 Open Access
 Total Downloads : 424
 Authors : Myunggon Yoon
 Paper ID : IJERTV4IS110273
 Volume & Issue : Volume 04, Issue 11 (November 2015)
 Published (First Online): 16112015
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Experimental Identification of Thrust Dynamics for a MultiRotor Helicopter
Myunggon Yoon
Department of Precision Mechanical Engineering GangneungWonju National University,
South Korea
AbstractIn this paper we propose a simple experimental procedure for an identification of the thrust dynamic for a multi rotor helicopter. As a case study, we experimentally confirm that the transfer function from a PPM speed command for an ESC (electrical speed controller) driving a BLDC (brushless DC) motor to the thrust force generated by a propeller can be modeled as a simple firstorder system
Keywords Multirotor Helicopter; Drone; Thrust Dynamics

INTRODUCTION
Multirotor helicopters informally called as drones, attracted much attention and interest from both academic community and general public. Various applications of such helicopter for search and rescue operation, mapping, aerial photograph, surveillance and so on, have been proposed in diverse field. Recently toylevel commercial drones are also widely used in academic community, e.g. see [1,2,3].
A small batterypowered drone is composed of mechanical frames, a set of motors with propellers, battery and electrical boards for stabilization, sensing, communication and navigation guidance. A typical drone, which is considered in our case study, is shown in Fig. 1. For a controller design and implementation for drones one needs to have a dynamic modeling of a whole drone system.
Fig. 1 A Typical Drone (Case Model)
Drones typically have simple mechanical structures and hence a dynamic modeling of its mechanical part, i.e., the rigid body dynamics, is well known [3].
A real difficulty however is how to characterize the dynamic behavior of a BLDC motor, ESC and aerodynamic forces and moments generated by propellers installed on motors. This difficulty also comes from the fact that a commercial motor control unit, commonly called as an ESC (electrical speed controller) for a BLDC motor, has its own dynamical property, a set of selectable operational modes, communication protocol and even its own userconfigurable speed controller. In fact a precise dynamic modeling of an ESC itself is a hard task [4].
In this paper we propose an experimental approach for characterizing the dynamics of propeller thrust. The dynamic inputoutput relation from the ESC command to the thrust force is regarded as an unknown blackbox subsystem whose transfer function needs to be identified.

EXPERIMENT

Sensor Design
We designed and implemented two sensors; a force sensor to measure the thrust of a propeller and an optical sensor for the angular velocity of motor.
A thrust force is measured with a low cost loadcell type scale. The scale is composed of a strain gauge and an IC amplifier HX711 from AVIA Semiconductor Â© which includes an instrument amplifier and a 24bits AD converter. The digital signal from HX711 is captured by a microprocessor module (Arduino Due Â©) and then converted to an analog signal again for an easy monitoring with an oscilloscope.
A simple optical sensor system is made in order to measure the rotational angular velocity of a propeller. This sensor is composed of an infrared LED, an optical transistor and an OP amplifier in order to ensure a high voltage signal when the blade reflects an infrared ray from LED.
The force sensor and the velocity sensor are installed as shown in Fig. 2.
As a first step, the thrust sensor is calibrated making use of objects whose weights are measured with another precise scale. For this, we made the configuration of propeller and load cell in Fig. 2 upside down and hang objects from the motor center with a wire.
Fig. 2 Sensor Configuration
Fig. 3 Force Sensor Output
TABLE I. COMPONENTS SPECIFICATION
BLDC Motor
Motor Outer Diameter
58.5 mm
Stator Diameter
50.0 mm
Speed per Volt
340 RPM /V
Stator Number
12
Motor Poles
14
Weight
168 g
Propeller
Length
18 inches
Pitch
5.5 inches
Material
carbon fiber
Blade Root Thickness
3.3 mm
Load Cell
Capacity
5 kg
Resistance
1000
Material
Aluminum
Nonlinearity
0.05 %
ESC
Output (continuous)
40 A
Battery
Type
LiPo
Capacity
10000 mAh
Nominal Voltage
22.2 V
Discharging Rate
25C

Motor Electronic Speed Controller (ESC)
From a historical reason within the authors knowledge, most commercial ESCs are following a special driving protocol. Typically, the driving signal is PPM (pulse position modulation) signal with 50 Hz frequency (fixed mostly) and the duty ratio is between 5% and 10%.
In our experiment a PPM signal is made with a function generator (Agilent 33220A). With this signal, we were able to find that our BLDC motor starts to move with 6% duty ratio and reaches its maximum speed when the duty ratio reaches around 8.8 %.

Components Technical Specification
Several technical specifications of components which were used in our experiment are given in Table 1.


