Comprehensive System Identification of Ducted Fan UAVs

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Comprehensive System Identification of

Ducted Fan UAVs

A Thesis

Presented to the Faculty of

California Polytechnic State University

San Luis Obispo

In Partial Fulfillmentof the Requirements for the Degree of

Master of Science in Aerospace Engineering

by:

Daniel N. Salluce

January 2004


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Copyright 2004

Daniel Salluce

ALL RIGHTS RESERVED


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APROVAL PAGE

TITLE: Comprehensive System Identification of Ducted Fan UAVs

AUTHOR: Daniel N. Salluce

DATE SUBMITTED: January 2004

(SUBJECT TO CHANGE)

Dr. Daniel J. Biezad (AERO) ____________________________________

Advisor & Committee Chair

Dr. Mark Tischler (NASA/Army) ____________________________________

Committee Member

Dr. Jordi Puig-Suari (AERO) ____________________________________

Committee Member

Dr. Frank Owen (ME) ____________________________________Committee Member


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ABSTRACT

The increase of military operations in urbanized terrain has changed the nature of

warfare and the battlefield itself. A need for a unique class of vehicles now exists. These

vehicles must be able to accurately maintain position in space, be robust in the event of

collisions, relay strategic situational awareness, and operate on an organic troop level in a

completely autonomous fashion. The operational demands of these vehicles mandate

accurate control systems and simulation testing. These needs stress the importance of

system identification and modeling throughout the design process. This research focuses

on the unique methods of identification and their application to a class of ducted fan,

rotorcraft, and unmanned autonomous air vehicles. This research shows that a variety of

identification techniques can be combined to comprehensively model this family of

vehicles and reveals the unique challenges involved. The result is a high fidelity model

available for the purposes of control system design and simulation.


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ACKNOWLEDGMENTS

The author would like to give special recognition to Dr. Daniel J. Biezad,

Department Chair at Cal Poly, San Luis Obispo, CA and Dr. Mark B. Tischler, U.S.

Army Aeroflightdynamics Directorate Moffett Field, CA. Without their support,

guidance, and organizational efforts this research would never have been possible. Also,

Dr. Colin Theodore, Jason Colbourne, and the whole of the Army/NASA Rotorcraft

Division at Moffett Field proved to be invaluable resources and facilitators in the

completion of this project.


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TABLE OF CONTENTS

LIST OF TABLES........................................................................................................... viii

LIST OF FIGURES ........................................................................................................... ix

NOMENCLATURE ......................................................................................................... xii

CHAPTER 1 Introduction and Motivation

1.1 Vehicles Examined ............................................................................................1

1.2 Scope..................................................................................................................8

CHAPTER 2 Dynamic Model Identification Methods and Techniques

2.1 Identification Methods .................................................................................... 11

2.2 CIFER ............................................................................................................. 12

2.2.1 Flight Test Techniques..................................................................... 13

2.2.2 Bench Test Techniques.....................................................................14

2.3 Manufacturer Specifications ............................................................................14

2.4 Wind Tunnel Tests...........................................................................................15

CHAPTER 3 Vehicle Identification

3.1 Areas of Identification .....................................................................................16

3.2 Bare-Airframe ID.............................................................................................17

3.2.1 Aerovironment/Honeywell OAV......................................................17

3.2.2 Allied Aerospace MAV ....................................................................35

3.2.3 Trek Aerospace Solotrek...................................................................46

3.2.4 Hiller Flying Platform.......................................................................48

3.2.5 Vehicle Scaling Laws and Comparisons...........................................52

3.3 Servo Actuator Identification...........................................................................56

3.4 Sensor Identification ........................................................................................94

3.4.1 Accelerometer Identification ............................................................95

3.4.2 Rate Gyro Identification ...................................................................96

3.4.3 GPS Receiver Identification .............................................................98


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3.4.4 Magnetometer Identification...........................................................101

3.4.5 Pressure Altimeter Identification ....................................................102

CHAPTER 4 Flight Simulation

4.1 Simulated Sweeps ..........................................................................................104

4.2 Matlab Linear Model Determination .............................................................110

CHAPTER 5 Conclusions.............................................................................................119

BIBLIOGRAPHY............................................................................................................120

APPENDIX A OAV Proposal State Space Form.........................................................123

APPENDIX B Frequency Response Bode Plots for all Actuator Cases ......................124

APPENDIX C Actuator Generated TF Model Bode Plot Verification ........................135

APPENDIX D Actuator Time Domain Verification of Final Models..........................157


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LIST OF TABLES

3.1 OAV Measured Parameters during Flight Testing .......................................................18

3.2 OAV Frequency Range of Good Coherence (rad/sec) .................................................19

3.3 OAV Control Derivatives Extracted from Transfer Function Fits ...............................20

3.4 OAVDERIVID Identified parameters and Certainties ................................................23

3.5 OAVDERIVID Frequency Response Costs ................................................................23

3.6OAVEigenvalues and Associated Eigenvectors of [F]................................................24

3.7 MAV Physical Properties .............................................................................................35

3.8MAV Identified Stability Derivatives...........................................................................39

3.9 MAV Identified Control Derivatives............................................................................403.10 Final Flight Test Identified MAV Derivatives............................................................42

3.11 MAV Wind Tunnel Identified Derivatives and Flight Test Results...........................44

3.12Pitching Moment Derivatives and Solotrek Fan Speed..............................................47

3.13 Pitching Moment Coefficient Summary .....................................................................53

3.14 Pitching Moment with Blade Chord Summary...........................................................54

3.15 Manufacturer Specifications for Servo Actuators Tested...........................................57

3.16 Actuator Linkage Geometries.....................................................................................60

3.17 ActuatorCalibration Factors for Input and Output Channels to Degrees...................61

3.18 Frequency Sweep Used for all Actuators....................................................................62

3.19 Square Wave Parameters ............................................................................................63

3.20 Actuator BenchTest Matrix........................................................................................65

3.21 ActuatorNAVFIT Frequency Ranges for CIFER Cases............................................67

3.22 ActuatorNAVFIT Results for all Cases.....................................................................68

3.23 ActuatorNonlinear Characteristic Summary..............................................................74

4.1 Linmod, Wind Tunnel, and Flight Test Results for i-Star 9........................................114


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LIST OF FIGURES

Figure 1.1 Land Warrior OAV Concept ..........................................................................1

Figure 1.2 Hiller Helicopters Flying Platform 1958.....................................................3

Figure 1.3 Aerovironment / Honeywell DARPA Phase I OAV 2001 ..........................3

Figure 1.4 Trek Aerospace Solotrek Ducted Fan 2001.................................................4

Figure 1.5 Allied Aerospace i-Star MAV 9 Vehicle 2003..........................................4

Figure 1.6 Detailed view of 9 MAV Design..................................................................5

Figure 1.7 MAV Stator and Vanes...................................................................................6

Figure 1.8 Helicopter Body Axes System........................................................................7

Figure 1.9 Helicopter Body Axes System Applied to the Ducted Fan ............................7

Figure 1.10 Block Diagram of Basic DFCS Architecture ...............................................8

Figure 1.11 Comprehensive Identification Schematic.....................................................9

Figure 2.1 Sample Frequency Sweep Flight Test Command.........................................13

Figure 3.1 Roll rate response frequency domain verification........................................26

Figure 3.2 Pitch rate response frequency domain verification.......................................27

Figure 3.3 Yaw response frequency domain verification ..............................................29

Figure 3.4 Roll response time history verification.........................................................30

Figure 3.5 Pitch response time history verification .......................................................31

Figure 3.6 Yaw response time history verification........................................................32

Figure 3.7 Techsburg Wind Tunnel Setup for OAV......................................................33

Figure 3.8 Techsburg OAV Pitching Moment to Airspeed ...........................................34

Figure 3.9 On and Off Axis MAV Roll Frequency Responses .....................................36

Figure 3.10 On and Off Axis MAV Pitch Frequency Responses ..................................37

Figure 3.11 MAV Lateral Acceleration and Roll Rate Response to Roll Input ............40

Figure 3.12 MAV Longitudinal Acceleration and Pitch Response ...............................41

Figure 3.13 Pitching Moment Wind Tunnel Test Data for i-Star 9 .............................43

Figure 3.14 SolotrekWind Tunnel Test Results for Pitching Moment .........................46

Figure 3.15 Hiller Flying Platform Pitching Moment Data...........................................48

Figure 3.16 Drag over a Flat Plate Perpendicular to Flow.............................................49

Figure 3.17 Results of Removing Dummy Moment from Hiller Platform Test............50


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Figure 3.18 Actuators Tested and Relative Sizes ..........................................................57

