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3. Departmentof Applied Computers Systems and Communication Technologies BACHELOR'SPROGRAMMES • Computer systems and networks • Applied Informatics • Telecommunications 3

4. MASTERS PROGRAMS • Software technologies • Computer networks • Applied Informatics • Mobile communications • High-performance systems andtechnologies • Intelligent Systems (Robotics)

5. Lab 808 “Intelligent Systems & Robotics” Laboratoryequipment and environment for simulation and experimental demonstration of the control algorithms

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7. Main objectives • Duo-copter modeling • Derive the model based on theoretical principles and using a robotics approach. • Gain physical insight on the major effects governing helicopter behavior. • Provide a simple yet accurate helicopter model. • Path following controller design • Develop a controller based on a integrated guidance and control strategy.

8. Wide and valuable range of applications. Relevant research challenges, combining multiple fields of knowledge. Availability of increasingly accurate, reliable and miniaturized sensors. Motivations Autonomous vehicles

9. High maneuvering capabilities: Vertical flight trajectories (VTOL) and hovering High degrees of lateral and longitudinal motion control. Strongly coupled and naturally unstable nonlinear dynamic system. Motivations Autonomous duo-copter

10. Potential Applications • Types of applications • Operation problems in hostile environments or unreachable locations. • Precise or repetitive tasks. • Examples: • Topographical and geological surveying. • Volcano or forest fire surveillance missions. • Traffic and air pollution monitoring. • Cost-effective spraying of crops.

11. Topics • Mathematical modeling of a duo-copter • 6 DoF rigid body dynamics. • Main rotor: rotary-wing dynamics and aerodynamics. • Other components: fuselage, horizontal tailplane, vertical fin. • Path following controller design • Error space definition. • Gain-scheduled control theory.

12. Helicopter model description {U}- inertial frame {CM}- body-fixed frame

13. Rigid Body Dynamics • Equations of motion • where

14. Helicopter configuration

15. Main forces and moments side view top view

16. Main rotor - General description • Primary source of lift, propulsion and control. • Working principle: • Blade rotation on air generates aerodynamic lift (and drag) forces. • Variation of blade pitch angle is used to control these loads. • Opposite reaction to the lift force: the induced downwash (conservation of momentum)

17. Rotor blade motions: Rotation

18. Blade pitching - rotor control system Main rotor control variables Blade tip Blade root

19. Swash plate • Mechanical device used to transmit control inputs to the rotating blades.

20. Blade motions: flap and lag Flap angle β(ψ) Lag angle ζ(ψ)

21. Rotor aerodynamics • Momentum theory • Global theory based on the conservation laws of fluid dynamics. • Estimates the thrust generated by a propeller or rotor. • 2D airfoil theory • Applied to blade section elements. • Estimates local lift and drag as functions of local flow velocity and incidence.

22. Momentum theory • Hover • Vertical climb

23. Momentum theory (2) • Other flight regimes

24. Blade aerodynamics Lift Drag

25. Blade dynamics • Adopted model • Rigid blade, with centre hinge spring. • Flapping moment equilibrium

26. Blade dynamics (2) • Flapping moment equilibrium Flapping frequency ratio Lock number

27. Blade dynamics (3) • Derivation method • reference frames: {cm}, {hub}, {hw}, {b}, {bf}

28. Rotor dynamics • , vector of flapping angles for nb-bladed rotor. • Rotor flapping dynamics: • Transformation from Individual to Multi-blade coordinates (MBC), • Benefit: eliminate first order harmonics.

29. Multi-blade coordinates • Multi-blade coordinates Coning mode

30. Multi-blade coordinates (2) Longitudinal cyclic mode Lateral cyclic mode

31. Multi-blade coordinates (3) • Steady-state solution • MBC • IBC • Flapping modes

32. Forces Moments Main rotor forces and moments

33. Outputs Inputs State Main rotor block diagram

34. Tail rotor

35. Fuselage

36. Horizontal tail plane Vertical fin Empennage

37. Model assembly

38. Path following controller design • Problem: steer the helicopter, at fixed speed, along trimming paths defined in an inertial frame. • Path following strategy: • System equations are expressed in a generalized error space. • Problem is transformed into that of driving the error vector to zero.

39. Path following controller design Sequence of steps: i) selection of a set of relevant trimming paths, ii) linearization of the model about the selected trimming paths, iii) design of a linear path following controller for each linear model, iv) implementation of the resultant non-linear path following controller using the gain scheduling technique.

40. Simulation results

41. Simulation results Simulation beginning, 3D view with orientation

42. Simulation results Time evolution of blade pitch commands

43. Conclusions Main contributions: • Development of a dynamic helicopter model suitable for control purposes. • Establish a sound theoretical basis for control system design. • Design and implementation of a path following controller • Application of an integrated guidance and control strategy to the case of helicopters.

44. Directions for future work • Analysis of the developed model: • Trimming, stability, and response. • Model validation and identification from real data. • Redesign of path following controller: • Accommodate all trimming paths. • Include main rotor dynamics. • Address the problem in other frameworks.

45. Thank you for your attention and the patience ! 45