ABSTRACT
Title of Thesis: WIND FRAME STATE ESTIMATION
AND GUST REJECTION USING
BIO-INSPIRED FLOW SENSORS
William Dean, Master of Science, 2015
Thesis directed by: Professor J. Sean Humbert
Department of Aerospace Engineering
Growing demand for robust, low-computation sensing and control of micro-air
vehicles motivates development of new technology. A MEMS wind flow sensor has
been developed in-house, drawing inspiration from setae structures seen in biology.
The goal of this work is to validate the use of these new sensors for wind frame state
estimation and gust rejection. Three of these sensors were mounted on the surface
of a fuselage-like structure to estimate wind speed, angle of attack, and sideslip
angle. Static linear and nonlinear estimation model structures and parameters were
designed with time-domain equation-error system identification techniques. For
small angles, state estimation was demonstrated for both estimation schemes. Gust
rejection control was implemented to improve state regulation in the presence of a
lateral gust stream. A robust µ controller was implemented and displayed lateral
velocity and path perturbation attenuation.
WIND FRAME STATE ESTIMATION AND GUST
REJECTION USING BIO-INSPIRED FLOW SENSORS
by
William Alexander Dean
Thesis submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial fulfillment
of the requirements for the degree of
Master of Science
2015
Advisory Committee:
Professor J. Sean Humbert, Chair/Advisor
Professor Derek Paley
Professor Inderjit Chopra
c© Copyright by
William Alexander Dean
2015
Acknowledgments
It is with deep sincerity I thank everyone who has helped me and been part
of my life over the past few years. To start, I’d like to thank my advisor Dr. Sean
Humbert for offering me the opportunity and financial support to work as a graduate
student in the Autonomous Vehicle Laboratory, especially when I came to him
with no prior research experience. Two years under your supervision has allowed
me to learn more than I ever could have imagined. Next I have to thank Badri
Ranganathan and Hector Escobar, who were there to provide guidance and expertise
from start to finish. May this thesis serve written documentation of my debt to you
(as verbally agreed upon). Greg Gremillion, Andrew Kehlenbeck, Imraan Faruque,
and Jishnu Keshavan all deserve many thanks for their help along the way, whether
large or small. We may not have had the pleasure of working on the same projects,
but the company and conversation of Julia, Lina, and Mac was another great part
of working in this lab.
For their unwavering support, I thank my family. Mom and Dad, the col-
lege education you’ve provided has been the most defining experience of my life.
Words cannot express how grateful I am to be where I am today, all thanks to you.
Grandma and Mom-mom, I hope you understand how vital your love and support
was over the years. Making you guys proud has been my greatest achievement. I
love all of you more than anything else in the world. That goes for all my distant
family, as well; I wish I had the chance to you see more often.
To all the friends I’ve made along the way, you’re the best company anyone
ii
could ask for. Every single one of you has a bright future and I can’t wait to see
where we all end up. Shout out to my friends who’ve graced the company of C4.
You’re an awesome group of guys and are all destined for great things. Good luck
to all the upstanding brothers of Theta Tau in your future endeavors. Whatsoever
thy hand findeth to do, do it with thy might. To everyone else, keep up the good
work and I hope we’ll get the chance to catch up later in life.
Lastly, it is with pride I say thank you and farewell to the University of Mary-
land and the Department of Aerospace Engineering. This institution has provided
the structure behind the knowledge, temperament, professionalism, and friendships
I’ve gained. It is here I have learned to appreciate the notion that suffering builds
character, and there is no such thing as too much character. I would also like to
acknowledge the financial support provided by Aurora Flight Sciences, which gave
me the work to earn this degree.
iii
Table of Contents
List of Tables vi
List of Figures vii
List of Abbreviations x
1 Introduction 1
1.1 Motivation and Previous Work . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Strain Based Sensing . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Wind Frame Estimation and Gust Rejection . . . . . . . . . . . . . . 3
1.4 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.5 Outline of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Bio-Inspired Hair Sensing and Signal Processing 7
2.1 Sensor Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Signal Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Sensor Mount and Casing . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3 Wind Frame State Estimation 16
3.1 Wind Tunnel Experimental Setup . . . . . . . . . . . . . . . . . . . . 18
3.2 Initial Steps in Sensor Characterization . . . . . . . . . . . . . . . . . 19
3.3 Kapton Sensor Characterization . . . . . . . . . . . . . . . . . . . . . 23
3.4 System Identification and State Estimation . . . . . . . . . . . . . . . 30
3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4 Gust Rejection 42
4.1 Instrumentation and Flight Test Information . . . . . . . . . . . . . . 43
4.2 Gust Speed Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.3 Robust Controller Design . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.4 Theoretical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.5 Experimental Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
iv
5 Conclusion 79
5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.2 Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
A Additional Figures 83
v
List of Tables
3.1 Linear and Nonlinear Estimation Parameters . . . . . . . . . . . . . . 33
3.2 Updated Estimation Parameters . . . . . . . . . . . . . . . . . . . . . 36
4.1 Gust Speeds at Distances from the Nozzle of the Leaf Blower . . . . . 52
4.2 Block Diagram Labels . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.3 Stability Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
vi
List of Figures
2.1 Hair Sensor Design (to scale) . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 a. Sensor Geometry, b. Sensor Deflection Due to Flow (Credit: Badri
Ranganathan) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Sensor with Connected and Extended Paddles, Mounted . . . . . . . 11
2.4 Signal Conditioning Circuit with Picture of 3 Circuit Boards Next to
Quarter Dollar (to show size) . . . . . . . . . . . . . . . . . . . . . . 12
2.5 Mount in CAD (exploded view), and Semi-Assembled Sensor on Mount 14
2.6 Sensor Case in CAD, and Picture of Mounted Sensor in Case . . . . . 14
3.1 Body Frame Relation to Air-Relative Velocity [1] . . . . . . . . . . . 17
3.2 Initial Angle of Attack and Sideslip Angle Test Setup . . . . . . . . . 19
3.3 Initial Wind Speed Sweep Results . . . . . . . . . . . . . . . . . . . . 20
3.4 Initial Angle of Attack Sweep Results . . . . . . . . . . . . . . . . . . 21
3.5 Initial Sideslip Angle Sweep Results . . . . . . . . . . . . . . . . . . . 21
3.6 Kapton Sensor Design 2 (left), Design 3 (middle), and Design 4 (right) 24
3.7 Design 4 Forward and Reverse Wind Speed Tests . . . . . . . . . . . 24
3.8 Fuselage Mount in Wind Tunnel . . . . . . . . . . . . . . . . . . . . . 26
3.9 Wind Speed Sweep at α = 0◦, β = 0◦ . . . . . . . . . . . . . . . . . . 27
3.10 Angle of Attack Sweep at β = 0◦ . . . . . . . . . . . . . . . . . . . . 28
3.11 Sideslip Angle Sweep at α = 0◦ . . . . . . . . . . . . . . . . . . . . . 29
3.12 Linear Estimation Validation Test Errors . . . . . . . . . . . . . . . . 34
3.13 Nonlinear Estimation Validation Test Errors . . . . . . . . . . . . . . 35
3.14 Linear Estimation with Updated c′1 . . . . . . . . . . . . . . . . . . . 36
3.15 Linear Estimation with Updated c′2 . . . . . . . . . . . . . . . . . . . 37
3.16 Linear Estimation with Updated c′3 . . . . . . . . . . . . . . . . . . . 37
3.17 Linear Estimation with Updated c′4 . . . . . . . . . . . . . . . . . . . 38
3.18 Linear Estimation with Updated c′5 . . . . . . . . . . . . . . . . . . . 38
3.19 Linear Estimation with Updated c′6 . . . . . . . . . . . . . . . . . . . 39
3.20 Static Linear and Nonlinear Estimation at α = −15◦, β = 15◦, and
V = 2.5 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.1 AVL Flight Test Arena . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2 DJI FlameWheel 330 with ArduPilot Mega . . . . . . . . . . . . . . . 44
vii
4.3 Vicon Tracker Software . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.4 XBee-PRO Wireless Communication Module . . . . . . . . . . . . . . 46
4.5 Additional Battery and Voltage Regulator . . . . . . . . . . . . . . . 47
4.6 Signal Conditioning Board . . . . . . . . . . . . . . . . . . . . . . . . 47
4.7 Anti-aerodynamic Cardboard Surface . . . . . . . . . . . . . . . . . . 48
4.8 Quadrotor Vehicle As Used In Gust Rejection Experimentation . . . 49
4.9 Band-pass Filter Bode Diagram . . . . . . . . . . . . . . . . . . . . . 50
4.10 Raw Analog Signal vs. Filtered and Rectified Signal . . . . . . . . . . 51
4.11 Gust Estimation Block Diagram . . . . . . . . . . . . . . . . . . . . . 52
4.12 Gust Speed Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.13 System Model Used for Disturbance Rejection Controller . . . . . . . 54
4.14 M∆-Structure Block Diagram . . . . . . . . . . . . . . . . . . . . . . 60
4.15 Uncertainty and Performance Weighting Functions . . . . . . . . . . 62
4.16 General Control Configuration Block Diagram . . . . . . . . . . . . . 63
4.17 General Block Diagram Using Lower LFT Form . . . . . . . . . . . . 64
4.18 Block Diagram Formulation of Robust Performance as a Structured
Robust Stability Test . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.19 Singular Value Plot of M . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.20 Singular Value Plot of WPSG . . . . . . . . . . . . . . . . . . . . . . 68
4.21 Structured Singular Value Plot of N . . . . . . . . . . . . . . . . . . 68
4.22 Effect of Input Disturbance on Output . . . . . . . . . . . . . . . . . 70
4.23 Open Loop Transfer Function Comparison . . . . . . . . . . . . . . . 71
4.24 Trajectory Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.25 Lateral Velocity Comparison . . . . . . . . . . . . . . . . . . . . . . . 74
4.26 Open Loop Trajectories . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.27 Closed Loop Trajectories . . . . . . . . . . . . . . . . . . . . . . . . . 76
A.1 Complete Signal Processing Board Schematic . . . . . . . . . . . . . . 83
A.2 Initial Sensor 1 Wind Speed Sweep . . . . . . . . . . . . . . . . . . . 84
A.3 Initial Sensor 2 Wind Speed Sweep . . . . . . . . . . . . . . . . . . . 84
A.4 Initial Sensor 3 Wind Speed Sweep . . . . . . . . . . . . . . . . . . . 85
A.5 Initial Sensor 4 Wind Speed Sweep . . . . . . . . . . . . . . . . . . . 85
A.6 Initial Sensor 9 Wind Speed Sweep . . . . . . . . . . . . . . . . . . . 86
A.7 Initial Sensor 1 Angle of Attack Sweep . . . . . . . . . . . . . . . . . 86
A.8 Initial Sensor 2 Angle of Attack Sweep . . . . . . . . . . . . . . . . . 87
A.9 Initial Sensor 3 Angle of Attack Sweep . . . . . . . . . . . . . . . . . 87
A.10 Initial Sensor 4 Angle of Attack Sweep . . . . . . . . . . . . . . . . . 88
A.11 Initial Sensor 9 Angle of Attack Sweep . . . . . . . . . . . . . . . . . 88
A.12 Initial Sensor 1 Sideslip Angle Sweep . . . . . . . . . . . . . . . . . . 89
A.13 Initial Sensor 2 Sideslip Angle Sweep . . . . . . . . . . . . . . . . . . 89
A.14 Initial Sensor 3 Sideslip Angle Sweep . . . . . . . . . . . . . . . . . . 90
A.15 Initial Sensor 4 Sideslip Angle Sweep . . . . . . . . . . . . . . . . . . 90
A.16 Initial Sensor 9 Sideslip Angle Sweep . . . . . . . . . . . . . . . . . . 91
A.17 Linear Estimation at α = 0◦, β = 0◦, V = 3 m/s . . . . . . . . . . . . 91
A.18 Linear Estimation at α = 5◦, β = 5◦, V = 3 m/s . . . . . . . . . . . . 92
viii
A.19 Linear Estimation at α = 10◦, β = 10◦, V = 3 m/s . . . . . . . . . . . 92
A.20 Linear Estimation at α = 15◦, β = 15◦, V = 3 m/s . . . . . . . . . . . 93
A.21 Linear Estimation at α = 20◦, β = 20◦, V = 3 m/s . . . . . . . . . . . 93
A.22 Linear Estimation at α = −5◦, β = −5◦, V = 3 m/s . . . . . . . . . . 94
A.23 Linear Estimation at α = −10◦, β = −10◦, V = 3 m/s . . . . . . . . . 94
A.24 Linear Estimation at α = −15◦, β = −15◦, V = 3 m/s . . . . . . . . . 95
A.25 Linear Estimation at α = −20◦, β = −20◦, V = 3 m/s . . . . . . . . . 95
A.26 Nonlinear Estimation at α = 0◦, β = 0◦, V = 2.5 m/s . . . . . . . . . 96
A.27 Nonlinear Estimation at α = 5◦, β = 5◦, V = 2.5 m/s . . . . . . . . . 96
A.28 Nonlinear Estimation at α = 10◦, β = 10◦, V = 2.5 m/s . . . . . . . . 97
A.29 Nonlinear Estimation at α = 15◦, β = 15◦, V = 2.5 m/s . . . . . . . . 97
A.30 Nonlinear Estimation at α = 20◦, β = 20◦, V = 2.5 m/s . . . . . . . . 98
A.31 Nonlinear Estimation at α = −5◦, β = −5◦, V = 2.5 m/s . . . . . . . 98