Figure 3.19 Actuator Test Stand Apparatus...................................................................58

Figure 3.20 Cirrus CS-10BB Mounted on Wooden Strip..............................................58

Figure 3.21 Schematic Detailing Linkage Geometry.....................................................59

Figure 3.22 Sample Chirp Input, Response, and Square Wave Time History...............64

Figure 3.23 HS512MG Responses Illustrating Difference between 5V and 6V...........70

Figure 3.24 Sample Square Wave Response .................................................................72

Figure 3.25 Linear Fit for Max Rate Determination......................................................73

Figure 3.26 CS-10BB at 5V TH Illustrating Erratic Response at High Frequency.......75

Figure 3.27 94091 at 6V TH Illustrating Erratic Response at High Frequency.............75

Figure 3.28 94091 at 5V TH not Showing Erratic Response.........................................76

Figure 3.29 DS8417 FR Illustrating Mismatch in Linear Model...................................77

Figure 3.30 DS8417 TH Comparison to 1995 STI Findings .........................................78

Figure 3.31 Magnitude Comparison for Linear & Nonlinear Model to Bench Test .....81

Figure 3.32 Phase Comparison for Linear & Nonlinear Model to Bench Test .............82

Figure 3.33 Error Function Fr and NAVFIT Transfer Function Fit ..............................83

Figure 3.34Rise Time Ratio Phase Lag Relationship ...................................................85

Figure 3.35 Rise Time for Linear Model of DS8417 at 5V...........................................86

Figure 3.36 Sweep Amplitude and Natural Frequency with Rate Limiting ..................87

Figure 3.37 Simulink Actuator Blockset .......................................................................88

Figure 3.38 Configurable Actuator Parameters .............................................................89

Figure 3.39 2nd

Order Actuator Dynamics behind Mask ...............................................90

Figure 3.40 DS8417 at 5V Time Domain Validation ....................................................91

Figure 3.41 Accelerometer Model .................................................................................95

Figure 3.42 Accelerometer Stationary Noise Model .....................................................96

Figure 3.43 Rate Gyro Model ........................................................................................97

Figure 3.43 Rate Gyro Response to Constant 15 deg/sec for 10 sec .............................98

Figure 3.44 GPS Heading and Speed Model .................................................................99

Figure 3.45 GPS Error and Discrete Signal Model......................................................100

Figure 3.46 GPS Model Results...................................................................................101

Figure 3.47 Magnetometer Model ...............................................................................102


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Figure 3.48 Magnetometer Depiction at 5 Gauss for 5 Seconds .................................102

Figure 3.49 Pressure Altimeter Model.........................................................................103

Figure 3.50 Pressure Altimeter at 15 feet for 5 seconds ..............................................103

Figure 4.1 Simulink MAV Model................................................................................105

Figure 4.2 Custom PC and COTSSimulation Environment .......................................106

Figure 4.3 Simulink Sweep Generator GUI Built for Sweeps.....................................107

Figure 4.4 Simulink GUI Generated Sweep ................................................................108

Figure 4.5 MAV Flight Test Cross Coherence between Pitch and Roll controls ........109

Figure 4.6 Cross Control Decoupling Block Diagram.................................................111

Figure 4.7 LINMOD and Simulated Sweep Roll Frequency Response ......................115

Figure 4.8 Effect of Removing Cross Control Coupling to Response.........................116

Figure 4.9 Coupling Removed Illustrating linmodand Simulated Sweep Results......117

Figure 4.10 Comparison oflinmodand Flight Test Pitch Responses..........................118


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NOMENCLATURE

A Area v& Lateral body acceleration

a1 First Fourier Coefficient w Vertical body velocity

b1 Second Fourier Coefficient w& Vertical body accelerationBW Bandwidth Y Lateral Body Force

c Chord x State Matrix

C Nondimensional Coefficient X Longitudinal Body Force

CMPA Commanded Roll Rate Z Vertical Body Force

CMQA Commanded Pitch Rate Roll attitude

CMRA Commanded Yaw Rate Pitch attitude

CR Cramer-Rao Bound Heading attitude

F Plant Matrix n Natural Frequency

G Control Matrix n Normalized Natural FrequencyH1 Output Matrix Position Propeller Rotational Velocity

H2 Output Matrix Rate Density

I Inertia Propeller Coefficient

j Imaginary Variable Time Constant

L Rolling Moment Damping Ratio

M Pitching Moment Phase Angle

N Yawing Moment

p Roll body rate Subscripts

pmixer Lateral mixer signal

P Period c, Commandq Pitch body rate CG Center of Gravity

qmixer Longitudinal mixer signal col Collective

r Yaw body rate FS Full Scale

R Radius Lat Lateral

rmixer Pedal mixer signal (deg/sec) lon Longitudinal

s Frequency Domain Variable mixer Mixer

Rt Linear : Nonlinear Rise Time ped Pedal

NLRt Rise Time Nonlinear prop Propeller

LRt Rise Time Linear rad Radiansu Longitudinal body velocity xx X-plane in the Direction of X

u Input Control Matrix yy Y-plane in the Direction of Y

u& Longitudinal body acceleration zz Z-plane in the Direction of Z

v Lateral body velocity dot Time Derivative


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CHAPTER 1 INTRODUCTION AND MOTIVATION

1.1Vehicles Examined

Interest and application of ring-wing type unmanned aerial vehicles (UAVs) has

increased within recent years. The military and commercial uses for a vehicle capable of

hovering and forward flight while remaining small and unmanned are countless. Military

operations on urbanized terrain (MOUT) have become an area of concern for the United

States military within recent years. An increased need for policing and securing

urbanized areas has become apparent with the conflicts in Iraq and Mogadishu. It is this

type of environment that dictates the especially challenging design of small-scale UAVs1.

Because of the nature of MOUT, precise station-keeping requirements and overall

increased risk of collision with obstacles are important. Add to that the need for small and

back-pack carried vehicles and it becomes apparent why the ducted fan design is

appealing. The Defense Advanced Research Projects Agency (DARPA) advanced

concept technology demonstrator (ACTD) projects yielded submissions which included

the Kestrel organic air vehicle (OAV) and i-Star micro air vehicle (MAV). Figure 1.1

shows the typical application of the OAV envisioned by the US Army.

Figure 1.1 Land Warrior OAV Concept


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Commercial interest has also been seen by companies and organizations looking

for stable camera and surveillance platforms. Bridge inspection, traffic monitoring, and

search and rescue in hostile environments all can benefit from use of a small unmanned

vehicle capable of hovering flight. A unique class of small rotorcraft UAVs (RUAVs)

incorporating all of the characteristics yields a small design with certain design

difficulties. These RUAVs possess the problem of making a small-scale vehicle

unmanned along with the inherently unstable nature of rotorcraft dynamics. The ducted

fan RUAV design fulfills the collision and troop handling safety requirements. However,

these ducted fans introduce a strong tendency to correct themselves in pitch and roll with

longitudinal and lateral velocity, respectively.

These ducted fan RUAVs have low inertias with most of the weight near the

center of the vehicle. Their small size and weight make for stringent volumetric and mass

restrictions. This leads to lower performance subsystems, especially sensors and

actuators. High degrees of cross coupling due to strong gyroscopic effects are created by

the fast spinning propellers. The unconventional designs that have little or no knowledge

base established make physics based modeling difficult2. Most RUAV types include the

ability for a wide range of scales to be produced. Because of the relative simplicity of

construction, bigger and smaller vehicles alike can be produced. Usually shorter design

cycles due to limited funding and demanding project requirements leave these vehicles in

need of accurate models early in the design cycle. Flight vehicles are available very early

in the design sequence and make for easier flight test based identification. These

characteristics combine to mandate accurate dynamic models. This research work will

focus on the comprehensive identification of these models.


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The vehicles examined within the scope of this research are all very similar in

design in that they consist of mainly a ducted fan utilized for lift. The vehicles examined

are shown in Figures 1.2 1.5. Although the mission profiles for all of these vehicles

varies greatly, the two smaller scale surveillance vehicles, the Kestrel and the i-Star

MAV are most representative of future military operations on urbanized terrain (MOUT)

applications.

Figure 1.2 Hiller Helicopters Flying Platform 1958

Figure 1.3 Aerovironment / Honeywell DARPA Phase I OAV 2001


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Figure 1.4 Trek Aerospace Solotrek Ducted Fan 2001

Figure 1.5 Allied Aerospace i-Star MAV 9 Vehicle 2003

Figure 1.2 depicts the Hiller flying platform. This vehicle underwent some testing

of the pitching moment characteristics of ducted fans back in 19583. For this purpose it

was included in the study. Figure 1.3 shows the Aerovironment/Honeywell teamed effort

technology demonstrator for DARPA. This vehicle was used for flight testing and

parametric modeling as well as for the identification of sensor packages. Figure 1.4

shows the Trek Aerospace Solotrek. This unique design underwent comprehensive wind


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tunnel testing to study the characteristics of the ducted fan at varying propeller speeds.

