Research On Time Optimal Trajectory Optimization And Iterative Learning Error Control Of CNC Machine Tools

Computer numerical control machine tools have a large number of positioning auxiliary strokes when processing complex workpieces.In order to improve the working efficiency of the CNC machine tool,the running time of the auxiliary stroke should be reduced as much as possible.Therefore,it is necessary to optimize the trajectory of the auxiliary stroke with the minimum trajectory running time as the goal.In the existing traditional CNC machine tool auxiliary stroke interpolation methods,the trapezoid and S-shaped speed curve interpolation of straight lines and arcs are mostly used,and the jerk,acceleration time,maximum speed and other parameters need to be set manually.On the one hand,this is not conducive to the realization of intelligence of CNC machine tools;on the other hand,it is not conducive to the realization of high-speed motion control of CNC machine tools.This article focuses on how to achieve high-speed motion control of the auxiliary stroke of CNC machine tools to improve work efficiency and how to achieve high-precision motion control of CNC machine tools to improve processing quality.The main contents are as follows:(1)The dynamic model of CNC machine tools is established according to the second type of Lagrange's equation.The excitation trajectory is designed with the Fourier series as the variable and the condition number of the dynamic model observation matrix as the goal.Recursive least squares method is used to identify the dynamic parameters.The experimental results show that the identified dynamic model can better fit the actual model of the CNC machine tool.(2)In order to constrain the motor torque,a numerical integration time-optimal trajectory optimization method based on the dynamic model of CNC machine tools is proposed: based on the identified dynamic model,with motor speed,acceleration and torque constraints as constraints,and trajectory running time as the objective function,a mathematical model of the time-optimal trajectory optimization problem is established,and the numerical integration-like method is used to solve it.The simulation results show that the trajectory speed,acceleration and torque obtained by the optimization of the numerical integration-like algorithm all meet the constraint conditions.However,the experimental results show that the torque of some points on the trajectory obtained by the numerical integration-like algorithm is beyond the torque limit,which is caused by the mismatch between the theoretical dynamic model and the actual model.(3)Furthermore,in order to avoid the mismatch between the theoretical dynamic model and the actual model in the time-optimal trajectory optimization of CNC machine tools,thereby solving the problem of motor dynamic load overload,a dynamic-free time-optimal trajectory optimization reinforcement learning method is proposed: according to the kinematic constraints of the motor,a reinforcement learning environment for time-optimal trajectory optimization problems is constructed.Considering the characteristics of the time-optimal trajectory optimization problem,corresponding improvements are made to the SARSA algorithm's action,reward and action state value functions,so as to obtain an improved SARSA algorithm for the time-optimal trajectory optimization problem.An iterative interaction method with the real environment is proposed,which introduces dynamic torque constraints into the reinforcement learning environment through interaction with the real environment,and then the improved SARSA algorithm is used to solve the problem.Through continuous iteration,a time-optimal trajectory that satisfies both kinematics and dynamics constraints is finally obtained.The experimental results show that after multiple iterations,the trajectory speed,acceleration and torque obtained by the time-optimal trajectory optimization reinforcement learning method can meet the constraint conditions.(4)High-precision motion control of CNC machine tools.Aiming at the effects of non-linear disturbances such as the noise,friction and the gap between the screw and the screw nut of the CNC machine tool,using the characteristics of the repetitive work of the CNC machine tool,a dual-encoder-based iterative learning error control method is proposed:using the system identification method to identify the transfer function between the motor input and the workbench output.The error between the actual output of the load and the expected input is taken into account in the control,and based on this;an iterative learning method is used to control the error.Finally,the stability of the proposed dual-encoder-based iterative learning error control method is analyzed in the form of a lifting matrix.Experimental results show that the proposed dual-encoder-based iterative learning error control method can not only respond to input and disturbances to adapt to changes or uncertainties in the system model,but also can learn and compensate disturbances,frictions and un-modeled nonlinearities behavior.After several iterations,the maximum value and root mean square of the trajectory tracking error have been greatly reduced,and finally the high-precision motion control of the CNC machine tool is realized.