基于差分思想的高压油管压力控制

针对2019年“高教杯”全国大学生数学建模竞赛A题——高压油管的压力控制,提出了一种基于差分思想的高压油管内压力控制的建模方法。利用状态转换方程与分段式处理得出了增压阶段单向阀开启时长的控制方案,并进一步验证与分析了模型的精度。分析结果表明:高压油管内部压力稳定在100MPa与150MPa时,单向阀开启时长的相对误差分别是1.19%与0.40%,模型精度高达98%以上,基于差分思想的数学建模方法可以有效控制高压油管的内部压力,提高稳定性。

Aiming at the A question in 2019"Higher Education Cup"National Mathematical Contest in Modeling for College Students―pressure control of high pressure tubing,a modeling method of pressure control in high pressure tubing based on differential idea was proposed.The state transition equation and subsection processing are used to get the control scheme of the opening time of the one-way valve during the pressurization stage,and the accuracy of the model is further verified and analyzed.The analysis results show that when the internal pressure of high pressure tubing is stable at 100 MPa and 150 MPa,the relative error of one-way valve opening length is 1.19%and 0.40%respectively,and the model accuracy is over 98%.The mathematical modeling method based on difference idea can effectively control the internal pressure of and improve the stability of high pressure tubing.