Periodic Flap Control of a Helicopter Blade in Forward Flight

Abstract

The primary objective of this paper is to present new periodic control strategies for the control of flapping motion of an individual helicopter rotor blade in forward flight, which is represented by a differential equation with periodic coefficients. First, an algebraic procedure based on Chebyshev polynomial expansion is employed to control the periodic flapping motion. In this approach, the state vector and the elements of the periodic system matrix have been expanded in terms of shifted Chebyshev polynomials of the first kind over the principal period. Later, optimal control theory in conjunction with Floquet theory has been used to design full-state and observer-state feedback controllers. In the second method, the feedback controllers have been designed in the time-invariant domain through the application of a linear, invertible, periodic transformation known as Liapunov-Floquet (L-F) transformation to the periodic system model. It is shown that by using both methods the periodic control gains can be obtained as explicit functions of time and, therefore, a control scheme more suitable for real-time implementation can be achieved. The design procedures have been found to be much simpler in character when compared to those techniques that have appeared in the literature.