A.32 Nonlinear Estimation at α = −10◦, β = −10◦, V = 2.5 m/s . . . . . . 99
A.33 Nonlinear Estimation at α = −15◦, β = −15◦, V = 2.5 m/s . . . . . . 99
A.34 Nonlinear Estimation at α = −20◦, β = −20◦, V = 2.5 m/s . . . . . . 100
ix
List of Abbreviations and Symbols
AVL Autonomous Vehicle Laboratory
CAD Computer-Aided Design
IC Integrated Circuit
MAV Micro-Aerial Vehicle
MEMS Microelectromechanical Systems
UAV Unmanned Aerial Vehicle
A Area
C Capacitance
c Coefficient
d Disturbance
E Young’s Modulus
G Gain or Plant
I Identity Matrix
K Controller
L Length or Stability Derivative or Observer
M Moment
P Pressure or Stability Derivative
p Pressure or Roll Rate
R Resistance
S Sensitivity Function
s Laplace Variable
t Time
u Longitudinal Body Velocity or Control Input
V Velocity or Voltage
v Lateral Body Velocity
W Weighting Function
w Width or Vertical Body Velocity
x State
Y Stability Derivative
y Output
α Angle of Attack
β Sideslip Angle
∆ Change or Uncertainty
 Strain
µ Structured Singular Value
ν Gauge Factor
ρ Density or Weighting Factor
τ Time Period
φ Roll Angle
x
Chapter 1: Introduction
1.1 Motivation and Previous Work
Micro-air vehicles are becoming increasingly popular platforms for research,
commercial, and military applications. The source of most difficulties in developing
this type of technology is the limitation in size, weight, and power. These are
even more of a problem when coupled with the increased agility seen in small-
scale aircraft. Small Reynolds numbers, inertia, and flight speed are some of the
characteristics gained by these vehicles [2]. Thus, developing robust, light-weight,
low-power sensing and control capabilities is vital.
Biology serves as a rich source of inspiration for engineering new methods of
sensing and control. Flying insects are useful for this discussion as they demonstrate
robustly stable flight with similar constraints on payload and computing power.
Reynolds et al [3] discusses how a wind-sensing mechanism is used by insects for
navigation, and suggests that wind-sensitive setae may be involved. At the Uni-
versity of Maryland, a Kapton-based ’hair’ sensor has been developed to measure
wind flow. This was conceived from the setae structures seen in nature which are
commonly found covering the bodies of flying insects. Previous efforts to develop
similar sensors are discussed in [4], [5], [6], [7], [8], [9], and [10]. The sensor used
1
in this work is a robust, lightweight, free standing, long, directional sensor system
suitable for MAVs [11]. It is emphasized that no previous work with these types of
sensors has been done to perform estimation or gust rejection, as is discussed in this
thesis.
1.2 Strain Based Sensing
The flow sensing device developed at the University of Maryland, College
Park is a microelectromechanical system (MEMS) that utilizes strain gauge based
sensing. The sensor has two layers to it, a Kapton film as the structural layer and a
layer of gold strain gauge patterns. An analog signal conditioning board inputs the
sensor voltage readings, provides 2-stage instrumental amplification, and low-pass
filtering. The sensor (with casing and headers) and processing board weigh about
2.2 and 2.1 grams, respectively, and have maximum dimensions of 21.0 x 10.3 x 21.3
mm3 and 28.4 x 12.7 x 11.4 mm3, respectively. It should be noted that the size
and weight of the sensor, processing board, and associated hardware are designed
for rapid modification of the deployment strategy and not efficient payload design.
Optimization of the deployment of this technology will require extensive efforts in the
redesign of the power supply/regulation, signal processing, and mounting approach.
As such, optimal estimation and gust rejection will not be the goal of this research.
2
1.3 Wind Frame Estimation and Gust Rejection
Wind frame state estimation is well understood and relatively easy to per-
form on large-scale aircraft, particularly fixed-wing vehicles. However, this is not
the case for MAVs that cannot afford the weight and size of common windspeed
sensors. Pitot tubes, air data probes, and electromechanical vanes are some of the
more conventional methods for this type of estimation. Multiple (redundant) sensors
and bulky mechanical connections might be required for the conventional sensing
schemes [12]. Other problems seen with these types of sensors include digital band-
width limitations (imposed by the controlling architecture) and operational ranges
above the flight speeds of such small aircraft. Slow flight speeds are a problem be-
cause assumptions such as inviscid fluid are no longer valid and flow field models
in low Reynolds numbers are still underdeveloped [13]. Shen et al uses distributed
pressure information on the wing of a fixed wing MAV for pitch (or α) control [14],
but these sensors don’t offer the true wind speed or sideslip angle information that is
often desired. [15] uses hot-film flow sensors to perform wind frame state estimation,
where a neural network modeled the relationship between the sensors and estimated
states. A few downsides to this method include placing sensors on the aerodynamic
surfaces and the implementation of a complex, nonlinear neural network. Our goal
is to have access to all three wind frame states (α, β, and V ), with sensors located
on a fuselage-like structure and utilize a simple (static) estimation scheme. Most
MAVs are not fixed wing and don’t have large aerodynamics surfaces. Thus it is
desired that an alternative type of sensing device be made for MAV application.
3
Out-of-boundary-layer wind speed information can be obtained using hair sensors,
and consequently wind frame state estimation can be directly performed. With
proper location and orientation, it will be shown that is possible to measure angle
of attack, sideslip angle, and wind speed with these unique sensors.
The wind tunnel in the Autonomous Vehicle Laboratory (AVL) has a wind
speed range of 0.5 – 3.7 m/s and test section dimensions of 60 x 30 x 30 cm3. The
fuselage structure has a maximum diameter of 9.1 cm, which is the annular location
where the sensors are mounted, and has a tip-to-rear length of 10.6 cm. Angle
of attack and sideslip angle are varied by ± 30◦, with estimation equations being
calculated using data between ± 20◦.
Disturbances, such as (primarily) wind gusts, are known to have extremely
adverse effects on the performance of MAVs. Much effort has gone into developing
control strategies to subjugate these effects using pre-defined gust models, but the
turbulent and unpredictable nature of these disturbances makes it too difficult for
vehicles to react quick enough [16]. Simulation work provides promising results, but
requires numerous simplifications [17]. Flow field estimation has also been used for
disturbance rejection, which has incorporated effects such as blade flapping, blade
drag, induced flow, and non-conventional aircraft platforms [18] [19]. Unfortunately,
these models may not stay accurate for all conditions an MAV might be susceptible
to, and may be computationally intense. Given a way to directly measure the gust
disturbance, a vehicle’s performance could be vastly improved upon by cutting down
reaction time. Gust rejection will be implemented and serve as starting point for
improving MAV performance in the presence of gusts using hair sensors.
4
Feedback from a single sensor will be used on a quadrotor vehicle that was
modified to be more easily disturbed by lateral wind gusts. A µ-based H∞ con-
troller is designed to regulate lateral motion for an input disturbance with additive
uncertainty. Cartesian displacement from the nominal path is reduced by 17.1%
and lateral velocity is reduced by 19.7%.
1.4 Contributions
The purpose of this thesis is to present the first efforts in the implementation of
a unique, bio-inspired hair sensor for wind frame state estimation and gust rejection.
More specifically, the contributions are:
• Characterization of unique, bio-inspired hair sensors for the purpose of wind
frame estimation on a (MAV) fuselage-like structure. Previous work with
similar sensing technology has only been to estimate wind speed and doesn’t
take implementation on a micro-air vehicle into consideration.
• Development and validation of linear and nonlinear static estimation schemes
compatible with the bio-inspired hair sensors, for estimation of wind speed,
angle of attack, and sideslip angle in a wind tunnel. This is an expansion
on the previous contribution in that all previous work hasn’t implemented
similar sensing technologies for wind frame estimation. Utilizing this type of
sensing technology for wind frame estimation provides a starting point for the
development of a new light-weight, low-computation sensory system ideal for
small unmanned aerial vehicles.
5
• Robust formulation of a gust rejection controller, which uses gust speed feed-
back from bio-inspired hair sensors. When estimating a disturbance directly,
rejecting (input) disturbances is typically performed using feedforward control.
This strategy isn’t conducive to the formulation of robustly stable control, so
a different approach was considered where the effect of the gust was reduced
using gust state feedback.
• Implementation of the robust controller on a small quadrotor vehicle with a
bio-inspired hair sensor to demonstrate the gust rejection capability. These
types of sensors haven’t previously been deployed on a free-flying vehicle. This
contribution provides validation of the robust feedback control and the appli-
cability of the unique, bio-inspired sensors for use on a micro-air vehicle.
1.5 Outline of Thesis
The next chapter will discuss the sensor’s design and signal processing circuit
board. Chapter 3 will discuss wind frame estimation in a low speed wind tunnel
using three hair sensors mounted on a fuselage-like structure. The last chapter
will discuss a real-time gust estimation scheme, the methodology behind the design
of a robust µ-controller, then show performance of the controller on a quadrotor
vehicle with regards to lateral state regulation. The quadrotor will already possess
stability augmentation and the hair sensor feedback will act as additional outer loop
feedback.
6
Chapter 2: Bio-Inspired Hair Sensing and Signal Processing
The hair sensor used in these efforts has been developed by Badri Ranganathan
(advised under Dr. J. Sean Humbert) and Ivan Penskiy (advised under Dr. Sarah
Bergbreiter) at the University of Maryland. Funding was provided by Aurora Flight
Sciences, working under contract with the U.S. Army Research Laboratory. The
purpose of this research was to enable innovative capabilities for small unmanned
aircraft systems (SUAS), thus increasing performance of the fixed wing vehicles that
currently exist in the military.
Most of the material in this section is referenced from [11], and instead of
continuously referencing this paper I will simply state that this work should not be
considered as one of my contributions. Instead, this chapter should be considered
background material, in which I had a partial contribution.
2.1 Sensor Design
Strain gauge sensing was chosen in order to satisfy bidirectional sensing and
provide relatively simple fabrication requirements. Kapton [20] polyimide film was
used as the structural component of the sensor, which provided a durable substrate
that maintains the desired mechanical properties after the fabrication process. With
7
a gold strain sensing layer laid on top, the Kapton layer will deform based on
the magnitude and direction of the flow. The deflecting portion of the sensor is
designed with multiple cantilever structures where pairs of cantilevers are connected
to paddles. Figure 2.1 displays a top-down image of the hair sensor as it seen in
computer aided design (CAD).
Figure 2.1: Hair Sensor Design (to scale)
There are four cantilever-paddle structures per sensor. Three interfacing ter-
minals exist: ground, power, and signal (Vout). The sensing strain gauge patterns
are located on the roots of the cantilevers, and are connected in series. As each
paired cantilever-to-paddle structure deforms, the nominal resistance will change
according equation 2.1.
∆R
R0
= (1 + 2ν) (2.1)
8
R0 is the nominal resistance of the gauge,  =
∆L
L
is the strain (L being
nominal length of the gauge), and (1 + 2ν) is the gauge factor (about 2 for gold).
The strain is the variable dependent on wind velocity, because the applied (total)
pressure over the structure is a function of velocity.
P = pstatic + 12ρairV
2 (2.2)
Where pstatic is the static pressure that will be considered constant (since the
altitude will hardly vary), ρair is the air density (also constant), and V is the wind
speed perpendicular to the cantilever structure. Deflection will occur when there
is a difference in pressure on each face of the cantilever structure. Assuming the
flow velocity is only non-zero on the upstream side, the difference in pressure will be
equal to 12ρairV
2. For simplicity, I will simply use P as the pressure difference. The
