1. POLI di MI tecnicolano Numerical Simulation of Aero-Servo-Elastic Problems, with Application to Wind Turbines and Rotary Wing Vehicles Carlo L. Bottasso Politecnico di Milano COMPDYN 2007 Rethymno, Crete, Greece, June 13-15, 2007

2. Aero-Servo-Elasticity of Rotorcraft POLITECNICO di MILANO DIA Acknowledgements Work in collaboration with: A. Croce, D. Leonello, L. Riviello, B. Savini; Work supported by: AgustaWestland, US Army Research Office, Leitner S.p.A.

3. Aero-Servo-Elasticity of Rotorcraft POLITECNICO di MILANO DIA Outline 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.

4. Aero-Servo-Elasticity of Rotorcraft POLITECNICO di MILANO DIA Multidisciplinary FEM Multibody Modeling finite element multibody Rotorcraft aeroelastic model: finite element multibody code (Bauchau & Bottasso 2001). arbitrarily complexnon-linearly stable Highlights: arbitrarily complex topologies, non-linearly stable 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.

5. Aero-Servo-Elasticity of Rotorcraft POLITECNICO di MILANO DIA Multidisciplinary FEM Multibody Modeling

6. Aero-Servo-Elasticity of Rotorcraft POLITECNICO di MILANO DIA Some Trends and Needs active controls Integration of complex multi-physics models with active controls (e.g., add virtual pilots to vehicle models, systematically explore operational envelope boundaries, etc.); Model reduction Model reduction (e.g., for model-based control); Model identification Model identification from experimental data; Real-time Real-time performance (e.g., for pilot-in-the-loop applications).

7. Aero-Servo-Elasticity of Rotorcraft POLITECNICO di MILANO DIA Three challenging applications : Simulation of maneuvers (Maneuvering Multibody Dynamics, MMBD); Finding periodic solutions (“trimming”); Control of wind turbine generators. Active Control of Complex Aero-Servo-Elastic Models

8. Aero-Servo-Elasticity of Rotorcraft POLITECNICO di MILANO DIA Limiting factors maneuvering regime Limiting factors (maximum loads, vibrations, noise, etc.) are experienced in the maneuvering regime and at the performance envelope boundaries. impossible to guess the controls complexlong durationwithin the performance envelope boundaries It is virtually impossible to guess the controls that will produce a complex maneuver of long duration, guaranteeing to stay within the performance envelope boundaries. Maneuvering Multibody Dynamics TDP Example Example: Cat-A continued take-off. Two model predictive problemsplanningtracking Two model predictive problems: trajectory planning & tracking.

9. Aero-Servo-Elasticity of Rotorcraft POLITECNICO di MILANO DIA Maneuvering Multibody Dynamics

10. Aero-Servo-Elasticity of Rotorcraft POLITECNICO di MILANO DIA Example: Cat-A Continued TO

11. Aero-Servo-Elasticity of Rotorcraft POLITECNICO di MILANO DIA MMBD: Model Predictive Planning & Tracking 1. Maneuver planning problem (reduced model) Reference trajectory 2. 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 cost Prediction window Steering window Prediction error 5. Re-plan with updated reduced model Updated reference trajectory Reference trajectory comprehensive model update Fly the comprehensive model along the reference trajectory and, at the same time, update the reduced model (learning).

12. Aero-Servo-Elasticity of Rotorcraft POLITECNICO di MILANO DIA Three challenging applications : Simulation of maneuvers (Maneuvering Multibody Dynamics, MMBD); Finding periodic solutions (“trimming”); Finding periodic solutions (“trimming”); Control of wind turbine generators. Active Control of Complex Aero-Servo-Elastic Models

13. Aero-Servo-Elasticity of Rotorcraft POLITECNICO di MILANO DIA Procedure Procedure: Given Given desired loads or velocities specifying the desired condition, Find Find resulting attitude and constant-in-time controls. Trimming Trim: steady Trim: control settings, attitude and cargo disposition for a desired steady (flight) condition. strongly Performance, loads, noise, handling qualities, stability, etc. depend strongly on the trim condition. Important remark: Rotorcraft systems excited by harmonic external loads; Periodic response Periodic response of all states and loads at trim. TRIM PROBLEM

