bergamasco phd thesis defence
TRANSCRIPT
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Dottorato in ingegneria dellinformazione
XXV ciclo
Continuous-time model identification with
applications to rotorcraft dynamicsMarco Bergamasco
Advisor: Prof. Marco LoveraTutor: Prof. Patrizio Colaneri
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2Index
Motivation and objectives: rotorcraft model identification
Continuous-time predictor-based subspace identification algorithm
Recursive continuous-time predictor-based subspace identificationalgorithm
Continuous-time Linear Parameter Varying model identification
Continuous-time model identification with applications to rotorcraft dynamics
Model uncertainty estimation: bootstrap approach
Black-box to grey-box model transformation in the frequency-domain
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Rotorcraft model identificationMotivation
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Translational velocities
Angular velocities
Attitude angles
Linear accelerometers
Aerodynamic angles
Longitudinal cyclic
Lateral cyclic
Collective
Pedal
Continuous-time model identification with applications to rotorcraft dynamics
Most helicopters are characterized by an unstable behaviour
Helicopter control systems design needs accurate models
Intrinsic limitations in physical modelling call for full or partial resort to
empirical modelling increasing attention given to system identification
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Rotorcraft model identificationMain issues and objectives
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Main difficulties in rotorcraft model identification:
Intrinsically multivariable (MIMO) problem
High order dynamics
Most rotorcraft vehicles are open loop unstable
need for closed-loop identification techniques
Community wants continuous-time, physically parameterised models
Continuous-time model identification with applications to rotorcraft dynamics
need for continuous-time identification techniques Advanced control techniques require uncertainty information
need for model uncertainty estimation
Objectives:
Continuous-time identification algorithm able to deal with closed-loop
MIMO systems
Model uncertainty estimation
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In the system identification community Subspace Model Identificationwas proposed about 20 years ago to handle black-box MIMO problems
in a numerical stable way
SMI has proved extremely successful in a number of industrialapplications
Intensively studied for discrete-time models
5Subspace model identification (SMI)
Continuous-time model identification with applications to rotorcraft dynamics
Predictor Based Subspace IDentification algorithm (PBSID, Chiusoand Picci, 2005) is the present state-of-the-art in the field
Identification of continuous-time systems has been studied in a numberof contributions only for open-loop setting
Main downside: impossibility to impose a fixed basis to the state spacerepresentation, i.e., the identified models are unstructured
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6Continuous-time PBSID algorithmModel class, assumptions, approach
Consider the MIMO LTI continuous-time system
(in innovation form for simplicity) where
Assumptions
Continuous-time model identification with applications to rotorcraft dynamics
e ener process (A,B,C,D,K) such that (A,C) observable and (A,[B K]) controllable
system possibly operating in closed-loop
Convert the model to discrete-time via an exact signals-based method
Apply the discrete-time PBSID SMI algorithm
Retrieve the original continuous-time model, i.e., (A,B,C,D,K)
Approach
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The family of Laguerre basis is defined as
Denote with the impulse response of the i-th Laguerre basis
Definitions
Continuous-time PBSID algorithmFrom continuous-time to discrete-time: Laguerre basis
Continuous-time model identification with applications to rotorcraft dynamics
)(1
tl
)(0
tl
)(2
tl
)(3
tl
)(4
tl
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Matrices
transformation
Signals
projection
Continuous-time PBSID algorithmFrom continuous-time to discrete-time: system transformation
Continuous-time model identification with applications to rotorcraft dynamics
Discrete index k: basis order
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9Continuous-time PBSID algorithmPredictor-based subspace identification 1/2
The system is considered in prediction form and the state equation isiterated ptimes
Continuous-time model identification with applications to rotorcraft dynamics
After some iterations, the data equation is obtained
in which the quantities contain input-output data
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past data
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10Continuous-time PBSID algorithmPredictor-based subspace identification 2/2
The state space matrices can be recovered from the data equationusing Least Squares techniques
Finally, the continuous-time state space model matrices are obtained
using the inverse of the matrix transformation
Continuous-time model identification with applications to rotorcraft dynamics
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Implementation issues: the computation of the signals transformations
can be critical (storage) but allows to deal with non uniform sampling
The data equation is algebraic, so data from different experiments canbe merged in the identification procedure
11Continuous-time PBSID algorithmComments
Continuous-time model identification with applications to rotorcraft dynamics
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12Recursive continuous-time predictor-basedsubspace identification algorithm
Objective: update the model estimation at the arrival of a new input-output sample (online estimation)
The computation of the projections on a finite window can faced bymodifying the basis functions to have compact support
Signals projection
Continuous-time model identification with applications to rotorcraft dynamics
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13Continuous-time Linear Parameter Varying modelidentification
