Time-periodic control of a multi-blade helicopter

Abstract

Abstract : The flap-lag equations of motion of an isolated rotor blade and those for a rigid helicopter containing four blades free to flap and lag are derived. Control techniques are developed which stabilize both systems for a variety of flight conditions. Floquet theory is used to investigate the stability of a rotor blade's flap-lag motion. A modal control technique, based on Floquet theory, is used to eliminate the blade's instabilities using collective and cyclic pitch control mechanisms. The technique shifts the unstable roots to desired locations while leaving the other roots unaltered. The control, developed for a single design point, is shown to significantly reduce or eliminate regions of flap-lag instabilities for a variety of off-design conditions. Both scalar and vector control are successfully used to stabilize the blade's motion. Coupling the flap-lag equations of motion of four rotor blades to a rigid airframe alters the flap, lg, and airframes roots. The airframe roots are stabilized using a combination of the body's pitch attitude and pitch rate feedback to the main rotor's longitudinal cyclic pitch. The modal control technique is used to eliminate multiple blade instabilities by first controlling a pair of unstable roots at a specific design point. The resulting closed loop system is a new linear system which periodic coefficients. Another modal controller is designed for this new system to shift a second pair of unstable roots to desired locations. This process is repeated until all instabilities are eliminated. Numerical inaccuracies, however, become noticeable when modal control is used more than once.