dimensions shown in figure 2.2 are known constants and can be used in the formulas
for moment of inertia I = wt
3
12 and area A = L
2
2 + 2wL1, where t is the cantilever
thickness.
9
Figure 2.2: a. Sensor Geometry, b. Sensor Deflection Due to Flow (Credit: Badri
Ranganathan)
Thus, strain can be written as eq. 2.3, and ∆R is a function of wind speed.
 =
Mt
2EI
=
12Mt
2Ewt3
=
6PAL1
Ewt3
=
6P (L22 + 2wL1)L1
Ewt2
(2.3)
Where L1 = 4.8 mm, L2 = 1.6 mm, w = 0.8 mm, t = 13 µm, and (Young’s Modulus)
E = 2.5 GPa.
Looking back at figure 2.1, the series connection of the sensing gauges can
be considered as a single (total) resistor that varies with wind speed. The pattern
below the sensing gauges is another set of strain gauges connected in series, known
as the reference resistor. This total resistance will not change as it is part of the
sensor that will not be allowed to deform. The total sensing resistance and total
reference resistance form a potential divider where the voltage (Vout) between them
varies with the sensing resistance and is sent to a signal conditioning circuit board.
10
Multiple designs were considered for the cantilever area, most relevant of which
is the design where the paddles are connected side-by-side and extended upward.
This provided more sensitivity to wind speed and prevented fluttering from happen-
ing in certain instances. Figure 2.3 is a picture of this design. It is glued to a 3D
printed structure that will be discussed in the mount and casing section.
Figure 2.3: Sensor with Connected and Extended Paddles, Mounted
The fabrication process for this sensor is outside the scope of this thesis. For
more information, refer to [11].
2.2 Signal Processing
The Vout signal can vary on the order of tens of microvolts up to millivolts,
due to variability in the fabrication process. Thus this signal will require signifi-
cant amplification and, consequently, low-pass-filtering. Two stage amplification is
performed by two instrumental amplifier chips, INA 326 from Texas Instruments.
11
These chips require two input voltages, Vin+ and Vin−. One will come from the
potential divider circuit on the sensor, and the other will come from a potential
divider formed by two potentiometers. This forms a Wheatstone network, where
the resistors are RS (sensing resistor), RR (reference resistor), RD1 (2 kOhm pot.),
and RD2 (2 kOhm pot.). Figure 2.4 displays this network along with a simplified
representation of the rest of the circuit. The complete schematic is shown in figure
A.1.
R S R D1
R R R D2
R f
C f
V out2
R 5
R 6
V DD V DD1INA -326 INA -326
V out1V in+ V in+
V in-V in-
Figure 2.4: Signal Conditioning Circuit with Picture of 3 Circuit Boards Next to
Quarter Dollar (to show size)
VDD represents the voltage supplied to the Wheatstone network, which was
set between 0.1v and 0.35v so as to reduce possible heat build-up from electrical
current. The amplifier chips are powered by 3.3v which is set by an IC regulator
from STMicroeletronics. This means the maximum voltage each chip can output is
12
3.3v, and that RD1, RD2 must be hand tuned until the first chip’s output is between
0 and 3.3v. In order to satisfy the same output range requirement in the second
amplifier chip, another potential divider is used to set one of the inputs to the second
stage. R5 is another 2 kOhm potentiometer that is adjusted by hand, and R6 is a
fixed resistor to prevent the possibility of shorting. VDD1 is also connected to the
3.3v provided by the regulator. The output of the second stage is then low-pass
filtered by Rf and Cf , which are chosen to set the cut-off frequency to 15.9 Hz.
The amplifier gains are set by a pair of fixed resistors for each chip. They
are R1,R2 and R3,R4 in figure A.1, which correspond to the first and second stage
gains, respectively. Those gains are G1 =
2R2
R1
and G2 =
2R4
R3
for the first and
second stage, respectively. The total gain has been varied from 400 to 4000 over the
course of the research, depending on the sensors’ resistances.
2.3 Sensor Mount and Casing
Since the sensor itself consists of only Kapton and gold traces, it is necessary
to develop a structure to support the sensor. An OBJET EDEN350 3D printer was
used to create this mounting structure, due to its rapid prototyping capability. The
mount is a three part design created in Solidworks. The sensor is super glued to one
of the parts, using Loctite 454 Instant Adhesive. 90◦ headers are used to interface
with the sensor’s terminals. The header-to-terminal connection is secured using the
other two parts of the mounting design. Figure 2.5 shows an exploded view of the
three part mount design in CAD and a picture of the sensor glued to one part with
13
the headers fastened between the other two parts.
Figure 2.5: Mount in CAD (exploded view), and Semi-Assembled Sensor on Mount
Altogether the sensor, mount, and headers weigh about 1.1 grams. The max-
imum dimensions (from end of cantilevers to tip of headers) are 21.9 x 17.7 x 7.5
mm3. As an additional means of protection and a more aerodynamic shape, a two
part case was designed. Figure 2.6 shows the two case parts in CAD next to a
picture of the mounted sensor inside the case.
Figure 2.6: Sensor Case in CAD, and Picture of Mounted Sensor in Case
The case also weighs about 1.1 grams, resulting in a sensor that weighs about
2.2 grams. The new maximum dimensions are 20.9 x 21.3 x 10.3 mm3. The signal
14
conditioning board weighs about 2.1 grams and has maximum dimensions of 28.4
x 12.7 x 11.4 mm3, resulting in a sensing package that weighs 4.3 grams and takes
up 8697.0 mm3 (or 8.697e-6 m3) of space (excluding wiring and other installation
materials).
2.4 Summary
By placing gold strain gauges on Kapton film, a bio-inspired hair sensor was
made to detect wind flow. The original design consists of four cantilever structures
per sensor, with the strain gauges placed at the roots. The change in resistance
of the gauges is proportional to the dynamic pressure (i.e. wind speed). With the
resistors on the sensor and two potentiometers on the signal conditioning board,
a Wheatstone bridge is formed. The difference in voltage provided by the bridge
is amplified using an instrumental amplifier, the output of which is compared to
another potential divider’s output voltage, and the difference is amplified using a
second instrumental amplifier. The output of the second amplifier is then low-pass
filtered before being considered as the final output voltage to be used for state
estimation and gust rejection. The sensor is mounted on a three part set of 3D
printed structures, which includes 90circ headers that interface with the sensor’s
terminals. Surrounding the mounted sensor is a protective casing that also provides
a more aerodynamic surrounding. The sensor and signal conditioning board weigh
about 4.3 grams and are very small in volume.
15
Chapter 3: Wind Frame State Estimation
Body frame coordinates are useful for understanding how an aircraft is moving
at any given moment, since the axes are fixed to the vehicle. This frame also
defines the aircraft’s orientation relative to the Earth (or inertial frame). However,
aerodynamic forces and moments are often best expressed in the wind frame. Like
the body frame, the wind axes have the origin at the vehicle’s center of gravity. The
axes are oriented with one axis in the direction of the velocity relative to the air
and the other two axes in directions similar to the body axes, but orthogonal to the
air-velocity axis. Figure 3.1 is a picture from [1] that shows the body axis states,
forces, and moments with the wind flow vector shown relative to the body frame.
16
Figure 3.1: Body Frame Relation to Air-Relative Velocity [1]
Lift and drag can nominally be assumed to act in the negative z and negative
x axes of the wind frame, respectively. A two angle Euler rotation relation can be
used to translate the aerodynamic effects back to body frame forces and moment.
Those angles are α and β shown in figure 3.1, which relate wind speed to body
velocity in the following equations:
u = V cosα cos β (3.1)
v = V sin β (3.2)
w = V sinα cos β (3.3)
Thus, given a sensor that measures windspeed and wind frame orientation, we
can directly calculate the translational motions of the aircraft. This chapter will
17
discuss the use of the hair sensors to estimate V , α, and β.
3.1 Wind Tunnel Experimental Setup
All experiments in this chapter are performed using the AVL’s (very) low
speed wind tunnel. This wind tunnel is fan-driven with a motor that is rated to
about 3000 rpm. This rpm corresponds to a wind speed of about 3.7 m/s. Particle
image velocity tests characterize the tunnel’s rpm to wind speed as an exponential
relationship where
V = 2.444 log(rpm)− 15.639 (3.4)
from 0.58 m/s to 4.69 m/s. A wind speed of 4.69 m/s requires the motor to be
over-driven to about 4000 rpm, so for safety reasons all tests were performed within
the range the motor is rated (up to 3.7 m/s). After the sensor outputs are processed
by the signal processing circuit boards, the voltage is read and recorded on a desktop
computer. For this we used BNC-2110 terminals on a National Instruments PCI-
6224 Data Acquisition system and interfaced with this system using Labview. This
setup introduced wall noise, which was dealt with by implementing another low-pass
filter in Labview with a 10 Hz cut-off frequency. Voltage readings were sampled at
1000 Hz. Those 1000 samples were averaged every second and the average was
recorded at the user’s discretion.
18
3.2 Initial Steps in Sensor Characterization
The first step taken towards state estimation was to measure the sensor’s
response over a wide range of orientations. These tests were performed at the
start of this research, when the sensor design was a little different. The cantilever
structure was made of silicon dioxide, shorter, extremely fragile, and consisted of
6 cantilever structures. Even with these differences, the information inferred from
these tests is still valuable for setting up a state estimation scheme. Figure 3.2 shows
the test setup with the old sensor.
Figure 3.2: Initial Angle of Attack and Sideslip Angle Test Setup
19
For the angle of attack tests, 0◦ refers to the tips of the cantilevers pointed
upstream, 90◦ is when the side of the cantilever that has the strain gauge patterns
on it is facing upstream (as shown in the the top left part of figure 3.2), and -90◦ is
when the strain gauge side is facing downstream. For the sideslip angle tests, 0◦ is
when the the strain gauge side is facing upstream and the sensor is rotated ± 90◦
about the vertical axis. Both angle sweep tests were varied by 10◦. Wind speed
tests were performed with the strain gauge side of the cantilevers facing upstream,
while mounted on the sideslip angle test stand. Figures 3.3, 3.4, and 3.5 display the
results from these tests for five different sensors.
Figure 3.3: Initial Wind Speed Sweep Results
20
Figure 3.4: Initial Angle of Attack Sweep Results
Figure 3.5: Initial Sideslip Angle Sweep Results
21
The y-axis for the wind speed and sideslip angle tests show the voltage as it
reads, while the angle of attack tests show the change in output. The change in
output was used to express angle of attack because the voltage reading needed to
be adjusted between 90◦ ranges to prevent the output from saturating the amplifier
limits. The starting (wind off) voltage is dependent on hand tuning the poten-
tiometers on the conditioning board. Also, the magnitude of change for these tests
is dependent on the resistance of each sensor, which varies from sensor to sensor.
Therefore, the information of interest lies in the trends of the data. Note that the
sign of the trend is different between sensors. This is a result of switching the po-
sition of ground and power to the sensor (a requirement to send the appropriate
voltages to the first stage amplifier on old conditioning board designs), effectively
switching the RS and RR resistors in the Wheatstone bridge. With all of these
considerations it is necessary to inspect each response individually. Each trend is
plotted on a graph with its appropriate y-axis in figures A.2 – A.16.
For wind speed tests, sensors 1 and 9 show fairly linear response without satu-
rating while sensors 2, 3, and 4 show a decaying rate of change. The linear response
is most desirable while the decaying response indicates a saturation effect. Visual
inspection revealed that the cantilevers were deflecting to the point of mechanical
saturation, corresponding to the voltage reading saturating. Data was not recorded
with the intention to investigate statistical characteristics of these sensors, as that
information will not be used in the estimation scheme. Visual inspection of voltage
readings in real-time revealed the signal-to-noise ratio was large enough (>10) for
the goal of performing first-time state estimation with this type of sensor.
22
Both angle sweep tests were performed at a constant wind speed of either 1.79
or 2.24 m/s, whichever speed elicited an informative response (i.e. not saturating
