两架公务机的数学模型及六自由度仿真

版本1.0.0.0 (28.6 KB 罗伯特·斯坦格尔
飞机飞行六自由度非线性仿真

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更新2015年11月4日

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FLIGHT.mis a tutorial program, heavily commented to make interpretation easy. It provides a full six-degree-of-freedom simulation of an aircraft, as well as trimming calculations and the generation of a linearized model at any flight condition chosen by the user [1]. Changes to aircraft control histories, initial conditions, flag settings, and other program control actions are made by changing the numbers contained in the code; there is no separate user interface. The code has been designed for simplicity and clarity not for speed of execution, leaving a challenge to the reader to find ways to make the program run faster. Numerous additions could be made to the code, including implementation of feedback control logic, simulation of random turbulence or microburst wind shear, and interfaces for real-time execution. No explicit or implicit warranties are made regarding the accuracy or correctness of the computer code.
FLIGHT.mis the script that calls program functions. Initial conditions are defined here, the three primary features (trim, linearization, and simulation) are enabled, and output is generated. Initial perturbations to trim state and control allow transient effects to be simulated. As shown, trimming for steady, level flight is accomplished by first defining a cost function, J, that contains elements of the state rate, then minimizing the cost using the Downhill Simplex (Nelder-Mead) algorithm contained in fminsearch. The longitudinal trimming parameters are stabilator angle, throttle setting, and pitch angle. The linear model is generated by numjac, a numerical evaluation of the Jacobian matrices associated with the equations of motion. The linear model is saved to disk files in the variables Fmodel and Gmodel. MATLAB's ode23, ode45, or ode15s integrate the equations of motion to produce the state history. The state history is displayed in time plots, with angles converted from the radians used in calculation to degrees. The reader can readily change the units of plotted quantities or add additional plots through minor modifications to the code. Any result (e.g., numerical values of the state history) can be displayed in the MATLAB Command Window simply by removing the semi-colon at the end of the line. The flag MODEL selects either a low-angle-of-attack, Mach-dependent model for BizJet A [2] or a high-angle-of-attack, low-subsonic model for Bizjet B.

AeroModelMach.muses aerodynamic and dimensional data contained in [2] with estimates of inertial properties of the generic business jet. Details of the configuration, such as sweep and aspect ratio of the wing and tail, are used in the estimates of Mach effects. Estimates of Mach effects are based on the Prandtl factor or the modified Helmbold equation. AeroModelAlpha.m for BizJet B is derived using handbook methods for estimating geometric, inertial, and aerodynamic characteristics. The model is first built using GeoMassAero.m, which saves three .mat files describing the airplane: InerGeo.mat, DataTable.mat, and RotCont.mat. AeroModelAlpha.m loads the .mat files for use in FLIGHT.m. The angle-of attack range extends from -10 to 90 deg based on conventional low-alpha and Newtonian high-alpha estimates. No Mach, landing gear, spoiler, or flap effects are considered.

EoM的运动方程。M用平面地球假设[1]表示。对俯仰角余弦施加了一个特别的限制,以防止在近垂直飞行中进行奇异计算。当俯仰角接近+/-90度时,这种便利引入了一个小误差。M指定一个停止条件,如果高度低于0,则在最后时间之前终止模拟。

通过最小化TrimCost中包含的纵向加速度(即轴向速度、法向速度和俯仰速率的变化率)的二次函数来计算微调控制设置。m[1]。TrimCost。m叫EoM。M来产生所需的加速度。方向余弦(或旋转)矩阵在函数DCM中实现。m[1]。矩阵将矢量从相对于地球的参照系转换为身体轴系。LinModel。m为线性时不变模型在修剪设置下产生状态和控制雅可比矩阵。在状态和控制的标称值处计算雅可比矩阵。WindField。m produces a three-component wind vector as a function of altitude, with linear interpolation between tabulated points [1]. 1976 U.S. Standard Atmosphere air density, air pressure, air temperature, and sound speed are generated as functions of altitude by Atmos.m.

斯坦格尔,飞行动力学,普林斯顿大学出版社,普林斯顿,2004。
[2] Soderman, P. T.和Aiken, T. N.,“带T型尾的小型无动力喷气式飞机的全尺寸风洞试验”,NASA TN D-6573,华盛顿特区,1971年11月。

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罗伯特·斯坦格尔(2022年)。两架公务机的数学模型及六自由度仿真(//www.ru-cchi.com/matlabcentral/fileexchange/53821-mathematical-models-and-six-degree-of-freedom-simulation-of-two-business-jet-aircraft), MATLAB中央文件交换。检索

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