POLI di MI tecnicolano Numerical Simulation of Aero-Servo-Elastic Problems, with Application to Wind...

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Itecn

ico

tecn

ico

lano

lanoNumerical Simulation of

Aero-Servo-Elastic Problems, with Application to Wind Turbines and

Rotary Wing Vehicles

Carlo L. BottassoPolitecnico di Milano

COMPDYN 2007 Rethymno, Crete, Greece, June 13-15, 2007

Numerical Simulation of Aero-Servo-Elastic Problems, with Application to Wind Turbines and

Rotary Wing Vehicles

Carlo L. BottassoPolitecnico di Milano

COMPDYN 2007 Rethymno, Crete, Greece, June 13-15, 2007

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POLITECNICO di MILANO DIA

AcknowledgementsAcknowledgements

Work in collaboration with:

A. Croce, D. Leonello, L. Riviello, B. Savini;

Work supported by:

AgustaWestland, US Army Research Office, Leitner S.p.A.

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OutlineOutline

• Multidisciplinary FEM-based multibody modeling;

• Active control of complex aero-servo-elastic models: three challenging applications;

• Adaptive identification of reduced models;

• Examples;

• Conclusions and outlook.

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Multidisciplinary FEM Multibody Modeling


Rotorcraft aeroelastic model: finite element multibodyfinite element multibody code (Bauchau & Bottasso 2001).

Highlights: arbitrarily complexarbitrarily complex topologies, non-linearly non-linearly stablestable energy decaying schemes.

Aerodynamic models: lifting lines; inflow models (Pitt-Peters, Peters-He); free-wake; CFD.

Other models: controllers; actuators (hydraulic, engine, etc.); sensors; unilateral contact.

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Some Trends and NeedsSome Trends and Needs

• Integration of complex multi-physics models with active active controlscontrols (e.g., add virtual pilots to vehicle models, systematically explore operational envelope boundaries, etc.);

• Model reductionModel reduction (e.g., for model-based control);

• Model identificationModel identification from experimental data;

• Real-timeReal-time performance (e.g., for pilot-in-the-loop applications).

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Three challenging applications :

• Simulation of maneuvers (Maneuvering Multibody Simulation of maneuvers (Maneuvering Multibody Dynamics, MMBD);Dynamics, MMBD);

• Finding periodic solutions (“trimming”);

• Control of wind turbine generators.

Active Control of Complex Aero-Servo-Elastic ModelsActive Control of Complex Aero-Servo-Elastic Models

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• Limiting factorsLimiting factors (maximum loads, vibrations, noise, etc.) are experienced in the maneuvering regimemaneuvering regime and at the performance envelope boundaries.

• It is virtually impossible to guess the controlsimpossible to guess the controls that will produce a complexcomplex maneuver of long durationlong duration, guaranteeing to stay within the performance envelope boundarieswithin the performance envelope boundaries.

Maneuvering Multibody DynamicsManeuvering Multibody Dynamics

TDP

ExampleExample: Cat-A continued take-off.

Two model predictive problemsTwo model predictive problems: trajectory planningplanning & trackingtracking.

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Maneuvering Multibody DynamicsManeuvering Multibody Dynamics

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Example: Cat-A Continued TOExample: Cat-A Continued TO

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MMBD: Model Predictive Planning & Tracking

MMBD: Model Predictive Planning & Tracking

1. Maneuver planning problem (reduced model)

Reference trajectory2. Tracking

problem (reduced model)

Trajectory flown by comprehensive model

4. Reduced model update

Predictive solutions

3. Steering problem (comprehensive model)

Prediction window

Steering window

Tracking cost

Prediction error

Prediction window

Tracking cost

Steering window

Prediction error

Tracking costPrediction window

Steering window

Prediction error

5. Re-plan with updated reduced model

Updated reference trajectory

Reference trajectory

Fly the comprehensive modelcomprehensive model along the reference trajectory and, at the same time, updateupdate the reduced model (learning).

