Active/passive Hybrid Control Of Shafting Vibration Based On Composite Magnetic Bearings

The control of propeller induced vibration(PIV)is of critical importance for reducing the acoustic radiation of underwater shell structures,such as submarine.The reason of PIV is the interaction force between propeller blade and non-uniform wake field.The force is transmitted along the propeller shafting system to the hull,causing acoustic radiation to the surrounding of submarine.The suppression of the vibration induced by the low frequency propeller is a very challenging problem,because the shafting does not allow the insertion of the soft elastic components to dissipate the low frequency vibration.Active vibration control technology can inhibit rear hull’s vibration while ensuring the total stiffness of isolation system,which can solve the above problem easily compared with passive vibration control methods.Besides,the actual submarine system has a lot of nonlinearity,parameter uncertainty and unknown disturbance,which requires the robustness and adaptability of the active control method The objective of this study is to design a nonlinear adaptive control scheme considering the driving characteristics of the magnetic bearings,system controllability,system uncertainty as well as nonlinearity.This control scheme can not only effectively reduce the energy transmission rate of propeller vibration energy to the hull,but also has adequate adaptability and robustness.Composite passive/active magnetic bearing is utilized as actuator in this scheme.This special bearing is a new type of bearing based on the mechanism of magnetic levitation,which has the advantages of non-contact,wearless,no friction and long life.This composite magnetic bearing not only has excellent controllability,but also improved the loading capacity and energy usage ratio compared with the traditional active magnetic bearings(AMBs).In order to achieve control objectives step by step,both permanent magnet bearings(PMBs)and active magnetic bearings are studied in advance.For PMBs in the low-speed and heavy-load bearing-rotor system,this study takes the simplified propeller propulsion shafting as the research object,considering the coupling between the magnetic field of magnetic bearings and the structure of shafting.On the one hand,the nonlinear factors of the magnetic force of the permanent magnetic bearing can be easily taken into account.On the other hand,this model can ensure the integrity and continuity of the structural characteristics of the system.On the basis of this model,the dynamic response of shafting under longitudinal and lateral blade frequency excitation is both studied.A robust and adaptive control scheme is applied to the control of thrust AMBs.In light of the strong nonlinear dynamic characteristics between the magnetic bearing and the propeller shaft system,a new back-stepping control scheme is developed,which can effectively prohibit the vibration energy of the propeller from transferring to the hull.Then,on the basis of the controller designed in the first step,an adaptive control scheme that can deal with the uncertainty of the system and the unknown excitation is proposed.The parameter estimator and perturbation estimator based on Lyapunov method are integrated into the control system,which guarantees the robustness and adaptability of the control method.Under the operating condition with strong nonlinearity and strong uncertainty,the controller can successfully suppress the hull’s vibration induced by propeller,thus effectively reducing the sound radiation of the hull.Finally,in order to improve the computational efficiency and convergence speed of the robust control scheme,a dynamic surface control(DSC)scheme based on RBF neural network is proposed.This method uses neural network to approximate the overall uncertainty of the system rather than individual system parameters,which is endowed with better expansibility and versatility.In addition,the permanent magnet/electromagnetic hybrid magnetic bearing is firstly applied in the specific underwater vehicle system.Because the stiffness of the passive magnetic bearing varys with the excitation frequency,the finite element model of the hull and the shafting is first established,and the information of frequency response function(FRF)between these key nodes is extracted.Then the two subsystems are synthesized by using the frequency response synthesis method considering the variable stiffness of each connection bearing(related to the blade frequency).As a result,the overall control equation based on FRF of the whole system is established.Then,according to this control equation,gradient optimization method is used to find the optimal control force of AMBs to suppress the vibration of the hull.Finally,in order to both reduce the vibration of the hull and the power consumption of the AMBs,a mixedweights optimal control scheme with a new objective function is designed to suppress both the amplitude of the electromagnetic force and the amplitude of the controlled freedom.And the optimal control force vector is derived from this mixed-weights optimal control scheme.