Multi-degree-of-freedom systems AAE 556 Aeroelasticity Multi-degree-of-freedom systems With feedback control AAE556 – Spring 2008 - 8

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 AAE556 – Spring 2008 - 8

Use the 2 DOF aeroelastic wing model add control surfaces Torsional springs wing tip wing root degrees of freedom AAE556 – Spring 2008 - 8

Add an aileron to outboard panel 2 added aileron AAE556 – Spring 2008 - 8

Static equilibrium - an end view aileron deflection adds lift and pitching (torsional) moment AAE556 – Spring 2008 - 8

Estimators for aileron aero co-efficients CLd and CMACd Define the flap-to-chord length ratio as E Limiting cases? AAE556 – Spring 2008 - 8

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 AAE556 – Spring 2008 - 8

Changes in lift and pitching moment on outboard panel 2 aileron AAE556 – Spring 2008 - 8

A closer look – the full equation set Aileron input AAE556 – Spring 2008 - 8

Applied torsional loads - math expressions Divide load matrix by KT so that AAE556 – Spring 2008 - 8

Gather together the terms in the loads matrix AAE556 – Spring 2008 - 8

Final equation set outputs inputs AAE556 – Spring 2008 - 8

Divergence condition We have applied an aileron deflection Nothing about divergence has changed - why? AAE556 – Spring 2008 - 8

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 AAE556 – Spring 2008 - 8

What difference does this make? This term is out of place. How did it get here again? It belongs over here with these guys. AAE556 – Spring 2008 - 8

Get the aileron control moment into the “correct” form notice the minus sign AAE556 – Spring 2008 - 8

Reduce the equations to nondimensional form The term G1 is called k in the notes, page 78 AAE556 – Spring 2008 - 8

Has the Divergence dynamic pressure changed? Compute the Determinant Why?? AAE556 – Spring 2008 - 8

Expand the stability determinant Polynomial 2nd order AAE556 – Spring 2008 - 8

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 AAE556 – Spring 2008 - 8

A closer look at the first crossing point Negative aileron action, load reduction AAE556 – Spring 2008 - 8

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 AAE556 – Spring 2008 - 8