AAE 556 Aeroelasticity Lecture 8 Multi-degree-of-freedom systems with feedback control Purdue Aeroelasticity

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 Purdue Aeroelasticity

Purdue Aeroelasticity Add an aileron surface to outboard panel 2 of previous example in Section 2.14 added aileron Purdue Aeroelasticity

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? Purdue Aeroelasticity

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 Purdue Aeroelasticity

Purdue Aeroelasticity Compute changes in lift and pitching moment on outboard panel 2 aileron due to aileron deflection about aero center @ ¼ chord of panel 2 Purdue Aeroelasticity

Purdue Aeroelasticity Write equilibrium equations in matrix form Two aileron torque terms are added Aileron input Purdue Aeroelasticity

Purdue Aeroelasticity Three applied aero torsion loads Nondimensionalize to identify aeroelastic terms Divide load matrix terms by KT so that Purdue Aeroelasticity

Combine the aileron load terms Purdue Aeroelasticity

The final equilibrium equation set outputs inputs Purdue Aeroelasticity

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? Purdue Aeroelasticity

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 Purdue Aeroelasticity

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. Purdue Aeroelasticity

Get the aileron control vector into the “correct” form notice the minus sign Purdue Aeroelasticity

Reduce the equations to nondimensional form Purdue Aeroelasticity

The divergence dynamic pressure has changed Compute the Determinant Purdue Aeroelasticity

Expand the stability determinant Polynomial 2nd order Purdue Aeroelasticity

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 Purdue Aeroelasticity

A close look at the first crossing point Negative aileron action, load reduction D Purdue Aeroelasticity

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 Purdue Aeroelasticity

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 Purdue Aeroelasticity