Reference no: EM133584527
Linear System Theory
Project
This semester you will need two downloadable documents. The first is On Stability and Control of Hypersonic Vehicles net coded as DSTO-TR-2358. On page 14 is a free body diagram for a common longitudinal dynamical model for a hypersonic vehicle. Included is a five dimensions state variable description of the five energy storage mechanisms of interest for the longitudinal component. The vehicle is assumed to have thrust vectoring at the tail and aero dynamic lift generated by the slight elevation of the nose within the shock cone. The state variables defined are: (1)δV (1/2m(δV)2)kinetic energy due to forward motion, (2)δα (1/2I(δα)2)work done to elevate the nose with respect to forward velocity, (3)δq(1/2I(δq)2) work done to achieve flight path curvature, (4)δθ (1/2I(δθ)2) work done to elevate the velocity vector with respect to horizon, and (5) δR (1/2(mg)(δR)2 potential energy change due to altitude i.e. work done against gravity.
A detailed analysis in the Appendices begins on page 23 and results in a state equation description on page 28. As the author's state, the aero dynamic stability depends on the eigenvalues of the A matrix having negative real parts. The subsequent analysis on page 6 (part b) establishes the criteria for negative real components of the eigenvalue (aerodynamic stability) for the A matrix.
The second document is a sample MatLab program for simulating a Neural Network Adaptive Controller with Pseudocontrol Hedging applied to limited authority adaptive controls system. The "plant model" (see definition Chptr. 8) is the description used for the aerodynamics state equations for a hypersonic vehicle. As noted in the supporting narrative, this model is "primitive" where a simple sinusoid state variable dependence and a square wave input is used to demonstrate the stability, efficacy, and adaptability of the Neural Controller. The state description is one dimensional as defined in the initiation of "xdot" to a 1D matrix. This state variable from the Neural controller's standpoint is thrust vector pitch angle labeled "δη" on page 28 above. There is a block diagram in Steven, Brian L., Lewis, Frank L., and Johnson, Eric N., Aircraft Control and Simulation: Dynamics, Controls, Design, and Autonomous Systems.
A major drawback of the simulation demonstration for convincing third parties of the applicability of the Neural Controller, is the "primitive" nature of the plant model. Your task is to start with the generally accepted 5D description and developed the necessary similarity transformations, etc. to support an improved code line(s) for the plant model. Your written documentation (≤ 10 pages) should address your suggested code enhancements and support your choice's validity via matrix development tools such as similarity transformations, reduction in dimensionality, etc. Note the Australian paper gives a strong "hint" when they demonstrated the reduction of the five dimensional, A matrix eigen problem to a single test regarding the relative position of the center of pressure and the center of mass. Note the due date listed on the computer for submission of the document is the last day of class.
Attachment:- Neural Simulation.rar