Its The Quadrotor System Engineering Essay

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CHAPTER 3

QUADROTOR SYSTEM

3.1 Introduction

In this chapter, quadrotor system will be described including the structure and hardware architecture design. The structure design will cover the material being used while hardware architecture design will cover the flight control board (FCB), actuator, sensor and remote controller for quadrotor. Several types of test platforms were developed as the experiment to the quadrotor attitude control system. The test platform also will be described in this chapter. An experiment of propeller lift thrust measurement was conducted and the result will also be shown in this chapter. In order to design the attitude control algorithm, a dynamical model of quadrotor must be determined. To determine the dynamical model of quadrotor, the kinematics and dynamics of quadrotor must be known first. It is also included in this chapter.

3.2 Hardware Design and Specification

To test the attitude flight stability, the real quadrotor must be developed. In developing the quadrotor, there will be structure and hardware architecture system. To get a better result, the selection of actuator, FCB, sensor and remote controller must meet the specification needed for the quadrotor system.

3.2.1 Quadrotor Structure

Quadrotor base structure is made from two 12mm X 12mm X 1000mm square hollow aluminum and attached in '+' frame. Aluminum was chosen because it is light-weight and low cost. The other material that can be used is carbon fiber which is lighter but costly. Four Brushless DC (BLDC) motors are attached at distance of 317.5mm from the center of each side of quadrotor axis. Then a propeller will be placed on top of each motor as illustrated in Figure 3.1. In the middle of the intersection of aluminum, main board, power distributor and battery were placed.

Figure 3.1: Quadrotor Structure Illustration

For quadrotor, there are two pairs of propellers that being used which are pusher-type and puller-type. Pusher-type propeller will spin clockwise while puller-type propeller will spin counter clockwise. The pusher-type propeller will be place on front and rear motor while puller-type propeller will be placed on right and left motor. This combination of propellers will counter the torque produced by motor. So, the quadrotor can eliminate torque produce by single direction of rotation for all motors. When all motors rotate at same speed, a pair of motors that rotate counter clockwise will counter the torque produced by a pair of motors that rotate clockwise. So the total torque produced will be zero and quadrotor body will not turn right or left in z-axis when in flight. The two types of propeller will be described in section 3.2.2.3. Figure 3.2 shows the real quadrotor that has been developed.

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Figure 3.2: Quadrotor

3.2.2 Hardware Architecture

Quadrotor is an UAV aircraft. The whole system is controlled by electrical system. The electrical system is used to control the flight stability of the quadrotor whether in semi-autonomous or autonomous mode. The battery supply the required power to the electrical system and the remote controller is used to control the movement of quadrotor. The sensor is read and processed by microcontroller which is embedded with the attitude control system by programming to be responded by the actuator. The main components for the quadrotor hardware are flight control board, sensors, electronic speed controller (ESC) and BLDC. All of them will be connected as quadrotor hardware architecture as shown in Figure 3.3.

Figure 3.3: Quadrotor Hardware Architecture

The hardware architecture shown is the whole connection of the quadrotor system. The sensors are connected to analog pins of microcontroller in FCB because the sensors output is in analog signal which are converted to digital by microcontroller later. The digitalized signals from sensors then will be used as feedback of an algorithm and being processed by microcontroller. The signal from radio controller is connected to digital pin to get the time width of the signal that will be used as control input for quadrotor movements. The processed data then sent to ESC to control the BLDC speed. The whole system is interrelated by each other to perform a closed-loop control.

3.2.2.1 Flight Control Board

Flight Control Board of quadrotor in this project is ArduIMU V2 Flat developed by DIYDrones which is a combination of microcontroller and sensors in a single small board. The small size of FCB can make the quadrotor easy to build and less space required. The Figure 3.4 shows the FCB that been used for this quadrotor project with size about 28mm X 39mm. The microcontroller that been used is ATmega328P from ATMEL corporation in Arduino Integrate Development Environment (IDE) programming. ATmega328p is an 8-bit microcontroller with 32k bytes flash program memory. This microcontroller can process the instruction up to 20MHz. With 8 channels of analog pin in TQFP package and 32 programmable input/output pins make this microcontroller is suitable for this project. The technical data of the microcontroller is provided in appendix x. But in this FCB, the developer just limits the pin out of the board that has 10 programmable input/output pins. The other pins already connected to sensors and some of them remain unconnected.

