LQR Reference Tracking Control of Boeing 747-100 Longitudinal Dynamics with CG Shifts

The stick-fixed longitudinal flight of Boeing® 747-100 is compared at three Mach-altitude conditions: 0.2 at sea-level; 0.5 at 20,000ft; and 0.9 at 40,000ft, as centre of gravity (CG) shifts. Velocity, pitch rate, attitude and altitude with elevator and throttle commands have been simulated for each flight condition. These simulations indicate stable complex eigenvalues with low stability margins. Stick-fixed flight is dominated by insufficiently damped long-period responses with an initial short-period effect. Dynamic stability and performance of the stick-free autopilot is investigated using a linear quadratic regulator (LQR) algorithm in the presence of CG shifts. Steady state convergence is achieved within a few seconds with acceptable flying qualities. The controller has been revised to cope with Mach-altitude constraints and demonstrates autopilot ability to mainain stable cruise flight. The results emphasise the plane is dynamically stable and satisfactorily trimmed at those CG cruise conditions.