Vibration and Optimal Control of a Composite Helicopter Rotor Blade

Helicopter vibration is an inherent characteristic of rotorcraft operations, arising from transmission dynamics and unsteady aerodynamic loading, posing challenges to flight control and longevity of structural components. Excessive vibration elevates pilot workload and accelerates fatigue damage in critical components. Leveraging advances in optimal control and microelectronics, the active vibration control methods offer superior adaptability compared to the passive techniques, which are limited by added weight and narrow bandwidth. In this study, a comprehensive vibration analysis and optimal control framework are developed for the Bo 105 helicopter rotor blade exhibiting flapping, lead-lag, and torsional (triply coupled) motions, where a Linear Quadratic Regulator (LQR) is employed to suppress vibratory responses. An analytical formulation is constructed to estimate the blade’s sectional properties, used to compute the coupled natural frequencies of vibration by the modified Galerkin method. An orthogonality condition for the coupled flap–lag–torsion dynamics is established to derive the corresponding state-space equations for both hovering and forward-flight conditions. The LQR controller is tuned through systematic variation of the weighting parameter Q, revealing an optimal range of 10²–10⁴ that balances vibration attenuation and control responsiveness. The predicted frequencies of the vibrating rotor blade are compared with the finite element modeling results and published experimental data. The proposed framework captures the triply coupled rotor blade dynamics with optimal control, achieves modal vibration reductions of approximately 60–90%, and provides a clear theoretical benchmark for future actuator-integrated computational and experimental studies.