RESULTS

Static Thrust
Period
Fig. 4 Velocity Sensor Output
The relation between known weights of objects and the output of thrust sensor is shown in Fig. 3. From a linear curve fitting of the data in Fig.3, we were able to obtain a linear relation between the thrust force and the load cell output.
The output of rotational velocity sensor was shown in Fig.4. From the rising edge of every second pulse we could measure the period, which gives the angular frequency of the motor rotor.
By changing the duty ratio of ESC over the range (6.0, 8.8) % with a step size 0.2%, we have measured the outputs of force and velocity sensors.
A measurement of angular velocity sensor with different duty ratios gave the results in Fig. 5. It is remarkable that with a small duty ratio the relation between the duty ratio and angular velocity is almost linear.
In addition, from the data of force sensor, we have obtained the relation between duty ratio and thrust force as shown in Fig. 6. By combining Fig. 5 and Fig. 6, we were able to find the relation between propeller angular velocity and static thrust force as shown in Fig. 7. It is clear from this result that the thrust force is a quadratic function of angular velocity. From a curve fitting of data in Fig. 7 we have found that the quadratic relation can be explicitly given
T = 1.24 Ã— 106 2 (1)
Fig. 5 Angular Velocity versus Duty Ratio
Fig. 7 Static Thrust versus Velocity
Operating point
Fig. 6 Thrust versus Duty Ratio
where T denotes the thrust force in Newton and denotes the angular velocity in RPM.
A wellknown theoretical value of the thrust is given as
Fig. 8 Thrust Step Responses
2
2
2 (2)
T =
4 Ã— 3600
where = 1.225 kg/m3 is the air density, and p denote the diameter and pitch of a propeller in meter unit [5]. By plugging our data = 18 (inches) and = 5.5 (inches) in Table 1 into the above thrust equation (2), we obtained the following theoretical relation between angular velocity and static thrust force which is quite close to our experimental result;
T = 1.09 Ã— 106 2 (3)

Dynamic Thrust
In order to characterize the dynamic behavior of thrust force, we captured the response of thrust force sensor after applying a step (PPM) command to our ESC unit as shown in Fig. 8.
Fig. 9 Normalized Step Response
The data in Fig. 8 strongly suggests that the dynamic response of thrust force with respect to a step PPM command for ESC unit can be modeled as a firstorder system, e.g. see [6].
For a more precise estimation of thrust dynamics, we normalized the responses in Fig.8 to obtain the normalized step response in Fig. 9. From Fig. 9, we could experimentally
obtain the rising time 0.25 (second) of thrust force output with respect to the PPM command input for ESC unit. Consequently we could identify the transfer function between PPM command () and thrust force () as follows;


CONCLUSION
From a series of elementary experiments along with some simple analysis, we could identify both the static and dynamic property of the propeller thrust for a multirotor helicopter. Even though our experiment was quite elementary without any
() =
+ 1/
() (4)
special instruments, our experimental results showed good agreement with theoretical predictions. We believe our results in this paper should be generalized and confirmed with more
where is an unknown constant which will be determined later and (), () are the Laplace transforms of the thrust force and PPM command for ESC, respectively.
For an estimation of the constant in (4), that is, the DC gain of the transfer function (4), we could use the experimental results in Fig. 6. We choose an operating (nominal) point around
= 7.0 % (5)
= 10.8
for a PPM command = + . In addition, from a linear approximation of the relation between (), () around the operating point (, ) in Fig.6, we could find a proportional coefficient 14.50 which corresponds to the DC gain of (4). This allowed us to find an equality relation
general communication protocols and userprogrammable parameters of ESC in future.
REFERENCES

G. M. Hoffmann, H. Huang, S. L. Waslander, C. J. Tomlin, Precision flight control for a multivehicle quadrotor helicopter testbed, Control Engineering Practice, 19(9), pp. 10231036, 2011

C. V. Junior Jose, Paula Julio C. De, Leandro Gideon V. and Bonfim Marlio C., Stability Control of a QuadRotor Using a PID Controller, Brazilian Journal of Instrumentation and Control, Control 1.1,pp. 1520, 2013

S. Bouabdallah, P. Murrieri, R. Siegwart, Design and control of an indoor micro quadrotor, Proceedings of the 2004 IEEE International Conference on Robotics and Automation, New Orleans, LA, 26 April1 May 2004.

N. A. Demerdash and T. W. Nehl, Dynamic Modeling of Brushless DC Motors for Aerospace Actuation, IEEE Transaction on Aerospace and Electronic Systems, 16 (6), pp. 811821, 1980.

Gabriel Staples, Electric RC aircraft guy. 2014. Propeller Static & Dynamic Thrust Calculation. [ONLINE] Available at:
http://www.electricrcaircraftguy.com/2014/04/propellerstatic
dynamicthrustequationbackground.html. [Accessed 15 November
= 14.50
= 58.0
15].
and thus finally we could find the following transfer function
() 58
=
(6)
() + 4
which is valid around our choice of an operating point at (, ) = (7%, 10.8 N).
Note that the operating point should be chosen from a required thrust of a single propeller in an actual design of a drone controller,