Finally, Figure 1.5 shows the Allied Aerospace i-Star MAV vehicle. Pictured is the 9

diameter vehicle. There is also a bigger cousin with a 29 diameter. Both of these

vehicles were used for actuator identification, flight testing, and simulation as part of

work for DARPA. Figure 1.6 shows a detailed view of the MAV.

Figure 1.6 Detailed view of 9 MAV Design

The basic design of the ducted fan UAV incorporates a small COTS power plant

that is centered inside a duct. The flow of air in the duct is passed over stators for flow

straightening and over vanes which allow actuation to generate moments. Figure 1.7

shows the vanes and stators on the bottom of the 9 MAV design.


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Figure 1.7 MAV Stator and Vanes

Great care is needed in specifying proper coordinate systems. It is not uncommon

to see these vehicles with their x-body axis out the nose, or main nacelle pointing up.

This causes issues because then the vehicle is at a 90 nose up orientation in hover. This

is a gimbal-lock orientation and is best avoided for standard Euler sequences. Figure 1.8

below illustrates the helicopter coordinate system used for this research and Figure 1.9

shows it applied to the ducted fan. Unless otherwise specified, all derivatives and

mention of moments are referred to in standard helicopter notation.

Duct

Stators

Camera &Proximity Sensor

LowerCenterBod

Vanes


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Figure 1.8 Helicopter Body Axes System

Figure 1.9 Helicopter Body Axes System Applied to the Ducted Fan

All moments and forces are represented as positive in the directions shown with moments

being applied in accordance with the positive right-hand rule.

XBody

YBody

ZBody


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Commanded

Inputs

Bare-Airframe

DynamicsDigital Flight

ControlServo-Actuators

Sensors

Vehicle

Response

1.2Scope

This research will focus on representing the entirety of the RUAV modeling.

Figure 1.10 shows a simplified block diagram depicting the operation of the vehicle.

Figure 1.10 Block Diagram of Basic DFCS Architecture

It can be seen that simply modeling the bare airframe and its dynamics is not

enough to capture the whole nature of the vehicle. Due to the small size and limited

performance actuators and sensor packages, these areas heavily influence the nature of

flight. To accurately model the vehicle for flight control and simulation purposes, a more

expanded diagram would be required. Figure 1.11 represents the identification effort of

this research.


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Figure 1.11 Comprehensive Identification Schematic

Figure 1.11 shows that a number of techniques (described in Chapter 2) applied to a large

range of components are required to model the system. Each of these areas will be the

Sensors &Telemetry

Vehicle Dynamics

Control System

IMU

Rate Gyros

GPS

Pressure

Altimeter

Rigid Body

Dynamics

Inner-

Loop

Closures

Outer-

Loop

Closures

Actuators

Unique Pitching

Moment

Characteristics

Accelerometers

CIFER

Wind Tunnel or Other Empirical Data

Manufacturer and Bench Data

SOURCES OF IDENTIFICATION


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focus of this research. Various vehicles will be looked at in order to build up this compete

picture of the operation of these ring wing UAVs.


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CHAPTER 2 METHODS AND TECHNIQUES

2.1 Identification Methods

A combination of the characteristics of these small RUAVs makes system

identification an important and integral part of the design cycle. The need for a high

performing and robust control system is paramount to vehicle survivability and mission

performance. The design of the flight control system requires an accurate model across a

variety of operating conditions and input frequencies.

As previous work shows2, the use of Froude scaling the natural frequencies of

vehicles reveals the natural frequency would increase by the square root of a scale factor

measured in length. For example, making the vehicle 4 times smaller would increase the

natural frequency by 2. So, as vehicles become smaller, they require a higher bandwidth

control system. The need to operate at higher frequencies and in more of the available

flight envelope requires accurate models across large ranges of input frequencies. The use

of frequency domain techniques lends itself very nicely to accomplishing this modeling

challenge.

The NASA/Ames Research Center tool CIFER

(Comprehensive Identification

from Frequency Responses) is primarily used to identify low order equivalent systems

and parametric state-space models required across broad frequency ranges. This tool is

used extensively for the modeling of system dynamics in this effort.

The reliance on small scale, low performance components and sensors makes

characterizing the errors and inconsistencies of components important. Without exclusive


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access to hardware inside of test vehicles, manufacturer data must be applied for error

and noise modeling. These tools and techniques combine to represent the comprehensive

identification of these vehicles.

2.2 CIFER

CIFER provides an environment and set of programs that perform the various

steps of the system identification process. Nonparametric modeling, in which no model

structure or order is assumed; in the form of frequency responses represented as Bode

plots are first extracted with CIFER. This then allows for the parametric modeling.

Transfer functions, low order equivalent (LOE) systems, or state-space models with

stability and control derivative representation3

are all used. The identification process can

be summarizes as4:

1. Nonparametric frequency response calculation from time history data

o Use of Chirp-Z Fast Fourier Transforms (FFT) and complex functions to generate

the frequency responses over multiple windows and samples2. Multi-input frequency response conditioning

o Off axis control inputs contribution to on axis response is removed

3. Multi-window averaging of frequency responses

o Combination of different window sampling sizes

4. Parametric models fit to frequency responses

o Transfer function models fit to single input single output (SISO) systems

o State-space models fit to all controls and states for parameter extraction

5. Time domain verification of parametric models

When complete, this procedure yields accurate models to be applied for a variety

of tasks. CIFER does require flight test time histories in which the vehicles modes have

been excited by frequency rich inputs. It is not limited to vehicle dynamics either. This

tool can be used anywhere frequency domain analysis is needed. CIFER is a powerful

tool that incorporates all of the tools to needed to model in the frequency domain.


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2.2.1 Flight Test Techniques

There are a number of techniques that need to be applied to ensure that the flight

test of the vehicle is useful and applicable to system identification. While outside the

scope of this research, it is sufficient to say that a combination of frequency rich

maneuvers as seen in Figure 2.1 and validation maneuvers like doublets are required. A

combination of sensing and telemetry equipment is needed to measure both the input

from the actuators and the vehicle response. Access to the IMU and servo signals is

required.

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0

5

10

15

0 15 30 45

ControlDeflection

(%)

Time (seconds)

ZeroDuration

ZeroDuration

FallTime

RiseTime

Sine Frequency Sweep

Figure 2.1 Sample Frequency Sweep Flight Test Command


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2.2.2 Bench Test Techniques

Bench testing was used in cases where components were to be tested without

actually installing them on the vehicle or testing them while in flight. This method was

primarily applied to the testing of the servo actuators. The search for and classification of

actuators meeting the requirements of the vehicles made it impractical to install the

numerous actuators on the vehicle for testing. In this case, the actuators were tested while

hooked up to specific measuring equipment. Frequency domain analysis with CIFER was

applied to determine the dynamic characteristics of the components.

2.3 Manufacturer Specifications

The use of commercial off the shelf (COTS) devices and components for the

buildup of inertial measuring units (IMU) on the vehicles provides for manufacturer

specifications and ratings of component performance. This is important when direct

access of the components and hardware in the loop (HIL) bench testing is not available.

The identification of the rate gyros, accelerometers, magnetometers, GPS receiver, and

actuators all benefited from the provision of manufacturer identified errors and

performance specifications. In general, these specifications are slightly optimistic and

reflect the specific measuring procedure applied by the manufacturer. Averages are

usually presented by manufacturers while component-specific results are required in

some modeling cases. Due to time constraints and availability of hardware for testing,


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manufacturer specifications are modeled and applied for the majority of telemetry and

measuring equipment aboard the vehicles.

2.4 Wind Tunnel Tests

Wind tunnel and other empirical data measured from the vehicles themselves play

an important role as well. As previously mentioned, these ducted fan RUAVs exhibit

unique corrective pitching moment characteristics due to large Mu and Lv derivatives.

Wind tunnel studies help to better characterize this. The need to accurately characterize

the behavior of the ducted fan in translational velocities has put emphasis on accurate

wind tunnel modeling. This type of physics-based modeling is used to draw some

conclusions regarding the nature of the strong pitching and rolling moment created when

the vehicle is in forward flight or in a cross-wind. It is also used to compare and correlate

the CIFER identified dynamics. In the case of the Solotrek vehicle, a wind tunnel was not

actually used. Similar techniques and methodology was applied to the vehicle although it

was suspended on top of a moving pickup truck. Regardless, wind tunnel tests and data

were used to validate and compare trends for most of the vehicles studied.