Consider a linear parameter varying model
with A, B, C, and Ddepend on measured parameters
Local approach:
Identification of N localmodels
Continuous-time model identification with applications to rotorcraft dynamics
The balanced realizations of Fs are interpolated
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Consider a dataset of Nelements
Model uncertainty estimation: bootstrap approach
Continuous-time model identification with applications to rotorcraft dynamics
Q d UAV
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Quadrotor UAVIntroduction
Experimental setup
Commercial UAV Equipped for outdoor flights
Sampling onboard at 100Hz
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Continuous-time model identification with applications to rotorcraft dynamics
u oma c exc a on
Attitude control (closed-loop)
YawLon/LatCollective
Q d t UAV
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Quadrotor UAVData consistency analysis
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Improve the data quality ensuring that the measured data are mutually
consistent, by enforcing kinematic constraints among measured
variables
Estimation of the instrumental errors: bias and scale factors
State equations Output equations
Continuous-time model identification with applications to rotorcraft dynamics
Approaches Output-Error
Unscented Kalman Filter
Q d t d li g
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Quadrotor modelingHover condition
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Continuous-time model identification with applications to rotorcraft dynamics
Stable modes Unstable modes
Experimental results
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Experimental resultsCollective and yaw models
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Collective Yaw
Continuous-time model identification with applications to rotorcraft dynamics
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Experimental results 20
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Experimental resultsLongitudinal and lateral models: TD validation
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Longitudinal Lateral
Continuous-time model identification with applications to rotorcraft dynamics
2121Rotorcraft model identification
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2121
The dynamics of a rotorcraft during steady flight (e.g., hover,forward flight)
Rotorcraft model identificationExample: control-oriented physical model
Continuous-time model identification with applications to rotorcraft dynamics
can be well described using a MIMO LTI continuous-time system
where the system matrices depend on unknown parameters (i.e.,physical parameters)
22Black-box to grey-box model transformation
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22Black-box to grey-box model transformationin the frequency-domain
Black-box identified model
Grey-box model structure
Continuous-time model identification with applications to rotorcraft dynamics
H
approach in frequency-domain
The estimation of the similarity transformation is not necessary
The non-smooth non-convex optimization problem can be solved using
some recent algorithms available in literature, see Apkarian & Noll 2006
23BO-105 Example Problem
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23BO 105 Example ProblemIntroduction
Continuous-time model identification with applications to rotorcraft dynamics
The BO-105 is a light, twin-engine, multi-purpose utility helicopter
Forward flight at 80 knots (unstable dynamics)
Nine-DOF simulator:
4 inputs
11 outputs
12 state variables
47 physical parameters
24BO-105 Example Problem
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24BO 105 Example ProblemResults: Eigenvalues estimation error
0.005
0.01
0.015
0.02
0.025
0.03
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real-
est|
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Black-boxmodel
Continuous-time model identification with applications to rotorcraft dynamics
1 2 3 4 5 6 7 8 9 10 11 120
0.005
0.01
0.015
0.02
0.025
0.03
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real-
est|
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1 2 3 4 5 6 7 8 9 10 11 12
Grey-boxmodel
25Collaboration with AWPARC/AgustaWestland
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25Collaboration with AWPARC/AgustaWestland
Research project between DEI(B) e AgustaWestland-PolitecnicoAdvanced Rotorcraft Center (AWPARC)
Experiment design for MIMO model identification, with application to
rotorcraft dynamics
Data consistency analysis
Continuous-time model identification with applications to rotorcraft dynamics
Model reduction (Principal Component Analysis)
Procedure for the data collection using the helicopter simulator of the
AgustaWestland
26Experiment design
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26pe e t des g
Input Design
Excite the dynamic system so that the data contain sufficient information
respecting the constraints
Continuous-time model identification with applications to rotorcraft dynamics
Piecewise constant Orthogonal multisines
Cost function
27AW149 model identification
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AW149 simulator: nonlinear model with 55 state variables
12 datasets: 3 for each input channel (1 cross-validation, 2 identification)
Continuous-time model identification with applications to rotorcraft dynamics
28Conclusions
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A novel algorithm to identify continuous-time models, based on asubspace identification method, has been proposed
Recursive implementation of the proposed approach has been studied
The extension for the estimation of continuous-time linear parametervarying models has been analysed
The model uncertaint estimation has been addressed usin a
Continuous-time model identification with applications to rotorcraft dynamics
bootstrap approach
The problem of the black-box to grey-box model transformation in the
frequency-domain has been faced
Simulation and real examples are taken into account to show theviability of the proposed approaches
29Thank you!
