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Study on Nonlinear Feedforward Control of Open-Channel Based on Adjoint Equation

Author(s): Xiaochen Guo; Wenxue Chen; Xiangpeng Mu; Yihong Wu; Zhiping Liu

Linked Author(s): Wenxue Chen, Zhiping Liu, Yihong WU

Keywords: Nonlinear optimal control; Open canal; Sensitivity analysis; Recedingoptimal; Feedforward control

Abstract: An optimal flow control methodology based on adjoint sensitivity analysis of Saint-Venant equations for open channel flows is presented. The objective of the controller is to maintain the constant downstream water level at the pool under external perturbation. The off-take discharge is selected as the input variable, and gate opening is the control variable. The inequality of the prediction horizon and the control horizon makes the control process more flexible. The control algorithm has two characteristics as nonlinear model prediction and receding optimization. The Saint-Venant equations and their strong nonlinear adjoint equations were discretized by means of the implicit four-point finite-difference scheme firstly proposed by Preissmann. Firstly, the nonlinear modeling prediction is adopted, and then the sensitivity of the gate opening, i.e. the gradient of the gate opening to the objective function, is calculated, and finally the gate opening is obtained through an iterative minimization procedure. And the optimal model is solved by means of quasi-Newton method which has the merits as fast convergence and more numerical stability. The simulation result shows that the proposed control method is more effective and robust than the gate stroking method. And the controlled water level variation is small. Furthermore, this method could be used in operation of the canal systems.


Year: 2009

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