Mechatronics Lab 3 Group B

8/9/2019 Mechatronics Lab 3 Group B

1/23

UNIVERSITY AT BUFFALO

2010

Authored by: Jenna Curry, Ian Duncan, Ian Clark, Chris Van Loon, Ilya Gartseev

Lab 3 Group B

Speed Control of a DC Motor


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Table of Contents

Abstract 2

Introduction 2

Theoretical Background 2

Wiring Diagram 4

Components List 7

Photographs 8

User Instructions 9

Code Walk Through 9

Comments on Our Controller and Gain Selection Logic 10Simulation 10

Results 11

Limitations 18

Appendix 19

References 22


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Lab 3 Group BSpeed Control of a DC Motor

Abstract

In this experiment we explored the control of a DC motor with a microcontroller. A Basic Stamp II microcontroller

was used in this case with a small fan and Stampplot software. Open loop and closed loop control were both used.

An encoder was made to measure the angular motion of the fan. These parts were accomplished successfully and are

outlined in the following report.

IntroductionThe control of a DC motor is an example of one of the many ways microcontrollers can be used to control a process.

To start our examination we created a sensor to measure the angular motion of the fan. This consisted of a disk

which was half white and half black paired with an infrared emitter and detector.

A transistor coupled with the PWM output of the Basic stamp of the was used to drive the fan. The PWM output

allowed the speed of the fan to be varied. By measuring the speed with a sensor and comparing it to the set speed the

PWM output can be changed to account for error.

The last part of the experiment involved sending data to a computer running the Stampplot software. The data was

sent through a serial port. This allowed us to plot the voltage output to the fan and the rpm. The plots generated

gave a good picture of the performance of our system and any disturbances that arose or were introduced.

Theoretical Background

Voltage Divider

A voltage divider is a simple circuit that produces an output voltage that is a

fraction of the input voltage being supplied. A simple example of a voltage

divider, seen adjacent, consists of two resistors in series, and is commonly

used to create reference signal.

The point of this type of circuits is to be able to control voltage by altering the

resistors used. Often time you cannot alter you power supply, but with

circuits like these it allows us to control the voltage we want to be supplied to a

specific circuit as to not overload it.

DC Fan


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Our DC fan has its theory embedded in the motor that drives it. The Brushless DC (BLDC) motor one the types of

electric motors that are often utilized and in our case it is a synchronous direct current powered which has an

electronic communication system versus a mechanical commutator or brushes. A BLDC is equivalent to a reversed

DC motor in the sense that the magnets moves while the conductor remains stationary.

In our lab we are utilizing a brushless DC fan which is rated at 12 VDC and draws 90mA. It has a cut off voltage of

approximately 3.5VDC. Our BLDC fan is not like a normal DC motor, where operation is still attainable despite the

polarity switch.

DC motors provide substantial speed control for acceleration and deceleration. The basis for this precision is rooted

in the fact it is rooted in how the power supply is connected directly to the field of the motor which allows for a more

precise control.

Brushless motors are more precise when making use of speed operations and torque control. They require adequate

and appropriate control because of entirely electric operation. They are relatively more expensive than brushed

motors but are more precise.

Pulse Width Modulation (PWM)

Pulse-width modulation uses a square waveform to approximate an analog signal or generate voltages somewhere in

between the on and off voltage. By varying the width of this square wave the average voltage will change. Pulse

width modulation can allow a digital device, such as the Basic Stamp to output an analog voltage. This is done by

quickly alternating between high and low and using a resistor and capacitor combination to essentially average the

outputs over time.

Open Loop Control

This is a method that can be used by a controller to modify the operating state of a system to achieve a desired

output. This is one of the simpler forms of control that can be used, since it depends only on the current state and a

model of the system. There is no feedback loop to determine how closely the current state of the system matches the

desired state of the system. This system generally works well if the system has a constant load. For example, if a

constant speed is desired, the model of the system would provide a value for the output voltage necessary for a

certain state and load of the system that is required to achieve that speed. Since there is no feedback if the load

changes, the same voltage value will still be output to the system but will result in a different speed. If the load

changes often, then the speed will fluctuate. Thus, open loop control will succeed in delivering accurate, desired

results only for a system with constant or known variations.