but still responding for the majority of the sweep). Figure 3.4 shows that the outputs
are most sensitive to angle of attack changes about the 0◦ orientation. Figure 3.5
shows that the orientation of greatest sensitivity is ± 90◦. These orientations are
when the cantilevers are aligned with the flow, unlike the wind speed tests where
the cantilevers are orthogonal to the flow. Moving forward towards performing
state estimation, these orientations of greatest sensitivity will be the orientation of
zero-pose.
3.3 Kapton Sensor Characterization
Chronologically skipping iterations of sensor designs and tests, the Kapton
sensor discussed in Chapter 2 is now the design that needs to be characterized for
state estimation. At this point it should be noted that the thickness of the Kapton
film used for wind tunnel tests and estimation is 12 µm. A slightly thicker film will
be used in Chapter 4. These 12 µm sensors tend to curl, which is a result of the fab-
rication procedure. Similar tests as the ones in the previous section were performed
with Kapton sensors of four designs. Design 1 was with the paddles unconnected
(see figure 2.1), design 2 was connected directly across, design 3 was connected and
extended downward, and design 4 was connected and extended upward (see figure
2.3). The CAD outlines are shown in figure 3.6.
23
Figure 3.6: Kapton Sensor Design 2 (left), Design 3 (middle), and Design 4 (right)
These designs were made to reduce the flutter effects that were seen in design
1. Design 4 showed the most desirable results, with effectively no flutter and the
greatest sensitivity to wind speed. Shown below are wind speed sweep tests per-
formed for three sensors of this design, which are mounted in a test stand similar to
the sideslip angle stand shown in figure 3.2.
Figure 3.7: Design 4 Forward and Reverse Wind Speed Tests
24
For this test and those from here on out the y-axis is shown as change in output.
Zero flow initial conditions will be taken into consideration separately. The output’s
trend vs. flow direction is reversed in future tests to give a more intuitive result.
Recall that was a capability that was not yet developed for the initial tests. There
is a clear bidirectional trend in the change in output. However, the initial increase
in voltage at low speeds is concerning. This is credited to thermal effects, where the
voltage change due to mechanical deflection becomes greater than thermal effects
around 2 m/s. Thus, state estimation will be performed at wind speeds greater than
2 m/s so that directionality may be more easily distinguished.
To estimate all three states of interest (α, β, V ), three hair sensors were
mounted on a fuselage-shaped structure. The angle of attack and sideslip angle
sensors are located on the port (left) side and top of the mount, respectively. Both
are oriented with the cantilevers aligned with the flow (as discussed in the previous
section) and are shown in figure 3.8. In order to disambiguate the pose estimations
from variations at different wind speeds, a third sensor is necessary to estimate wind
speed separately. This third sensor was mounted on the starboard (right) side and
oriented with the strain gauge side of the sensor facing the incoming flow. It is
shown in figure 3.8 (bottom left) that sensor curl is towards the strain gauge side of
the cantilevers.
25
Figure 3.8: Fuselage Mount in Wind Tunnel
Tangential flow of incompressible fluid over a sphere is Vθ = 32V∞ sin(θ) [21],
so we expect the flow speed at the sensor to be higher than the freestream wind
speeds by a similar amount. For reference, θ is 0◦ along the axis aligned with the
front top of the fuselage. A wind speed sweep test with the fuselage at zero-pose
(α = 0◦, β = 0◦) is shown below, in figure 3.9.
26
Figure 3.9: Wind Speed Sweep at α = 0◦, β = 0◦
It is clear that the wind speed at the sensor has increased since the wind speed
output doesn’t decrease at low speeds before becoming positive. This is indicative
that the thermal effects are less than the mechanical effects at all speeds. The
wind speed sensor takes a quadratic form until about 3 m/s. This implies that the
wind speed sensor output is proportional to the dynamic pressure, agreeing with the
analysis in section 2.1. Saturation in the change in output starts around 3 m/s and
appears to be complete around 3.7 m/s. Knowing this, it was decided to perform
estimation in the 2–3 m/s wind speed range. It should be noted that angle of attack
and sideslip angle sensor outputs are non-zero as the wind speed changes. This
is due to the non-uniformity in the inherent curl. Non-zero output will be taken
into consideration by using the output reading at zero-pose as the reference voltage,
27
instead of the zero wind speed reading as the reference. The wind speed sensor will
still use the wind-off reading as its reference.
Wind tunnel tests were performed with [−30 → 30]◦ angle sweeps for α and
β separately (i.e. α = [−30 : 30]◦ while β = 0◦ and β = [−30 : 30]◦ while α = 0◦),
at angle increments of 5◦. These α and β sweeps were performed at constant wind
speeds of 2, 2.5, and 3 m/s. Figures 3.10 and 3.11 display the results for these tests
Figure 3.10: Angle of Attack Sweep at β = 0◦
28
Figure 3.11: Sideslip Angle Sweep at α = 0◦
In general, it can be inferred that the sensor responses are proportional to their
corresponding states and wind speed squared (dynamic pressure). Angle of attack
readings show unexpected nonlinearities past ±20◦, which is likely an attribute of
the sensor curl. An equally undesirable effect is seen in the sideslip angle sensor
when V=3 m/s, more precisely from [−20 → −25]◦. This is a result of a bi-modal
plastic-like effect which is also attributed to the non-uniform curl. Therefore, sensor
responses from [−20 → 20]◦ will be used for identification of estimation equation
parameters. It should be noted that there were slight changes in the outputs of the
α sensor during the β tests (and vice versa), but mostly at angles outside of ±20◦.
It is reasonable to suspect that the sensors will have outputs correlated to the states
corresponding to the other sensors, but those effects will be taken into consideration
29
by the system identification procedure.
3.4 System Identification and State Estimation
Linear and nonlinear output models were constructed using least squares solu-
tions with the data presented in figures 3.10 and 3.11. Using α, β, and V as states,
the output model structures are as follows:
Linear:
y1 = c1α (3.5)
y2 = c2β (3.6)
y3 = c3V (3.7)
Nonlinear:
y1 = c4αV 2 (3.8)
y2 = c5βV 2 (3.9)
y3 = c6V 2 (3.10)
The nonlinear model structure was determined using stepwise regression. Step-
wise regression is a statistical technique that uses forward selection and backward
elimination for modeling. This methodology is referenced from [1].
30
Variables Meaning Dimension
N number of samples scalar
n number of regressors (model terms) scalar
Θ model parameters n x 1
X matrix of regressors N x n
z measured output N x 1
y true output N x 1
ν measurement noise (or residual) N x 1
p current number of terms in the model scalar
Fp partial F ratio scalar
s2 fit error variance scalar
SSR regression sum of squares scalar
The goal is to find the best Θ that minimizes ν in z = y + ν = XΘ + ν.
Using the cost function J(Θ) = 12(z −XΘ)
T (z −XΘ), it is known that the Θ that
minimizes J (called Θˆ) is the least squares solution:
Θˆ = (XTX)−1XT z (3.11)
The purpose of stepwise regression is to determine what regressors that X
should incorporate. A step-by-step procedure is given below:
1. Starting with a pool of candidate regressors, partial correlations are calculated
for each candidate with the measured output z
31
2. Add the regressor with the highest partial correlation to the model
Partial correlation: rjz =
Sjz
√
SjjSzz
(3.12)
where,
X = [ζ1 ζ2 · · · ζn], Sjz =
N∑
i=1
[ζj(i)− ζj][z(i)− z],
Sjj =
N∑
i=1
[ζj(i)− ζj]
2, Szz =
N∑
i=1
[z(i)− z]2
3. Fp is calculated for all regressors in the model. All regressors with Fp below the
cut-off value (Fpcut−off =20 for 95% confidence) are removed from the model.
Fp =
SSR(Θˆp+1)− SSR(Θˆp)
s2
(3.13)
4. Use least squares modeling to orthogonalize the remaining candidates with re-
gressors in the model (model the candidates with the regressors in the model).
This removes variation (correlated to the output) in the remaining candidates
that is already included in terms already in the model. Treat the residuals as
the new pool of candidate regressors.
5. Repeat steps 1–4 until no more regressors can be added without subsequently
being removed from the model.
The regressors considered were α, β, V , αV , βV , V 2, αV 2, and βV 2. Note
that the linear models were also calculated in a similar fashion, except the only
regressors considered for each output were α, β, and V . The coefficients resulting
from the solution 3.11 are shown in table 3.1.
32
Table 3.1: Linear and Nonlinear Estimation Parameters
Parameter Value % Error
c1 0.009 8.34
c2 0.0097 10.31
c3 0.3317 1.84
c4 0.0014 4.80
c5 0.0015 6.06
c6 0.0672 2.77
To perform static estimation, a simple inversion was performed. The estima-
tion equations then become:
Linear:
α =
y1
c1
= c′1y1 (3.14)
β =
y2
c2
= c′2y2 (3.15)
V =
y3
c3
= c′3y3 (3.16)
where c′1 =
1
c1
= 111.1, c′2 =
1
c2
= 103.1, c′3 =
1
c3
= 3.01
Nonlinear:
α =
y1c6
c4y3
=
y1c′4
c′6y3
(3.17)
β =
y2c6
c5y3
=
y2c′5
c′6y3
(3.18)
V =
√
y3
c6
=
√
c′6y3 (3.19)
33
where c′4 =
1
c4
= 714.3, c′5 =
1
c5
= 666.7, c′6 =
1
c6
= 14.88
Since the data used to identify these parameters was for tests where only one
state was changed at a time, it is a reasonable prediction that these parameters only
work well for uncoupled pose estimation. During validation tests both α and β were
varied at the same time. A sweep of tests from [α β] = [-20 -20]◦ → [20 20]◦ (i.e. a
diagonal sweep from down-and-left to up-and-right) at 5◦ increments was performed
to test the performance of the estimation equations. Figures 3.12 and 3.13 show
the average error during the first 2–3 seconds of the tests after the wind tunnel is
allowed to reach the desired speed. It takes approximately 5 seconds for the wind
tunnel to settle to the intended speed. Only the first few seconds are used in the
error averaging because the signal can sometimes drift.
Figure 3.12: Linear Estimation Validation Test Errors
34
Figure 3.13: Nonlinear Estimation Validation Test Errors
The raw data for these tests is shown in figures A.17 – A.34. Note that the
beginning of the tests show non-zero readings which depend on the references when
the wind tunnel is running. While these results show that there is at least some
capability to estimate pose in a wind tunnel, a manual adjustment of the estimation
coefficients was performed to reduce the overall error results of the static estimation.
These new errors were found by using the raw sensor data and recalculating the
estimations with different coefficients. The resulting coefficients are shown in table
3.2 and the shifted errors are shown in figures 3.14 – 3.19.
35
Table 3.2: Updated Estimation Parameters
Parameter Old Value New Value
c′1 111.1 93
c′2 103.1 81
c′3 3.01 5.5
c′4 714.3 901
c′5 666.7 633
c′6 14.88 21.5
Figure 3.14: Linear Estimation with Updated c′1
36
Figure 3.15: Linear Estimation with Updated c′2
Figure 3.16: Linear Estimation with Updated c′3
37
Figure 3.17: Linear Estimation with Updated c′4
Figure 3.18: Linear Estimation with Updated c′5
38
Figure 3.19: Linear Estimation with Updated c′6
Similar improvements resulted from the gain changes for both linear and non-
linear estimation coefficients. Improving the V estimation error was intuitive, in that
the gains could simply be increased to reduce errors. α estimation errors weren’t
found to have room for improvement. There was arguable room for improvement
for β estimation, in that it was possible to improve negative angle estimation with
the cost or worsening positive angle estimation. The improved negative angle esti-
mation outweighed the worsened positive angle estimation and was the motivation
for the new gain. Using intuition, it is hypothesized that the negative angles are
more easily estimated because of the location of the sensors on the fuselage struc-
ture. Looking back at the images in figure 3.8 we see that at negative angles of
attack the sideslip angle sensor is most ’exposed’ to the incoming flow. At positive
39
angles of attack there is likely some amount of flow separation effects that reduce
the sensor’s effectiveness. An analogous hypothesis can be said about the angle of
attack sensor’s effectiveness being dependent on its location and the sideslip angle.
As an additional measure to validate the estimative capabilities of these sensors, a
final test was performed at α = −15◦, β = 15◦, and V = 2.5 m/s with these updated
coefficients. Note that this orientation was chosen to support the hypothesis and
simply to try an untested orientation.
Figure 3.20: Static Linear and Nonlinear Estimation at α = −15◦, β = 15◦, and
V = 2.5 m/s
As before, the results shown in figure 3.20 are collected after the wind tunnel