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CHAPTER 3 VEHICLE IDENTIFICATION

3.1 Areas of Identification

As mentioned in Chapter 2, the comprehensive identification of these vehicles

requires modeling and testing of the bare-airframe dynamics as well as all of the systems

and components onboard which directly affect the flight characteristics of the vehicle.

Figure 1.11 of Chapter 1 illustrates the areas of identification. The tools and techniques

outlined in Chapter 2 will be applied to the bare-airframe of the vehicles with conclusions

being drawn for scaling and correlation. COTS actuators will then be analyzed for there

dynamics and nonlinearities. Finally, all of the sensors and telemetry equipment used in

observation for the control system will be analyzed and modeled.


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3.2 Bare-Airframe ID

The bare-airframe dynamics are perhaps the most unique aspect of these vehicles

and the way they fly. A small inertia with a large concentration of mass near the center of

the duct is inherent in the design. Combined with this, there is heavy coupling between

pitch and roll due to the gyroscopic effects of the fast spinning propeller. All of the

vehicles looked at utilize fixed pitch propellers. Figure 1.11 showed that the pitching

moment characteristics together with the whole of the bare-airframe rigid body dynamics

characterize the vehicle in uncontrolled flight.

3.2.1 Aerovironment/Honeywell OAV

The goal of the CIFER

system identification was to achieve an accurate Multi-

Input Multi-Output (MIMO) state-space model to support flight control development and

vehicle sizing for the DARPA Phase I test vehicle. The frequency range of interest was

0.1 10 rad/sec. Frequency response analyses show that the important dynamic

characteristics in this frequency range are the rigid body dynamics.

Examination of the eigenvalues of the identified model reveals low frequency

unstable periodic modes in both the pitch and roll degrees of freedom. Excellent matches

between the model and flight data for the on-axis time responses confirm the accuracy of

the of the identified state-space dynamic model.


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The CIFER identification is based on a set of flight test data gathered while flying

the prototype vehicle. The data was recorded at a nominal data rate of 23 Hz and included

vehicle rate and control mixer inputs. These are presented in Table 3.1.

Table 3.1 OAV Measured Parameters during Flight Testing

Parameter Measured Value

pmixer CMPA

qmixer CMQA

rmixer CMRA

p PP

q QQ

r RR

Frequency responses were generated with CIFERs FRESPID tool from the test

data gathered from flying the proposal vehicle. Frequency ranges from ~0.35 20

(rad/sec) were used with four windows. The data was processed through MISOSA to

remove the effect of off-axis control inputs during the sweeps. COMPOSITE was used to

combine the four windows of data into a single response.

The frequency ranges used for the dynamic model identification were the ranges

when the coherence was good (values above 0.6). These frequency ranges are listed in

Table 3.2 and are used in the state space model identification in DERIVID. Examination

of the off-axis frequency responses indicates no significant cross-couplings between the

longitudinal and lateral degrees of freedom. These couplings are therefore not included in

the state space model. This is unique to this vehicle and differs from other vehicles tested.

It may be due to lack of excitation during flight test.


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Table 3.2 OAV Frequency Range of Good Coherence (rad/sec)

Because no significant cross-coupling between the longitudinal and lateral degrees of

freedom was observed, the state-space form would be modeled after the transfer

functions. The identified transfer functions appear as Equations 3.1-3.2.

ppmixer

= 18.68s(s + 0.0032)e0.0477s

(s + 2.0983)[0.5761,1.7921] (Equation 3.1)

q

qmixer=

21.07s2e0.0653s

(s +1.9496)[0.7616,1.9349] (Equation 3.2)

r

rmixer=

20.81e0.0718s

s (Equation 3.3)

The 3rd

order denominator forms known as a hovering cubics (Equations 3.4 and

3.5) exemplify the dynamic modes for the longitudinal and lateral directions5. The control

derivatives for the state-space model were initially set as the free gain terms in the

numerators of the transfer functions. These values appear in Table 3.3.

( )3 2lateral hover v P v P vY L s Y L s gL = + + (Equation 3.4)

( )3 2longitudinal hover u q u q us X M s X M s gM = + + + (Equation 3.5)

CMPA CMQA CMRA

P 1-8 - -Q - 1-8 -

R - - 3-10


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Table 3.3 OAV Control Derivatives Extracted from Transfer Function Fits

Derivative Value

L 0.326

M 0.343

N 0.339

A state space form comprised of a set of four matrices (F, G, H1, and H2) known

as a quadruple was set up. This can be seen as Equations 3.6 3.13. The state vector ( x )

is presented as equation 3.8 (the subscript "rad" indicates that these quantities have the

units of rad and rad/sec). The three controls were pmixer, qmixer, and rmixer, as seen in

Equation 3.10 ( u ). The removal of cross-coupled terms yielded a final stability matrix

(F) to be fitted to the data (Equation 3.11). While the units of the states are in rad, rad/sec,

and ft/sec; the data is in deg/sec. A conversion factor of 57.3 (deg/rad) was multiplied

through the H1 matrix (Equation 3.13) and divided through the initial values of the

control derivatives (Table 3.3) in the G matrix (Equation 3.12). CIFER then tuned the

parameters in the F and G matrices to match the state space models frequency responses

to those for the flight test data.

x Fx Gu= +& (Equation 3.6)

1 2y H x H x= + & (Equation 3.7)

rad

rad

rad

rad

v

p

x u

q

r

=

(Equation 3.8)


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p

y q

r

=

(Equation 3.9)

mixer

mixer

mixer

p

u q

r

=

(Equation 3.10)

0 0 0 0 0

0 0 0 0 0

0 1 0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 1 0 0

0 0 0 0 0 0

v

v P

u

u q

r

Y g

L L

F X g

M M

N

=

(Equation 3.11)

0 0

0 0

0 0 0

0 0

0 00 0 0

0 0

mixer

mixer

mixer

mixer

mixer

p

p

q

q

r

Y

L

XG

M

N

=

(Equation 3.12)

1

0 57.3 0 0 0 0 0

0 0 0 0 57.3 0 0

0 0 0 0 0 0 57.3

H

=

(Equation 3.13)

It is worthwhile to note that many of the derivatives were set to zero in the

identification process. Because of the lack of acceleration data, the on-axis damping

parameters Xu, Yv, and Zw were unable to be determined in the model and were thus

removed from the CIFER model (fixed to a value of 0). A closer examination of the


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transfer functions (Equations 3.1-3.3) will show that the longitudinal and lateral modes

are heavily reliant on the values of Lv and Mu, respectively. If these derivatives were the

only ones in the hovering cubic forms (Equations 3.4 and 3.5), the equations would

reduce to the degenerate forms seen in Equations 3.14 and 3.15. These forms contain one

real and one complex root for negative values of Lv and Mu. These roots describe the

dynamics of the system and show that Lv and Mu are the dominant terms required to

depict the three modes.

3

lateral hover vs gL = (Equation 3.14)

3

longitudinal hover us gM = (Equation 3.15)

CIFER allows for a measure of merit, or cost, of the final model fit to the

frequency responses. Lower costs are better fits. The final model had an excellent

average cost of 23.6. For the best possible fit, pure time delays were identified as

0.04205, 0.08730, and 0.07189 seconds for roll, pitch, and yaw responses, respectively.

The longitudinal delay was bigger in both the state space model and the transfer function

fits. However, the Cramer-Rao bound for the longitudinal delay was rather big (29%)

revealing that it was a correlated term in the minimization process. This may be due to

CIFER adjusting the value to make up for inconsistencies in the model or it is due to the

pitch sensor or flight control computer. All other Cramer-Rao bounds were acceptable,

(CR< 15%) indicating good reliability of the identified derivatives.

Table 3.4 contains the identified variables and their respective certainty during the

identification. A comparison with the control derivatives extracted from the transfer

functions (Table 3.3) reveals very close matches.


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Table 3.4 OAV DERIVID Identified Parameters and Certainties

Table 5 shows the cost functions for the transfer functions. They were all very acceptable.

Table 3.5 OAV DERIVID Frequency Response Costs

The asymmetric design of the vehicle accounts for the difference in the values

between Lv and Mu. Figure 1.3 depicts the fact that the OAV design has nacelles or cargo

pods making it asymmetric. The ratio of the identified values (Lv : Mu = 0.7510) reflects

the relationship of the lateral and longitudinal inertias specified (Iyy : Ixx = 0.6312).


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The final CIFER

identified state space dynamic model is presented in Appendix A.

The eigenvalues and their associated eigenvectors are given below in Table 3.6.

