Filter-Expanded Linear Quadratic Regulator and Its Application in Wind Turbine Vibration Control

In the domain of vibration control, a common scenario arises where two conflicting $H_{2}$ norm performance indicators require simultaneous improvements. In this article, a novel control method known as the filter-expanded linear quadratic regulator (FELQR) is proposed to effectively address this challenge. In comparison with the linear quadratic regulator (LQR) method, the FELQR method demonstrates considerable advantages in managing two conflicting $H_{2}$ norm performance indicators. The primary contribution lies in establishing a constraint relationship between any two outputs of a linear vibration control system during the offline tuning of the state feedback gain. Leveraging this constraint relationship, a filter design process for the FELQR method is provided. By capitalizing on the disparate impact of gain tuning on the two outputs, the FELQR method attains a higher upper bound of vibration control performance compared with the LQR method. To validate the proposed FELQR method, simulations and experiments are conducted to assess its performance and robustness. The obtained results provide sufficient evidence supporting the efficacy of the FELQR method. Furthermore, a theoretical explanation is provided to elucidate the observed outcomes.