Ducted-Fan Force and Moment Control via Steady and Synthetic Jets
Comprehensive System Identification of Ducted Fan UAVs
-
Upload
andrew-whipple -
Category
Documents
-
view
220 -
download
0
Transcript of Comprehensive System Identification of Ducted Fan UAVs
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
1/174
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
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
2/174
ii
Copyright 2004
Daniel Salluce
ALL RIGHTS RESERVED
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
3/174
iii
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
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
4/174
iv
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.
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
5/174
v
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.
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
6/174
vi
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
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
7/174
vii
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
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
8/174
viii
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
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
9/174
ix
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
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
10/174
x
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
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
11/174
xi
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
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
12/174
xii
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
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
13/174
- 1 -
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
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
14/174
- 2 -
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.
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
15/174
- 3 -
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
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
16/174
- 4 -
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
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
17/174
- 5 -
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.
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
18/174
- 6 -
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
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
19/174
- 7 -
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
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
20/174
- 8 -
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.
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
21/174
- 9 -
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
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
22/174
- 10 -
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.
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
23/174
- 11 -
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
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
24/174
- 12 -
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.
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
25/174
- 13 -
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.
-15
-10
-5
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
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
26/174
- 14 -
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,
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
27/174
- 15 -
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.
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
28/174
- 16 -
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.
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
29/174
- 17 -
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.
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
30/174
- 18 -
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.
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
31/174
- 19 -
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
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
32/174
- 20 -
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)
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
33/174
- 21 -
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
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
34/174
- 22 -
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.
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
35/174
- 23 -
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).
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
36/174
- 24 -
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
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
37/174
- 25 -
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.
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
38/174
- 26 -
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.
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
39/174
- 27 -
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
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
40/174
- 28 -
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.
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
41/174
- 29 -
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.
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
42/174
- 30 -
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
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
43/174
- 31 -
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
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
44/174
- 32 -
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.
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
45/174
- 33 -
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
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
46/174
- 34 -
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.
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
47/174
- 35 -
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.
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
48/174
- 36 -
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.
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
49/174
- 37 -
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
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
50/174
- 38 -
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.
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
51/174
- 39 -
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
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
52/174
- 40 -
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
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
53/174
- 41 -
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.
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
54/174
- 42 -
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
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
55/174
- 43 -
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.
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
56/174
- 44 -
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
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
57/174
- 45 -
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).
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
58/174
- 46 -
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
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
59/174
- 47 -
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.
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
60/174
- 48 -
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)
PitchingMoment(ft-lbs)
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
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
61/174
- 49 -
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)
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
62/174
- 50 -
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)
PitchingMoment(ft-lbs)
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.
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
63/174
- 51 -
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.
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
64/174
- 52 -
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
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
65/174
- 53 -
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.
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
66/174
- 54 -
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
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
67/174
- 55 -
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.
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
68/174
- 56 -
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
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
69/174
- 57 -
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.
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
70/174
- 58 -
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
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
71/174
- 59 -
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.
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
72/174
- 60 -
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.
-
7/29/2019 Comprehensive System Identification of Ducted Fan UAVs
73/174
- 61 -
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