1. AAE 556 Aeroelasticity Lecture 8
Multi-degree-of-freedom systems
with feedback control
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2. Purdue Aeroelasticity
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 – Section 2.21
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3. Purdue Aeroelasticity
Add an aileron surface to outboard panel 2 of previous example in Section 2.14
added aileron
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4. Purdue Aeroelasticity
Static equilibrium equations change aileron deflection adds lift and pitching (torsional) moment
The end view, looking inboard
How do lift and pitching moment depend on aileron movement?
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5. Review - The flap-to-chord ratio determines the aileron aero derivative values
Big letter, little letter? What’s the diff?
All-movable section
Nose-down pitch
center of pressure behind ¼ chord
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6. Purdue Aeroelasticity
Compute changes in lift and pitching moment on outboard panel 2 aileron due to aileron deflection
about aero ¼ chord of panel 2
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7. Purdue Aeroelasticity
Write equilibrium equations in matrix form Two aileron torque terms are added
Aileron input
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8. Purdue Aeroelasticity
Three applied aero torsion loads Nondimensionalize to identify aeroelastic terms
Divide load matrix terms by KT
so that
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9. Combine the aileron load terms
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10. The final equilibrium equation set
outputs
inputs
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11. Purdue Aeroelasticity
The divergence condition still comes from the determinant of the aeroelastic stiffness matrix on the left hand side
We have applied an aileron deflection
Nothing about divergence has changed - why?
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12. Feedback control laws what are they?
Nature already has designed 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 between aileron deflection on the outer panel and twist of the inner panel
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13. What difference does this make? Look at the equilibrium equations
This term is out of place.
How did it get here?
The aileron term belongs over here with these guys.
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14. Get the aileron control vector into the “correct” form
notice the minus sign
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15. Reduce the equations to nondimensional form
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16. The divergence dynamic pressure has changed
Compute the Determinant
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17. Expand the stability determinant
Polynomial
2nd order
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18. Purdue Aeroelasticity
Plot the Stability Determinant vs. dynamic pressure parameter for different k (=G) values
Crossing points are different
Positive values of k mean that the aileron increases load in response to positive q
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19. A close look at the first crossing point
Negative aileron action, load reduction D
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20. Purdue Aeroelasticity
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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21. Homework for next Friday?
Five problems handed out in class and posted on-line
Watch for updates
Helpful hints for maximizing points
FBD’s
Definitions
Stability is a perturbation event
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