many 2ms interrupts have occurred. In one of the interrupts, the output compare register (OCR2) is enabled which compares TMR2 to a value in the register and outputs either 1 or 0. In the remaining interrupts, OCR2 is disabled to keep the output to 0. To go even further, the interrupt could be at 20ms, setting the pulse to 1 and then another interrupt could be implemented for 1ms before the PWM is started. That way, 255 positions would be possible. As good as it sounds; the 8-bit resolution is not able to provide full 255 positions, or even 127 positions. The Arduino has problems of outputting steps from an 8-bit resolution. An 8-bit resolution is able to output results close to the 16-bit resolution; however, it is coupled with possible instability and jittering.

13 Servo Motor for the Dagu - Hoang 13 Conclusion In conclusion, the minimum step size was found by using the modified script Testing Sweep in conjunction with the Dagu connected to the Arduino. It was possible to see each step due to setting up a high delay between each step. Two steps were measured, and the distance between those two steps were noted down. Having that distance, and using a predetermined distance between the Dagu and the wall, it is possible to calculate the angle. A smaller angle was preferable. In this document, two resolutions were being tested on 8-bit and 16-bit with 16- bit being the better one, because it allowed the servo to be more accurate. Using the 8-bit resolution, it was possible to get results similar to the 16-bit resolution, however with drawbacks such as possible jittering and instability of the servo. The real minimum number of bits is determined to be at least 10 bits. 8 bits is not enough to serve the purposes of Mission Payload. The 16-bit resolution provided a better result; hence it was chosen to control the servo and the Dagu.

14 Servo Motor for the Dagu - Hoang 14 References Azega Hill, Gary