system identification of rotorcraft

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System Identification of Rotorcraft

Rebecca Creed, Mechanical Engineering, University of DaytonAndrea Gillis, Aerospace Engineering, University of Cincinnati

Urvish Patel, EE-CompE Accend, University of Cincinnati

Dr. Kelly Cohen, Faculty Mentor, University of CincinnatiMr. Wei Wei, Graduate Mentor, University of Cincinnati

June 28, 2013

Part of NSF Type 1 STEP Grant, Grant ID No.: DUE-0756921

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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.

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2012 Colorado Wildfire• The progression of the fire could not be

anticipated.• Once the fire had become an issue, the best

way to access it was unknown.• An autopilot equipped rotorcraft would be able to use a camera and assess the situation.

Image courtesy of csmonitor.com

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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

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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

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So, what is System Identification?

SystemInputs Outputs

Given the inputs to a system, a system model can predict the outputs

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Simple Example: Pushing a Sled

Input is the “pushing” force applied to the sled

Output is the sled’s movement

Sled• Push(force)• Acceleration• Velocity• Displacement

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System Inputs and Outputs

• 4 inputs– Yaw– Pitch– Roll– Thrust

• 9 outputs– 3 attitudes– 3 angular rates– 3 accelerations

Aeroquad System

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System Identification FlowchartFlight Testing

Data Processing

Data Evaluation

System Model

Validation

System Identified!

CIFER

MATLAB

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Flight Test• Inputs given to the rotorcraft by controller

• Outputs recorded by the sensor stick (IMU)

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How the quad-rotor worksYaw Control

spin cw/counter-cw

Roll Controlmove right/left

Pitch Controlmove forward/backward

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Data ProcessingFlight Testing

Data Processing

Data Evaluation

System Model

Validation

System Identified!

Record raw data in MATLAB program

Filter recorded data

Reformat data for use in CIFER

Filter Data

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Sensor stick used in

Rotorcraft – 9DOF

Accelerometer ADXL345

Noisy Data

Picture from: www.sparkfun.com

Filtered Data

FilterNext Step

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Kalman Filter

• Kalman filter finds the optimum averaging factor for each consequent state and also remembers some information about previous state

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Kalman Filter for Linear System x = filtered value p = estimated error q = processed noise r = Sensor Noise k = Kalman gain

• p = p + q• k = p / (p + r)• x = x + k * (measured – x)• p = (1 – k) * p

Kalman Predictor Equation

Measurement Update Equation

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Result from Kalman Filter

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

X axis

RegularKalman

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Moving average• Similar results as Kalman filter for our system• Moving average is less efficient than Kalman

filter

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Results of Moving average

-6

-4

-2

0

2

4

6

X axis

RegularMoving average

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-2

-1.5

-1

-0.5

0

0.5

1

1.5

X axis

RegularKalmanMoving average

Moving average and Kalman

Regular

Kalman

Moving Average

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Data Evaluation – CIFER

CIFER • stands for Comprehensive Identification from

Frequency Responses

• Advanced tool used for System Identification

• 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/

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Data Evaluation – FRESPID

– First Step:

FRESPID COMPOSITE NAVFIT

Finds the frequency response of our data

Uses windowing to combine FRESPID

results

Finds a transfer function from our

combined frequency response

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• Frequency response relates the inputs and outputs of our data

Input Data

Output Data

Frequency Response

Data Evaluation – FRESPID

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Data Evaluation – COMPOSITE

– Second Step:

FRESPID COMPOSITE NAVFIT

Finds the frequency response of our data

Uses windowing to combine FRESPID

results

Finds a transfer function from our

combined frequency response

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Data Evaluation – COMPOSITE• COMPOSITE combines parts of the frequency

responses that have the best coherence

FRESPID Frequency Response COMPOSITE Frequency Response

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Data Evaluation – NAVFIT

– Last Step:

FRESPID COMPOSITE NAVFIT

Finds the frequency response of our data

Uses windowing to combine FRESPID

results

Finds a transfer function from our

combined frequency response

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Data Evaluation – NAVFIT• NAVFIT fits a transfer function

to the COMPOSITE frequency response

COMPOSITE Frequency Response

Transfer Function Phase and Magnitude

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• CIFER produces transfer functions for three motions• These transfer functions model the Aeroquad system

and must be stable

Transfer Function =

Data Evaluation – Stability

𝐴𝑠+𝐵𝑠2+𝐶𝑠+𝐷

𝑖

𝑠

Poles should be on this side! Stable Example

𝐻 (𝑠 )= 𝑠+2𝑠2+2 𝑠+1

𝑟𝑜𝑜𝑡𝑠 : 𝑠=−1,−1

Negative real roots

Unstable Example

𝐻 (𝑠 )= 𝑠+2𝑠2−𝑠+1

𝑟𝑜𝑜𝑡𝑠 : 𝑠=0.5 ±0.866 𝑖

Positive real roots

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UAV Advantages• Maneuverability• Capable of indoor flight• Safer for Crews• Endurance• Cost• Sushi Delivery

Image courtesy of http://www.todaysiphone.com/2013/06/yo-sushi-delivering-food-on-ipad-controlled-trays/

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Progress

*Plan to submit Journal paper and Conference paper from this research

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TimelineWeek 1 2 3 4 5 6 7 8

Literature and technical Review

Learn how to fly AR Drone

Flight testing

Data ProcessingSystem Identification

Paper

Presentation

Poster

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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 BO-105

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?