The Receptance-based Active Optimal Vibration Control Method And Its Application In Suppression Of Bridge Flutter

Flutter instability is the most important problem in wind-resistant design of long-span suspension bridges.Active aerodynamic measures based on control surfaces have recently become a research hotspot in suppression of bridge flutter.The system matrices of bridge-control surfaces（i.e.mass,damping and stiffness matrices）have to be known for existing researches based on the conventional active control theory.During the construction of system matrices,numerous errors,however,are inevitably introduced from the process of modelling,model reduction,observer design and so on such that the established theoretical model are incompatible with the practicalities of actual structure dynamic characteristics.So,the control effectiveness cannot be guaranteed.In recent years,a new theory for active vibration suppression called receptance method is proposed in Aerospace Engineering Community.This method uses measured receptances,which reflect the actual structure dynamic characteristics rather than system matrices to design controller so the above-mentioned errors are avoided.This research introduces the receptance method into the field of civil engineering while developing it theoretically and then apply to the active control of bridge flutter.The main research outcomes are presented as follows.（1）The H₂-optimal vibration control using receptance-based regional eigenvalue assignment is proposed.The pole-residue expression ofH₂-norm of transfer matrix is derived.The weighted sum ofH₂-norm of transfer matrices composed of closed-loop receptance matrix and the transfer matrix from the external input to the control input is chosen as the objective of optimisation.The closed-loop eigenvalues are assigned to prescribed regions rather than precise positions,which provide flexibility for optimising the closed-loop performance and control efforts.The working of the method and its advantages over the standardH₂-control are demonstrated numerically with a two-degree-of-freedom mass-spring-damping system.Considering that the response in a certain frequency band is focused in practical application,and the frequency response function obtained by modal test fitting is only in a limited frequency band,the expression of frequency-limitedH₂-norm of transfer matrix is derived.（2）The robust stability control based on receptance method is proposed.In view of the uncertainty of single element in the open-loop receptance matrix,it is considered that the poles of the objective transfer function can be placed to the specified position while its zeros can be kept unchanged by receptance-based active control,so as to broaden the value range of the uncertain parameter to ensure the stability of the system and improve the robust stability.The same two-degree-of-freedom mass-spring-damping system is used to verify the effectiveness of proposed method.（3）These two proposed theories are applied to the suppression of bridge flutter.A suspension bridge sectional model is chosen as numerical example.The leading-and trailing-edge control surfaces are designed for this deck sectional model.The numerical wind tunnel CFD is used to demonstrate the effective applications in flutter optimal control and robust stability control,respectively.