A strategy to suppress limit cycle oscillations in helicopter ground resonance including landing gear nonlinearities

Ground Resonance (GR) in helicopters is a potentially dynamic instability commonly involving the coalescence of the blade lag mode with the fuselage motion. Linear techniques can be employed to identify the unstable rotor speeds with acceptable level of accuracy for some problems. However, structural nonlinearities can induce limit cycle oscillations (LCOs) that can define new GR boundaries and limit the helicopter operational landing envelope. Although there are different strategies to control design, stabilize a GR including nonlinearities is still a relevant challenge. In this context, this article presents a novel approach to suppress LCO during GR including structural nonlinearities. Two different cases of nonlinearities on the landing gear are considered. The first one includes a quadratic damping typically related to the hydraulic shock absorbers, and the second case considers the addition of a hardening stiffness combined with dry-friction. The proposed approach is based on the Fuzzy Takagi-Sugeno modeling and a polytopic representation of the system with these nonlinear terms is developed. It is used a Lyapunov's stability function and Linear Matrix Inequalities (LMIs) to solve a convex optimization problem for finding a controller gain to suppress the LCOs in a range of rotor speeds where they take place. Numerical simulations are carried out to demonstrate the approach and it is shown that an unique control gain can asymptotically stabilize the system responses to assure a safe landing envelope.