Comprehensive Error-based Sliding Mode Control For Uncertain Hybrid Mechanism

In order to further improve the load capacity and flexibility level of existing electrophoretic coating transport equipment,our research group developed a novel hybrid mechanism for electrophoretic coating and conveying of automobiles by combining parallel and serial mechanisms in a complementary way in terms of structure.This paper takes this hybrid mechanism as the research object and focuses on studying its high-performance trajectory tracking control method.At present,the research difficulties of achieving high-performance trajectory tracking control of the hybrid mechanism are mainly: end-effector movement accuracy problem and uncertainty problem.Since hybrid mechanisms currently mostly adopt joint space control,hybrid mechanisms with multiple branches and multiple active joints are affected by various factors such as controller time delay error,desired trajectory curvature,and multi-joint asynchrony when realizing trajectory tracking motion,which will cause large end-effector movement errors in the task space of the hybrid mechanism.In addition,there are many uncertainties in the control system of the hybrid mechanism during actual operation,such as friction forces of each active joint;modeling errors caused by screw clearance,connecting rod tilt and uneven vehicle load changes;external environmental changes when the vehicle enters and exits the electrophoretic liquid tank,etc.,which will reduce the control performance of the hybrid mechanism and even cause instability of the mechanism.Therefore,different from existing hybrid mechanism control methods that only focus on tracking errors along the instruction point direction,this paper introduces contour errors orthogonal to the desired trajectory,by establishing a new type of comprehensive error that combines end pose contour error with end tracking error in task space,and proposes a new comprehensive error-based sliding mode control method for the hybrid mechanism to improve its system robustness and convergence performance of end-effector movement error and tracking performance.The main work completed in this paper is as follows:(1)The kinematics and dynamics of the proposed hybrid mechanism are analyzed.The analytical solutions of the forward and inverse kinematics of the mechanism are obtained,and the Jacobian matrix is derived.The Lagrange method is used to establish a standard dynamic model and a dynamic model with aggregated uncertainties of the hybrid mechanism in task space,and MATLAB software is used for simulation verification and result analysis to verify the necessity and accuracy of the established dynamic model with aggregated uncertainties of the hybrid mechanism in task space.(2)A new comprehensive error is established in task space.In view of the problem of endeffector movement accuracy of hybrid mechanism,a new end-effector pose contour error is designed,which can not only reflect the position accuracy of hybrid mechanism end-effector orthogonal to desired trajectory direction,but also reflect its orientation accuracy.Then,in order to consider the end-effector movement accuracy along instruction point and orthogonal to desired trajectory,a new comprehensive error is established in task space,which combined with end pose contour errors and end tracking errors,and the rationality analysis of comprehensive error establishment is carried out.(3)A comprehensive error-based sliding mode control method for hybrid mechanism is proposed.In order to solve the problems of end-effector movement accuracy and uncertainty at the same time,based on the newly established comprehensive error,a comprehensive error-based continuous non-singular fast terminal sliding mode control algorithm(CE-NFTSMC)for hybrid mechanism is designed to improve the robustness and end-effector movement accuracy of uncertain hybrid mechanism system,improve the convergence speed of system,and suppress sliding mode control jitter.The Lyapunov stability proof of designed controller is completed,and simulation experiments are carried out through MATLAB software.The results show that compared with tracking error-based continuous non-singular fast terminal sliding mode control(NFTSMC),the proposed algorithm can effectively improve the movement accuracy of hybrid mechanism end-effector orthogonal to desired trajectory direction;Compared with comprehensive error-based constant-velocity reaching law sliding mode control(CE-SMC),the proposed algorithm can effectively improve system convergence performance and tracking performance,and suppress sliding mode control jitter.(4)Based on “upper computer + lower computer” distributed control system experimental platform according to hybrid mechanism control requirements and actual task demand of electrophoretic coating transportation,a comprehensive error-based sliding mode control system for hybrid mechanism is constructed.Through prototype comparative experiment with NFTSMC,the effectiveness of proposed method is further verified.