Figure 3.4: Flight Control Board

The sensors combined in the FCB are 3-axis gyroscopes and 3-axis accelerometers. These two sensors are combined together by an algorithm to sense the orientation of the quadrotor. Gyroscope is used to sense the rate of rotation in an axis and measured in radian per second (rad/s) while accelerometer is used to measure the inclination due to gravity effect. But both of them have drawback if been used separately. Gyroscope intends to be drifted in time while accelerometer is sensitive to vibration. Because of a lot of vibration produced in quadrotor in flight, accelerometer alone cannot be used although it can measure the orientation of quadrotor. The drift of gyroscope is the rate of rotation value not comes back to zero even though the rotation has stopped. The FCB is placed at the center of the quadrotor structure on a simple board to reduce the wiring to the motor and receiver. The placement of FCB is shown in Figure 3.5. Both of the sensor will be filtered and fusion using an algorithm that will be discussed in Chapter 4.

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Figure 3.5: Placement of FCB on Quadrotor Structure

3.2.2.2 Power Source

Quadrotor is high power consumption UAV because of its 4 BLDC motors. Each of them can drain about 4 Amperes current depends on the type of motor used. Because of the high current operation usage, a suitable type of battery must be used to support the system. Lithium Polymer (Li-Po) is the suitable battery because of its high discharge rate and capacity. In this project, the Li-Po battery being used is three cells which give 11.1V with 3300mAh discharge capacity. The Li-Po battery being used in this project is shown in Figure 3.6.

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Figure 3.6: LiPo Battery

3.2.2.3 Brushless DC Motor, Electronic Speed Controller and Propeller

Brushless DC motor is selected as the actuator because of the advantages than brushed DC (BDC) motor. BLDC motor has wide speed range than BDC motor because of its no mechanical limitation imposed by brushes which operate in contactless operation. The BLDC motor efficiency is higher than BDC motor because of no voltage drop across brushes as BDC motor. The comparison of the BLDC and BDC motors are listed in Table 3.1. The model of BLDC motors that been used in this project is Robbe ROXXY 2827-35. The Figure 3.7 shows the BLDC motor that been used for this project. This motor is out runner-type with high torque for direct drive. Means, the propeller can be attached directly on the motor using propeller mount. BDC motor usually needs gear reduction before attaching the propeller because it cannot support direct drive that most of BLDC can. With the speed of 760 rotation per minute (RPM) per volt without load, it can speed up to 8,436 RPM without load because the voltage used to drive this motor is 11.1V.

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Figure 3.7: Robbe ROXXY 2827-35 BLDC Motor

Table 3.1: comparison of the BLDC and BDC motors

Comparison

BLDC

BDC

Control

Three phases of driving coils control (need special driver)

Two wire control (simple driver)

Maintenance

Less required maintenance due to absence of brushes

Replaceable brushes for extended life (Need to replace brushes)

Speed

Higher speed range - no mechanical limitation imposed by brushes/commutator

Lower speed range due to mechanical limitations on the brushes

Thermal characteristic

Reduced size due to superior thermal characteristics. Because BLDC has the windings on the stator, which is connected to the case, the heat dissipation is better

Poor heat dissipation due to internal rotor construction

Noise

Low electric noise generation

Brush Arcing will generate noise causing EMI

Speed/Torque

Speed/Torque- flat, enables operation at all speeds with rated load

Speed/torque is moderately flat. At higher speeds, brush friction increases, thus reducing useful torque

