Optimum Design of a PID Controller for the Adaptive Torsion Wing Using GA

Abstract

This paper presents the optimum design of a PID controller for the Adaptive Torsion Wing (ATW) using the genetic algorithm (GA) optimiser. The ATW is a thin-wall, twospar wingbox whose torsional stiffness can be adjusted by translating the spar webs in the chordwise direction inward and towards each. The reduction in torsional stiffness allows external aerodynamic loads to deform the wing and maintain its shape. The ATW is integrated within the wing of a representative UAV to replace conventional ailerons and provide roll control. The ATW is modelled as a two-dimensional equivalent aerofoil using bending and torsion shape functions to express the equations of motion in terms of the twist angle and plunge displacement at the wingtip. The full equations of motion for the ATW equivalent aerofoil were derived using Lagrangian mechanics. The aerodynamic lift and moment acting on the aerofoil were modelled using Theodorsen’s unsteady aerodynamic theory. The equations of motion are then linearized around an equilibrium position and the GA is employed to design a PID controller for the linearized system to minimise the actuation power require. Finally, the sizing and selection of a suitable actuator is performed.