Bergamasco PhD thesis Defence

7/30/2019 Bergamasco PhD thesis Defence

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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

3

Translational velocities

Angular velocities

Attitude angles

Linear accelerometers

Aerodynamic angles

Longitudinal cyclic

Lateral cyclic

Collective

Pedal


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

4

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


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)


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


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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7

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


)(1

tl

)(0

tl

)(2

tl

)(3

tl

)(4

tl


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8

Matrices

transformation

Signals

projection

Continuous-time PBSID algorithmFrom continuous-time to discrete-time: system transformation


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


After some iterations, the data equation is obtained

in which the quantities contain input-output data

-

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



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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



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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



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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


The balanced realizations of Fs are interpolated


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14

Consider a dataset of Nelements

Model uncertainty estimation: bootstrap approach


Q d UAV


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Quadrotor UAVIntroduction

Experimental setup

Commercial UAV Equipped for outdoor flights

Sampling onboard at 100Hz

15


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


Approaches Output-Error

Unscented Kalman Filter

Q d t d li g


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Quadrotor modelingHover condition

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Stable modes Unstable modes

Experimental results


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Experimental resultsCollective and yaw models

18

Collective Yaw



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Experimental results 20


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Experimental resultsLongitudinal and lateral models: TD validation

20

Longitudinal Lateral


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


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


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


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

||

real-

est|

|

Black-boxmodel


1 2 3 4 5 6 7 8 9 10 11 120

0.005

0.01

0.015

0.02

0.025

0.03

||

real-

est|

|

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


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


Piecewise constant Orthogonal multisines

Cost function

27AW149 model identification


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27

AW149 simulator: nonlinear model with 55 state variables

12 datasets: 3 for each input channel (1 cross-validation, 2 identification)


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


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


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


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.


- -


Journal of Sound and Vibration, Volume 331, Issue 1, Jan 2012, pages 27 40.


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



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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.


[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.

Documents

Bergamasco PhD thesis Defence