System Identification
of Rotorcraft
Rebecca Creed, Mechanical Engineering, University of Dayton
Andrea Gillis, Aerospace Engineering, University of Cincinnati
Urvish Patel, EE-CompE Accend, University of Cincinnati
Dr. Kelly Cohen, Faculty Mentor, University of Cincinnati
Mr. Wei Wei, Graduate Mentor, University of Cincinnati
July 11, 2013
Part of NSF Type 1 STEP Grant, Grant ID No.: DUE-0756921
1
Introduction
• Natural disasters take thousands of lives
every year.
• Many first responders perform dangerous
rescue missions to save lives.
• Technology will allow first responders to
assess the situation more quickly and
efficiently.
2
2013 Arizona and 2012 Colorado Wildfire
• The progression of the fire could not be anticipated
due to severe weather conditions.
• Accurate situational awareness and fire growth
predictive capability can be obtained using a UAV
and intelligent software.
• An autopilot stabilized
UAV (rotorcraft) would be
able to collect information
using a camera
Image courtesy of csmonitor.com
3
UAV Advantages
•
•
•
•
•
•
Maneuverability
Capable of indoor flight
Safer for Crews
Endurance
Cost
Sushi Delivery
Image courtesy of http://www.todaysiphone.com/2013/06/yo-sushidelivering-food-on-ipad-controlled-trays/
4
Why Autopilot?
• Easy to use with simple controls
• Increase the range of the rotorcraft
– Without autopilot, the rotorcraft must remain in
the operator’s line of sight
• A dynamic model is necessary to develop an
autopilot
5
System Identification
• A dynamic model is a representation of the
behavior of a system (for this case, rotorcraft)
• Two options for creating a dynamic model
– System Identification
– Wind Tunnel Testing
• Placing the rotors in a wind tunnel is complex
– Simulation
• Based on the moment of inertia
6
Research Goals
– Study the characteristics of Aeroquad.
– Use System Identification and CIFER software to
develop and validate the dynamic model of
Aeroquad.
– Report the findings so process can be repeated in
the future.
7
So, what is System Identification?
Inputs
System
Outputs
Given the inputs to a system, a system
model can predict the outputs
8
Simple Example: Pushing a Sled
Input is the “pushing”
force applied to the sled
•
Push(force)
Output is the sled’s
movement
Sled
•
•
•
Acceleration
Velocity
Displacement
9
System Inputs and Outputs
• 4 inputs
–
–
–
–
Yaw
Pitch
Roll
Thrust
• 9 outputs
– 3 attitudes
– 3 angular rates
– 3 accelerations
Aeroquad System
10
System Identification Flowchart
Flight Testing
Data Processing
MATLAB
Data Evaluation
CIFER
System Model
Validation
System Identified!
11
Flight Test
• Inputs given to the rotorcraft by
RC Controller from Futaba.
• Outputs recorded by the 9 DOF Sensor stick
from Open Hardware.
12
How the quad-rotor works
Roll Control
move right/left
Yaw Control
spin cw/counter-cw
Pitch Control
move forward/backward
13
Data Processing
Flight Testing
Data Processing
Data Evaluation
Record raw data in
MATLAB program
Filter recorded
data
System Model
Validation
Reformat data for
use in CIFER
System Identified!
14
Filter Data
Sensor stick used
in Rotorcraft –
9DOF
Next Step
Accelerometer
ADXL345
Filtered Data
Noisy Data
Filter
Picture from: www.sparkfun.com
15
Result from Kalman Filter
5
X axis
4
3
2
1
0
Regular
-1
Kalman
-2
-3
-4
-5
-6
We designed new and unique Kalman Filter !
16
Moving average and Kalman
5
X axis
4
Regular
3
2
Kalman
1
Regular
0
Kalman
-1
Moving average
-2
-3
Moving Average
-4
-5
-6
17
Data Evaluation
CIFER
• Advanced program used for System Identification
• Stands for Comprehensive Identification from
Frequency Responses
• Developed by the U.S. Army and the University of
California Santa Cruz
• We use CIFER to identify the Aeroquad system
CIFER image from: http://uarc.ucsc.edu/flight-control/cifer/
18
Data Evaluation
First Step – find the frequency response
• Frequency response relates the inputs and outputs of our data
Output Time History Data
100
80
60
40
20
0
-20
-40
-60
-80
-100
0
10
20
30
40
50
Time (seconds)
60
Pitch Output (degree/second)
Pitch Input (Percentage)
Input Time History Data
100
80
60
40
20
0
-20
-40
-60
-80
-100
0
10
20
30
40
50
60
Time (seconds)
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Coherence
Phase (Deg) Magnitude (DB)
Data Evaluation – Frequency Response
Frequency (Hz)
A coherence value closest to 1 shows that the inputs and
outputs correlate well.
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Data Evaluation
Next step: transfer function fit
• CIFER fits a transfer function to the frequency
response
What is a Transfer Function?
The transfer function relates the inputs to the outputs of a system
Transfer Function = 𝐻 𝑠 =
𝑌 𝑠
𝑋 𝑠
=
𝐴𝑠+𝐵
𝑠2 +𝐶𝑠+𝐷
CIFER finds the coefficients of this transfer function
21
Data Evaluation – Stability
• CIFER produces transfer functions for three motions
• These transfer functions model the Aeroquad system
and must be stable(by doing a closed loop system
identification, the system is stable)
Transfer Function = 𝐻 𝑠 =
Roots of the
denominator
should be on
this side!
