A periodic H₂ state feedback controller for a rotor-blade system

Many engineering applications have as their main component rotor-blade systems whose dynamics can be represented by a linear time-varying model. Since rotor-blade systems exhibit periodic dynamics, standard linear time-invariant analysis and synthesis techniques cannot be directly used and are not able to guarantee closed-loop stability and performance. Although there exist many results for periodic systems, the design of controllers for such systems is, in general, a difficult task. Its practical application is challenging, from the computational and experimental aspects. This paper presents the application of a periodic H2 control problem in a rotor-blade system in order to attenuate the tip vibration. The proposed control design is based on a periodic Riccati differential equation (PRDE). The Floquet-Lyapunov theory is used to represent the dynamics in an adequate coordinate system, so that the PRDE can be efficiently solved. A robustness analysis is also perfomed. Numerical experiments show the effectiveness of the proposed approach.