is ramped to the desired wind speed. The root mean square error of the linear
estimator is 2.59◦ for α, 2.35◦ for β, and 0.68 m/s for V . The root mean square
error of the nonlinear estimator is 1.99◦ for α, 1.11◦ for β, and 0.16 m/s for V .
Both estimators show acceptable levels of performance. Thus, the use of static
estimators with these bio-inspired hair sensors is sufficient for state estimation of
40
this fuselage-like structure in the flow speed regime seen in the AVL’s wind tunnel.
3.5 Summary
The goal of this chapter was to show that wind frame state estimation can be
performed with bio-inspired hair sensors. Early testing revealed that the sensor out-
puts were most sensitive to angle variation about orientations where the cantilever
arrays were aligned with the flow. A sensor design where the cantilever paddles
were connected and extended upward performed the best in terms of low aerody-
namic flutter and greatest amount of mechanical sensitivity to wind flow. Three
sensors were mounted on a fuselage-like structure. Estimation was limited to wind
speeds of 2 – 3 m/s for the most amount of bidirectionality in the sensor response,
and orientations from -20◦ – 20◦ to avoid nonlinearities. Using stepwise regression
and method of least squares, static linear and nonlinear estimation equations were
developed. The estimation coefficients were adjusted to minimize errors seen in
validation tests. One final validation test was performed using these modified pa-
rameters. This test served as the final piece of validation that these sensors can
be used for wind frame estimation. It was also hypothesized and shown that the
effectiveness of the sensors’ estimation capabilities is dependent on their position on
the fuselage structure and orientation of the structure.
41
Chapter 4: Gust Rejection
Performing state estimation on a quadrotor vehicle was originally the next goal
for these sensors. Two sensors were mounted on a quadrotor with the intention to
perform system identification again. Ideally, the sensor readings would be correlated
to translational and rotational velocity (depending on their location relative to the
center of gravity). The translational velocities seen in the AVL’s flight test area do
not exceed 2 m/s and there was little correlation found between the vehicle velocities
and the sensor readings. Multiple sensor designs were used for these tests (like those
seen in figure 3.6). Once design 4 (same design used in wind tunnel estimation) was
implemented it was found that the sensors were becoming correlated with body
accelerations. The explanation for this is that as the length and paddle size of the
cantilevers increased, the inertia about the root of the cantilevers was large enough
to cause deflection due to acceleration. Instead of attempting to design hair sensors
that could act as accelerometers the goal was shifted towards gust rejection. Past
experimentation revealed that lateral gust speeds of at least 10 m/s were necessary to
significantly perturb a quadrotor vehicle. Since the 12 µm sensors will be saturated
well before that speed (only shown in figure 3.9, but known from undocumented
tests), we must use a stiffer (thicker) Kapton sensor. 23 µm thick Kapton sensors
42
were found to be suitable for this purpose. This chapter will discuss the use of
a single 23 µm thick hair sensor used to improve the performance of a quadrotor
vehicle in the presence of wind gusts.
4.1 Instrumentation and Flight Test Information
Figure 4.1: AVL Flight Test Arena
All tests were performed in the AVL’s flight test area (shown above in figure
4.1), which is 5.5 m2 in floor space. A DJI FlameWheel 330 quadrotor vehicle, inte-
grated with an ArduPilot Mega avionics package, was used for this experimentation
and is shown in figure 4.2.
43
Figure 4.2: DJI FlameWheel 330 with ArduPilot Mega
A Vicon Tracker system was used to record true rigid body motion and feed-
back height measurements to allow the quadrotor to hold a reference altitude. All
tests were performed with altitude hold engaged, thus incorporating this feedback
into the vehicle dynamics. A picture of the Vicon Tracker software interface is shown
in figure 4.3.
44
Figure 4.3: Vicon Tracker Software
Sensor data was wirelessly transmitted using XBee wireless communication
modules and recorded using LabView at a rate of about 50 Hz. One of the devices
is shown below.
45
Figure 4.4: XBee-PRO Wireless Communication Module
Wind gusts were generated with a TORO Ultra Blower Vac (leaf blower).
The vehicle was given a constant forward velocity, where it would pass a constant
wind gust directed at the vehicle’s left side. The average distance of the quadrotor
from the tip of the gust source’s nozzle was about 0.5 m, where the gust speed was
measured to be about 9.6 m/s. Gust speed at varying distances from the source were
measured with a hand-held La Crosse anemometer (model number: EA-3010U) and
used for gust speed estimation.
When the motors are throttled, there is a decrease in the 5 volts that the
ArduPilot is capable of supplying. Since the hair sensor (and first potential divider
on signal conditioning board) needs its own power supply, a separate 7.4 volt (2-cell
LiPo) battery and 5 volt regulator (PTR08060) are used. They are shown below in
46
figure 4.5.
Figure 4.5: Additional Battery and Voltage Regulator
Fixed 5.5 kOhm resistors are used to step the voltage down from the regulator
to the hair sensor and first stage potential divider, to about 0.2 volts (it varies
for each sensor since each sensor’s total resistance can be different). As another
reference, figure 4.6 displays an up-close picture of the signal conditioning board’s
top side.
Figure 4.6: Signal Conditioning Board
The last addition to the quadrotor vehicle is an (anti-)aerodynamic surface
meant to reduce the gust speed at which the vehicle would be significantly per-
47
turbed. This is necessary to guarantee that the sensor won’t mechanically saturate,
which would prevent it from estimating gust speed. For this, a rectangular piece of
cardboard provided a light-weight and stiff structure that could be easily modified.
Figure 4.7 shows the 10.2 x 22.6 cm2 cardboard surface that was mounted in the
x-z (forward-down) plane of the vehicle.
Figure 4.7: Anti-aerodynamic Cardboard Surface
3D printed parts were designed to hold all of these necessary components
for on-board gust speed estimation and rejection. The vehicle with all of these
components is shown in figure 4.8.
48
Figure 4.8: Quadrotor Vehicle As Used In Gust Rejection Experimentation
4.2 Gust Speed Estimation
Static estimation of the gust speed was performed, then be fed back for gust
rejection. The 0 – 3.3v signal from the output of the conditioning board cannot be
directly used for static estimation, as a reference voltage would be needed (like in
chapter 3). Instead of manually setting a reference, the non-zero offset of the signal
was removed with a band-pass filter. This was be performed by the ArduPilot which
can convert the analog signal to digital through one of the available servo pins. The
high-pass part of this filter removes the offset and drift effects. The low-pass part of
this filter reduces the high frequency content that wasn’t filtered out by the low-pass
filter on the conditioning board. This high frequency content was largely due to the
49
turbulent nature of the gusts generated from the leaf blower. A bode magnitude
plot of the band-pass filter is shown in figure 4.9.
Figure 4.9: Band-pass Filter Bode Diagram
This is a 2nd order Butterworth filter with the frequency range of 0.87 – 8.47
rad/s being passed (> -3dB). An overshooting effect is seen in the output from the
band-pass filter. To compensate for this, half-wave rectification was used. This
rectification is applicable in this situation because the experiments use only unidi-
rectional wind gusts. With the sensor connections configured so that the left side
wind gusts will cause the signal to increase, a threshold level of 0.1v was used.
In other words, any output from the band-pass filter less than 0.1 is set to 0. A
50
comparison of the raw analog signal to the filtered signal is shown in figure 4.10.
Figure 4.10: Raw Analog Signal vs. Filtered and Rectified Signal
The final step in this process is static estimation, which is effectively a scaling
factor to convert from units of voltage to m/s because the estimation equation
structure was assumed linear: V = cy. Nonlinear estimation would have been
considered if this method didn’t show good enough performance in conjunction with
the control law. c=38.6 (19% error) was determined using the least squares solution
with two tests batched together. In these tests the sensor was exposed to the flow at
distances where the gust speed was measured by the hand-held anemometer. Table
4.1 displays these measured gust speeds.
Gust speeds were only taken in a straight line from the nozzle because the gust
stream maintained a small width. The value of c served only as a starting point
51
Table 4.1: Gust Speeds at Distances from the Nozzle of the Leaf Blower
Distance (m) Gust Speed (m/s)
0.5 9.61
0.75 7.60
1.0 5.81
1.25 4.92
1.5 3.58
since the gain of the controller will be hand-tuned to bring the controller magnitude
within a reasonable (conservative) range. A block diagram of this estimation process
is shown in figure 4.11.
Figure 4.11: Gust Estimation Block Diagram
This estimation process does not approximate with good accuracy given the
limited window of operation of this sensor and unsophisticated estimation scheme.
It does, however, offer a ’conservative’ estimate that will not drift from 0 unless a
significant gust is affecting the vehicle. Figure 4.12 shows the estimation of the gust
speeds listed in table 4.1.
52
Figure 4.12: Gust Speed Estimation
The data used for the estimate above is part of the data used in the estimation
parameter calculation. The root mean square error of this test is 2.34 m/s, which
is too small to accurately describe the error of the estimation scheme since the zero
gust speeds are all perfectly correct. Note that only the gust at about 9 m/s is
well noticed by the sensor. This is acceptable since that is the gust speed that the
vehicle will be subjected to, on average.
4.3 Robust Controller Design
At first thought, a static feedforward control law might seem like the best
way to perform gust rejection. In the most ideal situation, feedforward control can
53
entirely eliminate the effect of the measured disturbance on the process output [22].
In the future, that might be correct but an alternative control method was designed
for this research. One sensor was able to estimate the gusts over only a small
portion of the vehicle, while the entire vehicle passed the gust disturbance in the
experiments. In an attempt to compensate for this unmeasured disturbance affecting
the vehicle, a robustly stable µ-controller was designed using gust speed feedback.
Robust stability means that the controller provides (or maintains) system stability
for a range of plant uncertainty. The methodology behind the controller synthesis
and performance analysis was referenced from [23]. The block diagram used for this
design is shown below in figure 4.13.
Figure 4.13: System Model Used for Disturbance Rejection Controller
This system is modeled with additive uncertainty, input disturbance, and per-
formance measured at the output. The uncertainty models that were considered
were output uncertainty and additive uncertainty. For this system, the uncertainty
model has no clear relation to the physics of the system. Whether the disturbance
was considered to affect the output or input was also arbitrary, depending on how
one interprets the effect of gust disturbances on the vehicle. The four possible com-
54
binations of uncertainty model and disturbance location were considered. Additive
uncertainty and input disturbance were chosen to allow the highest bandwidth in
the performance weighting (will be discussed in more detail later). Performance was
chosen to be measured at the output because the goal of disturbance rejection is
to reduce the effects of the disturbance on the states. The state labels and block
names are listed in table 4.2.
Table 4.2: Block Diagram Labels
Name General Meaning Physical Value
v Signal available to controller Negative of the gust estimate
u Control inputs Lateral control input
u∆ Input to the uncertainty block Weighted control input
y∆ Output from uncertainty block Uncertainty added to output
y Output from the plant Lateral states
w Exogenous input Lateral gust
z Regulated output Weighted states
K Controller Gust rejection controller
G Plant Lateral Dynamics
WU Uncertainty weighting function
∆ Uncertainty block
WP Performance weighting function
Before moving on with the controller synthesis; G, WU, and WP need to be
defined. The plant incorporates lateral dynamics for the states v (lateral velocity),
55
p (roll rate), φ (roll angle), and vg (gust velocity). The linear time-invariant (LTI)
state-space equations of motion are written as