Closed Loop Control

This is a method that uses feedback from the system to more accurately control the system. By using the feedback, or

error signal, it is possible to determine the difference between the state of the system and the desired state. There are

many different techniques of closed loop control, but one of the most widely used and the one that was used in this

lab is called PID (Proportional-Integral-Derivative) Control. This method is used to keep the state of the system

constant and uses three methods together to achieve this goal. The Proportional part of the control involves changing


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the output proportionally to the current error between the state and the desired state. If this could be enacted

instantaneously, the observed error could be corrected instantaneously, and the system would behave as desired.

However, while the output is being adjusted to correct for the error and the new state of the system is being

obtained, the conditions of the system can be changing. Thus, the new state can still contain error. To help predict

and minimize the error, two additional terms are used. The Derivative part of the control involves an error term that

is proportional to the rate at which the error is changing. This term can help the system to react more quickly or tonot overshoot the desired value since using the rate of change of the error can help to predict whether the system is

approaching the desired state. The Integral term of the controller takes into account the duration that an error has

existed. Thus, the longer the error has existed and the greater the magnitude of this error, the larger the integral

error term will be. Essentially, the Integral term attempts to eliminate long term error but can cause the system to

overshoot the target value in certain cases because previous errors are taken into account. This process may appear

complex, but is experienced intuitively every day in activities such as driving a car. In this lab, PWM was used to

output the voltage level calculated by the closed loop controller and was used to maintain a constant speed of a fan.

The weight of each of the error terms, the limitations on this particular system and the results of the controlled fan

system are discussed below.

Wiring Diagram

The schematic of the Lab 3 hardware is shown in the figure below.


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BS2

P0

5

P1

6

P2

7

P3

8

P4

9

P5

10

P6

11

P7

12

P8

13

P9

14

P10

15

P11

16

P12

17

P13

18

P14

19

P15

20

ATN

3

RES

22

TX

1

RX

2

U1

BS2-IC

Lab3.SpeedControlofaDCMotor

GroupB

P8

P13

P14

Version1

CS

1

VIN(+)

2

VIN(-)

3

GND

4

VCC

8

CLK

7

VREF

5

DO

6

U2

ADC0831

P13

GND

VD

D

P14

Tx

R1

10k

C1

1uF

3 2

1

8 4

U4

LM358N

R2

10k

R3

10k

Q1

2N3904

VIN

+88.8

kRPM

U1:A(OP)

U1:A(+IP)

Q1(E)

R3(1)

R4

1k

R6

1k

P15

P15

12

64

U3

QRB1114

R5

100R

R7

220R

Q2

2N3904

R8

1k

R9

220R

P8

P2

P2


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The integrated circuit U1 depicts Basic Stamp II (BS2) module.

The bottom-left part of the schematic drawing depicts control circuit for the opto-reflective sensor. The component

U3 is an opto-reflective switch QRB1114. The component Q2 is a transistor for amplifying output of opto-reflective

switch. The signal P8 goes to the input port of BS2 module.

The upper part of the schematic drawing depicts the control circuit for the fan. The operation amplifier U4 serves as

buffer between the processor port and fan powering circuit. Because the Op-Amp can only supply ~20mA, the

transistor Q1 (2N3904) is used for powering the fan.

The integrated circuit ADC0381 is an 8-bit successive approximation analog-to-digital converter with a serial I/O

and configurable input multiplexers with one channel.

The figure below is the wiring diagram for the device


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Components List

Quantity References Value Order Code

9 resistors

1 R5 100, 1/4W, 5% 150-010111

3 R1, R2, R3 10K, 1/4W, 5% 150-01030

3 R4, R6, R8 1K, 1/4W, 5% 150-01020

2 R7, R9 220, 1/4W, 5% 150-02210

1 capacitor

1 C1 1 uF electrolytic capacitor 201-01050

4 integrated Circuits

1 U1 BS2-IC, Basic Stamp II module BS2-IC

1 U2 ADC0831 ADC0831

1 U3 QRB1114 QRB1114

1 U4 LM358 602-00015

4 Miscellaneous

1 StampWorksTM

Board of Education 28803

1 Fan 12 VDC brushless fan 700-00040

1 Q1, Q2 2N3904 500-00001

1 All parts are fromhttp://www.parallax.com
http://www.parallax.com/http://www.parallax.com/http://www.parallax.com/http://www.parallax.com/


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Photographs

The following are photographs taken of our device when completed.


