Sliding Mode Synchronization Control Of A Bilaterally Symmetrical Type Hybrid Mechanism

To remedy the defects of the existing automobile electro-coating conveying systems with the cantilever beam structure,our research group developed a bilaterally symmetrical type hybrid mechanism for automotion electro-coating conveying.To further improve the motion control performance on the basis of its mechanical properties,this paper focuses on the high performance motion control of the bilaterally symmetrical type hybrid mechanism.To achieve this goal,two main problems need to be solved: the synchronization problem and the uncertainty problem.The reasons are shown as follows.Firstly,hybrid mechanisms generally have multiple active joints,and the synchronization and coordination among the active joints influence the security,reliability and control accuracy of the system.Besides,the hybrid mechanism studied in this paper is a bilaterally symmetrical type mechanism with three parallel-serial combined active joints in each side.The whole mechanism is equivalent to two groups of hybrid mechanisms moving synchronously when the mechanism is running.Therefore,it demands higher synchronization performance.Secondly,the control system of hybrid mechanism is affected by modeling error,friction,external disturbance and other uncertainties.These uncertainties directly influence the control performance of hybrid mechanisms.In order to solve the synchronization problem,this paper introduces the synchronization control theory.A coupling synchronization error is designed,which is coupled of the synchronization error among active joints and the synchronization error between two ends of the connecting rod.The convergence of the coupling error can ensure the synchronization among active joints and the synchronization between two ends of the connecting rod.Furthermore,a novel compound error is designed by combining the coupling synchronization error and the tracking error of the end-effector of the hybrid mechanism.The convergence of the compound error can further guarantee the tracking accuracy of the end-effector and the synchronization of the system.The rationality of the designed compound error is proved.Considering the strong robustness,fast response speed and other advantages of sliding mode control,the sliding mode control strategy is introduced in this paper to solve the uncertainty problem.Firstly,a compound error constant speed sliding mode synchronizaition controller is designed to solve the synchronization problem and the uncertainty problem of the system.However,due to the existence of the switching function in the constant speed reaching law,the system remains the chattering problem.To solve this problem,the switching function is replaced by a norm function,and a compound error chattering-free sliding mode synchronization controller is designed.Since the norm function is a continuous function,the robustness of the compound error chattering-free sliding mode synchronization controller is decreased.Therefore,a compound error super-twisting sliding mode synchronization control algorithm is further proposed by replacing the norm function with an integral function.The proposed control algorithm can further improve the synchronization,robustness,response speed and tracking accuracy of the system while keeping the control system chattering-free,and can realize the high performance control of the hybrid mechanism.In this paper,we firstly summarize the development of automobile electro-coating conveying equipment and hybrid mechanisms,and introduce current researches of synchronization problem and uncertainty problem of hybrid mechanisms in detail.Secondly,we briefly introduce the components of the hybrid mechanism and its working principle.Then based on the established inverse kinematics,the Jacobi matrix of the mechanism is calculated.Besides,the desired motion trajectory is designed according to the engeering application requirements of the mechanism.Thirdly,the dynamic model of the hybrid mechanism,including the uncertainly factors,such as friction and external disturbance,is established by Lagrange method in Cartesian space.The dynamic model is simulated by MATLAB to verify the correctness of it.Fourthly,we design a coupling synchronization error,which is coupled of the synchronization error among active joints and the synchronization error between two ends of the connecting rod.Then a novel compound error is designed by combining the coupling synchronization error and the tracking error of the end-effector.The rationality of the compound error is proved.Based on the novel compound error,a compound error constant speed reaching law sliding mode synchronization controller is designed,and its stability and convergence are proved.The MATLAB simulation results verify the effectiveness of the designed controller of improving the synchronization performance and solving the uncertainty problem of the system.Further research shows that,since the existence of the switching function in the control law,the system has the chattering problem.To solve this problem,a compound error chattering-free sliding mode synchronizaiton controller is designed by replacing the switching function with a norm function.Its stability and convergence are proved and the MATLAB simulation results veritify the effectiveness of the designed controller to solve the chattering problem.Since the norm function is a continuous function,the robustness of the compound error chattering-free sliding mode synchronization controller is decreased.To further improve the robustness of the system while keeping the system chattering-free,a compound error super-twisting sliding mode synchronization control algorithm is proposed by replacing the norm function with the integral term.Its stability and convergence are proved.MATLAB simulation results show that the proposed compound error super-twisting sliding mode synchronization control algorithm can further improve the synchronization,robustness,response speed and tracking accuracy of the system and realize the high performance control of the hybrid mechanism.Finally,the general framework of the sliding mode synchronization control system for the hybrid mechanism is designed,and its hardware and software platform are respectively constructed.Then the debug of the prototype of the hybrid mechanism is completed,and the motion control experiment of the proposed compound error super-twisting sliding mode synchronization control algorithm is completed based on it.The correctness and effectiveness of the proposed compound error super-twisting sliding mode synchronization control algorithm is verified by the experiment results.