流体管道水锤抑制的时间尺度变换控制

Control of water hammer suppression via time-scaling technique

中文关键词  水锤模型  分段一次线性控制变量参数化  时间尺度变换  敏感性分析

英文关键词  water hammer model  piecewise-linear control parameterization  time-scaling technique  sensitivity analysis

中文摘要

      在流体管道运行中, 打开的阀门突然关闭会造成管道内部流体对阀门及管壁的巨大压力冲击, 这种现象叫 做水锤效应, 严重威胁流体管道的健康运行. 基于此, 本文研究了阀门关闭过程中抑制水锤效应的最优边界控制问 题. 水锤模型由一组非线性时空演化方程描述, 本文首先通过半离散方法得到一个有限维模型. 然后, 采用分段一 次线性控制变量参数化方法及灵敏度分析方法, 结合时间尺度变换方法, 推导其梯度形式. 最后, 结合非线性优化 求解器, 完成边界最优控制设计. 仿真结果显示时间尺度变换方法能够更有效地抑制水锤效应. 考虑到实际工程中 的控制量为阀门相对开度, 在得到阀门处的流量和压力的最优变化过程后, 本文给出了阀门相对开度随时间的演化 关系.

英文摘要

      During the fluid pipeline running, sudden closure of an open valve in the pipeline network causes a huge pressure shock toward the valve and pipeline wall. This phenomenon, called water hammer, threatens the healthy operation of the fluid pipeline. Thus, an optimal boundary control problem of water hammer suppression during valve closure is studied. The water hammer model can be described as a set of nonlinear spatio-temporal equations, including a boundary control at the end of the pipeline. First, the method of lines (MOL) is applied to reduce the water hammer model to a finite dimensional model. Then, the piecewise-linear control parameterization method and sensitivity analysis method combined with the time-scaling technique are proposed to derive the gradients of the objective function. Finally, nonlinear optimization techniques are used to solve the optimal control problem. Numerical results show the time-scaling technique can suppress water hammer more effectively. Since the practical control input is the degree of the valve opening, the optimal changes of valve relative opening with time evolution are given based on the optimal boundary control and the corresponding pressure changes.