Sliding mode robust control of supersonic three degrees-of-freedom airfoils

Abstract

The robust aeroelastic control of a three-degrees-of-freedom (3DOF) linear and non-linear wing-flap system under sliding mode control (SMC) and operation in supersonic flight speeds is presented. Open-and closed-loop aeroelastic responses to blast and sonic-boom excitation in the wingflap system with uncertainty, as well as flutter analysis, are investigated along with the implementation of a Sliding Mode Observer (SMO). The effectiveness of control in reducing the amplitude of oscillation and preventing flutter instability is demonstrated. NOMENCLATURE a = Non-dimensional elastic axis position measured from the mid-chord, positive aft B = Ratio of the nonlinear to the linear pitching stiffness M, H, K= Mass, damping, and stiffness matrices b = Half-chord length e = Non-dimensional leading-edge flap position measured from the mid-chord, positive aft , a c F F = Aerodynamic and control load vectors , , h α β = Plunging, pitching, and flap displacements , I I α β = Mass moment of inertia per unit span of the wing-flap system about the elastic axis (EA) and of the flap about the flap axis (FA) of rotation, respectively , , h k k k α β = Stiffness parameters in plunging, torsional stiffness of the wing and flap about the EA , , ea L M H β = Total lift per span, aerodynamic moment, and hinge moment , , a ea l m h β = Non-dimensional aerodynamic lift, moment, and torque m = Airfoil mass per unit span M F , M f = Flutter speed and flight speed ρ ∞ = undisturbed density , U V ∞ = free stream speed and its nondimensional counterpart , r r α β = Non-dimensional radii of gyration of the wingflap system about EA , S x α α = Static unbalance about EA and its nondimensional counterpart , S x β β = Static unbalance about FA and its nondimensional counterpart , t τ = Time variable and its nondimensional counterpart κ = Polytropic gas coefficient

Extended Nonsingular Terminal Sliding Surface for Second-Order Nonlinear Systems

“…where 1 > 0, 0 < 1 / 1 < 1, and 1 and 1 are positive odd integers [8][9][10]. However, though the conventional terminal sliding surface in (3) ensures finite time convergence, it suffers from the singularity problem and has a restriction on the exponent of the power function [14].…”

“…Sliding mode control (SMC) method, which is also called a variable structure system (VSS), is one of nonlinear robust control schemes. It has been widely used because of its invariance properties to parametric uncertainties and external disturbances [5][6][7][8]. In conventional sliding mode control systems, sliding surfaces have been designed such that the overall system in the sliding mode is asymptotically stable.…”

Nonsingular finite-time second order sliding mode attitude control for reentry vehicle

“…0 e e e = = = Once the auxiliary control W is identified, according to (17), the actual control torque M can be calculated as follows:…”

“…It is insensitive to parameter variations and external disturbances under matching conditions [16], and has fast dynamic response, making it a potential approach for flight control system [17,18]. The sliding mode control method is utilized to design the attitude controller for the RLV in [19,20], where a sliding mode manifold is firstly designed such that states of the flight control system on the sliding mode manifold exhibit desired attitude tracking behavior, then the control strategy is designed to drive the system states to the sliding mode manifold and guarantee system motion on it thereafter.…”