Goal: analyze aircraft longitudinal dynamics to determine if the be- havior is acceptable, and if not, then modify it using feed back control Note that we could (and will)work with the full dynamics model but for now, let's focus on the short period approximate model from

Recall from 6-2 that the derivative stability derivative terms zai, and Mi ended up on the lhs as modifications to the normal mass and Inertia terms displaced air is \entrained\and moves with the aircraf rounding These are the apparent mass effects- some of the sur Acceleration derivatives quantify this effect Significant for blimps, less so for aircraft e Main effect: rate of change of the normal velocity w causes a transient

State Space Basics State space models are of the form x()= Ax(t)+ Bult) y(t)= Cx(t)+ Dult) with associated transfer function G()=C(sI-A)

Matrix Diagonalization Suppose a is diagonizable with independent eigenvectors use similarity transformations to diagonalize dynamics matrix

mu Xuu+ Xww-mg cos 000+ m(wi-qUo) Zuu+ Zww Ziw+ Zgq-mg sin+ Iyyq Muu+ Mww+ Mww+ Mq+ There is no roll/yaw motion, so=0. Control commands△x,△z,and△ MC have not yet been specified

Note can develop good approximation of key aircraft motion(Phugoid) using simple balance between kinetic and potential energies. Consider an aircraft in steady, level flight with speed U and height ho. The motion is perturbed slightly so that

For general applications in 3D, often need to perform 3 separate rotations to relate our inertial frame to our body frame Especially true for aircraft problems There are many ways to do this set of rotations -with the variations be based on the order of the rotations All would be acceptable

Static stability is all about the initial tendency of a body to return to its equilibrium state after being disturbed To have a statically stable equilibrium point, the vehicle must develop a restoring force/ moment to bring it back to the eq. condition Later on we will also deal with dynamic stability, which is concerned with the time history of the motion after the disturbance

Aircraft Performance Accelerated horizontal flight-balance of forces -Engine thrust TLift(toV)

一、回顾FEM和F一D 二、一维实例 三、一二三维的有限差分矩阵 四、高斯消元的代价 五、Krylov法 六、通讯下限 七、基于改善通讯的预条件器