Research On Active Disturbance Rejection Control Strategy Of Magnetic Levitation Ball Systems

Magnetically suspended technology makes objects in a contactless suspension state by using magnetic force.It has the advantages of high speed,no pollution and no mechanical contact.It is widely used in the fields of space,transportation,industry and so on.The magnetic suspension sphere is an important experimental device to verify the magnetic suspension technology.It is a non-linear open-loop unstable system.The design of controller for magnetic levitation sphere system is confronted with the influences of modeling error,external disturbance,balance point drift and other uncertain disturbances,which bring great challenges to the high performance control of magnetic levitation sphere position.In order to achieve high-performance control of magnetic suspension sphere system under multi-source uncertain disturbances,an auto-disturbance rejection control strategy is proposed,which considers the internal and external disturbances as"comprehensive disturbances".Using the advantage that the design of auto-disturbance rejection controller is not entirely dependent on the precise mathematical model of the system,an extended state observer is constructed to realize on-line estimation of multi-source uncertain disturbances and to implement feed-forward compensation.The nonlinear uncertain system is transformed into a disturbance-free linear integral cascade form,and the state feedback controller is further designed to achieve high-performance control of the magnetic suspension sphere system.The main research contents are as follows:（1）Based on the analysis of the structure and working principle of the magnetic suspension sphere system,the mathematical model of the system is built and linearized.（2）A linear ADRC method based on model-assisted linear extended state observer（LESO）is presented to improve the control performance of the system.By incorporating the known LESO model information into the LESO design process,the convergence of the model-assisted LESO is analyzed and compared with the simulation of LADRC and PID when the model is completely unknown.（3）To further suppress the influence of multisource uncertain disturbances with high frequency measurement noise on the system control performance,a linear active disturbance rejection control（LADRC）method based on an improved extended state observer is presented.In view of the frequency characteristics of multi-source uncertain disturbances in a magnetic suspension sphere system,a LADRC method for magnetic levitation sphere based on cascade extended state observer is presented.The convergence of CESO（Cascade Extended State Observer,CESO）is analyzed by using the disturbance frequency stratification method.The feasibility of this method is verified by simulation.By comparing the performance of the magnetic suspension sphere under LADRC and PID control when the extended state observer is CESO_（1）,CESO_（2）,CESO_（3）,the general rule between the number of CESO layers and the speed/accuracy of state estimation is given,and the superiority of the control strategy is verified.（4）In order to further improve the performance of linear ADRC control based on CESO,on the basis of research（3）,fractional order PD is used instead of conventional linear PD state feedback control law to improve the robustness of the system.The effectiveness of the proposed control method is verified by simulation.By improving the self-disturbance rejection controller,this paper effectively suppresses the influence of multi-source uncertain disturbance with high frequency measurement noise on the system control performance,expands the range of ESO bandwidth,reduces the sensitivity of ESO to high frequency measurement noise,improves the system comprehensive disturbance estimation/control accuracy,and has the advantages of simple structure,easy implementation and strong disturbance rejection ability.