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y
Continuous-time model identification with applications to rotorcraft dynamics
3030Rotorcraft model identification
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Frequency-domain approaches Advantage: computationally fast (few data-points)
Advantage: deal with unstable system in a very natural way (phase signs)
Drawback: long and expensive experiments (frequency sweeps)
Iterative time-domain approaches (e.g., OE, EE, etc.)
Main issues and objectives
Continuous-time model identification with applications to rotorcraft dynamics
van age: s or er, c eaper, an sa er exper men s sequences
Drawback: computationally slow (a lot of data-points)
Drawback: some tricks are needed in order to deal with unstable system
NON-iterative time-domain approaches (e.g., subspace methods)
Advantage: computationally efficient and robust
Advantage: shorter, cheaper, and safer experiments (3211 sequences)
Drawback: no control on state space basis of identified models.
31Publications
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Journals
[J.1] L. Vigano', M. BERGAMASCO, M. Lovera, A. VargaOptimal periodic output feedback control: a continuous-time approach and a case studyInternational Journal of Control, Volume 83, Issue 5 May 2010 , pages 897 914.
[J.2] M. BERGAMASCO, M. Lovera
Continuous-time predictor-based subspace identification using Laguerre filtersIET Control Theory & Applications, Volume 5, Issue 7, May 2011, pages 856 867.
[J.3] M. BERGAMASCO, M. Lovera
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Continuous-time model identification with applications to rotorcraft dynamics
Journal of Sound and Vibration, Volume 331, Issue 1, Jan 2012, pages 27 40.
[J.4] M. BERGAMASCO, M. Lovera
Identification of linear models for the dynamics of a hovering quadrotorSubmitted, provisionally accepted.
[J.5] G. van der Veen, J.-W. van Wingerden, M. BERGAMASCO, M. Lovera, M. Verhaegen
Closed-loop subspace identification methods: an overview
Submitted, provisionally accepted.
32Publications
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Book chapters
[BC.1] M. BERGAMASCO, M. LoveraSubspace identification of continuous-time state-space LPV models
Linear parameter-varying system identification, World Scientific, 2011, pages 233-262
[BC.1] M. Lovera, M. BERGAMASCO, F. Casella
LPV modelling and identification: an overviewBook chapter - In press
Continuous-time model identification with applications to rotorcraft dynamics
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34PublicationsI i l f 2 2
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International conferences 2/2
[C.8] M. Sguanci, M. BERGAMASCO, M. Lovera
Continuous-time model identification for rotorcraft dynamics
16th IFAC Symposium on System Identification, Brussels, Belgium, 2012.
[C.9] F. Della Rossa, M. BERGAMASCO, M. Lovera
Bifurcation analysis of the attitude dynamics for a magnetically controlled spacecraft
51th IEEE Conference on Decision and Control, Maui, U.S., 2012.
[C.10] M. BERGAMASCO, M. Lovera
State space model identification: from unstructured to structured models with an Hinf approach
Joint 2013 IFAC SSSC, TDS, FDA Conference, Grenoble, France, 2013.
Continuous-time model identification with applications to rotorcraft dynamics
[C.11] M. BERGAMASCO, M. LoveraRotorcraft system identification: an integrated time-frequency domain approach
2nd CEAS Specialist Conference on Guidance, Navigation & Control, Delft, Netherlands, 2013.
[C.12] M. BERGAMASCO, M. Lovera
Spacecraft Attitude Control based on Magnetometers and Gyros
2nd CEAS Specialist Conference on Guidance, Navigation & Control, Delft, Netherlands, 2013.
[C.13] M. BERGAMASCO, F. Della Rossa, L. Piroddi
Active noise control of impulsive noise with selective outlier elimination
2013 American Control Conference , Washington, U.S., 2013.