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User Instructions

The set of user instructions below are to operate Group Bs BSII setup. It assumes the program has been

loaded to the modules memory and the power supply is plugged in.

The basic operation of this setup is to observe and monitor speed control of the DC fan. There is no button necessary

to activate the fan, neither are there any buttons to control its speed. It is monitored via opto-reflective switch and itsspeed is controlled via the code implemented in the Basic Stamp. This sensor along with the code allows it to vary its

speed based on the feedback it is receiving DC fan.

Operation of the fan can come from being able to alter the code by following the instructions below.

To change parameters:

Change set speed between 2000 and 6000 in the code under set-speed in the main routine of the code. Change Kp and Kd.

* NOTE: To set value for Kp

and Kd

[Value = x/65536]*

To run

Press play button within the Basic Stamp editor Close Debug Window Open Stamp Plot program and choose Basic x-y plot Connect to desired port with connect button

Code Walkthrough

Our code begins by declaring the size and names of most variables used in the system. This is followed by specifying

the pins to be used to drive the fan and used the ADC. The constants, variables and pins used by the optical encoder

are then given. This ends the declarations section.

The main routine starts by assigning initial values to variables. Next, commands are sent to the Stampplot software to

initialize plotting and set program parameters to our liking. Last the main program loop is started and the code

moves to various subroutines in order.

The first subroutine calculates the error between the set speed and the measured speed. This is performed by

subtracting one from the other. This gives the magnitude of the error. Also calculated is the sign of the error to beused in future calculations.

The next subroutine uses the error calculated in the first for proportional control. The user sets proportional gain

adjusts the amount change made in the system. The selection of this gain is discussed in the following section. Also,

the gain is multiplied using the multiply high command (**), which allows you to multiply fractions in increments of

1/65535.


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A derivative control subroutine follows the proportional control. This subroutine evaluates the rate at which the

error is changing and changes the system accordingly. Again a user set gain (derivative gain) is used to adjust the

amount of change made.

These two error adjustments are then combined with the previous PWM value to obtain the new one. This is then

outputted to the pin which drives the fan.

The final subroutine of the code reads the optical encoder, converts the value to rpm and outputs the value to the

StampPlot software. The input from the encoder takes 1 second and it counts the number of cycles completed by the

signal.

Comments on Our Controller and Gain Selection Logic

Unfortunately, due to the resolution and sampling time of the system, we have selected coefficients strictly

based on resolution. The proportional and derivative gain values were selected in multiples of 1/60 due to the

resolution. The smallest error you could possibly have (besides 0) would be 60. Therefore, in order to constitute aPWM change at all, the error would need to be multiplied by 1/60 to produce a positive or negative 1 PWM jump.

When applying these coefficients it ended up working out nicely in terms of speed control. I would also like to

comment on the uniqueness of our controller. Our controller uses elements of Proportional, Derivative and Integral.

The proportional part was simply employed by multiplying the error by a constant. The derivative part was employed

by taking the difference between the current error and the previous error and dividing them by 1 second(time for 1

cycle). The Integral part was a bit of a make shift implantation as when the PWM value was determined (adding of

both the proportional part and the derivative part) the original value of the PWM was also included. This is basically

integral control as you are summing the error up to this point.

Simulation

To check our regulator, we developed a Simulink model of the system, which is shown in the figure below.

The blocks with yellow background represent the fan. We chose a first-order periodic link for the fan's

approximation and added the dead zone nonlinearity. The parameter of the dead zone and the gain of the object were

identified experimentally with good precision. The time constant To was identified roughly through step response of

the open loop system. The blocks of yellow background are calculated continuously.

FanScope

ZOH 1/z

-K-

K2

-K-

K1

-1

Z

-1

Z

10/255

6180/10

To.s+14000


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The blocks in red are calculating only once per second as well as in the real system. The representation of the

regulator blocks is exactly the same as in the program code. The constants K1 and K2 are also equal to the ones used

in the program code. The results of simulation (one of them is shown in the figure below with set speed = 4000,

Kp=.01667, Kd=.03333) are pretty the same as results of experiment with real hardware (see results section for

comparison).

ResultsOpen Loop Control

Before implementing closed loop control of the system, our group decided to look at the characteristics of the open

loop system. To do this we sent PWM voltages to the motor and read the speeds with the tachometer discussed

earlier. The table below demonstrates the voltage readings to the fan, the RPM read from the encoder, the PWM

signal used to generate the voltage, and the theoretical voltage expected for that PWM setting.


