Relaxed Static Stability Aircraft Design via Longitudinal Control ...

[ ] [ ] [ ] [ ]Zα/= V 1 α Zα/ ˙α˙q M α + M + V˙αZ α / V M q + M ˙αq M δ + M [δ˙αZ e ] (6)δ / Vwhere α is the aircraft angle of attack, q is the aircraft pitch rate, δ e is the elevatordeflection angle, V is the aircraft frestream velocity, and [Z α ,M α ,M ˙α ,M q ,Z δ ,M δ ]are dimentional stability derivatives. Note that every dynamic state is affected bythe elevator deflection control input signal.Control Systems DesignThe control system considered consist of an output feedback controller, where the gainscan be expressed as:[ ]αu = δ e = [k α ,k q ](7)qwhere stability of the closed loop system is guaranteed by selecting negative control gainvalues as seen in Fig. 7.150Root Locus2Root Locus100α/δ e1.5q/δ e1Imaginary Axis500-50-100Imaginary Axis0.50-0.5-1-1.5-150-300 -250 -200 -150 -100 -50 0Real Axis-2-3 -2.5 -2 -1.5 -1 -0.5 0Real AxisFig. 7: Root Locus of the Closed Loop SystemDesign VariablesTable 2 lists the design variables, their bounds, and the initial design used in the optimizationproblem. Note that most of the coupling variables described will be repeatedfor each flight condition analyzed. At the system level, 61 design variables are takeninto consideration, from which 19 are global design variables and 42 are coupling designvariables. The global design variables include the main non-dimensional geometricvariables which define the aircraft configuration. Coupling variables include 4 flight conditionindependent terms (engine scaling factor, MTOW, fuel and engine weights), whilethe rest are distributed over the different flight conditions. For example, 12 coupling11