Stability Control System for a Propeller Powered by a Brushless DC Motor

(BLDC)

Final Proposal: ET494

Codey Lozier

Christian A. Thompson

Advisor: Dr. Mohammad Saadeh

September 15, 2014

AbstractThe following paper proposes a design for a stability control system for a propeller powered by a brushless DC motor. The prototype will consist of various mechanical, and electrical components that systemically work together to stabilize a beam in the horizontal position. This stabilization will result by placing a brushless DC motor, paired with a propeller, on each end of a horizontal beam. When energized the motor will rotate the propellers and produce a lift force. A lift force introduced at each end of the beam will allow the beam to change position. A perpendicular shaft will be attached at the center of the beam to provide support, and a sensor known as an incremental rotary encoder will be attached on the opposing end of the shaft. The rotary encoder will output a signal that represents the angular position of the shaft. The angular position of the beam will be compared to a reference position, 180 degrees with respect to the ground. The difference between the reference position and current position of the horizontal beam will produce an error. In order to manipulate the error signals a microcontroller will be implemented into the design. When an error is produced the system will respond by changing the signals used to energize the BLDC motors, resulting in a change in position of the horizontal beam.

1. Introduction

Control systems provide engineers the ability to regulate an environment with desired behaviors. Therefore, it is imperative that an engineer understands the methods required to develop a stable control system. The following paper proposes a design for a stability control system for a propeller powered by a brushless DC motor.

The design will consist of a horizontal beam that will support two brushless DC ( BLDC ) motors, each attached with a propeller, that will be placed on opposite ends of the horizontal beam. In order to support the beam a shaft will be incorporated into the design. One end of the shaft will be fixed at the middle of the horizontal beam, and the opposite end of the shaft to a sensor known as an incremental rotary encoder. In order to move the beam to a horizontal position, 180 degrees with respect to the ground, a lift force must be introduced at each end of the beam. Controlling the amount of lift force will be accomplished by controlling the speed at which each propeller rotates. While the beam changes position the rotary encoder will output a signal that represents the current angular position of the horizontal beam. This angular position will be constantly compared to a reference position, 180 degrees. The difference in angular position between the current position and reference position will produce an error. Using negative feedback an error will be produced until the horizontal beam is positioned at 180 degrees. Achieving stability without manually controlling the commutation of each motor will be accomplished using methods in feedback control. Autonomous stability can be achieved by controlling the lift force introduced at each end of the horizontal beam, with respect to the current angular position, and by incorporating techniques found in control theory to the system.

This proposal will explain the function of the main components of the proposed control system, and explain the methods that will be used to acquire autonomous stability. The methods used in the design, construction, and evaluation of the prototype can be used in various applications that involve feedback control systems.

1.1 Project Deliverables- Research all components needed to design the control system- Understand how the signals of each component are transmitted and read- Gain knowledge of LabVIEW driven environment- Design an experimental prototype using electrical components, and one BLDC

motor- Gain knowledge of control systems- Implement a control system that uses a PID controller- Incorporate a second BLDC motor to system- Modify system to operate using two BLDC motors- Research paper

2. Background

The following sections provide a brief background of the concepts researched, and primary components used for this project.

- Brushless DC motor- Propeller ( Lift Force )- Incremental Rotary Encoder- Control Systems

2.1 Brushless DC Motor (BLDC)A motor is a mechanical device that converts electrical energy into mechanical energy. This mechanical energy is used to turn the shaft of a motor through a process called commutation. The type of motor used in this project is known as a brushless DC (BLDC) motor. The BLDC motor used in this project can be seen in Figure 1.

Figure 1: A2208-12 Brushless DC Motors by Mystery

A BLDC motor is typically constructed with a three-phase winding topology with star connection. In order to generate motion each drive phase consists of one terminal driven high, one terminal driven low, and one terminal left floating. In order to control the speed at which the motor spins, the motor’s characteristics must be obtained. Table 1 displays equations used to describe an ideal motor.

Table 1: Equations Used in an Ideal Motor

Variable Symbol Equationrevolutions per minute RPM RPM=KV (E )

back electromotive force BEMF BEMF= RPMK v

torque τ τ=KT ( I )

Kt = motor torque constantKv = motor constant

In BLDC motors the positions of current carrying windings can be found by allowing Kt to become a periodic function of electrical angle. BLDC motors are also ideal due to the

fact that they can be operated using electronic signals. These electronic signals are represented as a train pulses. The process of producing said pulses is possible using pulse-width modulation (PWM). This process is later explained in Section 3 of this paper.

