Periodic motion suppression based on control of wing rock in aircraft lateral dynamics

Wing rock prevention is an important objective for an aircraft that needs to fly and maneuver at moderate to high angles of attack. This phenomenon is characterized as a periodic motion (or limit cycle), and needs to be avoided at all costs. A candidate mechanism for the wing rock limit cycle is the inertia coupling between an unstable lateral-directional (Dutch roll) mode with a stable longitudinal (Short period) mode. The coupling mechanism is provided by the nonlinear interaction of motion related terms in the complete set of motion equations. A methodology for preventing the limit cycle accomplished by adding a control function to the original equation of wing rock motion is presented in this paper. To analyze the state variables of the system, the complete set of nonlinear equations of motion including effective linear control function was solved. Numerical model constructed for A-4D and a Mig-21 Aircraft is solved to illustrate the results. The numerical results show that it was sufficient to use a linear control function including both roll attitude and roll rate for suppressing wing rock motion without any error in desired time. A good agreement between the numerical results and the published work is obtained for limit cycle oscillation existence at different values of damping ratio for almost the same roll angle.