x˙
x˙d



 =




A GdCd
0 Ad








x
xd



+ Bu + Bdd
y =
[
0 1
]




x
xd




(4.1)
where x =








v
p
φ








, y = xd =vg, u =uR
Augmenting the original state space (A,B) model with the gust dynamics is
necessary for state feedback. First-order Gauss-Markov processes have been used to
model wind dynamics for the purpose of disturbance rejection in [24]. The shaping
filter for the gust is then represented as
x˙d =
−1
τ
xd + ρd (4.2)
where τ=3.2 sec is the correlation time of the wind, ρ=1 is a weighting fac-
tor, and d (as seen in 4.1) is a white noise process that drives the gust dynamics.
Thus (Ad,Bd,Cd,Dd) = (-0.3125,1,1,0). The vehicle’s lateral dynamics (A,B) was
be populated with first-order stability derivatives, which were calculated using sys-
tem identification. The disturbance’s effect on these dynamics was defined by Gd.
This matrix (3x1 here) was set equal to -A(:,1) (negative of the first column of A),
56
which can be interpreted as a gust moving in the positive y-axis (body frame) and
is equivalent to the vehicle moving in the negative y-direction [25].
The rest of the state space model is written as
A =








Yv Yp g
Lv Lp Lφ
Pv 1 Pφ








,B =












YR
LR
PR
0












Bd =












0
0
0
1












Gd =








−Yv
−Lv
−Pv








(4.3)
g is the gravitational constant. The bare frame (non-stabilized) dynamics of
a quadrotor typically have Lφ, Pv, Pφ, YR, and PR equal to 0. With the ArduPilot
avionics providing stability augmentation, it was found (using stepwise regression,
again) that some of these terms hold significant weight in the open loop dynamics.
Closed loop will refer to the gust feedback control loop (outer loop), where open loop
will refer to the dynamics that include inner loop feedback (provided by ArduPilot).
Open loop flight data was used to assign values to the stability derivatives. They
are listed in table 4.3.
57
Table 4.3: Stability Derivatives
Name Value % Error
Yv -0.3380 6.85
Yp -0.2812 7.75
YR -0.0644 160
Lv 1.3324 19.2
Lp -0.5652 82.5
Lφ -32.0842 6.04
LR 11.3946 15.4
Pv 0.0175 56.5
Pφ -1.0410 7.37
PR 0.4348 17.2
These values result in the system being unstable. More specifically, there is
one pole that is slightly in the right-half plane. This results in the system being un-
dectectable, which is necessary for the controller synthesis. We know that dynamics
are actually stable because of the avionics. To avoid spending excessive time to get
slightly different parameters that result in system stability (and thus detectability)
a few parameters were adjusted within their respective error bounds until the unsta-
ble pole moved to the left-half plane. These adjusted parameters are: Lv=1.0824,
Lp=-0.9652, and Lφ=-33.584. Now the system can be written as
58



x˙
x˙d



 =












−0.3380 −0.2812 9.81 0.3380
1.0824 −0.9652 −33.584 −1.0824
0.0175 1 −1.041 −0.0175
0 0 0 −0.3125
















x
xd



+












−0.0644
11.3946
0.4348
0












u +












0
0
0
1












d
y =
[
0 0 0 1
]




x
xd




(4.4)
which from now on will be referred to as x˙ = Ax + Bu+ Bdd, y = Cx
At this point it may be noticed that the plant G(s) = C(sI − A)−1B = 0,
since the only observed state is not dependent on vehicle’s states and is not affected
by control inputs. Thus, an observer must be constructed so full state feedback can
be assumed for the controller synthesis. A Luengberger observer was used for this
purpose. The state estimate dynamics are
˙ˆx = Axˆ + Bu+ Bdd+ L(y − yˆ)
yˆ = Cxˆ
(4.5)
L will simply be a static gain matrix which defines the observer dynamics. Nor-
mally, L is designed such that the observer dynamics are ten times faster (i.e. eigen-
values are 10x further in the left-half-plane) than the full-state-feedback closed-loop
dynamics. This is not possible with this system because of the lack of observability.
59
In fact, only the observer dynamics associated with the gust state can be modified
by L. So L will simply be a (4x1) matrix of ones. A qualitative interpretation of this
observer is that it acts as an estimator of the states as they would change due only
to effects from the disturbance. Now the controller will be synthesized assuming full
state feedback.
WU and WP are the last quantities to define before proceeding with the
controller synthesis. These weighting functions act as tuning knobs for the controller.
They can be set to enforce high performance in the controller with the trade-off of
losing guaranteed nominal performance and robust stability. WU can be thought of
as a weight which normalizes the uncertainty perturbation from the nominal plant
(Gn) to be less than 1, where the identified plant is G = Gn + WU∆ (for additive
uncertainty). The system can be expressed in M∆ form, shown in figure 4.14, where
M is found by inspection of figure 4.13 while ignoring the disturbance input.
Figure 4.14: M∆-Structure Block Diagram
60
M = WUK(I + GK)−1 = WUKS (4.6)
S is the (output) sensitivity transfer function and I is the identity matrix
The bound for uncertainty perturbation of 1 comes from the small gain theo-
rem, which says that if ||M||∞ <1 the system is robustly stable. This assumes ∆ is
full complex in structure (unstructured) and ||∆||∞ <1. The uncertainty weighting
that was used in the final controller design was
WU = 0.3
s
2
+ 1
s
32
+ 1
(4.7)
This weight enforces 30% uncertainty at low frequencies, starts to increase at 2
rad/s, and allowing 478% uncertainty at high frequencies. It was found that robust
stability was guaranteed for this system, while performance was difficult to achieve.
WP is a weight designed to enforce the nominal performance objective, which
is to suppress effects on the output from an input disturbance. 4.8 is derived by
inspection of 4.13 (ignoring the uncertainty) and reveals that the SG is the quantity
that reflects how the controlled system performs.
z = WPy, y = G(w − u) = G(w −Ky)→ y = (I + GK)−1Gw = SGw
→ z = WPSGw
(4.8)
||WPSG||∞ < 1
Attenuation of the input disturbance is improved when SG is low in magni-
tude. Therefore a high magnitude is desired in WP. This was sought for frequencies
61
up to (<) 10 rad/s, but not for frequencies higher than that since the open loop
system response drops off for frequencies that high. The final weight was designed
with a bandwidth frequency of 5 rad/s because of implementation issues. As the
bandwidth was allowed to increase, the controller dynamics pushed the limits of sta-
bility, which resulted in unstable control signals during real-time implementation.
The performance weighting function that was used in the final controller design is
WP =
s
5
+ 5
s+ (5)(0.3)
I (4.9)
I is the 4x4 identity matrix, which is necessary to weigh all states respectively.
Figure 4.15 shows the bode magnitude plots of these two weighting functions.
Figure 4.15: Uncertainty and Performance Weighting Functions
Now, proceeding with controller synthesis, a general control configuration must
62
be constructed. The block diagram for this is shown in figure 4.16, where P is
determined by inspection of 4.13.
Figure 4.16: General Control Configuration Block Diagram








u∆
z
v








= P








y∆
w
u








=








0 WU WU
WP WPG WPG
−I −G −G
















y∆
w
u








(4.10)
For robust stability, it was assumed that the perturbation ∆ was unstructured.
This is the most conservative test for robust stability. ∆ could have been structured
using our knowledge of the plant uncertainty, but the results revealed that was not
necessary. Robust performance is a test similar to robust stability, except another
performance ∆ (∆P) is joined with the uncertainty ∆ (in block-diagonal fashion).
63
This results in a new perturbation quantity that always has structure. Thus, a
structured singular value (µ) must be calculated to determine robust performance.
A structured singular value is a generalization of the singular value and the spectral
radius [23], defined as:
µ(M) ,
1
min {km| det(I − kmM∆) = 0 for structured ∆, σ¯(∆) ≤ 1}
(4.11)
where σ¯ is the singular value and km is scalar. Note that µ(M) = σˆ(M) when
∆ is unstructured.
It is desired that µ be less than 1, as a value of 1 indicates there is a pertur-
bation just large enough to make I −M∆ singular. Regarding robust performance,
the quantity for which µ is calculated is a linear fractional transformation (LFT) of
P to N.
Figure 4.17: General Block Diagram Using Lower LFT Form
N =