They have been normalized to the dominant mode. The eigenvectors are the

corresponding state values which identify the modes. The larger values indicate the states

which are dominant in the modes. A value of 1 in the eigenvector indicates which state is

the primary mode. From the eigenvectors and eigenvalues some interesting dynamics can

be noted.

Table 3.6 OAV Eigenvalues and Associated Eigenvectors of [F]

Mode #(Aperiodic Yaw Subsidence)

Mode #2(Lateral Low Frequency Periodic)

Mode #3(Aperiodic Roll Subsidence)

real imaginary real imaginary Real imaginary

0.00E+00 0.00E+00 9.25E-01 -/+1.60E+00 -1.85E+00 0.00E+00

[zeta, omega] [zeta, omega] [zeta, omega]

[0.000E+00, 0.000E+00] [-.500E+00, 0.185E+01] [0.000E+00, 0.000E+00]

V 0.00E+00 0.00E+00 V -8.20E-02 +/-1.42E-01 V 1.64E-01 0.00E+00

P 0.00E+00 0.00E+00 P 1.00E+00 -/+1.13E-08 P 1.00E+00 0.00E+00

PHI 0.00E+00 0.00E+00 PHI 2.70E-01 +/-4.68E-01 PHI -5.40E-01 0.00E+00

U 0.00E+00 0.00E+00 U 0.00E+00 0.00E+00 U 0.00E+00 0.00E+00

Q 0.00E+00 0.00E+00 Q 0.00E+00 0.00E+00 Q 0.00E+00 0.00E+00

THETA 0.00E+00 0.00E+00 THETA 0.00E+00 0.00E+00 THETA 0.00E+00 0.00E+00

R 1.00E+00 0.00E+00 R 0.00E+00 0.00E+00 R 0.00E+00 0.00E+00

Mode #4(Aperiodic Pitch Subsidence)

Mode #5(Longitudinal Low Frequency Periodic)

real imaginary real imaginary

-2.04E+00 0.00E+00 1.02E+00 -/+1.76E+00

[zeta, omega] [zeta, omega]

[0.000E+00, 0.000E+00] [-.500E+00, 0.204E+01]

V 0.00E+00 0.00E+00 V 0.00E+00 0.00E+00

P 0.00E+00 0.00E+00 P 0.00E+00 0.00E+00

PHI 0.00E+00 0.00E+00 PHI 0.00E+00 0.00E+00

U 2.76E-01 0.00E+00 U -1.38E-01 -/+2.39E-01

Q -3.55E-02 0.00E+00 Q 1.78E-02 -/+3.08E-02

THETA 1.00E+00 0.00E+00 THETA 1.00E+00 +/-2.21E-08

R 0.00E+00 0.00E+00 R 0.00E+00 0.00E+00


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The identified state-space model yielded 7 eigenvalues. Two of these were

complex pairs, and three real. These 7 eigenvalues depict 5 modes. Mode #1 is the yaw

mode which was modeled with no yaw damping, thus the value of 1 for the yaw rate state

(r). Mode #2 is associated with the 2nd

order periodic denominator term in the hovering

cubic because of the high values for the lateral velocity (v) and roll rate (p) states. This is

a low frequency unstable mode. Likewise, Mode #5 is from the 2nd

order term in

longitudinal hovering cubic. This is seen by the larger eigenvectors for the states of

longitudinal velocity (u) and pitch rate (q). The remaining eigenvectors identify the 1st

order, aperiodic subsidence modes for roll (Mode #3) and pitch (Mode #4). These

eigenvalues are very close to the modes of the transfer function models (Equations 1-3).

The excellent agreement between the flight data and model can be seen in the

following frequency responses comparing the parametric state space model and the actual

flight test data.


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Figure 3.1 Roll rate response frequency domain verification

It can be seen in Figure 3.1 that the roll rate model fits very well in the regions of

good coherence. Only where there are dips in this signal to noise ratio does the model

start to yield poor results. These results were obtained without linear acceleration data.


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Better sensors, at higher sampling rates together with linear acceleration data will yield

closer matches across broader frequency ranges.

Figure 3.2 Pitch rate response frequency domain verification


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The pitch rate response seen in Figure 3.2 illustrates the accuracy of the state-

space model in regions of good coherence as well. The coherence is the ratio of output

power that is linearly related to input power. This means that high noise in this channel,

or wind gusts during the sweep can produce lower coherence. It can be seen that the

accuracy of the state-space model for the pitch rate deteriorates quickly at lower

frequencies.


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Figure 3.3 Yaw response frequency domain verification

The model revealed that there was no natural yaw damping for this vehicle. The

unstable hovering cubic is prevalent in the 1-3 (rad/sec) region. The fit was accurate at

higher frequencies before noise in the channel becomes a problem, as seen in Figure 3.3.


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The identified models were compared with data taken by Aerovironment during

flight testing. It can be seen that the on-axis responses have an excellent match for all 3

controls. The quality of the match confirms that the identified model is accurate.

Figure 3.4 Roll response time history verification


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Figure 3.4 shows that even though the lateral dynamics were modeled without a

roll damping term, the control surface effectiveness term and Lv in the hovering cubic

accurately pick up the nature of the response.

Figure 3.5 Pitch response time history verification


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Likewise, Figure 3.5 above shows that the longitudinal degree of freedom is

captured and represented in the state-space model very accurately.

Figure 3.6 Yaw response time history verification

Figure 3.6 shows the accuracy of the yaw degree of freedom. It stays accurate

regardless of being modeled as the simple integrator form with no yaw damping.


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It can be seen that the Aerovironment Proposal prototype OAV was successfully

modeled with a state-space model. The identified model shows good agreement for both

the time and frequency responses. The identified system showed an unstable periodic

mode in the pitch and roll responses. Time delays were determined for all three channels.

The ratio of the lateral to longitudinal moment terms Lv and Mu reflect the ratio of the

inertias Iyy to Ixx. All of the modes dictated by the hovering cubic forms were identified,

but because of a lack of acceleration data the speed damping force derivatives could not

be accurately identified. The identified transfer function modes closely match the modes

of the identified state space dynamic model.

After flight test was completed for the purposes of identification, the OAV design

was further analyzed in the wind tunnel. The vehicle was put into the Virginia Tech

Stability Wind Tunnel by Techsburg, Inc. without the payload nacelles. A photograph of

the setup is shown as Figure 3.7.

Figure 3.7 - Techsburg Wind Tunnel Setup for OAV


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Although part of a larger control surface and augmentation experiment, the

vehicle was tested in a baseline configuration similar to that seen in Figure 1.3. From the

tests, pitching moment information was extracted with varying wind speeds. Figure 3.8

shows the results of that test.

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-50 -40 -30 -20 -10 0 10 20 30 40 50

u (fps)

M(

ft-lbf)

Figure 3.8 Techsburg OAV Pitching Moment to Airspeed

As Figure 3.8 shows, there is a unique pitching moment created when the vehicle

experiences some wind velocity across the duct. This is illustrated by the slope of the

tangent line depicted as a dotted line. In this case, the dimensional derivative about the

hover condition is 0.011. This is a corrective moment for velocities below some critical

velocity. A negative pitching moment is then created above this critical speed. In the case

of OAV as tested, this occurs at roughly 10 fps.


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3.2.2 Allied Aerospace MAV

Flight test was performed on the MAV vehicle in a similar manner as was

described in the previous section for the OAV. Table 3.7 below shows the physical

properties for the vehicle as it was tested.

Table 3.7 MAV Physical Properties

Physical Quantity Value

Mass (slugs) 0.233

C.G. (below duct lip - inches) 2.25

Propeller Speed (rad/sec) 1884.0

Ixx (slug-ft^2) 0.021

Iyy (slug-ft^2) 0.021

Izz (slug-ft^2) 0.021

Iprop (slug-ft^2) 0.00012*

* value obtained from Allied Aerospace that contains the inertia of all of the rotating components.

Frequency responses for on and off-axis are presented as Figure 3.9. These include the

removal of off-axis control contributions by using the CIFER tool MISOSA.


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F040P_COM_ABCDE_pcmd_pb - p/lat

F040P_COM_ABCDE_pcmd_qb - q/lat

F040P_COM_ABCDE_pcmd_rb - r/lat

-50

-10

30MAGNITUDE(DB)

-150

50

250PHASE(DEG)

0.1 1 10 100FREQUENCY (RAD/SEC)

0.2

0.6

1

COHERENCE

Figure 3.9 On and Off Axis MAV Roll Frequency Responses

Figure 3.9 shows the roll, pitch and yaw rate frequency responses to roll control.

Here there is good coherence for the on-axis responses, but no coherence in the off-axis

direction. The roll rate frequency response has a good coherence from 0.5 to 12 rad/sec

and this portion of the frequency response is used in the identification.


