Optimal Vibration Control of a Triply Coupled Helicopter Rotor Blade

Helicopter vibration is an inherent feature of rotorcraft operation, arising from multiple sources including transmission dynamics and unsteady aerodynamic loading, and it poses significant challenges for both flight control and structural integrity. Excessive vibration not only increases pilot workload but also accelerates fatigue damage of mechanical components. While complete elimination is infeasible, active vibration control provides a systematic means of mitigating harmful responses. Enabled by advances in modern control theory and microelectronics, active techniques offer superior adaptability compared to passive methods that suffer from weight penalties and limited bandwidth. In this study, an optimal control framework based on a Linear Quadratic Regulator (LQR) is developed to attenuate vibration in a hingeless rotor blade system exhibiting triply coupled flap, lead-lag, and torsional motions. The governing state-space model is derived using orthogonality conditions for flap–lag–torsion coupling under both hovering and forward-flight conditions. Principal aerodynamic forces and moments are incorporated, and the LQR, whose performance is strongly dependent on the weighting parameter Q, is tuned to minimize vibration amplitude under both impulsive and periodic excitations. The results demonstrate significant attenuation across all modes, establishing a theoretical benchmark for active vibration suppression that is independent of actuator-specific implementation and suitable for guiding future experimental validation.