Active Vibration Control Of An Axially Moving System With High Acceleration/Deceleration

Axially moving structures are widely applied in many areas of modern mechanical,aerospace,marine,electronic,civil and automotive engineering due to the advantages of low damping,small stiffness,light weight,good flexibility,low energy consumption and so on.The structures can generally exhibit vibration,owing to the effects of the rotor eccentricity,motor excitation,its flexibility property and external disturbances.However,the unwanted mechanical vibration of the structures can degrade the performance of the system,shorten the service life of the material,limit the associated manufacturing process productivity and affect the processing precision of the product.What is more,it would lead to serious production accidents and then bring economic losses.With the development of system performance and production accuracy towards high precision day by day,the vibration suppression of axially moving systems has become an important research area and gained more concern of the experts and scholars at home and abroad in recent decades.The axially moving system can be identified as a typical distributed parameter system(DPS)with infinite-dimensional characteristics in the mathematical sense.The flexible structure is expressed by an infinite number of modal,which makes the control design more difficult.As per the existing literature,research on vibration control of axially moving systems mainly focuses on passive control and active control.The passive control is to achieve the vibration suppression via the optimization of material or stiffness,but it is limited with the increase of control precision.The active control is to control the vibration by designing the controller,and the research approaches mainly include modal approach,distributed control and boundary control.The modal approach is to implement control design based on the truncated finite-dimensional model,which would lead to control spillover and make the system unstable.The distributed control might yield better control performance,but it will make the controller difficult to implement in practice due to requiring many more distributed sensors and actuators.Boundary control can overcome the drawbacks arising from the above-mentioned methods and is successfully applied in the vibration suppression field of the axially moving system.In this paper,an axially moving belt system of Surface Mount Technology equipment(SMT)is considered.The active boundary control scheme is utilized to suppress the vibration of the belt system,achieving the application of active control theory and method in precision electronic manufacturing equipments.The main research work of this dissertation is summarized as follows:1.The background,research significance and status of axially moving systems are introduced,and then the research progresses of DPS,Lyapunov's direct method,active vibration control for axially moving systems,backstepping and nonsmooth nonlinearities are emphatically elaborated.Finally,the relevant theories and methods are presented.2.By studying the system dynamics,the geometric nonlinear characteristics,the relationship between acceleration or velocity and system parameters and so on,the energy method,Hamilton principle and variation operator are applied to obtain the dynamical model of the axially moving belt system,whose dynamics is represented by a partial differential equation(PDE)and a set of ordinary differential equations.3.The active vibration control problem of the axially moving belt system with high acceleration/deceleration(H-A/D)and system parametric uncertainties under unknown spatiotemporally-varying distributed disturbance and time-varying boundary disturbance is considered.Based on the original infinite-dimensional model of the system,the robust adaptive boundary control is developed to suppress the vibration and stabilize the system at the small neighborhood of its original position combining with Lyapunov theory,robust adaptive control technique and S-curve acceleration/deceleration(Sc-A/D)method.Besides,the disturbance observer is introduced to attenuate the effects of unknown external disturbance and the adaptive laws are employed to compensate for the system parametric uncertainties.With the proposed control,the control spillover phenomenon produced by the traditional truncated model-based methods is avoided,the stability of the closed-loop system is demonstrated and the uniform boundedness of the closed-loop signals is ensured.Finally,the finite difference method is used to carry out the numerical simulation and the results verify the effectiveness of the proposed controllers.4.The boundary control problem of the axially moving system with H-A/D in the presence of spatiotemporally-varying tension and external disturbances is investigated.Based on the infinite-dimensional PDE dynamics of the system and the principle of ScA/D,the finite-dimensional backstepping,Lyapunov's direct method and disturbance observer technique are exploited to construct a boundary controller with disturbance observer aiming at restraining the vibration and tracking the boundary disturbance.Subsequently,the uniform bonudedness of the controlled system under external disturbances and the exponential stability under free vibration are proven based on strict mathematical analysis.Finally,the control performance of the closed-loop system is validated via simulations.5.The boundary control issue of an axially moving system with H-A/D subject to the input saturation constraint is raised.In order to suppress the vibration of the presented system and handle the constraint effects of the input saturation,the state feedback and output feedback boundary control with an auxiliary system are developed.In addition,high-gain observers are utilized to estimate those unmeasurable system states.The uniformly bounded stability of the controlled system is analyzed through Lyapunov's synthetic method.Finally,the comparison results further show that the proposed controllers can stabilize the presented system with a better performance despite the exist of the input saturation.