2.2 Propeller (Lift Force)In order to produce a lift force at the ends of the horizontal beam, a propeller is attached to each motor. A concept used for most multicopter designs is the 2:1 thrust-weight ratio. Propellers are typically sold using the length of the propeller and the pitch. The difference in pitch can be seen in Figure 2 below.

Figure 2: Propeller Pitch

The prototype will be applied different loads throughout the evaluation. If a load is applied when the horizontal beam is stabilized thus producing an error, the prototype has a small amount of time to respond to the error. So an appropriate motor-propeller combination will need to be found.

Figure 3: Free Body Diagram of Plane

A free body diagram of a plane in flight can be seen in Figure 3. The figure shows that the lift force is the opposite of the weight. Just like a propeller blade the wing of an airplane is shaped with one side having more surface area than the other.

Using Figure 4 it can be seen that the air on the top of the wing has to move faster over a greater surface area to keep up with the air below the wing.

Figure 4: Side View of Wing

According to Bernoulli’s Principle which states that there must be a proportional decrease in pressure, if there is an increase in speed, resulting in a pressure difference between the propellers thus resulting in lift.

Figure 5: Flow through Propeller

P2 < P1 and P3 > P4 = P1 = PatmFigure 6: Pressure Variation along Mainstream

Figure 7: Velocity Variation along Mainstream

Continuity It is not possible to have a velocity discontinuityV2 = V3 = VBecause A2 = A3 = A

The propeller produces a pressure difference across the plain. The air accelerates as it approaches the propeller because of the low pressure in front of the propeller. According to Figure 7 the pressure is continuous from 1 to 2 (in front of the propeller) and from 3 (behind the propeller) to 4. The pressure jump from 3-2 represents the pressure energy the propeller blade creates.

The flow accelerates before and after it passes through the propeller, hence:

m=ρ A1 V 1=ρAV =ρ A4V 4

The speed through the propeller is the average between the free stream and the slipstream (V1 and V4):

V=V 1+V 4

2

Thrust=( p3−p2 ) A

The result in the difference in the air pressure is an upward net force called LIFT é . The air under the wing or the propeller blade moves slower and exerts more of a force than the air moving above the blade.

Since the force under the blade is greater than the force above the blade, the resulting force is positive or UP. A diagram of the forces involved when using a propeller can be seen in Figure 8.

Figure 8: Forces Involved When Using Propeller

2.3 Rotary EncoderThere are two mechanical configurations for “shaft” encoders that have been researched, linear and rotary. Linear encoders are used to measure linear motion or speed. The second configuration, rotary encoders, is used for angular measurements.

The type of encoder that best suites this project will be an incremental rotary encoder. An incremental encoder outputs digital pulses with respect to light and dark regions insider the encoder’s optical code wheel. An encoder also outputs a specific value called an index, which is considered the absolute position of the code wheel. Figure 9 is an example of an incremental encoder.

Figure 9: Incremental Shaft/Rotary Encoder

2.4 Control Systems In order for the system to stabilize when an error is produced, a fast and precise response is required from the BLDC motors. This will be achieved with a closed loop system using negative feedback. A general block diagram of control system and the components in a control system can be seen in Figure 10.

Figure 10: General Block Diagram of Control System

The squares represent the sub-systems that make up the control system. The arrows represent signals that are input/output through each sub-system. Table 2 displays a list of the components, description, and the signals associated with the components in Figure 10.

Table 2: Description of Components and Signals Used in a Control System

Component Symbol DescriptionController C Used to process error signal using a transfer function.

System ( plant ) P Represents the components that are physically controller.Sensor s Provides the signal representing the current state of the

system.Signal Symbol Description

Reference r Desired value or state of system, and is compared to the measured output.

Measured Error e Difference between desired output, and measured output.System Input u Control signal, or controller output

System Output y Current state of plant

3. Current ProgressThe following sections involve the progress made, and an updated list of components used to design the project. New components or software that has been incorporated to the project include:

- National Instruments: AT Multifunction I/O Board, E Series - SCB-68A Connector Block- LabVIEW

The following sections explain each component of the control system, along with the electrical components, and software associated with the system.

