Abstract
In this paper, we propose an efficient computational boundary control strategy for reducing water pressure shock effects generated by the suddenly operation of the valve closure located at the end of a fluid flow pipeline. First, we model the dynamic of the fluid flow transmission system as a coupled hyperbolic partial differential equations (PDEs), and then the water pressure suppression problem is formulated as a finite-time PDE-constrained optimal control problem. Second, we directly parameterize the time-varying boundary control input as a set of basic piecewise-quadratic functions which are needed to be optimized, the penalty function method is also introduced to deal with the inequality control constraint. As a result, the original PDE-constrained problem is transformed as a sequence of parameter optimization problems which can be easily solved by using existing gradient-based methods such as sequential quadratic programming (SQP). The exact gradient formulas of the cost function are derived analytically by using adjoint-based sensitivity analysis method. Finally, numerical simulations are illustrated to demonstrate our designed computational optimal boundary controller can significantly reduce the water pressure shock and fluctuation in the fluid flow transmission system.
Highlights
When a valve located at the end of a fluid flow pipeline is suddenly closed, the abrupt halting of fluid flow will generate very huge pressure shocks and fluctuations propagation along the pipeline, which would affect the security of the pipeline system, severe cases may even damage the entire pipeline transmission networks
We focus on solving a water pressure suppression control problem for a class of fluid flow transmission systems modeled by a set of hyperbolic partial differential equations (PDEs)
Different from using the control vector parameterization (CVP) method to the conventional ODE-constrained optimal control problems obtained from the original PDE problems via various model reduction techniques such as in [13], [21], [29], in this paper, we extend the control parameterization method and directly use it to solve the original PDE-constrained Problem Q1
Summary
When a valve located at the end of a fluid flow pipeline is suddenly closed, the abrupt halting of fluid flow will generate very huge pressure shocks and fluctuations propagation along the pipeline, which would affect the security of the pipeline system, severe cases may even damage the entire pipeline transmission networks. In [12], a predictive control method based on the method of characteristics is proposed for the suppression of the pressure surges in crude oil pipelines modeled by a class of hyperbolic PDEs. In this paper, we focus on solving a water pressure suppression control problem for a class of fluid flow transmission systems modeled by a set of hyperbolic PDEs. The valve is taken as a boundary controller working at the end of the pipeline and needs to be designed optimally so that the water pressure suppression can be mitigated quickly. 4) Numerical simulation results demonstrate our designed optimal boundary control can significantly reduce the water pressure shock and fluctuation.
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