Cost

Higher cost of construction

Low cost of construction

Every motor needs controller so the motor can function according to the needs. Same as BDC motor, BLDC motor needs motor controller to control the speed of the motor. The controller of the motor is called electronic speed controller (ESC) as shown in Figure 3.8. The BLDC motor is controlled by using three phases of driving coils operation. The three blue wires must be connected to BLDC motor. The red and black wire connected to power source and the servo cable connected to the signal controller. This type of ESC controls the BLDC motor speed by varying the standard servo pulse width modulation (PWM). Standard servo PWM vary from 1ms to 2ms with 25ms in cycle time. If servo pulse width time is 1ms, the degree of servo rotation is at zero degree and if the pulse width time is 2ms, the degree of servo rotation is at 180 degree. But for BLDC operation, 1 ms pulse width time is for stop while 2ms pulse width time is for full speed.

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Figure 3.8: Arrowind Electronic Speed Controller

As mention in section 3.2.1, the propeller type will be used is pusher and puller type. This combination of propeller called contra-rotating propeller. The thrust produced by the propeller is same if the size and pitch is the same but in different rotation. Figure 3.9 shows the contra-rotating propeller that been used for this project. For this project, the size of propellers been used are 10 inch with 4.5 inch pitch. The code to indicate the propeller is 'propeller size X pitch'. The unit measured is in inch.

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Figure 3.9: 10X4.5 Contra-Rotating Propeller

An experiment was conducted on the contra-rotating propeller to relate the effect of varying PWM to the speed of motor that effect to the thrust produced. The experiment is conducted by placing a propeller attached to BLDC on a platform which is placed on a digital scale to measure how much lift force is produced. The experiment setup for thrust measurement is shown in Figure 3.10. There are many configuration of experiment setup regarding this measurement such as in (ref).

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Figure 3.10: Experiment Setup for Thrust Measurement

The experiment is conducted by giving the PWM to ESC from range 1.1ms to 1.9ms. The thrust produced by the propeller measured in gram (g) and then converted to Newton (N). Each BLDC motor attached with propeller will undergo this experiment. The result will be shown in Figure 3.11 and Table 3.2. The full results of the experiment are included in Appendix x.

Figure 3.11: Thrust Measurement Result

Table 3.2: Thrust Measurement Result

PWM code

Thrust (N)

Front Motor (1)

Right Motor (2)

Back Motor (3)

Left Motor (4)

1100

0.000

0.000

0.000

0.000

1200

0.308

0.265

0.239

0.275

1300

0.756

0.710

0.684

0.714

1400

1.218

1.208

1.159

1.191

1500

1.774

1.676

1.702

1.712

1600

2.520

2.285

2.360

2.409

1700

3.277

3.001

3.142

3.146

1800

4.167

3.823

3.987

3.993

1900

4.450

4.543

1.354

4.491

From the experiment results as shown in Figure 3.11 and Table 3.2, the range taken is from 1100 which represent 1.1ms to 1900. After linearize the result, the equation thrust force Fi generated by motor i, i = 1, 2, 3 and 4 be:

(Equation 3.1)

Where and are thrust factor.

3.2.2.4 Remote Control

Remote control is used as input controller to the quadrotor attitude control system. An operator is needed to control the movement of quadrotor unless the quadrotor system is autonomous. The remote control comes in pair which is transmitter and receiver. The remote control chosen for this project is Futaba 2.4GHz 6EX as shown in Figure 3.12. The receiver is R617FS. This remote control is using 2.4GHz spectrum for the better connection than using the conventional radio frequency (RF) system which is tend to signal loss due to noise or frequency overlap. Using 2.4GHz the connection between transmitter and receiver is better. This remote control consists of 6 channels for controlling aircraft. For quadrotor, the only four control channels are needed which are yaw at channel 1, pitch at channel 2, throttle at channel 3 and roll at channel 4. This configuration is not fixed and can be changed by the operator to meet their convenient.

