Abstract
With advancements in modern flight vehicle design, an increased demand for maneuverability is observed, often requiring flight vehicles to operate under conditions involving a high angle of attack and large rudder angle. However, the prevalent linearized model of flight vehicle longitudinal dynamics in aerospace engineering is primarily tailored for launch vehicles, relying on assumptions such as small angle of attack and control surface deflection. Consequently, establishing a linearized model of flight dynamics applicable under conditions of the high angle of attack and large rudder angle is necessary.
This paper uses the small perturbation method to establish a linearized model of the rigid-flexible coupling flight dynamics for flight vehicles, which is then compared and analyzed with the commonly used model in aerospace engineering. Initially, the vector-form flight dynamic equations are projected onto the specified coordinate system, resulting in matrix-form scalar equations. Subsequently, the general linearized form of the dynamic equations in matrix form is derived, and the equation coefficients for the longitudinal dynamic model are obtained. High-precision linearization of the nonlinear expressions for inertia forces and moments owing to control surface deflection is performed, yielding linearized expressions that accurately describe the influence of the perturbation in the angle of attack and rudder angle on these forces and moments. A rigid-flexible coupling multibody system comprising a flexible body and rigid rudder is used as an example to compare simulation results of the linearized model derived in this paper, the traditional linearized model, and the original nonlinear model under the high angle of attack and large rudder angle, verifying the high simulation accuracy of the proposed model.
By comparing the coefficients of the dynamic equations derived in this paper with those in the commonly used model in aerospace engineering, we observe that when the angle of attack and the rudder angle are considered small, the coefficients of the dynamic equations obtained in this paper can be simplified to match those of the commonly used model in aerospace engineering. However, unlike the commonly used model in aerospace engineering, the linearized expressions for inertia forces and moments owing to control surface deflection in this paper include not only the increments of control surface deflection acceleration but also the increments of the rudder angle and angle of attack. Simulation results indicate that the linearized model derived in this paper produces results close to those of the nonlinear model than those of the traditional linearized model.
When the angle of attack and the rudder angle are small, the simulation results of the simplified linearized models are relatively close to those of the linearized model derived in this paper. However, under the high angle of attack and large rudder angle, a considerable discrepancy is observed between the simulation results of the linearized models that treat the angle of attack or rudder angle as small quantities and the linearized model derived in this paper. In such cases, treating the angle of attack or rudder angle as small quantities may lead to substantial errors. The research presented in this paper offers a high-precision linearized model that can be used for the guidance and control system design of a flight vehicle.
