Optimal criteria for H2 performance of the classic vibration control systems and an improved fixed structure method

In the field of vibration control, the analytical expressions for the optimal performance and optimal controller of classic vibration control systems remain unsolved. In this paper, this problem is partially solved. For several common performance indicators and inputs in classic vibration control systems, analytical expressions for the optimal controller and optimal value of the performance indicator are provided in this paper, which can be used to directly calculate the optimal value of the performance indicator and the Bode diagram of the optimal controller. Then, a fractional-order mechanical network design method is proposed in this paper. Compared with network synthesis method, the proposed mechanical network design method can realise better performance while satisfying constraints on the number of elements and network structure. Finally, the response of a 5 MW NREL wind turbine under seismic acceleration and wind loads is simulated to validate the effectiveness of the proposed mechanical network design method. Simulation results show that the designed fractional-order mechanical network has outstanding performance, and the analytical expression of the optimal controller can be used to efficiently guide the tuning of the mechanical network.