C:\Documents and Settings\Zul Azfar\Desktop\futaba6EX-24G3.jpgC:\Documents and Settings\Zul Azfar\Desktop\134-1908-large.jpg

Figure 3.12: Futaba 2.4GHz 6EX Transmitter with R617FS Receiver

3.3 Quadrotor Kinematics

The quadrotor movements are similar to helicopter which can move on pitch, roll, yaw, take-off, landing and hover. Each rotation of propeller generates vertically upward lifting force. Movement control of quadrotor is achieved by commanding different speeds to each motor. Figure 3.13 shows the illustration of speed variation in quadrotor movement. The quadrotor control movements are also explained in [10]-[13].

Figure 3.13: Speed Variation in Quadrotor Movement

Below are the descriptions how to control the movement of quadrotor:

Hovering, take-off and landing ()

To perform hovering, take-off or landing, all four propellers must rotate simultaneously at the same speed. To take-off the rotation of propeller must be higher to produce a lifting force greater than the total quadrotor weight while to landing the rotation of propeller must be slowly decreased to let the quadrotor getting low to the ground. The hovering can be achieved by producing the lifting force that same as the total quadrotor weight.

Pitch ()

In pitch, speed of M1 and M3 is changed conversely to perform forward and backward movement. To move forward, the speed of M3 must be greater than the M1 while to move backward, the speed of M1 must be greater than M3. The other two motors must maintain the current speed to stabilize the quadrotor.

Roll ()

For roll, speed of M2 and M4 is changed conversely to perform right and left movement. To move right, the speed of M2 must be greater than M4 while to move left, the speed of M4 must be greater than M2. The other two motors must maintain the current speed to stabilize the quadrotor.

Yaw ()

To perform yaw, the speed of motor in pair (M1 and M3) and (M2 and M4) are changed conversely. To rotate the quadrotor body to the right, the speed of M2 and M4 must be greater than the speed of M1 and M3 while to rotate the quadrotor body to left, the speed configuration is inversed The yaw happened because of the interruption of the neutralize torque effect of the motor. When the torque is high to the right rotation then the body quadrotor will rotate to the right.

3.4 Quadrotor Dynamics

In modeling quadrotor dynamics, there are two frame have to be defined as a reference which are Earth Inertial frame (E frame) and quadrotor fixed-body frame (F frame). The frame shown in Figure 3.14:

Figure 3.14: Quadrotor body and earth inertial frame

The quadrotor mathematical model derived based on a few assumptions as described in [14]:

Quadrotor body is rigid and symmetrical

Propellers are rigid with fixed pitch.

There is no air friction on quadrotor body.

Free stream air velocity is zero.

Drag torque td is proportional to propeller speed with d as drag constant.

There are difference ways to describe quadrotor dynamics such as quaternion, Euler angle and direction matrix. However, in designing attitude stabilization control, there must be a reference in axis angle so the designed controller can achieve a stable attitude control. In quadrotor flight, all angle references in each axis must be approaching zero as it in stable flight when take-off, landing or hover.

Quadrotor orientation is given by three Euler angles which are roll angle 𝜙, pitch angle 𝜃 and yaw angle 𝜓. These three Euler angles form the vector 𝜴𝑻= (𝜙, θ, ψ). The position of the vehicle in the inertial frame is given by the vector q𝑻= (𝑥, y, z). The transformation of vectors of the body fixed frame to the inertial frame is given by the resultant transformation matrix of z, y and x axis, 𝑹 as below:

(Equation 3.2)

Where c denoted for cos; s for sin. The thrust force generated by each motor j, j=1, 2, 3, and 4 is:

(Equation 3.3)

Where b is the thrust factor and [rad/s] is the rotational speed of motor j.

The thrust force applied to the airframe from the four motors is given by:

(Equation 3.4)

The differential equation for acceleration of the quadrotor can be described in Equation 3.5 as below:

(Equation 3.5)

Where g is gravity (9.81ms-1) and m is the weight of the quadrotor.

Vector T described the torque applied to the quadrotor's body as shown in Figure 3.14. Torque can be calculated by using Equation 3.6. So, the vector T can be defined as:

(Equation 3.6)

(Equation 3.7)

Where F and are the force produced from the propeller while L and are the length of the lever. b and d are thrust factor and drag factor respectively.