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F040Q_COM_ABCDE_qcmd_qb - q/lon

F040Q_COM_ABCDE_qcmd_pb - p/lon

F040Q_COM_ABCDE_qcmd_rb - r/lon

-50

-10

30MAGNITUDE(DB)

-150

50

250PHASE(DEG)

0.1 1 10 100FREQUENCY (RAD/SEC)

0.2

0.6

1COHERENCE

Figure 3.10 On and Off Axis MAV Pitch Frequency Responses

Figure 3.10 shows the pitch, roll and yaw rate frequency responses to pitch

control. As with the roll control responses, there is good coherence for the on-axis

response, but no coherence for the off-axis responses. This would indicate that there is

very little cross-coupling and the pitch and roll responses are essentially uncoupled. It is

uncertain why the gyroscopic coupling is not evident in the flight tests. A similar


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approach was used for the accelerometer information. The parametric state space model

was setup as shown in Equation 3.16.

0 0 0 0 0

0 0 0 00 1 0 0 0 0 0 0

0 0 0 0 0

0 0 0 0

0 0 0 0 1 0 0 0

u Xu g u Xlon

q Mu Mq Mp q Mlonlat

v Yv g v Ylat lon

p Lq Lv Lp p Llat

= +

&

&&

&

&

&

(Equation 3.16)

The derivatives Mp and Lq result from the gyroscopic moments produced by the

rotating inertia of the propeller. This coupling is one of the unique aspects of the

vehicles dynamics. Taking into account the angular momentum of the spinning propeller

and dividing by the inertia of the total vehicle yields the moment produced by the

gyroscopic effects. This is shown as equations 3.17 and 3.18.

prop

q

xx

IL

I

= (Equation 3.17)

prop

pyy

I

M I

= (Equation 3.18)

The values for Mp and Lq therefore can be used for the determination of propeller

inertia. This is possible because the rotational speed of the propeller remained mostly

constant and the inertia of the vehicle changed negligibly due to fuel burned. This is

useful because the inertia of the small propeller while spinning is hard to measure in any

type of simple experiment. A time delay was also added to the dynamics to account for

transport delays in the electronics.


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A 0th/2nd order transfer function is included in the identification to take into

account the actuator dynamics. The form of this transfer function is as follows:

TF=n 2

s2

+ 2n +n2

The values of the damping and natural frequency of the actuator used were

obtained from bench tests of the actuator dynamics presented in section 3.3 for the

Airtronics 94091 servo actuator running at nominally 5 volts. The natural frequency for

this case is 28.2 rad/sec and the damping ratio is 0.52.

The DERIVID utility was used to identify the elements of the state-space model.

The stability derivative results are shown Table 3.8.

Table 3.8 MAV Identified Stability Derivatives

COUP02

Derivativ e Param Value CR Bound C.R. (%) Insens.(%)

X u -0.1090 0.04395 40.33 10.92

Mu 0.5014 0.03412 6.805 2.729

Mq

0.000 + ... ... ... ... ... ...

Mp 0.000 + ... ... ... ... ... ...

Yv -0.1090 * ... ... ... ... ... ...

Lq 0.000 + ... ... ... ... ... ...

Lv -0.5014 * ... ... ... ... ... ...

Lp 0.000 + ... ... ... ... ... ...

Ipr op 0.000 + ... ... ... ... ... ...

+ Eliminated during model structure determination

y Fixed value in model

* Fixed derivativ e tied to a free derivative

Yv = 1.000E+00* X u ( COUP02 )

Lv =-1.000E+00* Mu ( COUP02 )

The value of the rotating inertia (Iprop) was insensitive in the identification and

was dropped from the list of active elements. This is because there was no good

coherence in the off-axis roll and pitch rate responses, which result for the gyroscopic


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effects from the rotating inertia. Ultimately this made for the coupling derivatives in the

model to become zero as well.

The control derivatives were identified as shown in Table 3.9.

Table 3.9 - MAV Identified Control Derivatives

COUP02

Derivativ e Param Value CR Bound C.R. (%) Insens.(%)

X lon -0.2841 0.01692 5.955 2.058

M lon -0.2343 0.01103 4.705 2.149

Yl at 0.2495 0.01876 7.519 2.544

L lat -0.1789 0.01056 5.902 2.614

lat 0.06767 * ... ... ... ... ... ...

lon 0.06767 4.599E-03 6.796 3.272

* Fixed derivativ e tied to a free derivativelat = 1.000E+00* lon ( COUP02 )

Figure 3.11 shows the identified models roll and lateral acceleration responses for the

roll sweep.

Flight results

COUP02 - Identification Results

-40

-20

0

20

40

Magnitude(DB)

p/lat

-150

-100

-50

0

50

100

150Phase (Deg)

0.1 1 10 100Frequency (Rad/Sec)

0.2

0.4

0.6

0.8

1 Coherence

-60

-40

-20

0

20Magnitude(DB)

ay/lat

-200-150

-100

-50

0

50

100Phase (Deg)

0.1 1 10Frequency (Rad/Sec)

0.2

0.4

0.6

0.8

1 Coherence

Figure 3.11 MAV Lateral Acceleration and Roll Rate Response to Roll Input


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Figure 3.12 shows the same for the longitudinal acceleration and pitch rate response to

pitch input.

Flight results

COUP02 - Identification Results

-40

-20

0

20

40

Magnitude(DB)

q/lon

-150

-100

-50

0

50

100

150 Phase (Deg)

0.1 1 10 100Frequency (Rad/Sec)

0.2

0.4

0.6

0.8

1 Coherence

-60

-40

-20

0

20

Magnitude(DB)

ax/lon

-400

-350

-300

-250

-200

-150

-100 Phase (Deg)

0.1 1 10Frequency (Rad/Sec)

0.2

0.4

0.6

0.8

1 Coherence

Figure 3.12 MAV Longitudinal Acceleration and Pitch Rate Response to Pitch Input

The combination of Figure 3.11 and Figure 3.12 show that the identified model

agrees with the flight test data. There are some inconsistencies, but overall the costs of

the fits were low and the model agrees with flight test results. The final identified

parameters are outlined in Table 3.10.


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Table 3.10 Final Flight Test Identified MAV Derivatives

Derivative Param Value

X u -0.1090

Mu 0.5014

Mq 0.000 +

Mp 0.000 +

Yv -0.1090 *

Lq 0.000 +

Lv -0.5014 *

Lp 0.000 +

Ipr op 0.000 +

X lon -0.2841

M lon -0.2343

Ylat 0.2495

L lat -0.1789

lat 0.06767 *

lon 0.06767

+ Eliminated during model structure determination

y Fixed value in model

* Fixed derivativ e tied to a free derivative

Mp= 8.971E+04* Ipop ( PIT21 )

Lq=-8.971E+04* Ipop ( PIT21 )

Yv = 1.000E+00* X uLv =-1.000E+00* Mulat = 1.000E+00* lon

The identification of the MAV vehicle benefited from also having wind tunnel

tests performed by Allied Aerospace. These tests were completed to build up a nonlinear,

test data based, table-lookup bare airframe and control simulation. MAV is a family of

vehicles. Both the larger 29 vehicle and smaller 9 vehicle were put into the wind tunnel

with the fans spinning at various speeds while the attitude and wind velocity was varied.

This was done to determine moment and force values with angle of attack and beta as

well as lateral, longitudinal, and vertical velocities.

There were issues with the 9 wind tunnel results. To illustrate the wind tunnel

method for the MAV (which is similar to the wind tunnel tests performed for OAV by


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Techsburg) the pitching moment response to gusts was analyzed. Figure 3.13 shows a

summary of the data collected for the pitching moment.

i-Star-9 Pitching Moment Characteristics

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0 20 40 60 80 100 120 140

Shroud Velocity (fps)

PitchingMoment(ft-lb)

Figure 3.13 Pitching Moment Wind Tunnel Test Data for i-Star 9

Figure 3.13 shows that a linearization was completed for the first 30 knots and is

shown. The slope of this line represents the dimensional derivative Mu. What is curious

here, and will be discussed in further detail in the next sections, is the nature of the

pitching moment response to increases in speed. As the vehicle experiences a cross wind

in hover, it will pitch in the positive direction. This represents a corrective moment.

However if the gust is strong enough, it will actually experience a negative moment.

The method illustrated above was repeated for all of the major flight derivatives

to obtain the values portrayed in Table 3.11. Table 3.11 compares both 9 and 29

vehicles as well as the 9 flight test results where appropriate.


