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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
飞机飞行的六自由度非线性仿真

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更新2015年11月04

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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.m使用[2]中包含的空气动力学和尺寸数据,估计通用商务射流的惯性特性。在Mach效果的估计中使用诸如翼和尾部的扫描和纵横比的配置的细节。Mach效果的估计基于Prandtl因子或修改的Helmbold方程。使用手册方法来估算几何,惯性和空气动力学特性的手册BET For Bizjet B.该模型是首次使用Geomassaero.m建造的,它保存了三个.MAT文件,描述了Airplane:Inergeo.mat,DataTable.mat和Rotcont.mat。Aeromodelalpha.m加载.MAT文件以用于航班。基于传统的低α和牛顿高alpha估计,攻击范围从-10到90°延伸。没有考虑马赫,着陆装置,扰流板或襟翼效果。

EOM.M的运动方程是使用平地的假设写入的[1]。施加了俯仰角余弦的余弦的临时限制,以防止近垂直飞行中的单数计算。当俯仰角接近+/- 90°时,此权宜程引入小错误。函数Event.M指定如果高度低于零,则终止在最终时间之前的模拟的停止条件。

通过最小化纵向加速度的二次函数(即轴向速度,正常速度和俯仰率的变化率)的二次函数来计算修整控制设置。Trimcost.M调用EOM.M以生成所需的加速度。方向 - 余弦(或旋转)矩阵在DCM.M.m [1]的函数中实现。该矩阵将来自地球相对帧的向量变换到身体轴框架。LinModel.m在Trim设置下产生用于线性,时间不变模型的状态和控制雅可比矩阵。Jacobian矩阵在状态和控制的标称值评估。Windfield.m作为高度的函数产生三分风向量,在制表点之间具有线性插值[1]。1976年,美国标准气氛空气密度,气压,空气温度和声速产生为Atmos.m的高度的功能。

[1] Stengel,Flight Dynamics,Princeton大学出版社,普林斯顿,2004年。
Soderman, P. T.,和Aiken, T. N.,“小型无动力喷气飞机T型尾翼全尺寸风洞试验”,NASA TN D-6573,华盛顿特区,1971年11月。

引用

Robert Stengel(2021年)。两架公务机的数学模型及六自由度仿真(//www.tianjin-qmedu.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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