Vector TG described as the gyroscopic torques. The gyroscopic torque is produced by the effect of rotation of propeller. The vector TG defined as:

(Equation 3.8)

Where IM is the motor inertia

Using Equation 3.7 and 3.8 with the inertia matrix ° (which is a diagonal matrix with the inertias °ð’™ð’™, °ð’šð’š and °ð’›ð’› on the main diagonal), a second set of differential equations is obtained:

(Equation 3.9)

We know that the movement of quadrotor is achieved by varying the speed of the motor. The rotational speed of each motor denotes as the input variable for the transformation of the quadrotor movement using the obtained model. Therefore, the input variables can be defined as below:

(Equation 3.10)

Where equal to 𝑇 as in Equation 3.4 denotes the thrust force applied to the quadrotor body; denotes the force which leads to the roll torque; denotes the force which leads to the pitch torque and denotes the force which leads to the yaw torque.

However, the gyroscopic torques also depend on the rotational velocities of the motors, so the vector = (,,,) of the transformed input variables. We assume that:

(Equation 3.11)

By combining Equation 3.5 and Equation 3.9, overall dynamic model yield in the form as below:

(Equation 3.12)

Then, the entire dynamical model above can be rewritten in state variable form of

Where is the vector of state variables.

(Equation 3.13)

Using equation Equation 3.11 and Equation 3.12, we can obtain:

(Equation 3.14)

Attitude Control Algorithm Using Fuzzy PID

In designing attitude control for quadrotor, a transfer function from mathematical model must be obtained for analysis for implementing the best suitable controller. The quadrotor dynamics must be simple enough before being implemented to the control algorithm. There are some of the terms that we can neglect which are gyroscopic torque and Coriolis-centripetal terms as mentioned in [19]. The considerations of neglecting those terms are as below: 

The gyroscopic torque terms can be neglected because the motor inertias are small.

The Coriolis-centripetal terms can also be neglected since the motion of the quadrotor can be assumed close to the hovering condition; the angular changes which come from cross coupling of angular speeds are smaller than the main.

From equation 13, we take the equation for roll, pitch and yaw as written below.

(14)

Then, after removing the two terms that can be neglected, the equation become simpler as below.

(15)

By applying Laplace Transform on equation 15, a set of transfer function for controlling roll, pitch and roll are obtained separately.

(16)

3.5 Identification of the Constant

An experiment was conducted on propeller to select the suitable size and pitch. The selection of propeller is important for quadrotor to perform smoothly in flight. The experiment is conducted by placing a propeller attached to BLDC on a platform which is placed on a digital scale to measure how much lift force is produced. The experiment setup for lift force measurement is shown in Fig. 3.3. There are many configuration of experiment setup regarding this measurement such as in (ref). Each propeller size and pitch will produce different lift force. So the suitable selection of size and pitch of propellers are needed for the quadrotor movement is not too aggressive or too slow response when the speed of motor is changed. It will make the quadrotor hard to control and will have poor flight especially in stability.

Table 3.1: Quadrotor Constants

Parameter

Value

Unit

Remark

g

9.82

m/s2

Gravity

m

1.125

kg

Quadrotor mass

L

0.3175

m

Lever length

Ixx=Iyy

1.63-10-2

kg.m2

Inertias around X and Y axis

Izz

2.87-10-2

kg.m2

Inertias around Z axis

b

kg.m2

Thrust factor

d

kg.m2

Drag factor

A1

- 6.8768

N

Thrust factor of front motor (1)

A2

- 6.6811

N

Thrust factor of right motor (2)

A3

- 6.7354

N

Thrust factor of back motor (3)

A4

- 6.808

N

Thrust factor of left motor (4)

B1

0.006

N

Thrust factor of front motor (1)

B2

0.0058

N

Thrust factor of right motor (2)

B3

0.0058

N

Thrust factor of back motor (3)

B4

0.0059

N

Thrust factor of left motor (4)

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