Theoretical Study On Control Synchronization Of Nonlinear Vibration Systems Under Two-exciters And Multi-machine Excitation

Vibration machinery is widely used in coal mining,chemical,metallurgy,electric power,construction,food,medicine,environmental protection and other fields.It can process,classify,de-sludge,dewater,recycle and remove different materials.With the continuous development of modern industry and agriculture,the requirements for vibration machinery are constantly improving,and the vibration machinery is developing in the direction of intelligence,high precision and high efficiency.Vibration body is subject to the inertial force,friction and impact force of the material.In order to more accurately analyze the synchronous performance of the exciter in the vibration mechanical system working,in the study of the vibration mechanical synchronization performance,the influence of the material should be considered.With the continuous development of vibration machinery,higher requirements are placed on the synchronous performance of vibration machinery,the synchronous motion accuracy of vibration machinery limits the application of vibration machinery.Therefore,the multi-exciter excitation vibration system control synchronization theory needs further research to adapt to the high-precision,intelligent development needs.Through the research on the synchronization theory of nonlinear vibration machinery-material system,it has important significance and application value in theory and engineering practice.Many studies on the synchronous performance of vibrating machinery neglect the factors affecting the synchronous motion of the material.In order to better understand the synchronous theory of the actual working conditions,this paper deduces nonlinear vibration machinery-material system dynamics model excited by two or more exciter with the consideration of the influence of materials.The vibration synchronization theory is used to analyze the influence of material nonlinear force on the synchronous motion of the co-rotating double exciter.The correctness of the application of synchronization theory is verified by simulation and experimental comparison.In order to improve the synchronization precision of the two exciters and multi-vibrators in the vibrating machinery-material system,a cross-coupling control strategy and the adjacent cross-coupling control strategy are respectively combining with the adaptive global sliding mode control algorithm are proposed.The experiment verified the effectiveness of the control system.The proposed control system considers the coupling dynamics characteristic between the exciters.The global sliding mode is used in the control system to solve the robustness problem of the sliding mode control arrival stage.The control system can be used for the nonlinear vibration machinery-material system,the total uncertainty is adaptively approximated,suppressing the chattering of the system and making the system’s response more stable.The proposed controller is used to control the multi-exciter in the vibrating machinery-material system,realizing high-precision synchronous motion,and analyzing the vibration characteristics and motion state of the vibrating mechanical system under the nonlinear force of the material.This article mainly studies the following aspects in detail:(1)For the synchronization problem of the vibrating machinery-material system under the excitation of two co-rotating exciters under the condition of far resonance,the synchronization condition and the synchronization state stability condition of the synchronous motion are obtained by the small parameter averaging method.Through the simulation and experimental comparison analysis,the correctness of the application of synchronization theory is verified.Through the establishment of the vibration machinery-material system dynamics model and the analysis and discussion of its synchronous motion performance,it provides a theoretical basis for more accurate analysis of the synchronous performance of the vibration mechanical system.In order to improve the precision of synchronization control,a controller combining cross-coupling control strategy and RBF adaptive global sliding mode algorithm is proposed.The stability of the control system is proved by Lyapunov stability theorem and Barbalat lemma.The effectiveness of the controller is further verified by comparison with the master-slave controller.The controller is used to control the vibrating machinery-material system,which realizes the synchronous movement of the two co-rotating vibration exciters in the system,and the system forms a stable elliptical motion trajectory in the working direction.The cross-coupling control synchronization method realizes the precise synchronous motion of the vibrating machinery-material system,which provides a new method for the design and application of the vibrating mechanical system and expands the application range of the vibrating mechanical system.(2)Two reverse-rotation exciter excited dynamic models of the vibrating mechanical-material system are established.The model considers the influence of the nonlinear force of the material on the synchronous motion of the vibrating mechanical system.In order to improve the synchronous motion effect,a controller combining the cross-coupling control strategy and the adaptive global sliding mode algorithm is proposed for the vibration machine-material system.The controller considers the coupling characteristics between the two reverse-rotation exciters.Firstly,the accuracy of the controller-controlled vibration mechanical system is verified by experimental methods.Then,the proposed cross-coupling controller is used to control the vibration mechanical system considering the material,and the synchronous motion of the two reverse rotary exciter excited vibration mechanical-material system is realized,and the synchronization performance and control precision are improved.(3)Aiming at the synchronous motion of multi-exciter with more than three exciters in the nonlinear vibration machinery-material system,the dynamic model of nonlinear vibration mechanical system under the excitation of the homodromy three exciters and the reverse rotation of four exciters and the excitation of multiple exciters considering the influence of materials are derived.Aiming at the problem of speed and phase synchronization of multi-vibrators,a controller based on RBF network adaptive global sliding mode algorithm and adjacent cross-coupling control strategy is established.The stability of the controller is proved by Lyapunov’s theorem.The effectiveness of the adjacent cross-coupling controller is verified by numerical simulation.The adjacent cross-coupling strategy considers the coupling between adjacent exciters and improves the control accuracy of the multi-exciter speed and phase.The RBF adaptive global sliding mode algorithm can adaptively learn the total uncertainty of the nonlinear vibration system,suppress the chattering of the system and make the response of the system more stable.Accurate control of the nonlinear vibration system is achieved by the control of the adjacent cross-coupling controller.The vibrating mechanical system obtained stable elliptical vibration and linear vibration under the conditions of three-exciters co-rotating and four-exciters reverse rotation.By analyzing the influence of parameter changes in the nonlinear vibration machinery-material system on the proposed controller,the robustness of the control system is illustrated.