14. Aero-Servo-Elasticity of Rotorcraft POLITECNICO di MILANO DIA Formulation of Rotorcraft Trim Problem system outputs Define system outputs (problem dependent): Wind tunnel trim: components of rotor loads in fixed system; Free flight: capture gross vehicle motion. 1.Trim constraints 1.Trim constraints: where are desired values for the outputs; 2.Trim conditions 2.Trim conditions: 3.Periodicity conditions 3.Periodicity conditions: (See Peters & Barwey 1996) y ¤ e y = y ¤ ; 8 t ; _ e u = 0 ; 8 t ; e x ( t + T ) = e x ( t ) + e z ; 8 t : e y = 1 T Z t + T t e g ( e x ; e u ) d t ;

15. Aero-Servo-Elasticity of Rotorcraft POLITECNICO di MILANO DIA Model Predictive Trimming Procedure Procedure: Predict non-linear reduced model Predict system response using a non-linear reduced model; steer Compute controls to steer the system for a short time horizon; Update Update reduced model based on predicted-actual output errors; Iterate Iterate, shifting prediction forward (receding horizon control).

16. Aero-Servo-Elasticity of Rotorcraft POLITECNICO di MILANO DIA Three challenging applications : Simulation of maneuvers (Maneuvering Multibody Dynamics, MMBD); Finding periodic solutions (“trimming”); Control of wind turbine generators. Control of wind turbine generators. Active Control of Complex Aero-Servo-Elastic Models

17. Aero-Servo-Elasticity of Rotorcraft POLITECNICO di MILANO DIA Control of Wind Turbine Generators Goals: wind turbulencegusts Regulate wind turbine by adjusting blade pitch (and possibly generator torque) to react against wind turbulence and gusts. fatigue damagepower output Minimize fatigue damage and maximize power output.

18. Aero-Servo-Elasticity of Rotorcraft POLITECNICO di MILANO DIA Reduced model Reduced model: few dofs, captures gross to-be-controlled response. Comprehensive multibody- based model Comprehensive multibody- based model: many dofs, captures fine scale solution details. Reduced Model Identification System Identification This procedure is common to all three previous problems.

19. Aero-Servo-Elasticity of Rotorcraft POLITECNICO di MILANO DIA Goal Goal: reduced modelpredicting the behavior of the plant Develop reduced model capable of predicting the behavior of the plant with minimum error (same outputs when subjected to same inputs); self-adaptive Reduced model must be self-adaptive (capable of learning) to adjust to varying operating conditions, and to react to disturbances. Predictive solutions Prediction (tracking) window Steering window Prediction error to be minimized Reduced Model Identification

20. Aero-Servo-Elasticity of Rotorcraft POLITECNICO di MILANO DIA Reduced Model Identification Comprehensive (multibody based) governing equations: where are the states, the controls, the Lagrange multipliers. capture the to-be-controlled outputs Define outputs that capture the to-be-controlled outputs: reduced parametric Find reduced parametric model such that when i.e. captures the gross motion the reduced model captures the gross motion of the comprehensive one (plant). e u e x e ¸ e y = e h ( e x ) : e f ( _ e x ; e x ; e ¸ ; e u ) = 0 ; e c ( _ e x ; e x ) = 0 ; f ( _ y ; y ; u ; p ) = 0 ; e y e y ¼ y e u = u,

21. Aero-Servo-Elasticity of Rotorcraft POLITECNICO di MILANO DIA Reduced Model Formulation Neural augmented reference model Neural augmented reference model: Reference (problem dependent) analytical model Reference (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 re f ( _ y ; y ; u ) = 0 ; yuyu

