木塑材料3DP打印机运动控制系统轨迹跟踪研究

Research on trajectory tracking of motion control system ofwood-plastic material 3DP printer

针对木塑材料3DP打印机运动控制系统X轴负载较大而导致CoreXY机构在进行开环控制时打印精度较差的问题,研究3DP打印机的模型预测控制(MPC)智能轨迹跟踪算法,提高打印精度和打印速度。基于黏结剂喷射(3DP)成型工艺和CoreXY机构的传动特点设计了木塑材料3DP打印机运动控制系统,提出了一种适用于3DP打印机的MPC轨迹跟踪策略。采用笛卡尔坐标系下近似圆形切片的打印轨迹作为参考轨迹,建立CoreXY机构A、B电机闭环系统的预测模型,运用MPC理论将打印速度和精度的多约束最优控制问题变为带约束的二次函数进行求解,对比参考轨迹与实际打印轨迹之间的误差,进而研究不同打印速度对轨迹跟踪效果的影响。对仿真结果进行分析计算得出,打印速度在80~400 mm/s范围内,3DP打印机的喷胶位点均可实现对参考轨迹的较准确跟踪,A、B电机皮带位移最大横向误差分别为0.0097和0.0060 mm,X、Y轴横向误差的平均绝对误差分别为0.357和0.362 mm。对比PID控制,MPC控制策略的各项衡量指标都更优,且参数更易整定,横向误差更小,提高了3DP打印机喷射路径的准确度和效率。随着打印速度的降低,MPC控制器的横向误差逐渐减小,系统的轨迹跟踪效果更准确和稳定,最终绘制参考轨迹与实际轨迹形状基本重合。

Wood additive manufacturing technology can help reduce the cost of 3D printed products and reduce carbon footprint.Aiming at addressing the problem that CoreXY mechanism has poor printing accuracy when performing open-loop control due to the large load of X-axis in the motion control system of wood-plastic 3DP printer,the intelligent trajectory tracking algorithm of model predictive control(MPC)of 3DP printer was investigated to improve printing accuracy and printing speed.The motion control system of wood-plastic material 3DP printer was designed based on three-dimensional printing(3DP)molding process and transmission characteristics of the CoreXY mechanism,and an MPC trajectory tracking strategy adapted to 3DP printer was proposed.The print trajectory of an appro-ximate circular slice under the cartesian coordinate system was used as the reference trajectory,the prediction model and loss function of the closed-loop system of A and B motors of CoreXY mechanism was established.Then the multi-constraint optimal control problem of printing speed and precision was transformed into a quadratic function with constraints,which can be solved using the model predictive control theory.By comparing the errors between the reference trajectory and the actual printing trajectory and comparing the effectiveness of the MPC and PID controls,the influence of different printing speeds on the trajectory tracking effect was studied.The simulation results were analyzed and calculated.It was concluded that the reference trajectory could be tracked accurately at the spray glue sites of 3DP printers within the range of 80-400 mm/s.The maximum lateral error of belt displacement of A and B motor was 0.0097 mm and 0.0060 mm,respectively.The average absolute error of X and Y axis lateral error was 0.357 mm and 0.362 mm,respectively.Compared with the PID control,the MPC control strategy had advantages of better indicators,easier parameter tuning and smaller lateral error,which improved the accuracy and efficiency of 3DP printer jet path,and solved the problems of parameter mismatch and low adaptability in traditional controls.With the decrease of the printing speed,the lateral error of MPC controller was gradually reduced,and the track tracking effect of the system was more accurate and stable.The MPC control strategy can update the prediction model within the control area according to the reference trajectory,solving the problem of actual printing deviation caused by mechanical structure in the X and Y axes,and effectively adjusting the actual motor speed and trajectory to enhance 3D printing efficiency.