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For the first StampPlot picture shown below, the set point for the RPM was set to 5160 RPM , the derivative

coefficient was set to .03333 and the proportional coefficient was set to .01667. The results are demonstrated below.

Notice how there is no overshoot and the final value is reached very quickly. This combination served as one of the

better coefficient combinations we used. For this plot we also stored the data saved by stamp plot. This is tabulated

below.

And the resulting plot is shown below:


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This is useful for tabulated real data and analyzing it with more powerful software.

The next test runs demonstrated a change in set point with the same controller settings. These set points were 4000

and 6000 RPM and are shown below:

0

1000

2000

3000

4000

5000

6000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53

RPM

Time (s)

RPM vs Time


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Next, our group decided to experiment with interference of the device. Our first experiment included blocking the

emitter after the device had reached the set point (4500 RPM). This had the effect of sending a 0 RPM reading to the

device. In order to compensate, the controller forced the output to 255 PWM and set the fan to maximum speed.

After un-blocking the device, the fan (from a high speed, read as 0) returned to the originally programmed speed of

4500 RPM. Notice in the following plot how the speed first overshoots in the negative direction. By accomplishing

this experiment, we have effectively reversed the response of the motor from a rising response to a falling one.

The next experiment our group performed was to simulate something hitting the fan to reduce its speed. This was

accomplished by lightly applying pressure to the fins of the fan. Once the pressure was applied and the speed reduced,

the controller would start to compensate by increasing the voltage. At this point the pressure was released and the fan

would speed up (due to the increased voltage). At this point he controller would again compensate and allow the

speed to drop. This was accomplished twice in the plot below.


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In this next experiment, our group decided to change the coefficients to see the effects. In the next plot, we doubledboth the gains so that:

Kp= .03333

Kd = .06667

This forced the system to oscillate, but eventually reach its final value as you can see in the plot below:

Next, we set the derivative gain equal to 0 to see how the system would respond. Kp was returned to its original

value. As you can see in the plot below, the system responded well, but was slightly slower to react initially.


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Next, our group attempted to create an unstable system. This was accomplished by keeping Kp the same and settingKd to ten times its original value. The plot below shows a saturated value of RPM (meaning the max 10V was

applied) . The motor would then saturate at 0 RPM (which is not read by the tachometer due to the fact that it would

take 1 second to read the data) causing an unstable system.


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Limitations

Low resolution

Unfortunately, due to the physical nature of our device, it has very low resolution in RPM. The encoder shown

below had to be used because any other encoder with higher resolution would force us to loose pulses and get

inaccurate readings of RPM. This played a part in only being able to get 60 RPM resolution.

Low Sampling Time

Because the system had to get enough samples to get an accurate reading for RPM, the cycles command had to be

initialized for 1 full second. This only allowed us to get one piece of data every second. This had negative effects on

our closed loop control of the system, as well as the resolution of RPM. The RPM value was calculated by the

following equation:

RPM = Opto_Count*60/CyclesPerRev

The Opto_Count value (collected over 1 second) had to be multiplied by 60 to get to RPM. The CyclesPerRev had

to be 1 due to encoder restraints, therefore, this was the best resolution we could hope for while still being able to

use closed loop control.


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Appendix


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References

parallax.com

Process Control Student Guide, Parallax

http://en.wikipedia.org/wiki/PID_controller

http://en.wikipedia.org/wiki/Control_theory

http://en.wikipedia.org/wiki/Open-loop_controller

Basic Stamp Manual

Handout For Lab 2

PBasic Syntax Manual

Wikipedia contributors. "Brushless DC electric motor." Wikipedia, The Free Encyclopedia. Wikipedia, The Free

Encyclopedia, 7 Apr. 2010. Web. 12 Apr. 2010.

"HowStuffWorks "How Electric Motors Work"" Howstuffworks "Electronics" Web. 12 Apr. 2010.

.

"Motors & Drives." Tri-State. Web. 12 Apr. 2010. .

Wikipedia contributors. "Voltage divider." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 28

Mar. 2010. Web. 12 Apr. 2010

"Voltage Dividers." Web. 12 Apr.

2010..

Mechatronics Lab 3 Group B

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