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Table 3.11 MAV Wind Tunnel Identified Derivatives and Flight Test Results

I-Star Vehicle

9Derivative29

Wind Tunnel Flight Test

uX - 0.476 - 0.344 -0.1090

vY - 0.476

(Fixed to Xu)

- 0.344

(Fixed to Xu)

-0.1090

(Fixed to Xu)

wZ - 0.349 - 0.212 n/a

vL

- 0.046

(Fixed to Mu)

0.004

(Fixed to Mu)

-0.5014

(Fixed to Mu)

pL 0 0 0

uM 0.046 0.003 0.5014

qM 0 0 0

pM n/a n/a 0

qL n/a n/a 0

wN - 0.056 - 0.006 n/a

rN 0 n/a n/a

lonX - 0.190 - 0.157 -0.2841

latY 0.156 0.123 n/a

colZ - 0.012 - 0.264/100 n/a

latL - 0.218 - 0.418 n/a

lon - 0.387 - 0.548 -0.2343

pedN 0.669 0.555 n/a

colN -0.005 - 0.057/100 n/a


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Table 3.11 shows that all of the dimensional derivatives for the 29 vehicle are

larger than the 9 values. This is to be expected because the larger vehicle should

experience larger forces and moments to go with its increased mass and inertias. It also

shows that the flight test and wind tunnel results are all of the same sign and fairly close.

The only exception is that of the difficult derivative Mu. Wind tunnel testing revealed a

much smaller value for this critical derivative (0.003) than the flight test (0.5014).


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3.2.3 Trek Aerospace Solotrek

Although nothing like the other vehicles examined, the Trek Aerospace (now

Trek Entertainment, Inc.) Solotrek does possess ducted fan technologies which are

common to the MAV and OAV. One of the Solotreks ducted fans (Figure 1.4) was

inserted into the NASA Ames 7 x 10 wind tunnel at Moffett Field for aerodynamic

testing. Forces and moments were recorded with various wind tunnel and fan speeds

while the ducted fan was mounted at 90 to the flow.

The pitching moment was recorded with varying forward speeds and propeller

RPM. The results of that test are shown in Figure 3.14. This data could be used for

determination of dimensional pitching moment derivatives.

0

20

40

60

80

100

120

140

160

180

200

0 20 40 60 80 100 120

Wind Tunnel Speed (fps)

PitchingMoment(ft-lbs)

1800 rpm2200 rpm

2600 rpm

3000 rpm

Figure 3.14 SolotrekWind Tunnel Test Results for Pitching Moment


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Figure 3.14 shows how increasing the fan speed increases the pitching moment.

By fitting lines to the data for 0 to 20 knots, a linear representation of the pitching

moment derivative is obtained for this low speed condition. This is shown in Figure 3.14

as dashed lines. The slopes of these lines are the dimensional derivatives. They are

summarized in Table 3.12. Figure 3.14 also shows that some critical velocity may exist

when the derivative will actually swing to negative. This is seen in the 1800 RPM case to

be around 70 fps.

Table 3.12 Pitching Moment Derivatives and Solotrek Fan Speed

Fan Speed(rpm)

Pitching Moment Derivative Mu

ft-lb

ftsec

1,800 1.034

2,200 1.376

2,600 1.933

3,000 2.589

This wind tunnel testing was the extent of identification work completed for the Solotrek

vehicle.


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3.2.4 Hiller Flying Platform

The Hiller Flying Platform along with a dummy mannequin was attached to the

top of a truck and possessed equipment to measure moments and forces as it was driven

at Moffett Field in 1958. The results of the tests by Sacks3

are the basis for the pitching

moment identification.

The primary data of concern is that of the pitching moment directly measured

with increasing truck speed. The results of those runs are presented in Figure 3.15.

0

50

100

150

200

250

300

350

400

450

0 20 40 60 80

Speed (fps)


Figure 3.15 Hiller Flying Platform Pitching Moment Data

The truck test was performed with the fan running at the speed required to keep

the vehicle in hover. However, it also contained a dummy 6 foot tall, 175 lb man.

Because this comparison is primarily focused on the pitching moment characteristics of


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the duct, the effects of the man need to be removed from the above moments. This is

done by approximating the man as a flat plate (6 x 2). While crude, this investigation is

merely to establish a trend with the pitching moment characteristics of ducted fan

vehicles.

The relationship for the drag on a flat plate for Re > 1000 is presented as Figure 3.16.

Figure 3.16 Drag over a Flat Plate Perpendicular to Flow

With the approximation in size of the man, a drag coefficient of CD = 1.1 is found

from Figure 3.15. It follows that the drag of the man will vary with velocity as in

Equation 3.19.

21 v2

plate DD AC= (Equation 3.19)


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It is known that the dummy was placed directly on top of the platform, so it is

assumed that the drag will have a moment arm of 3 feet above the platform, or half the

height of the plate used to approximate the drag. This allows the determination of

moment produced with airspeed due to the dummy. This is calculated and then subtracted

from the actual data in Figure 3.15 to produce Figure 3.17.

0

50

100

150

200

250

300

350

400

450

0 20 40 60 80

Speed (fps)


Hiller Test Results

Approximate Dummy Moment

Approximate Duct Pitching

Moment

Linear Fit for 20 knts

Figure 3.17 Results of Removing Dummy Moment from Hiller Platform Test

It can be seen that the moment from the dummy is increasing with truck speed.

Removing the effect of the dummy produces the green line. This is then used to fit a line

to determine the average slope from 0 to 20 knots (33.8 fps). This slope of this dashed

line is the dimensional pitching moment derivative, Mu.


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ft-lb

ftsec

5.11PLATFORM

uM =

This dimensional derivative is naturally much larger than the other values looked

at for the other vehicles. This makes sense because this is a much larger vehicle. It is a

positive number for hover. However, it will go negative if the wind velocity reaches some

critical speed. In this case, that velocity is 55 feet per second. This follows the trend of

the other vehicles.


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3.2.5 Vehicle Scaling Laws and Comparisons

It becomes apparent that the ducted fans looked at all share some basic

characteristics in one way or another. One of the main advantages of the RUAV designs

mentioned in Chapter 1 is that these vehicles can hover. Hovering flight leaves these

vehicles highly susceptible to wind in station-keeping applications. Of particular interest

is the derivative Mu. This derivative characterizes the vehicle very well in hovering flight

(as seen with OAV flight test: Equation 3.15) in the hovering cubic. To understand the

nature of the vehicles and fully characterize and identify their flight, some time is needed

to understand the pitching moment characteristics.

In order to compare the pitching moment characteristics of the four vehicles, Mu

must be nondimensionalized to take into account the size of the vehicles, the propeller

effects, and the ducts themselves. To do this, the nondimensional pitching moment

definition for rotorcraft is applied:

( )2M

MC

R R=

M ~ pitching moment

~ density

~ blade rotation speed (rad/sec)

R ~ duct radius

A ~ duct area

This method primarily accounts for duct size with the radius terms, and fan speed .

Because the condition we are most interested in is low speed around hover, we

look at the derivative about zero to 20 knots airspeed for the vehicles. In other words, the

slope of a line fit to the pitching moment vs. airspeed data is calculated for only the low

speed condition. This value is then nondimensionalized with the above method. It is


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apparent that the size of the duct is the driving factor in the aerodynamic pitching

moment. In fact, this nondimensionalization by the third power of the radius follows what

was observed for ducted fans by Sacks3.

This approximation of the way the pitching moment varies with duct size is used

to compare the three vehicles. The geometries of the vehicles are used here to determine

the dimensional and nondimensional parameters for comparison (Table 3.13).In the case

of the Solotrek fan, the four different fan speeds are presented.

Table 3.13 Pitching Moment Coefficient Summary

VehiclePitching Moment Derivative Mu

ft-lb

ftsec

Nondimensional

CMu

Flying Platform 5.11 7.95 x 10-5

Wind Tunnel 0.011 1.09 x 10-5

OAV

Flight Test 0.00643 6.52 x 10-5

1,800 RPM 1.034 3.21 x 10-5

2,200 RPM 1.376 2.86 x 10-5

2,600 RPM 1.933 2.87 x 10-5

Solotrek

3,000 RPM 2.589 2.90 x 10-5

Wind Tunnel 0.00323 1.30 x 10-6

i-Star 9

Flight Test 0.5014 2.01 x 10-4

i-Star 29 0.11652 1.14 x 10-6

It is evident from Table 3.13 that the values are within the same order of

magnitude and show positive speed stability for most of the vehicles and methods. Wind

tunnel values seem to differ from the other values. The largest values are seen with the

flight test for MAV and wind tunnel results for OAV. The values for the different fan

speed for the Solotrek duct are all closely related, demonstrating that the same method is

nondimensionalizing well for vehicles of varying prop speeds.


