Computational Optimal Control Of Pipeline Flows

Nowadays,Various pipeline flow transportation systems(petroleum chemical pipeline,urban drainage pipeline,water supply pipeline)are playing more and more important roles in the human production and life.Compared with other transport systems,it has the advantages of high efficien-cy,safety and economy.However,water hammer happens frequently.In severe cases,these may even cause the pipeline to rupture,wasting a lot of manpower and material resources.Thus,to ensure the security and stability of the pipeline system,it is important to research on the computa-tional optimal control of pipeline flow.The main contents and contribution of this dissertation are summarized as follows:1.When fluid flow in a pipeline is suddenly halted,a pressure surge or wave is created within the pipeline.This phenomenon,called water hammer,can cause major damage to pipelines,including pipeline ruptures.We model the problem of mitigating water hammer during valve closure by an optimal boundary control problem involving a nonlinear hyperbolic PDE sys-tem that describes the fluid flow along the pipeline.The control variable in this system represents the valve boundary actuation implemented at the pipeline terminus.To solve the boundary control problem,we first use the method of lines to obtain a finite-dimensional ODE model based on the original PDE system.Then,for the boundary control design,we apply the control parameterization method to obtain an approximate optimal parameter s-election problem that can be solved using nonlinear optimization techniques such as SQP. Finally,we give simulation results demonstrating the capability of optimal boundary control to significantly reduce flow fluctuation.2.We considers an optimal boundary control problem for fluid pipelines with terminal valve control.The goal is to minimize pressure fluctuation during valve closure,thus mitigating water hammer effects.We model the fluid flow by two coupled hyperbolic PDEs with given initial conditions and a boundary control governing valve actuation.To solve the optimal boundary control problem,we apply the control parameterization method to approximate the time-varying boundary control by a linear combination of basis functions,each of which depends on a set of decision parameters.Then,by using variational principles,we derive formulas for the gradient of the objective function(which measures pressure fluctuation)with respect to the decision parameters.Based on the gradient formulas obtained,we propose a gradient-based optimization method for solving the optimal boundary control problem.Numerical results demonstrate the capability of optimal boundary control to significantly reduce pressure fluctuation.3.The Chapter 4 proposes a new time-scaling approach for computational optimal control of a distributed parameter system governed by the Saint-Venant PDEs.We propose the time-scaling approach,which can change a uniform time partition to a nonuniform one.We also derive the gradient formulas by using the variational method.Then the method of lines is ap-plied to compute the Saint-Venant PDEs after implementing the time-scaling transformation and the associate costate PDEs.Finally,we compare the optimization results using the pro-posed time-scaling approach with the one not using it.The simulation result demonstrates the effectiveness of the proposed time-scaling method.