| Abstract: | When a valve is suddenly closed in fluid transport pipelines, a pressure surge or shock is created along the pipeline due to the momentum change. This phenomenon, called hydraulic shock, can cause major damage to the pipelines. In this paper, we introduce a hyperbolic partial differential equation (PDE) system to describe the fluid flow in the pipeline and propose an optimal boundary control problem for pressure suppression during the valve closure. The boundary control in this system is related to the valve actuation located at the pipeline terminus through a valve closing model. To solve this optimal boundary control problem, we use the method of lines and orthogonal collocation to obtain a spatial-temporal discretization model based on the original pipeline transmission PDE system. Then, the optimal boundary control problem is reduced to a nonlinear programming (NLP) problem that can be solved using nonlinear optimization techniques such as sequential quadratic programming (SQP). Finally, we conclude the paper with simulation results demonstrating that the full parameterization (FP) method eliminates pressure shock effectively and costs less computation time compared with the control vector parameterization (CVP) method. |
