This paper presents an active control strategy, based on a time-varying linear–quadratic optimal control problem, to attenuate the tip vibration of a two-dimensional coupled rotor-blade system whose dynamics is periodic. First, a periodic full-state feedback controller based on the linear–quadratic regulator (LQR) problem is designed. If all the states are not available for feedback, then an optimal periodic time-varying estimator, using the Kalman–Bucy filter, is computed. Both the Kalman filter gain and the LQR gain are obtained as the solution of a periodic Riccati differential equation (PRDE). Together, these gains provide the observer-based linear–quadratic–Gaussian (LQG) controller. An algorithm to solve the PRDE is also presented. Both controller designs ensure closed-loop stability and performance for the linear time-varying rotor-blade equation of motion. Numerical simulations show that the LQR and the LQG controllers are able to significantly attenuate the rotor-blade tip vibration.
- Linear time-varying systems
- Linear–quadratic–Gaussian controller
- Periodic systems
- Rotor dynamics
- Vibration control
Camino, J. F., & Santos, I. F. (2019). A periodic linear–quadratic controller for suppressing rotor-blade vibration. Journal of Vibration and Control, 25(17), 2351–2364. https://doi.org/10.1177/1077546319853358