𝑌 𝑠
𝑋 𝑠
=
𝐴𝑠+𝐵
𝐴𝑠 + 𝐵
𝑠𝑠22+𝐶𝑠+𝐷
+ 𝐶𝑠 + 𝐷
Stable Example
𝑖
𝐻 𝑠 =
𝑠
𝑠+2
𝑠 2 + 2𝑠 + 1
𝑟𝑜𝑜𝑡𝑠: 𝑠 = −1, −1
Negative real roots
Unstable Example
𝐻 𝑠 =
𝑠+2
𝑠2 − 𝑠 + 1
𝑟𝑜𝑜𝑡𝑠: 𝑠 = 0.5 ± 0.866𝑖
Positive real roots
22
Results
• Transfer Functions of Aeroquad
– Roll:
2.495 𝑠 − 0.1304
𝐻 𝑠 = 2
𝑠 + 64.32 𝑠 + 317.4
roots: -5.385, -58.934
– Pitch:
−7.895 𝑠 + 0.3096
𝐻 𝑠 = 2
𝑠 + 212.8 𝑠 + 981.2
roots: -4.715, -208.084
– Yaw:
𝐻 𝑠 =
0.1353
𝑠 + 6.199
roots: -6.199
*Notice all roots are negative representing a stable system !!
23
Validation
• CIFER also finds the state-space representations
from the pitch, roll, and yaw frequency responses
– Separate sets of data for pitch, roll, and yaw were
used
– Angular rates of the output were predicted from
the input angular rates
Inputs
(percentages)
State-space Model
Outputs
(angular rates)
24
Pitch Output (radians/second)
Validation – Pitch
Time (seconds)
25
Roll Output (radians/second)
Validation – Roll
Time (seconds)
26
Yaw Output (radians/second)
Validation – Yaw
Time (seconds)
27
Summary
• Observed the connection between our research and
potential societal impact… saving lives during
fires/natural disasters
• Learned to fly quad-rotor using RC controls
• Data collected from flight tests utilized to develop
dynamic model using system identification
• A new and unique Kalman filter was developed and
its effectiveness was demonstrated.
• The model was validated with additional flight test
data!
28
Timeline
Week
1
2
3
4
5
6
7
8
Literature and
technical Review
Learn how to fly
AR Drone
Flight testing
Data Processing
System
Identification
Paper
Presentation
Poster
29
Publications
• Conference: 9th Annual Dayton Engineering
Sciences Symposium (DESS 2013), October
29, 2013, Wright State University, Dayton,
Ohio
• Journal: Computer Application in
Engineering Education, Wiley Periodicals,
Inc.
30
References
•
Bestaoui, Y., and Slim, R. (2007). “Maneuvers for a Quad-Rotor Autonomous Helicopter,” AIAA Infotech@Aerospace
Conference, held at Rohnert Park, California, May 7-10, pp.1-18
•
Chen, M., and Huzmezan, M. (2003). “A Combined MBPC/2 DOF H∞ Controller for a Quad Rotor UAV,” AIAA Guidance,
Navigation, and Control Conference and Exhibit, held at Austin, Texas, August 11-14, n.p.
•
Esme, B. (2009). “Kalman Filter For Dummies.” Biligin’s Blog,
<http://bilgin.esme.org/BitsBytes/KalmanFilterforDummies.aspx> (Mar. 2009).
•
Guo, W., and Horn, J. (2006). “Modeling and Simulation For the Development of a Quad-Rotor UAV Capable of Indoor
Flight ,” AIAA Modeling and Simulation Technologies Conference, held at Keystone, Colorado, August 21-24, pp.1-11
•
Halaas, D., Bieniawski, S., Pigg, P., and Vian, J. (2009). “Control and Management of an Indoor Health Enabled,
Heterogenous Fleet,” AIAA Infotech@Aerospace Conference, held at Seattle, Washington, April 6-9, pp.1-19
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•
References
Koehl, A., Rafaralahy, H., Martinez, B., and Boutayeb, M. (2010). “Modeling and Identification of a Launched Micro Air Vehicle: Design and
Experimental Results,” AIAA Modeling and Simulation Technologies Conference, held at Toronto, Ontario Canada, August 2-5, pp.1-18
•
Mehra, R., Prasanth, R., Bennett, R., Neckels, D., and Wasikowski, M. (2001). “Model Predictive Control Design for XV-15 Tilt Rotor Flight
Control,” AIAA Guidance, Navigation, and Control Conference and Exhibit, held at Montreal, Canada, August 6-9, pp. 1-11.
•
Milhim, A., and Zhang, Y. (2010). “Quad-Rotor UAV: High-Fidelity Modeling and Nonlinear PID Control,” AIAA Modeling and Simulation
Technologies Conference, held at Toronto, Ontario, Canada, August 2-5, pp. 1-10.
•
Salih, A., Moghavvemi, M., Mohamed, H., and Gaeid, K. (2010). “Flight PID controller design for a UAV quadrotor,” Scientific Research and
Essays, ????, Vol. 5, No. 23, pp. 3660-3667.
•
Tischler, M.B., and Cauffman, M.G. (2013). “Frequency-Response Method for Rotorcraft System Identification: Flight Applications to BO105 Coupled Fuselage/Rotor Dynamics,” University Affiliated Research Center: A Partnership Between UCSC and NASA Ames Research
Center, pp. 1-13.
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Questions?
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