3.1 ControllerThe components dedicated to the Controller include:

- Arduino Uno Microcontroller board- AT Multifunction I/O board

3.1.1 Arduino UnoThe Arduino Uno is based on the ATmega128P microcontroller. This component will be dedicated to providing the PWM signals sent to the electronic-speed controller. This microcontroller can also be programmed using LabVIEW, making the design of the control system easier. Figure 11 provides the pin layout of the Arduino Uno microcontroller board.

Image Retrieved from Arduino Mega 2560 Datasheet

Figure 11: Arduino Uno Pin Layout

3.1.2 AT-MIO-AI E SeriesThe AT-MIO-AI E Series is a multifunction data acquisition board developed by National Instruments. The DAQ board must be interfaced with a computer that supports EISA or 16 bit ISA expansion slot. The DAQ can be seen in Figure 12.

Figure 12: Multifunction E Series DAQ Board

In order to implement this DAQ board into the project, certain accessories had to be obtained. In order to communicate with the DAQ device, the SCB-68A connector block (Figure 13a) along with a SHS68-68-D1 shielded conductor cable (Figure 13b) needed to be incorporated into the project.

(a) Connector Block (b) Shielded Conductor Cable

Figure 13: SCB-68A Connector Block & SH68-68-D1 Shielded Conductor Cable

The signals from the rotary encoder are sent to the SCB-68A connector block, which sends the signals to the DAQ board. Figure 14 displays the wire connections from the rotary encoder to the connector block.

Figure 14: Wire Connections from Rotary Encoder to Connector Block

3.2 Plant SystemThe following sections introduce components that make up the plant system of project. These components include:

- Brushless DC Motor- Electric Speed Controller- Carbon Fiber Propeller

3.2.1 Brushless DC MotorThe motor that was chosen to stabilize the horizontal beam of the system is the A2208-12 1800Kv Brushless Motor by Mystery. A datasheet of the motor is not provided by the manufacturer; therefore further testing will need to be performed to determine the characteristics of the motor.

The shaft of the motor will have a propeller attached, and will be powered using a brushless speed controller. By fixing the motor onto a shaft coupler the motor is capable of lifting the beam to a stable position. Figure 15 provides a photo of the motor without a propeller, and an image of the motor mounted on the horizontal beam.

Figure 15: A2208-12 Brushless DC Motor

Operation of the BLDC motor is accomplished by using a modulation technique known as pulse-width modulation (PWM). The PWM signals are sent to the electronic speed controller.

3.2.2 Electronic Speed ControllerThe 30A Brushless Speed Controller by Hobbywing is a sensorless electronic speed controller (ESC) that is typically used for high power RC systems. Figure 16 below shows a photo of the ESC when not connected to the BLDC motor.

Figure 16: Hobbywing Flyfun 30A Brushless Speed Controller

Figure 17 below displays the wire diagram of ESC. Like most components the black wire is the ground wire ( - ), and the red power ( + ) wire is supplied with a DC voltage. The blue arrow points to the wires, control signals, dedicated to operating/programming the ESC. Of the three wires the black wire is the ground, and the white wire is used to receive the PWM signal sent from the Arduino Mega. Using PWM also allows one to omit the red wire.

Image Retrieved from Sensorless Brushless Speed Controller Manuel

Figure 17: Hobbywing Flyfun 30A Brushless Speed Controller Wire Diagram

According to National Instruments, PWM is a technique used to generate an analog signal using a digital source. The signal consists of a train of HIGH & LOW or ON &

OFF pulses. Two components that define a PWM signal are the duty cycle, and frequency. The duty cycle is a ratio of the time a signal is active in one period. This process is best shown using Figure 18, and the example below.

Retrieved from: http://www.bristolwatch.com/picaxe/adc_pwm_demo.htm

Figure 18: PWM Signal with 25% Duty Cycle

By referencing Figure 18, and Table 3 below, the following steps can be used to calculate the variables of a signal with a period of 2ms, and a duty cycle of 25%.