22. Aero-Servo-Elasticity of Rotorcraft POLITECNICO di MILANO DIA Reduced Model Formulation Remarknotadequate Remark: reference model will not, in general, ensure adequate predictions, i.e. when Augmented reference model unknowndefect where is the unknown reference model defect that ensures when if we knewperfect prediction Hence, if we knew, we would have perfect prediction capabilities. d f re f ( _ y ; y ; u ) = d ( y ( n ) ;:::; y ; u ) ; e u = u. e u = u. e y 6 = y e y = y d

23. Aero-Servo-Elasticity of Rotorcraft POLITECNICO di MILANO DIA Reduced Model Formulation Approach Approach: parametric function - Approximate the unknown defect using a parametric function (neural network); Adjust - Adjust the function parameters to ensure good approximation of the defect (hence, good predictions). Reasons for using a reference model Reasons for using a reference model: even before any learning - Reasonable predictions even before any learning has taken place (otherwise would need extensive pre-training); small quantity - Easier and faster adaption: the defect is typically a small quantity, if the reference model is well chosen.

24. Aero-Servo-Elasticity of Rotorcraft POLITECNICO di MILANO DIA Results Rotorcraft maneuver problem: pitch rate for multibody, reference, and neural-augmented reference with same prescribed inputs. Short transient = fast adaption Black: multibody model Red: reference model Blue: reference model +neural network Good prediction, even for changing flight condition Good prediction, even for changing flight condition.

25. Aero-Servo-Elasticity of Rotorcraft POLITECNICO di MILANO DIA Results Rotorcraft trim problem: rotor thrust for multibody, reference, and neural-augmented reference with same prescribed inputs. Black: multibody model Red: reference model Blue: reference model +neural network

26. Aero-Servo-Elasticity of Rotorcraft POLITECNICO di MILANO DIA Results Rotorcraft trim problem: defect and remaining reconstruction error after adaption. d i " i Red: defect Blue: remaining reconstruction error

27. Aero-Servo-Elasticity of Rotorcraft POLITECNICO di MILANO DIA Results Wind turbine control problem: tower-tip velocity for multibody, reference, and neural-augmented reference with same prescribed inputs. Black: multibody model Red: reference model Blue: reference model +neural network Fast adaption Good prediction, even with turbulent wind Good prediction, even with turbulent wind.

28. Aero-Servo-Elasticity of Rotorcraft POLITECNICO di MILANO DIA Results Wind turbine control problem: defect and remaining reconstruction error after adaption. d i " i Red: defect Blue: remaining reconstruction error

29. Aero-Servo-Elasticity of Rotorcraft POLITECNICO di MILANO DIA Optimal Control Problem Optimal Control Problem (with unknown internal event at T 1 ) Cost function: Constraints and bounds: - Initial trimmed conditions at 30 m/s - Power limitations Application: Rotorcraft Minimum Time Obstacle Avoidance

30. Aero-Servo-Elasticity of Rotorcraft POLITECNICO di MILANO DIA Minimum Time Obstacle Avoidance

31. Aero-Servo-Elasticity of Rotorcraft POLITECNICO di MILANO DIA Minimum Time Obstacle Avoidance Trajectories at 1 st iteration Trajectories at 4 th iteration Effect of reduced model adaption: Red: tracked trajectory Blue: planned trajectory

32. Aero-Servo-Elasticity of Rotorcraft POLITECNICO di MILANO DIA Minimum Time Obstacle Avoidance Pitch vs. time at 1 st iteration Pitch vs. time at 4 th iteration Effect of reduced model adaption: Red: tracked trajectory Blue: planned trajectory

33. Aero-Servo-Elasticity of Rotorcraft POLITECNICO di MILANO DIA Conclusions Observations: aero-servo-elasticityflight mechanics Computational procedures now blend traditionally separate disciplines, e.g. aero-servo-elasticity with flight mechanics; so complex experimental data Mathematical models of vehicles are becoming so complex that there is a trend to use methods for analyzing experimental data (e.g. stability analysis, system identification, etc.); Outlook: These trends will continue (virtual lab); Real-time simulation; Human behavior models.