Thesis (M.Sc.) - Cairo University - Faculty of Science - Department of Astronomy and Meteorology

In this work the problem of aircraft stability augmentation (SAS) system has been addressed. The coupled lateral-longitudinal dynamics of the aircraft is formulated in the wind coordinate reference frame. The problem is solved using the Linear Quadratic Regulator (LQR) controller, in which we have the advantage of controlling and extremizing some parameters in a real time. By the virtue of technique, a closed loop solution valid for generic initial condition is obtained. The method is applied to a real problem and compared to the other methods such as open loop and closed loop using time impulse, step and doublet responses. The other methods fail in obtaining the required stability in a real time. The dynamics of the problem is a complicated set of six nonlinear coupled second order differential equation for the transnational and rotational motion. However, within certain condition, they can be decoupled and linearized with longitudinal and lateral equation. The simplified equation for an unstable dynamical system, which requires the use of a certain controller to achieve desired accuracy within reasonable time frames in addition to achieve stabilizing of the system. In this work, we have used (MATLAB) to design an autopilot that control the motion of an aircraft. We solved the problem using the classical control of multiple input {u2013} multiple output (MIMO) and then we used an autonomous Linear Quadratic Regulator (LQR) to optimize out solution within reasonable time but the (LQR) technique can do this in addition to extremizing some of variables and/or input of problem. We applied the results to a specific airplane using its Jacobean of equilibrium state and the worst initial conditions and the results have been simulated to verify the capability of the technique

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