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• Simulation of maneuvers (Maneuvering Multibody Dynamics, MMBD);

• Finding periodic solutions (“trimming”);Finding periodic solutions (“trimming”);

• Control of wind turbine generators.


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ProcedureProcedure:

• GivenGiven desired loads or velocities specifying the desired condition,

• FindFind resulting attitude and constant-in-time controls.

TrimmingTrimming

Trim:Trim: control settings, attitude and cargo disposition for a desired steadysteady (flight) condition.

Performance, loads, noise, handling qualities, stability, etc. depend stronglystrongly on the trim condition.

Important remark: Important remark:

• Rotorcraft systems excited by harmonic external loads;

• Periodic response Periodic response of all states and loads at trim.

TRIM TRIM PROBLEPROBLE

MM

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Formulation of Rotorcraft Trim Problem

Formulation of Rotorcraft Trim Problem

Define system outputssystem outputs (problem dependent):

• Wind tunnel trim: components of rotor loads in fixed system;

• Free flight: capture gross vehicle motion.

1.1. Trim constraintsTrim constraints:

where are desired values for the outputs;

2.2. Trim conditionsTrim conditions:

3.3. Periodicity conditionsPeriodicity conditions:

(See Peters & Barwey 1996)

y¤

ey = y¤; 8t;

_eu = 0; 8t;

ex(t + T) = ex(t) + ez; 8t:

ey =1T

Z t+T

teg(ex; eu)dt;

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Model Predictive TrimmingModel Predictive TrimmingProcedureProcedure:

• PredictPredict system response using a non-linear reduced modelnon-linear reduced model;

• Compute controls to steersteer the system for a short time horizon;

• UpdateUpdate reduced model based on predicted-actual output errors;

• IterateIterate, shifting prediction forward (receding horizon control).

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• Simulation of maneuvers (Maneuvering Multibody Dynamics, MMBD);

• Finding periodic solutions (“trimming”);

• Control of wind turbine generators.Control of wind turbine generators.


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Control of Wind Turbine GeneratorsControl of Wind Turbine Generators

Target value

Predicted output

Actual output

Projected controls u

d du/ t=0

Past Future

t

t+T Prediction horizonp

t+T Steering windows

t+T Control horizonc

Goals: Goals:

• Regulate wind turbine by adjusting blade pitch (and possibly generator torque) to react against wind turbulencewind turbulence and gustsgusts.

• Minimize fatigue damagefatigue damage and maximize power outputpower output.

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Reduced modelReduced model: few dofs, captures gross to-be-controlled response.

Comprehensive Comprehensive multibody-based modelmultibody-based model: many dofs, captures fine scale solution details.

Reduced Model IdentificationReduced Model Identification

System

System

Identifica

tio

Identifica

tio

nn

This procedure is common This procedure is common to all three previous to all three previous problems.problems.

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GoalGoal:

• Develop reduced modelreduced model capable of predicting the behavior predicting the behavior of the plantof the plant with minimum error (same outputs when subjected to same inputs);

• Reduced model must be self-adaptiveself-adaptive (capable of learning) to adjust to varying operating conditions, and to react to disturbances.

Predictive solutions

Prediction (tracking) window

Steering window

Prediction Prediction error to be error to be minimizedminimized


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Comprehensive (multibody based) governing equations:

where are the states, the controls, the Lagrange multipliers.

• Define outputs that capture the to-be-controlled capture the to-be-controlled outputsoutputs:

• Find reduced parametricreduced parametric model

such that when

i.e.

the reduced model captures the gross motioncaptures the gross motion of the comprehensive one (plant).

euex e

ey = eh(ex):

ef ( _ex; ex; e; eu) = 0;

ec( _ex; ex) = 0;

f ( _y;y;u;p) = 0;

ey

ey ¼y eu = u,

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Reduced Model FormulationReduced Model Formulation

Neural augmented reference modelNeural augmented reference model:

• Reference (problem dependent) analytical modelReference (problem dependent) analytical model:

For example, in this work:

- Rotorcraft problems: 2D rigid body model, actuator-disk rotor (blade element theory + uniform inflow).