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Table 3.13 reveals that this method may not be accounting for the entirety of

dominant characteristics for ducted fan vehicles. This is seen in the way the Solotrek

differs from the other smaller chord vehicles. To account for more specific geometries, a

method which better characterizes the propellers was also investigated. This

nondimensionalization uses the chord and radius of the rotating propellers to

nondimensionalize the pitching moment:

( )2M

MC

R R

bc

R

=

=

M ~ pitching moment

~ density

~ blade rotation speed (rad/sec)

R ~ duct radius

A ~ duct area

b ~ # of blades

c ~ mean blade chord

Table 3.14 represents the results of this method.

Table 3.14 Pitching Moment with Blade Chord Summary

Vehicle

Pitching Moment Derivative Muft-lb

ftsec

NondimensionalCMu

Flying Platform 5.11 4.48 x 10-4

Wind Tunnel 0.011 1.03 x 10-4

OAV

Flight Test 0.00643 6.15 x 10-4

1,800 RPM 1.034 2.90 x 10-4

2,200 RPM 1.376 2.58 x 10-4

2,600 RPM 1.933 2.60 x 10-4

Solotrek

3,000 RPM 2.589 2.61 x 10-4

Wind Tunnel 0.00323 2.45 x 10

-5

i-Star 9 Flight Test 0.5014 3.80 x 10-3

i-Star 29 0.11652 5.20 x 10-5

This method yields values similar to the previous methods in Table 3.13. The

numbers here are more closely related and show that the nondimensionalization is an


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adequate way to characterize the different pitching moment characteristics for these

vehicles. It is can be seen that the derivatives for the i-Star class of vehicles differ

considerably from the other ducted fans analyzed. In the case of the wind tunnel results

for these two vehicles, the 9 value (2.45 x 10-5

) and the 29 value (5.20 x 10-5

) are of the

same order of magnitude, but an order lower than all of the other vehicles. This suggests

that there may be something unique about the i-Star design, or that there was something

unexplainable happening with the wind tunnel tests of the vehicles. Flight test revealed

that the 9 vehicle actually had a very large value for Mu (3.80 x 10-3

). This is an order

larger than the other vehicles, and a full two orders greater than the wind tunnel results

for the same vehicle. This could be due to the fact that Mu was found to be so dominant in

the identification.

To briefly summarize and conclude, all four of the ducted fan vehicles exhibit

likeness in pitching moment characteristics. The only anomaly seen is with the i-Star

vehicle which shows relatively higher and lower CMu values in comparison to the other

vehicles and the method of identification.


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3.3 Servo Actuator Identification

The goal of the actuator test program was to measure a set of data that was used to

identify models of the actuator dynamic response characteristics. These actuator models

include linear transfer functions of the input/output relationships as well as non-linear

actuator properties such as actuator rate and position limits.

The identification was performed using the CIFER. Linear 0th

/2nd

order transfer

functions capturing the actuator dynamics were identified. Testing allowed for the

determination of the maximum angular rates and positions using linear curve-fitting of

the square wave responses. An explanation of the construction of the actuator block

diagrams built is also included. The actuators are a critical part of the flight control

system and it is important to have accurate models of the dynamics and limits of the

actuators themselves. Individual blocks were created for each actuator corresponding to

each of the tested 5 volt and 6 volt conditions. This section also includes a time domain

validation of the actuator models.

The goal of bench testing the control surface actuators was to collect a set of

bench test data that will be used to identify the actuator dynamics. This test data was also

used to determine the position and rate limits of the actuators. The significance of other

non-linear actuator properties, such as hysteresis and stiction, are also evaluated from the

bench test data.

The bench testing was carried out in accordance with CIFER flight test techniques

wherever possible. Five separate actuators from four manufacturers were tested. The


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actuators varied in size, weight, cost, and performance. The manufacturers specifications

are presented in Table 3.15. Figure 3.18 shows the relative sizes of the actuators tested.

Table 3.15 Manufacturer Specifications for Servo Actuators Tested

MODEL NUMBER WEIGHT TORQUE RATE L W D

(oz) (oz/in@ 4.8V) (deg/sec) (in) (in) (in)

JR PROPO DS8417 2.03 82.0 600.0 0.73 1.52 1.32

HITEC HS-512MG 0.80 42.0 352.9 0.39 1.33 1.18

JR PROPO DS368 0.80 53.0 285.7 0.50 1.12 1.17

AIRTRONICS 94091 0.32 18.0 500.0 0.44 0.91 0.87

CIRRUS CS-10BB 0.19 7.0 1000.0 0.37 0.90 0.61

Figure 3.18 Actuators Tested and Relative Sizes

The test apparatus was comprised of a rigid aluminum base stand with allowances

for the actuators to fit inside without moving. For the smaller actuators, small wooden

strips were used to ensure rigid mounting. The actuator horns were connected to horns on

potentiometers using clevises. The potentiometers offered little to no load resistance. The

mechanical apparatus can be seen in Figure 3.19.


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Figure 3.19 Actuator Test Stand Apparatus

A close up of the small Cirrus CS-10BB servo mounted on the test fixture in the wooden

strip is presented as Figure 3.20.

Figure 3.20 Cirrus CS-10BB Mounted on Wooden Strip


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It is noticeable from the figure that the servo horn and the potentiometer horn are

not the same length. This means that the deflection of the potentiometer horn will not be

the same as the deflection of the servo horn. All attempts were made to keep these

lengths the same.

Measurements of all the actuators and the various geometries accounting for the

aforementioned differences were taken with precision calipers and recorded as seen in the

schematic in Figure 3.21.

Figure 3.21 Schematic Detailing Linkage Geometry

It is apparent that because the center-center distance is different from the horn-

horn measurement, the servo deflection will not be 90 when the potentiometer is at 90.

The geometries for all of the actuators are presented in Table 3.16.


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Table 3.16 Actuator Linkage Geometries

HORN SERVO INPUT POT

SERVO VOLTHORN-HORN

(in)

SERVOHORN

(in)

POTHORN

(in)

CENTER-CENTER

(in)MIN MAX

MIN(deg)

MAX(deg)

MIN(10

3)

MAX(10

3)

MIN MAX

SE

PO9

5 3.482 0.994 0.975 3.460 -40 60 -40.741 34.174 -50 50 1810 3728 91DS8417

6 3.482 0.994 0.975 3.460 -40 60 -40.741 34.174 -50 50 1809 3727 91

5 3.688 0.757 0.669 3.719 -60 68 -46.419 30.644 -40 40 1851 3895 87JR94091

6 3.688 0.757 0.669 3.719 -60 68 -46.419 30.644 -40 40 1854 3882 87

5 3.527 0.495 0.468 3.539 -45 60 -48.610 32.539 -50 50 2102 4086 88DS368

6 3.527 0.495 0.468 3.539 -45 60 -48.610 32.539 -50 50 2102 4085 88

5 3.51 0.509 0.469 3.544 -55 50 -43.471 39.408 -50 50 1880 3870 86HS12MG

6 3.51 0.509 0.469 3.544 -55 50 -43.471 39.408 -40 40 1987 3670 86

5 3.67 0.504 0.468 3.652 -45 60 -43.814 39.785 -50 50 1930 3963 92CS-10BB

6 3.67 0.504 0.468 3.652 -45 60 -43.814 39.785 -50 50 1935 3969 92

The most non-linear case was observed for the HS12MG where problems with the

horns also resulted in binding and interference at larger deflections. For this reason, the

maximum commanded deflection was limited to 80% of the maximum actuator

deflection when testing this actuator.

The potentiometer apparatus was located next to Allied Aerospaces HIL

simulation test stand. This utilized the ADC and DAC capabilities of the vehicle

hardware to feed the actuators the Pulse Width Modulation (PWM) from the stimulus

files prepared in accordance with CIFER flight test techniques.

The two primary measurements required for the CIFER identification were the

sweep commanded into the actuator and the potentiometer reading as a result of the

actuator moving. Because of the nature of the recording equipment, calibration factors

were required to convert the input and output signals to degrees. These calibration factors

were determined using the geometries shown in Table 3.16 and are presented in Table

3.17.


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Table 3.17 ActuatorCalibration Factors for Input and Output Channels to Degrees

CALIBRATION FACTOR

IN Channel OUT ChannelSERVO VOLTAGE

(degrees/unit input) (servo deg/POT units)

5 0.000749 0.0391DS8417

6 0.000749 0.0391

5 0.000963 0.0377JR94091

6 0.000963 0.0380

5 0.000811 0.041DS368

6 0.000811 0.0409

5 0.000829 0.0416HS12MG

6 0.001036 0.0492

Documents

Comprehensive System Identification of Ducted Fan UAVs