Saint-Venant Reduced Order Model for Water Level Control in Open Channels

Dalmas, Violaine; Robert, Gérard; Besançon, Gildas; Duby, Georges

doi:10.1109/cdc.2018.8619438

Cited by 2 publications

(5 citation statements)

References 15 publications

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“…As depicted in Algorithm 1, an MPC scheme is implemented by solving the static optimization problem of Equation (11) repeatedly as time recedes. The S-V equations formulate the prediction model that predicts the future dynamics with undetermined control.…”

Section: Formulation Of Pde-constrained Model Predictive Control With...mentioning

confidence: 99%

“…The S-V equations formulate the prediction model that predicts the future dynamics with undetermined control. Since the S-V equations are unsolvable analytically, a framework based on the adjoint analysis method is established to solve the optimization problem in Equation (11). By applying the Lagrange multiplier method and variational calculation, the gradients of the objective functional with respect to the control variables are derived.…”

Section: Formulation Of Pde-constrained Model Predictive Control With...mentioning

confidence: 99%

“…Step II Solve the finite horizon optimization problem min u(t )∈U J s.t. %(1), (2), ( 3), ( 4), ( 6), (8) (11) Step III Apply the value of u(t ) at the first time to the plant.…”

Section: Repeat the Following Steps At Each Control Horizonmentioning

confidence: 99%

“…The ordinary differential equations model was developed by a control parameterization method [10]. A reduced order model based on the S‐V equations was proposed with the WKB method [11]. These simplified models used in finite‐dimensional control weaken the representation of the infinite‐dimensional dynamics present in the distributed system.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

PDE‐constrained model predictive control of open‐channel systems

Xie,

Zeng,

Zhang

et al. 2023

IET Control Theory & Appl

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A PDE‐constrained model predictive control (MPC) algorithm for open‐channel systems based on the Saint‐Vevant(S‐V) equations is investigated in this paper. The S‐V equations, which precisely model the dynamics of open‐channel systems, are quasi‐linear hyperbolic partial differential equations (PDEs) without analytical solutions. Directly applying the S‐V equations to an MPC controller design becomes sophisticated. In this work, the calculus of variation is used to obtain the adjoint equations and the adjoint analysis method is utilized to deduce the gradients of the MPC optimization problem. Particularly, the physical constraints involving both the state and control variables are also considered. A gradient‐based optimization algorithm in combination with the numerical computation of Preissmann implicit scheme is proposed to solve the constrained MPC optimization problem. The control performances of the developed PDE‐constrained MPC algorithm with respect to the controlled water levels and gate openings are compared with those of the MPC controller designed for the linearized model. All the simulation tests are carried out on an aqueduct reach in Yehe Irrigation District in Hebei Province, China. The results show that the proposed PDE‐constrained MPC algorithm is a promising method in dealing with the constraints in terms of hyperbolic PDEs, control variables and state variables simultaneously.

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Section: Formulation Of Pde-constrained Model Predictive Control With...mentioning

confidence: 99%

Section: Formulation Of Pde-constrained Model Predictive Control With...mentioning

confidence: 99%

“…Step II Solve the finite horizon optimization problem min u(t )∈U J s.t. %(1), (2), ( 3), ( 4), ( 6), (8) (11) Step III Apply the value of u(t ) at the first time to the plant.…”

Section: Repeat the Following Steps At Each Control Horizonmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

PDE‐constrained model predictive control of open‐channel systems

Xie,

Zeng,

Zhang

et al. 2023

IET Control Theory & Appl

View full text Add to dashboard Cite

show abstract

“…where (15a) and (15b) are derived by applying the recurrence relation (8) to the expressions defining the determinants (indicated above the numbered equalities determining det(K 1 ) and det(K 2 ) respectively). By putting ( 8), ( 14) and (15) together, the characteristic polynomial p A (x) and the characteristic equation of matrix A in variable x can be expressed as follows:…”

Section: Analysis Of the Modelmentioning

confidence: 99%

Asymptotic analysis of a control–oriented open channel flow model

Vasara

Selek

Ikonen

2021

2021 9th International Conference on Systems and Control (ICSC)

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This paper presents the development and mathematical analysis of an open-channel flow model. A tanksin-series model relying on systems engineering perspectives is constructed. Through a series of assumptions, the obtained nonlinear model is approximated by a linear dynamics, and its asymptotic modal behavior is analysed in infinite dimensions using rigorous mathematical machinery. The analysis exploits the repeating tridiagonal structure of the system matrix using Chebyshev polynomials and elaborates the dependence of the modal dynamics on the so-called flow coefficient, which accounts for the description of the flow of the model. The analysis presented in this paper reveals that using constant flow coefficient for flow description in cascade arrangement of liquid storages results in physically meaningless asymptotic modal behavior. The asymptotic modal behavior is well defined if the flow coefficient is an affine function or higher-order polynomial of the number of elements in the cascade structure.

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Saint-Venant Reduced Order Model for Water Level Control in Open Channels

Cited by 2 publications

References 15 publications

PDE‐constrained model predictive control of open‐channel systems

PDE‐constrained model predictive control of open‐channel systems

Asymptotic analysis of a control–oriented open channel flow model

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