−WUKS −WUSI
WPS WPSG



 (4.12)
64
which can be re-interpreted as the block diagram transformation shown in
figure 4.18. Also, SI is the input sensitivity function.
Figure 4.18: Block Diagram Formulation of Robust Performance as a Structured
Robust Stability Test
Finding the controller, K, that minimizes µ(N) requires an iterative process
known as DK-iteration. This methodology is referenced from [23]. Note that MAT-
LAB’s robust controller toolbox offers a function to compute this controller. This
process finds the controller that minimizes the peak value over all frequencies of the
upper bound min
D∈D
σ¯(DND−1), where D is the set of matrices that commute with ∆.
i.e.
min
K
(min
D∈D
||DND−1||∞) (4.13)
The iterations are initialized with an appropriately structured D(s), that is
stable, then proceeds with the following steps:
• K-step: synthesize an H∞ controller for the upper bound, while holding D(S)
fixed. Note that the H∞ synthesis formula is also discussed in [23].
65
• D-step: Find D that minimizes the upper bound at all frequencies, while
holding N fixed.
• Fit the magnitude of D(jω) at each element to a stable minimum-phase trans-
fer function D(s) and repeat the previous steps until the H∞ norm no longer
decreases by the designed improvement tolerance level.
Combining this controller and simple observer in the equation 4.14 yields the
controller that is implemented on the vehicle.
Kfinal = K(sI− (A−BK− LC))−1L
=
−2.311s7 + 253.4s6 + 243.4s5 + 3846s4 + 8029s3 + 25180s2 + 15130s+ 2984
[s9 + 30.34s8 + 456.1s7 + 4357s6 + 27560s5
+113500s4 + 293700s3 + 436900s2 + 278600s+ 27960]
(4.14)
4.4 Theoretical Analysis
The first test to check is to make sure the controller maintains stability for a
range of perturbations weighted by WU. Recall that this is guaranteed if ||M||∞ <1.
The infinity norm of a matrix is the equivalent of the supremum of the maximum
singular value. Noting that the upper left component of N (in 4.12) is M, it is also
equivalent to compute the structured singular value (µ) of that portion of N with
an unstructured perturbation. µ of the upper left portion of N is shown in figure
4.19 and reveals that the system is robustly stable. The computation of µ is too
66
computationally intense to get an exact value, but upper and lower bounds can be
computed. If these bounds are sufficiently tight (as seen in figures 4.19, 4.20, and
4.21), then we can be confident that the computed values are correct. [23] provides
greater detail on this subject.
Figure 4.19: Singular Value Plot of M
Also note that the bottom right portion of N is the weighted relationship
between input disturbance and output. If the maximum µ(WPSG) <1, with a
fully complex block structure, then nominal performance is achieved. Figure 4.20
reveals that this level of performance was not achieved by the synthesized controller.
67
Figure 4.20: Singular Value Plot of WPSG
Figure 4.21: Structured Singular Value Plot of N
68
Figure 4.21 is shown for completeness, but it is known that robust perfor-
mance will not be satisfied since nominal performance isn’t satisfied. The trends
in figures 4.20 and 4.21 are nearly identical, meaning (not so surprisingly) nominal
performance criteria was the primary cause of the controller not achieving robust
performance.
Even though the test for nominal performance was unsatisfied, we can still
analyze the effects of the controller on the system to see how much improvement it
offers. The performance weight was designed to reduce SG, which relates the input
disturbance to the output. Without feedback, G relates the input disturbance to
the output. These are compared in figure 4.22. Note that the K used to compute
S is the controller without the observer dynamics. This is necessary to make GK
square, and thus (I + GK) invertible.
69
Figure 4.22: Effect of Input Disturbance on Output
There is clear improvement at frequencies up to 6.9 rad/s, where SG is slightly
larger than G, until about 25.1 rad/s, where the singular values fall off together
(as expected by performance weight design). As the performance bandwidth was
increased, the peak of SG moved towards higher frequencies without decreasing
in magnitude. This played an additional factor in the final choice of performance
weight, as it was another reason not to push the performance requirements of the
bandwidth.
In order to analyze the system performance with regard to the controller that
includes the observer dynamics, we are limited to looking at open loop performance.
This is because the implemented controller is SISO and the only way we can analyze
G is by considering full state output, which makes GK non-square and (I+GK)
70
non-invertible. In other words, only the gust state is used in feedback but we must
consider C to be identity again, so G isn’t a static gain of 0. Furthermore, the
system has been augmented with a gust state and is designed as a regulator. So
while the controller can’t regulate the gust itself, it can regulate the states as they
are affected by the gust. For good tracking performance G can be compared to GK,
where K now contains the observer dynamics (as shown in eq. 4.14).
Figure 4.23: Open Loop Transfer Function Comparison
Significantly large magnitude of the open loop transfer function indicates good
tracking (and disturbance rejection). Figure 4.23 shows that the reference tracking
qualities were already very good for the uncontrolled G and that GK starts with
decent low frequency performance, but falls off fairly quickly. To compensate for
this, K can be multiplied by a static gain. A gain of 10 is chosen to show that the
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open loop tracking and disturbance rejection performance can be brought back to
the low frequency performance quality of the uncontrolled plant. Increasing the gain
of K also reduces SG by a significant amount, as figure 4.22 shows. It isn’t clear
how much the gain of K can be increased without reaching saturation issues. During
implementation it was seen that the magnitude of the generated control input did
not map to the magnitude range that the control input accepts. In addition, the
input generated was limited to 67% of the maximum possible lateral input. This
was to leave room for manual inputs to have the capability to over power the inputs
generated by the hair sensor, in the event of unstable behavior. So the controller
gain will be increased until expected deflection of the sensor cantilevers results in
the maximum allowed control input.
4.5 Experimental Analysis
Experimental implementation results will be used to validate the applicability
of these sensors for gust rejection. The experimental procedure was to have the
quadrotor vehicle hover at a position with its heading pointed along a path perpen-
dicular to the gust stream. The vehicle was given a forward motion impulse input
(from a human pilot), then left to move in a straight line until being perturbed by
the gust. The vehicle was pushed laterally, giving it a non-zero lateral velocity. The
closed loop results reveal the vehicle responded to the gusts and reduced the lateral
velocity. Two quantities are used to quantify the gust rejection performance; lateral
velocity, v, and cartesian displacement from the projected (undisturbed) path. Ten
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trajectory segments were used in the performance comparison (each), which were
chosen such that the open loop and closed loop tests were as close to each other as
possible until the vehicle displayed signs that they were affected by the gust. This
was the choice in trajectories because it guaranteed approximately equal distances
from the gust source, and thus equal levels of applied disturbance. The cartesian
trajectory comparison is shown in figure 4.24, and the lateral velocity is shown in
figure 4.25. The individual trajectories are shown in figures 4.26 and 4.27.
Figure 4.24: Trajectory Comparison
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Figure 4.25: Lateral Velocity Comparison
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Figure 4.26: Open Loop Trajectories
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Figure 4.27: Closed Loop Trajectories
Figure 4.24 reveals there was a 17.1% reduction in mean cartesian displacement
from the projected undisturbed trajectory, when the hair sensor feedback was active.
Note that this value would increase if there was more room for the vehicle to move
after being affected by the gust. The length of the trajectories is determined by
when human pilot commands took control to prevent flying into the wall. Figure 4.25
reveals a 19.7% reduction in the root-mean-square value of the lateral velocity. These
numbers are not as impressive as one might expect for a device that can directly
sense wind velocity, but are still indicative of the applicability of these sensors. Thus,
the goal of first-time implementation of these sensors for gust rejection is achieved.
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4.6 Summary
A single hair sensor was deployed on a quadrotor vehicle, which (including
the signal conditioning board) was powered by a 2-cell LiPo battery with a 5v
voltage regulator. Rigid body motion during flight tests was recorded using a Vicon
Tracker system. Voltage readings from the output of the signal conditioning board
were transmitted using an XBee wireless communication module. Vicon data was
recorded at the same frequency as the sensor data using Labview. The vehicle used
was a DJI FlameWheel 330, controlled by an ArduPilot Mega. An anti-aerodynamic
surface was mounted on the vehicle to increase sensitivity of the vehicle to lateral
gusts, so the hair sensor would not saturate when exposed to gusts that would affect
the vehicle.
Gust speed estimation was performed by passing the analog signal (from the
conditioning board) into the ArduPilot, using a band-pass filter and half-wave rec-
tifier, and multiplying by a static linear estimation gain. Band-pass removes the
non-zero offset of the signal, removes drift effects, and reduces high frequency con-
tent within the gust. Half-wave rectification removes overshoot effects resulting from
the band-pass filter. The static gain is the estimation coefficient determined by a
least-squares solution of the sensor readings compared to actual gust speeds. This
estimation scheme isn’t expected to perform exceptionally well, but was found to
perform well enough during experimentation.
A robust µ-controller was chosen to be implemented to generate gust rejecting
control inputs. Additive plant uncertainty was used, with the disturbance affecting
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the input, and performance weighted at the output. The plant contains lateral
dynamics, augmented with lateral gust dynamics. The gust dynamics were defined
as a first-order Gauss-Markov process with a correlation time of 3.2 seconds. The
stable vehicle dynamics were determined using time-domain system identification. A
static Luenberger observer was constructed to provide state estimates to a controller
designed for full state feedback. The lack of observability meant the dynamics of the
observer could only be as fast as the vehicle dynamics. To reduce the effect of the
input disturbance on the output, the performance weight was designed to reduce
SG at frequencies up to where the open loop plant falls off.
A controller was synthesized attempting to achieve robust performance, by
means of DK iteration. The controller was found to be robustly stable, but unable
to achieve the level of nominal performance set by the weighting function. That
being said, frequency domain analysis showed that there would still be reduction of
the effect of input disturbances on the output. The controller was implemented in
hardware to attempt gust rejection. 10 tests were performed with the vehicle flying
past the gust disturbance with and without gust speed feedback (20 tests total).
The distance the vehicle was perturbed from the nominal (undisturbed) path was
reduced by 17.1%, when comparing the mean trajectories. The root mean square of
the lateral velocity was reduced by 19.7%.
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Chapter 5: Conclusion
5.1 Summary
The work in this thesis demonstrates that unique bio-inspired hair sensors,
developed at the University of Maryland, can be used for state estimation in a
wind tunnel and for gust rejection on a micro-air vehicle. Chapter 2 discusses
the sensor’s design, signal conditioning board, and sensor support/casing. The
sensor has two parts to its structure: Kapton polymer film acting as a cantilever
structure that deforms with wind flow, and gold strain gauge patterns which vary
in resistance when the Kapton cantilevers deform. The signal provided from the
sensor varies by an amount so small that it requires two-stage amplification. A