Table 3: Variables Used to Calculate Duty Cycle

Variable DescriptionTon Time signal is active or ONToff Time signal is not active or OFF

Ton + Toff Period or complete cycle

DC=T on

T on+T off=25 %

Period=T=Ton+T off=1 msT on=DC× (T on+T off )=0 . 25×2 ms=0 .5 msT off=T−T on=2 ms−0 .5 ms=1. 5 ms

DC=T on

T on+T off=0 .5ms

0 .5ms+1 .5ms=0 . 5

2=0 . 25×100=25 %

3.2.3 Propeller An 8x4.5 carbon fiber propeller replaced the propeller that was used in the motor/prop combination found Figure 15. When the BLDC was powered with the new propeller, some changes had to be made due to the increase in lift force produced by the new propeller. Moving the project to a different location on the table was also carried out in order to provide a safer testing environment. A photo of the carbon fiber blades can be seen in Figure 19 below.

Figure 19: Carbon Fiber Propeller Blade

3.3 SensorThe following sections introduce the sensor that will output a signal representing the current state of the control system. The sensor introduced is:

- YUMO E6B2 Incremental Rotary Encoder

3.3.1 Incremental Rotary EncoderThe YUMO E6B2 Incremental Rotary Encoder, seen in Figure 20, was chosen due to its high resolution of 1024 pulses per revolution, and ability to handle loads of up to 30N. The encoder is fixed using a small bracket, and the shaft is kept stable using a pillow block.

Figure 20: YUMO E6B2 Rotary Encoder Setup

3.4 Laboratory Virtual Instrument Engineering Workbench (LabVIEW)LabVIEW is a powerful system-design platform and development environment that incorporates a graphical programming environment. LabVIEW can be used for numerous applications such as:

- Data Acquisition- Instrument Control- Test Automation- Analysis and Signal Processing- Industrial Control- Embedded Design

Programs in LabVIEW are called Virtual Instruments (VIs), and each VI contains two parts; a front panel and back panel. The front panel displays data using indicators, and controls. It also incorporates the use of tables, buttons, sliders, and graphs. An example of a front panel can be seen in Figure 21.

Figure 21: Example of Front Panel in LabVIEW

The back panel consists of a block diagram that contains that graphical source code to develop a VI. An example of a back panel can be seen in Figure 22.

Figure 22: Example of Back Panel in LabVIEW

Using a graphical programming approach makes the process of developing and testing the control system in this project easier. LabVIEW also has a large amount of resources available online.

For this project LabVIEW is going to be used to program the Arduino Uno microcontroller, and the multifunction DAQ device.

3.5 Conclusion of Current Progress1. Researched and acquired all components of project

- Gained understanding of how signals are transmitted, and read for each component.

2. Designed and constructed an experimental prototype of system3. Integrated components into experimental system4. Gained understanding of LabVIEW driven environment

- Designed VIs for all components5. Incorporated a Multifunction I/O Data Acquisition Device using LabVIEW

4. Future ProgressThe following section introduces the methods used to implement the type of control system that is going to be used in this project.

4.1 Proportional-Integral-Derivative (PID) ControllerA PID controller is a control loop feedback technique that is widely used in control systems. A block diagram of a PID controller can be seen in Figure 23.

Figure 23: Block Diagram of PID Controller

This three term controller uses three constant parameters that are labeled as:

- proportional (KP)- integral (Ki)- derivative (Kd) The transfer function of the PID controller looks like:

K p+K i

s+K p s=

K p s2+K p s+K i

s

Table 4 displays the characteristics of P, I, and D controllers.

Table 4: Characteristics of P, I, and D Controllers on Closed-Loop SystemResponse Rise Time Overshoot Settling Time S-S Error

Kp Decrease Increase Small Change DecreaseKi Decrease Increase Increase EliminateKd Small Change Decrease Decrease Small Change

In a closed loop system the error ( e ) produced by the system is sent to the PID controller. The signal output by the controller ( u ) is represented by the following equation:

u=K pe+K i∫edt +Kddedt

Once the signal (u) is established it is sent to the plant, and a new measured output ( Y ) is obtained.

There are other forms of PID controllers in which only two of the three terms are incorporated into a system. A PID controller will be introduced into the design of the control system, and depending on how the system reacts it may be reduced to only a two term controller.

4.2 Future Goals

October 2014- Develop a transfer function for experimental design- Incorporate a PID controller using LabVIEW

November 2014- Add a second BLDC motor on opposite end of beam- Modify control system using both motors- Design a final experimental prototype of system- Research paper