Single-Input/Single-Output Adaptive Flutter Suppression of a Three-Dimensional Aeroelastic System

Nomenclature  = estimated system matrix As0 = time invariant generalized aerodynamic stiffness matrix of the structural modes, As0 2 R 4 As1 = time invariant generalized aerodynamic damping matrix of the structural modes, As1 2 R 4 As2 = time invariant generalized aerodynamic mass matrix of the structural modes, As2 2 R 4 b = semichord of the wing, m B = estimated input matrix of control B = diagonal matrix of modal damping Ĉ = estimated output matrix of system D = matrix used in minimum-state rational function approximation e1 = estimated prediction error P t = gain matrix P s = estimated denominator polynomial of the transfer function of the controlled aeroelastic system K = stiffness matrix of elastic modes, diagonal for orthogonal elastic modes M = modal mass matrix involving elastic modes only, diagonal due to the orthogonality of elastic modes M = inertial coupling submatrix between control modes and elastic modes Qm s = transfer function of the reference model qd = dynamic pressure, Pa u = control input, rad V = flight speed, m=s v = measurement noise w = Gaussian random input to turbulence in spectral form x t = state vector of the aeroelastic system, including the first four modal displacements , modal velocities _ , aerodynamic state vector and actuator state vector Xa = aerodynamic state vector ym t = reference output signal, m=s Ẑ s = estimated numerator polynomial of the transfer function of the controlled aeroelastic system = generic individual control surface deflection as a function of time, 2 R, rad p = vector of the unknown parameters, p 2 R p = estimation of p = vector of the generalized modes, 2 R