signal conditioning board was constructed to provide amplification and filtering to
reduce the amplified noise. Chapter 3 discusses sensor response characterization,
motivation for sensor orientation and paddle configuration, and wind frame state
estimation. The characterization revealed that the sensors were most sensitive to
wind speed when the the largest amount of surface area was exposed to the flow and
to angle variation when the least amount of surface area was exposed (i.e. cantilever
array aligned with flow). Stepwise regression was used to determine linear and
nonlinear estimation equation model structure. Least squares solutions provided the
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estimation equation coefficients. Initial validation test errors were used to adjust the
estimation coefficients to allow better estimation at coupled (non-zero angle of attack
and sideslip angle) orientations. One final validation test at an untested orientation
provided the final piece of support to claim sensors are capable of windframe state
estimation. Errors for both estimation schemes are: 17.3% for linear α estimation,
15.7% for linear β estimation, 27.2% for linear wind speed estimation, 13.3% for
nonlinear α estimation, 7.4% for nonlinear β estimation, and 6.4% for nonlinear
wind speed estimation. Chapter 4 discusses instrumentation used for on-vehicle
implementation of the sensors, gust speed estimation, and gust disturbance rejection
via feedback control. The output from the signal processing board was passed
through a digital band-pass filter and half-wave rectifier before being used for static-
linear estimation of the gust speed. A robustly stable µ controller was designed to
reduce the effect of an input disturbance on the output. Poor observability of the
system required the construction of an observer, which served as an estimator of the
states as they were affected by the gust. Implementation of the controller resulted in
17.1% reduction in mean cartesian displacement from the projected (undisturbed)
path, and a 19.7% reduction in lateral velocity. While the gust rejection performance
is modest, the results serve as evidence of the ability to implement these unique
sensors for gust rejection.
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5.2 Contribution
The contribution of this research is the implementation of unique bio-inspired
hair sensors for estimation of wind frame states in a wind tunnel and for gust
rejection on a micro-air vehicle. More specifically, the contributions are:
• Characterization of unique, bio-inspired hair sensors for the purpose of wind
frame estimation on a (MAV) fuselage-like structure. Previous work with
similar sensing technology has only been to estimate wind speed and doesn’t
take implementation on a micro-air vehicle into consideration.
• Development and validation of linear and nonlinear static estimation schemes
compatible with the bio-inspired hair sensors, for estimation of wind speed,
angle of attack, and sideslip angle in a wind tunnel. This is an expansion
on the previous contribution in that all previous work hasn’t implemented
similar sensing technologies for wind frame estimation. Utilizing this type of
sensing technology for wind frame estimation provides a starting point for the
development of a new light-weight, low-computation sensory system ideal for
small unmanned aerial vehicles.
• Robust formulation of a gust rejection controller, which uses gust speed feed-
back from bio-inspired hair sensors. When estimating a disturbance directly,
rejecting (input) disturbances is typically performed using feedforward control.
This strategy isn’t conducive to the formulation of robustly stable control, so
a different approach was considered where the effect of the gust was reduced
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using gust state feedback.
• Implementation of the robust controller on a small quadrotor vehicle with a
bio-inspired hair sensor to demonstrate the gust rejection capability. These
types of sensors haven’t previously been deployed on a free-flying vehicle. This
contribution provides validation of the robust feedback control and the appli-
cability of the unique, bio-inspired sensors for use on a micro-air vehicle.
Development of the sensors is credited to Badri Ranganathan and Ivan Penskiy,
whom I assisted by providing feedback of my implementation efforts.
5.3 Future Work
Since this is the first attempt at wind tunnel state estimation and gust rejection
using bio-inspired hair sensors, there are many areas open to improvement. Some
of these areas could include the following:
• Continued refinement and creation of new sensor designs to expand range of
operation and improve performance
• More rigorous analysis of how the cantilevers deflect with wind speed and
orientation
• Improvement of the estimation scheme(s)
• Distribution of multiple sensors for improved detection of disturbances and/or
performing more advanced sensing and estimation techniques
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Appendix A: Additional Figures
Figure A.1: Complete Signal Processing Board Schematic
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Figure A.2: Initial Sensor 1 Wind Speed Sweep
Figure A.3: Initial Sensor 2 Wind Speed Sweep
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Figure A.4: Initial Sensor 3 Wind Speed Sweep
Figure A.5: Initial Sensor 4 Wind Speed Sweep
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Figure A.6: Initial Sensor 9 Wind Speed Sweep
Figure A.7: Initial Sensor 1 Angle of Attack Sweep
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Figure A.8: Initial Sensor 2 Angle of Attack Sweep
Figure A.9: Initial Sensor 3 Angle of Attack Sweep
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Figure A.10: Initial Sensor 4 Angle of Attack Sweep
Figure A.11: Initial Sensor 9 Angle of Attack Sweep
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Figure A.12: Initial Sensor 1 Sideslip Angle Sweep
Figure A.13: Initial Sensor 2 Sideslip Angle Sweep
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Figure A.14: Initial Sensor 3 Sideslip Angle Sweep
Figure A.15: Initial Sensor 4 Sideslip Angle Sweep
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Figure A.16: Initial Sensor 9 Sideslip Angle Sweep
Figure A.17: Linear Estimation at α = 0◦, β = 0◦, V = 3 m/s
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Figure A.18: Linear Estimation at α = 5◦, β = 5◦, V = 3 m/s
Figure A.19: Linear Estimation at α = 10◦, β = 10◦, V = 3 m/s
92
Figure A.20: Linear Estimation at α = 15◦, β = 15◦, V = 3 m/s
Figure A.21: Linear Estimation at α = 20◦, β = 20◦, V = 3 m/s
93
Figure A.22: Linear Estimation at α = −5◦, β = −5◦, V = 3 m/s
Figure A.23: Linear Estimation at α = −10◦, β = −10◦, V = 3 m/s
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Figure A.24: Linear Estimation at α = −15◦, β = −15◦, V = 3 m/s
Figure A.25: Linear Estimation at α = −20◦, β = −20◦, V = 3 m/s
95
Figure A.26: Nonlinear Estimation at α = 0◦, β = 0◦, V = 2.5 m/s
Figure A.27: Nonlinear Estimation at α = 5◦, β = 5◦, V = 2.5 m/s
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Figure A.28: Nonlinear Estimation at α = 10◦, β = 10◦, V = 2.5 m/s
Figure A.29: Nonlinear Estimation at α = 15◦, β = 15◦, V = 2.5 m/s
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Figure A.30: Nonlinear Estimation at α = 20◦, β = 20◦, V = 2.5 m/s
Figure A.31: Nonlinear Estimation at α = −5◦, β = −5◦, V = 2.5 m/s
98
Figure A.32: Nonlinear Estimation at α = −10◦, β = −10◦, V = 2.5 m/s
Figure A.33: Nonlinear Estimation at α = −15◦, β = −15◦, V = 2.5 m/s
99
Figure A.34: Nonlinear Estimation at α = −20◦, β = −20◦, V = 2.5 m/s
100
Bibliography
[1] Vladislav Klein and Eugene A Morelli. Aircraft system identification: theory
and practice. American Institute of Aeronautics and Astronautics Reston, VA,
USA, 2006.
[2] Yongsheng Lian, Wei Shyy, Dragos Viieru, and Baoning Zhang. Membrane wing
aerodynamics for micro air vehicles. Progress in Aerospace Sciences, 39(6):425–
465, 2003.
[3] Andy M Reynolds, Don R Reynolds, Alan D Smith, and Jason W Chapman. A
single wind-mediated mechanism explains high-altitude non-goal orientedhead-
ings and layering of nocturnally migrating insects. Proceedings of the Royal
Society B: Biological Sciences, 277(1682):765–772, 2010.
[4] Jack Chen, Jonathan Engel, Nannan Chen, and Chang Liu. A monolithic
integrated array of out-of-plane hot-wire flow sensors and demonstration of
boundary-layer flow imaging. In 18th IEEE International Conference on Micro
Electro Mechanical Systems, Miami, Florida, USA, pages 299–302, 2005.
[5] Gijs JM Krijnen, Marcel Dijkstra, John J van Baar, Siripurapu S Shankar,
Winfred J Kuipers, Rik JH de Boer, Dominique Altpeter, Theo SJ Lammerink,
and Remco Wiegerink. Mems based hair flow-sensors as model systems for
acoustic perception studies. Nanotechnology, 17(4):S84, 2006.
[6] Yu-Hsiang Wang, Tzu-Han Hsueh, Rong-Hua Ma, Chia-Yen Lee, Lung-Ming
Fu, Po-Cheng Chou, and Chien-Hsiung Tsai. A microcantilever-based gas flow
sensor for flow rate and direction detection. In Design, Test, Integration and
Packaging of MEMS/MOEMS, 2008. MEMS/MOEMS 2008. Symposium on,
pages 142–145. IEEE/RSJ, 2008.
[7] Yu-Hsiang Wang, Chia-Yen Lee, and Che-Ming Chiang. A mems-based air flow
sensor with a free-standing micro-cantilever structure. Sensors, 7(10):2389–
2401, 2007.
101
[8] JM Engel, Jack Chen, Nannan Chen, Saunvit Pandya, and Chang Liu. De-
velopment and characterization of an artificial hair cell based on polyurethane
elastomer and force sensitive resistors. In Sensors, 2005 IEEE, pages 4–pp.
IEEE, 2005.
[9] Mahdi M Sadeghi, Rebecca L Peterson, and Khalil Najafi. Micro-hydraulic
structure for high performance bio-mimetic air flow sensor arrays. In Electron
Devices Meeting (IEDM), 2011 IEEE International, pages 29–4. IEEE, 2011.
[10] C Song, AR Aiyar, S-H Kim, and MG Allen. Exploitation of aeroelastic effects
for drift reduction, in an all-polymer air flow sensor. Sensors and Actuators A:
Physical, 165(1):66–72, 2011.
[11] Badri N. Ranganathan, Ivan Penskiy, William Dean, Sarah Bergbreiter, and
Sean Humbert. Bio-inspired wind frame state sensing and estimation for mav
applications. In [ ], 2015.
[12] Sergio Callegari, Alessandro Talamelli, Michele Zagnoni, Alessandro Golfarelli,
Veronica Rossi, Marco Tartagni, and Enrico Sangiorgi. Aircraft angle of attack
and air speed detection by redundant strip pressure sensors. In Sensors, 2004.
Proceedings of IEEE, pages 1526–1529. IEEE, 2004.
[13] Gabriel Torres and Thomas J Mueller. Micro aerial vehicle development: de-
sign, components, fabrication, and flight-testing. In AUVSI Unmanned Systems
2000 Symposium and Exhibition, pages 11–13, 2000.
[14] He Shen, Yunjun Xu, and Charles Remeikas. Pitch control of a micro air vehicle
with micropressure sensors. Journal of Aircraft, 50(1):239–248, 2012.
[15] Haiping Fei, Rong Zhu, Zhaoying Zhou, and Jindong Wang. Aircraft flight
parameter detection based on a neural network using multiple hot-film flow
speed sensors. Smart materials and structures, 16(4):1239, 2007.
[16] Sam Zarovy, Mark Costello, Ankur Mehta, Greg Gremillion, Derek Miller,
Badri Ranganathan, J Sean Humbert, and Paul Samuel. Experimental study
of gust effects on micro air vehicles. In AIAA Atmospheric Flight Mechanics
Conference, 2010.
[17] Steven L Waslander and Carlos Wang. Wind disturbance estimation and rejec-
tion for quadrotor position control. In AIAA Infotech@ Aerospace Conference
and AIAA Unmanned... Unlimited Conference, Seattle, WA, 2009.
[18] Derrick Yeo, Elena Shrestha, Derek A Paley, and Ella Atkins. An empiri-
cal model of rotorcraft uav downwash model for disturbance localization and
avoidance. 2015.
[19] Nitin Sydney, Brendan Smyth, Derek Paley, et al. Dynamic control of au-
tonomous quadrotor flight in an estimated wind field. In Decision and Control
(CDC), 2013 IEEE 52nd Annual Conference on, pages 3609–3616. IEEE, 2013.
102
[20] Summary of properties for kapton polyimide films. http://www.dupont.com/
content/dam/assets/products-and-services/membranes-films/assets/
DEC-Kapton-summary-of-properties.pdf. Accessed: 2015-03-03.
[21] John David Anderson Jr. Fundamentals of aerodynamics. Tata McGraw-Hill
Education, 1985.
[22] Coleman Brosilow and Babu Joseph. Techniques of model-based control. Pren-
tice Hall Professional, 2002.
[23] Sigurd Skogestad and Ian Postlethwaite. Multivariable feedback control: anal-
ysis and design, volume 2. Wiley New York, 2007.
[24] Jyotirmay Gadewadikar, Frank L Lewis, Kamesh Subbarao, Kemao Peng, and
Ben M Chen. H-infinity static output-feedback control for rotorcraft. Journal
of Intelligent and Robotic Systems, 54(4):629–646, 2009.
[25] Robert C Nelson. Flight stability and automatic control, volume 2.
WCB/McGraw Hill, 1998.
103