| Trains get the electric energy through the mutual contact of pantograph and catenary in electrical railways,so the stable dynamic coupling state of pantograph and catenary plays a very important role in the process of electric energy transmission.With the increasing speed of trains,the coupling vibration of pantograph and catenary increases and the fluctuation of the contact force intensifies,which not only deteriorates the current quality of trains,but also damages the mechanical structure of pantograph and catenary,and reduces the performance of the system,thus reducing the contact force fluctuation is an important measure to ensure the safe and stable operation of trains and improve the current quality of trains.In order to reduce the fluctuation of contact force,the optimal control method of pantograph based on state estimation and the optimal control method considering actuator time delay are given in this paper.Meanwhile,the contact wire irregularity is considered.The effectiveness and robustness are verified based on nonlinear pantograph and catenary model at different speeds.Firstly,pantograph model and catenary model are established respectively.Pantograph model is divided into the multibody model of pantograph and the mass model of pantograph based on the structural characteristics.Catenary model is built based on the finite element method,in which the contact wire and messenger wire are constructed as a nonlinear cable element and the droppers are built as nonlinear truss elements based on the structural characteristics of catenary.Pantograph and catenary model are coupled by the penalty function method,and the effectiveness of pantograph and catenary model is verified,which provides a feasible basis for the following research.Secondly,the characteristics of contact force are analyzed,and considering the premise of safe and stable operation of trains,the control objective and performance output function are established.Considering the electromagnetic interference and environmental interference during the operation of pantograph and catenary system,the state information cannot be accurately obtained.The robust adaptive unscented Kalman filter algorithm is used to estimate the state information of pantograph,the results show that the estimation algorithm can accurately obtain state information under the condition of time-varying noise.Combining with the estimation algorithm,the optimal control algorithm is given,and the effectiveness and robustness of control algorithm at different operating speeds are verified on nonlinear pantograph and catenary model.The causes of contact wire irregularity are analyzed and the structure information of contact force is identified by power spectral density.Considering the condition of contact wire irregularity,the effectiveness of control algorithm is verified.The results show that control algorithm can effectively reduce the fluctuation of contact force.Finally,time delay of actuator in active control of pantograph is considered based on the fact that time-delay phenomenon exists in practical application and control system.Combining with the corresponding control objectives and state estimation,an optimal control algorithm considering time delay of actuator is given,the effectiveness of control algorithm and the robustness of control algorithm under parameter perturbation are verified on nonlinear pantograph and catenary model.Meanwhile,the effectiveness of control algorithm is verified under the condition of the contact wire irregularity.The results show that control algorithm can decrease the contact force fluctuation even if the actuator time delay exists.In this paper,the optimal control of pantograph is attemptted from the perspective of considering contact wire irregularity and actuator time delay.It can be found that this idea has good active control performance,which can provide idea for future research on the active control of pantograph. |