Study On Modeling And Control Method Of The Electromagnetic Active Vibration Isolation System

Vibrations emitted from large equipment and precision instruments not only affect the surrounding environment,but also reduce their performance.In recent years,a variety of vibration isolation systems and vibration control technologies have been developed and exploited effectively to control vibration for the purpose of keeping machinery performing at its best precision.The electromagnetic vibration isolation system,a typical active isolation system with controllable stiffness and damping coefficient,flexible and various control methods and fast response during in action,have been widely used in the field of processing equipment,measuring instruments,mechanical systems and other engineering applications.In this dissertation,optimization of internal components and system structure,nonlinear analysis and modeling,control strategy of an electromagnetic vibration isolation system,and control problems of the active electromagnetic system with multiple electromagnetic isolation units in parallel are studied based on the review and analysis of the relevant research.The main work of this dissertation is as follows:(1)The parameters of the vibration isolation components are optimized by COMSOL simulation and a simple and reasonable structure of the electromagnetic vibration isolation system is designed based on the model analysis of the common active vibration isolation system.The nonlinear relationships among the parameters of coil current,gap and electromagnetic force are achieved by COMOSOL Multiphysics and experiments respectively,which verify each other.A modeling method based on simulation and experimental data is proposed for the electromagnetic isolation system.Aiming at the problem that the control model of the electromagnetic vibration isolation system is difficult to establish,a modeling method based on mechanism and data is proposed based on the mechanical process of the vibration isolation system and the relationship between electromagnetic force and control current and gap.In order to verify the effectiveness of the proposed modeling method based on simulation and experimental data,the PID controller is introduced into the electromagnetic vibration isolation system for simulation and experiment.The simulation and experimental result demonstrates that the effectiveness of the modeling method and feasibility of the active control method.(2)A new active control method based on equivalent stiffness and damping coefficient is proposed for the electromagnetic isolation system to avoid the parameter tuning problem of a PID controller.In this method,the range of equivalent stiffness coefficient and damping coefficient of the electromagnetic force in the electromagnetic isolation system are calculated based on the required range of dynamic performance indexes.The optimal equivalent stiffness coefficient and damping coefficient are calculated in the range by the genetic algorithm.According to the nonlinear expression between electromagnetic force and coil current and gap,the relationship between the coil current and equivalent stiffness coefficient and damping coefficient.Then,the equivalent stiffness coefficient and damping coefficient can be satisfied by the controlled current in different gaps for meeting the required dynamic performance indexes.In order to realize the variable control parameters of the electromagnetic vibration isolation system and reduce the maximum overshoot and the number of oscillations of the system,the active control method with the piecewise equivalent stiffness and damping coefficient is proposed based on the piecewise control strategy to adopt the optimal control parameters at each control time and solve the conflict between the overshoot and the setting time in the time-domain performance of the system.The simulation and experimental results show that the control method based on the equivalent stiffness and damping coefficient can obtain the desired dynamic performance indexes and the control method based on the piecewise equivalent stiffness and damping coefficient can not only reduce the setting time of the system,but also ensure the stability of the electromagnetic vibration isolation system and the isolated object.(3)According to the state equation of an electromagnetic vibration isolation system,an active control method based on the linear quadratic regulator(LQR)approach and the co-evolutionary niche genetic algorithm(CNGA)is proposed to realize the optimal control for the control current of the vibration isolation system.For optimizing the weight matrices in the LQR controller,the co-evolutionary niche genetic algorithm is proposed to obtain the control current by calculating the objective function.In order to realize the time-varying control of the electromagnetic vibration isolation system to obtain different optimal control parameters at each control time based on the actual situation,the other active control method based on the receding horizon control(RHC)approach and the co-evolutionary genetic algorithm with variable length chromosomes(CGAVLC)is proposed for improving the performance of the optimal controller.In order to solve the problem of parameter selection of the objective function in the RHC controller,the co-evolutionary genetic algorithm with variable length chromosomes is presented.The lengths of chromosomes are utilized to represent and optimize the prediction horizon and the control horizon,and the values of chromosomes are used to represent and optimize the weights for displacement variations and the electromagnetic forces.According to the calculated optimal weight matrices,the optimal control variables at each time are obtained by solving the objective function in RHC controller.Simulation results,experimental results,and the comparison results with the state feedback control method demonstrate that the proposed active control methods can effectively control vibration and keep the stability of the electromagnetic vibration isolation system and the isolated object.(4)For the limited problem of isolation range and isolation force of a single isolation unit in the electromagnetic isolation system,the parallel electromagnetic isolation systems with multiple electromagnetic isolation units are designed and the controllers are constructed based on LQR and RHC methods,respectively.For the control problems of LQR and RHC controllers in the parallel electromagnetic isolation systems with multiple electromagnetic isolation units,the control performance index of the multiple units is transformed into the objective function based on the established model of the parallel electromagnetic isolation systems with multiple electromagnetic isolation units.Then,the co-evolutionary niche genetic algorithm for the LQR controller and the co-evolutionary genetic algorithm with variable length chromosomes for the RHC controller are utilized to optimize the weight matrices.Simulation and experimental results demonstrate that the active control methods based on the proposed objective function can effectively control vibration,ensure that multiple electromagnetic vibration isolation units have the same trajectory after being disturbed,keep the stability of the electromagnetic vibration isolation system and the isolated object,and reduce the influence of coupling vibration on the parallel system with multiple electromagnetic isolation units.