= CG position & velocity, pitch & pitch rate, rotor speed;

= main & tail rotor collective, lateral & longitudinal cyclics, available power.

- Wind turbine problems: actuator-disk rotor + springs to model tower flexibility.

= rotor speed, tower tip position & velocity;

= blade pitch, generator torque.

f ref( _y;y;u) = 0;

y

u

y

u

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RemarkRemark: reference model will notnot, in general, ensure adequateadequate predictions, i.e.

when

Augmented reference modelAugmented reference model

where is the unknownunknown reference model defectdefect that ensures

when

Hence, if we knewif we knew , we would have perfect predictionperfect prediction capabilities.

d

f ref( _y;y;u) = d(y(n); : : : ;y;u);

eu = u.

eu = u.ey 6= y

ey = y

d

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ApproachApproach:

- Approximate the unknown defect using a parametric parametric functionfunction (neural network);

- AdjustAdjust the function parameters to ensure good approximation of the defect (hence, good predictions).

Reasons for using a reference modelReasons for using a reference model:

- Reasonable predictions even before any learningeven before any learning has taken place (otherwise would need extensive pre-training);

- Easier and faster adaption: the defect is typically a small quantitysmall quantity, if the reference model is well chosen.

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ResultsResultsRotorcraft maneuver problem: pitch rate for multibody, reference, and neural-augmented reference with same prescribed inputs.

Short Short transient = transient =

fast adaptionfast adaption

Black: multibody model

Red: reference model

Blue: reference model +neural network

Good prediction, even Good prediction, even for changing flight for changing flight conditioncondition.

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ResultsResultsRotorcraft trim problem: rotor thrust for multibody, reference, and neural-augmented reference with same prescribed inputs.




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ResultsResultsRotorcraft trim problem: defect and remaining reconstruction error after adaption.

di"i

Red: defect

Blue: remaining reconstruction error

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ResultsResultsWind turbine control problem: tower-tip velocity for multibody, reference, and neural-augmented reference with same prescribed inputs.




Fast adaptionFast adaption

Good prediction, even Good prediction, even with turbulent windwith turbulent wind.

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ResultsResultsWind turbine control problem: defect and remaining reconstruction error after adaption.

di"i

Red: defect

Blue: remaining reconstruction error

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Optimal Control ProblemOptimal Control Problem (with unknown internal event at T1)

• Cost function:

• Constraints and bounds:

- Initial trimmed conditions at 30 m/s

- Power limitations

Application: Rotorcraft Minimum Time Obstacle Avoidance

Application: Rotorcraft Minimum Time Obstacle Avoidance

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Minimum Time Obstacle AvoidanceMinimum Time Obstacle Avoidance

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Trajectories at 1st iteration

Trajectories at 4th iteration

Effect of reduced model adaption:

Red: tracked trajectory

Blue: planned trajectory

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Pitch vs. time at 1st iteration

Pitch vs. time at 4th iteration

Effect of reduced model adaption:

Red: tracked trajectory

Blue: planned trajectory

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ConclusionsConclusions

Observations:

• Computational procedures now blend traditionally separate disciplines, e.g. aero-servo-elasticityaero-servo-elasticity with flight flight mechanicsmechanics;

• Mathematical models of vehicles are becoming so so complexcomplex that there is a trend to use methods for analyzing experimental dataexperimental data (e.g. stability analysis, system identification, etc.);

Outlook:

• These trends will continue (virtual lab);

• Real-time simulation;

• Human behavior models.

POLI di MI tecnicolano Numerical Simulation of Aero-Servo-Elastic Problems, with Application to Wind...

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Transcript of POLI di MI tecnicolano Numerical Simulation of Aero-Servo-Elastic Problems, with Application to Wind...