Nonlinear optimal control of a flapped-wing structure with freeplay and reduced stiffness

Abstract The aeroelastic behaviour of a flapped-wing with freeplay and reduced stiffness is highly nonlinear. The optimal control of a nonlinear system is desired to optimise a given structural performance. In this paper, two novelties (a new method to solve state dependent Riccati equation, and inclusion of damage effects on aero-servo-elastic system) are developed to optimally control the nonlinear aeroelastic behaviour of a flapped-wing section including freeplay and reduced stiffness. To design the optimal controller, the State Dependent Riccati Equation (SDRE) is utilised based on a combination of the Hamiltonian matrix and the Schur method. A three degree of freedom (DoF) aeroelastic wing structure with a control surface is mathematically modelled, including freeplay in control surface, cubic nonlinear spring for description of the torsional stiffness and reduced stiffness factor in torsional spring due to damage. The effect of freeplay, reduced stiffness and concentrated nonlinearity in torsional spring are analysed on aeroelastic response. The system response is determined by time marching of the governing equations using a Matlab code. Various simulations results for multiple flow velocities and nonlinear parameters prove the effectiveness of this control method in flutter suppression. It is also shown that the control surface freeplay leads to limit cycle oscillation at speeds less than flutter speed. Furthermore, the simulation results show that the presence of a damage – which reduces the stiffness in torsional spring – leads to an increase in the oscillation amplitudes.