1. Multi-degree-of-freedom systems
AAE 556 Aeroelasticity
Multi-degree-of-freedom systems
With feedback control
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2. Goals
Demonstrate how to increase divergence q of MDOF systems by adding a feedback control loop
Define stability conditions for controlled MDOF systems
Reading - Multi-degree-of-freedom systems - TAW p.76-85
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3. Use the 2 DOF aeroelastic wing model add control surfaces
Torsional springs
wing tip
wing root
degrees of freedom
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4. Add an aileron to outboard panel 2
added aileron
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5. Static equilibrium - an end view aileron deflection adds lift and pitching (torsional) moment
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6. Estimators for aileron aero co-efficients CLd and CMACd
Define the flap-to-chord length ratio as E
Limiting cases?
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7. Big letter, little letter?
The flap-to-chord ratio determines the value of aileron aero derivatives
Big letter, little letter?
All-movable section
Nose-down pitch
center of pressure behind ¼ chord
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8. Changes in lift and pitching moment on outboard panel 2 aileron
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9. A closer look – the full equation set
Aileron input
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10. Applied torsional loads - math expressions
Divide load matrix by KT
so that
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11. Gather together the terms in the loads matrix
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12. Final equation set
outputs
inputs
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13. Divergence condition We have applied an aileron deflection
Nothing about divergence has changed - why?
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14. A feedback control law what is it?
Nature already has a feedback relationship between aerodynamic loads and structural deflection - that is why part of the aero load is on the left-hand side of the equilibrium equation
Let’s put in an artificial feedback relationship of our choosing
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15. What difference does this make?
This term is out of place.
How did it get here again?
It belongs over here with these guys.
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16. Get the aileron control moment into the “correct” form
notice the minus sign
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17. Reduce the equations to nondimensional form
The term G1 is called k in the notes, page 78
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18. Has the Divergence dynamic pressure changed?
Compute the Determinant
Why??
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19. Expand the stability determinant
Polynomial
2nd order
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20. Crossing points are different
Plot the Stability Determinant vs. dynamic pressure parameter for different values of G1
Crossing points are different
Positive values of G1 mean that the aileron increases load in response to positive q
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21. A closer look at the first crossing point
Negative aileron action, load reduction
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22. Summary
When a control surface is added, its deflection creates just another load - unless…
the control surface deflection responds to surface deflection – using a control law that we choose.
A feedback control law changes Mother Nature’s aeroelastic feedback process and the divergence dynamic pressure changes
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