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Khadeeja Nusrath TK, Senior ScientistYoganathan, Project AssistantFlight Mechanics and Control Division,CSIR-NAL.

Modeling & Identification of Rotary Wing Unmanned Aerial Vehicle

❖Problem Statement

❖Challenges

❖Approach

❖Modeling & Identification

❖Rotorcraft Identification

❖Steps Involved &Tools Used

❖Results

❖Key take away

Content

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Problem Statement

Development of 6DOF linear state-space model which accurately captures the key dynamics of small-scale unmanned rotorcraft for model based control design.

System identification technique is used to develop the mathematical model using dynamic flight test data.

Mathematical

modelControl

design

• Design & execution of maneuverers which excites the modes of thevehicle.

• Reduced signal to noise ratio in the measurements.

• Unstable behaviour, tests needs to be carried out with autopilot.

• Determining the structure of the model.

• Good understanding of rotor aeromechanics.

• Highly non linear model across the operating conditions.

• Model identification at Low speed (hover ).

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Challenges

• Specially designed control inputs are applied.

• Tools for data processing.

• Sophisticated methods of system identification.

• Mathematical model based on the application.

• Model acceptance criteria.

• Model validation and release to user.

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Approach

Different approaches

• Wind tunnel testing.

• Nonlinear generic models. Uses 1st principles to build up models of the helicopter using knowledge andassumptions of the physical characteristics of each component aspect of thehelicopter.

• Derivative models from the flight test data using system identification techniques.

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Rotorcraft Model Development

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QUAD-M Process

Input u(t)Output y(t)

To determine the unknown parameters β such that model response Y matches measured response Z.

Interdisciplinary task which needs domain expertise.

• Flight mechanics

• Control theory

• Sensors

• Signal conditioning

• Numerical techniques

• Optimization

• Statistics

• Flight test techniques

• Flight mechanics Maneuvers Method

s

models

Measurements

M&I

Modeling & Identification

• Filtering ,Manuever extraction, Kinematic consistency checks.

Data preprocessing and sensor characterization

• Frequency domain analysis using phase , magnitude and coherence.

• Model order at different frequency range.

Non Parametric identification

• Model structure with sufficient degrees of freedom for the application to be developed.

Rotorcraft model development

• Using time domain identification techniques such as Output Error, Extended Kalman Filter for State Space Modeling.

• Transfer function modeling.

Parameter estimation

• Apply frequency domain and time domain critertia,statistical measures.

Model Validation

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Steps in Rotorcraft System Identification

Tools used @ each stage

Data preprocessing

&

Sensor characterization

MATLAB

Non Parametric identification

MATLAB

CIFER

Model development &

Parameter estimation

ESTIMA

MATLAB

Model Validation

CIFER

MATLAB

Documentation

MATLAB

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Data Acceptance: Coherence of input – output

Signal Filtering : accelerations

Data check independent of system identification to ensure that the measurements are error free and consistent

• Also called flight path reconstruction (FPR)

• Estimation of calibration errors (bias, scale factor, time delay errors…)

Basis for verifying compatibility of measurements is the use of kinematic relationships

Data Preprocessing & Sensor Characterization

Model Formulation

• Non parametric modelling

• Transfer function modelling• SISO models

• State space modelling• MIMO models

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✓ Characterize the whole system ✓ Physics based modelling✓ Time domain techniques ✓ Frequency domain techniques✓ On axis as well as cross coupling

derivatives

✓ Least no. of parameters which characterize the system.

✓ Initial values for MIMO modelling✓ Pole-zero modelling of on axis response✓ Numerator–denominator polynomials✓ Black box modelling

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• Input-output relationship of the vehicle dynamics is analyzed from the gathered data using frequency responses and coherence.

• Provides an excellent in sight to selecting the order of the model in the frequency range of interest

• Can be used to analyze the handling quality and stability margin of the vehicle

dlat_FRE_0B000_dlat_p

dlon_FRE_0B000_dlon_q

0

20

30

MA

GN

ITU

DE

(DB

)

-180

-90

0

90

PH

AS

E(D

EG

)

100

101

0.2

0.6

1

FREQUENCY (RAD/SEC)

CO

HE

RE

NC

E

p/dlat

q/dlon

Non Parametric Model Identification

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T

a e

T

c a e p

x = Ax + Bu

x = w u q θ p r v φ β β

u = δ δ δ δ

Helicopter State Variable Model

Long x x

A = x Lat x

x x Rotor

a

e

β : Long flap angle

β : Lat flap angle

Rotor States

c

a

e

p

δ :Collective

δ : Long Cyclic

δ : Lat Cyclic

δ : Pedal

Controls

Advanced Models for Rotorcraft Dynamics

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An appropriate mathematical model

which affects both the complexity and the

utility of the identified mode

Models of different order may be used

Measurements available

Frequency range of application

Degree of coupling between the

longitudinal and lateral directional

motions

Nearly 60 unknown derivatives

6DOF model found to be inadequate at higher frequencies

Time Domain Parameter Estimation

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Block diagram of Extended kalman filter

)(tu)(ty

)(̂ty-

+

error

EKFMathematical model

)ŷy(K 1k1kk1k +++ −+=

Dynamic System

Stabilized Output Error Method and Extended Kalman Filter are used for estimation

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0 10 20 30 40 50-0.4

-0.2

0

0.2

0.4

Control inputs

0 10 20 30 40 50-60

-30

0

30

60

p(d

eg

/s)

Measured Estimated

0 10 20 30 40 50-60

-30

0

30

60

q(d

eg

/s)

0 10 20 30 40 50-70

-35

0

35

70

r(d

eg

/s)

Dlon Dlat Dped Dcol

Derivative estimation is carried out

using output error method(OEM) and

Extended Kalman Filter(EKF).

Stability analysis carried out using

Eigen values & Eigen vectors.

Derivatives are compared with the

values from first principle

Results

Complementary dataset : Thetrajectories are simulated using theidentified model and compared withmeasured flight data.

Statistical analysis : Computation ofstandard deviation and Cramer-Raobounds

Frequency domain validation: Themeasured and model predictedresponses are compared in frequencydomain

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-20

0

20

40

60

Ma

gn

itu

de

(DB

)

-180

-135

-90

-45

0

45

90

Ph

as

e (

De

g)

100

101

0.2

0.4

0.6

0.8

1

Frequency (Rad/Sec)

Co

he

ren

ce

q/dlon(FLT)

q/dlon(EST)

Model validation

Frequency response match for model validation

• 6DOF State Space model for a small scale UAV rotorcraft was developed using system identification techniques.

• Both time & frequency domain algorithms were used.

• MATLAB® is used extensively in the work for

• Data processing.

• SISO modelling &MIMO modelling.

• GUI based for front end.

• Result generation & documentation.

• Future work

• Frequency domain parameter estimation using MATLAB®

• Development of end to end solution for RUAV identification using MATLAB®.

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Key Take Away

GUI based for front end