A periodic linear–quadratic controller for suppressing rotor-blade vibration

J. F. Camino*, I. F. Santos

*Corresponding author for this work

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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.
Original languageEnglish
JournalJournal of Vibration and Control
Issue number17
Pages (from-to)2351–2364
Publication statusPublished - 2019


  • Linear time-varying systems
  • Linear–quadratic–Gaussian controller
  • Periodic systems
  • Rotor dynamics
  • Vibration control

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