Open channel transient flow control by discrete time LQR methods

Garcia, Andre; Hubbard, Mont; Vries, J. J. de

doi:10.1016/0005-1098(92)90113-t

Cited by 43 publications

(22 citation statements)

References 7 publications

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“…As t is increased, a higher penalty is applied to depth deviations and gate velocities. The effect of a larger t specification will be less abrupt responses to changes in the disturbances [17]. The maximum deviations in gate openings ( u) are just the difference between the initial and final steady gate position.…”

Section: Linear Quadratic Regulatormentioning

confidence: 99%

“…The maximum deviations in gate openings ( u) are just the difference between the initial and final steady gate position. On the diagonal elements of Qx and R are nonzero and their values are determined from the flow transition and the corresponding wave equation response [17]. Conditions for the existence and uniqueness of the optimal solution are always met when diagonal penalization is used.…”

Section: Linear Quadratic Regulatormentioning

confidence: 99%

“…For practical applications, the values of these variables instead of the values of their derivatives must be known. Because of the presence of nonlinear terms, a closed-form solution of these equations is not available, except for very simplified cases [17]. The stability of a numerical solution of the equations can be investigated by studying whether an error grows or decays as the solution progresses in a marching (step by step) procedure.…”

Section: Mathematical Modelmentioning

confidence: 99%

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Fuzzy logic adaptive Kalman filtering in the control of irrigation canals

Durdu

2009

Numerical Methods in Fluids

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SUMMARYA fuzzy logic adaptive Kalman filtering methodology was developed for the automatic control of an irrigation canal system under unknown disturbances (water withdrawals) acting in the canal. Using a linearized finite difference model of open channel flow, the canal operation problem was formulated as an optimal control problem and an algorithm for gate opening in the presence of arbitrary external disturbances (changes in flow rates) was derived. Based on the linear optimal control theory, the linear quadratic regulator (LQR), assuming all the state variables (flow depths and flow rates) were available, was designed to generate control input (optimal gate opening). As it was expensive to measure all the state variables (flow rates and flow depths) in a canal system, a fuzzy logic adaptive Kalman filter and traditional Kalman filter were designed to estimate the values for the state variables that were not measured but were needed in the feedback loop. The performances of the state estimators designed using the fuzzy logic adaptive Kalman filter methodology and the traditional Kalman filtering technique were compared with the results obtained using the LQR (target loop function). The results of the present study indicated that the performance of the fuzzy logic adaptive Kalman filter was far superior to the performance of the observer design based upon the traditional Kalman filter approach. The obvious advantages of the fuzzy logic adaptive Kalman filter were the prevention of filter divergence and ease of implementation. As the fuzzy logic adaptive Kalman filter requires smaller number of state variables for the acceptable accuracy therefore, it would need less computational effort in the control of irrigation canals.

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Section: Linear Quadratic Regulatormentioning

confidence: 99%

Section: Linear Quadratic Regulatormentioning

confidence: 99%

Section: Mathematical Modelmentioning

confidence: 99%

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Fuzzy logic adaptive Kalman filtering in the control of irrigation canals

Durdu

2009

Numerical Methods in Fluids

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“…One is the so-called Saint Venant equations (Chow, 1959). From Saint Venant equations, a class of models are derived (discretized in Balogun, Hubbard, & De Vries, 1988;Garcia, Hubbard, & De Vries, 1992;Georges, 1994, and linearized in Baume & Sau, 1997;Chentouf, Xu, & Boulbrachene, 2001;Duviella, Charbonnaud, Chiron, & Carrillo, 2005;Litrico, 2001;Litrico & Georges, 1997, 1999a, 1999bLitrico, Georges, & Trouvat, 1998). The other principle is the water volume or mass balance principle (Corriga, Patta, Sanna, & Usai, 1979;Corriga, Sanna, & Usai, 1983;Schuurmans, Bosgra, & Brouwer, 1995;Schuurmans, Hof, Dijkstra, Bosgra, & Brouwer, 1999), with which some volume (mass) balance models are presented.…”

Section: Introductionmentioning

confidence: 99%

A modelling methodology for natural dam-river network systems

Zhuan

Zheng

Xia

2009

Control Engineering Practice

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a b s t r a c tAn approach for modelling a natural dam-river network system is proposed in this paper. Generally, the relationships among the variables of a natural dam-river network system are complex and difficult to describe. In this paper, some simple relationships among the water levels measured at a limited number of points of the network system are presented in such a way that a simple model is achieved. The model is identified and validated with the real time operational data. An example is given and the result shows the feasibility of the modelling methodology. It is believed that the proposed approach can be used in the operation of natural dam-river or river network systems.

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“…Usually numerical methods [3,4] have been used to obtain a solution of the Saint-Venant equations. The more typical numerical methods are the characteristic method [5], the finite difference method [6], and Preissman implicit scheme [7][8][9]. The implicit numerical schemes are simpler than the other approaches.…”

Section: Introductionmentioning

confidence: 99%

Discussion on Muskingum versus Integrator-Delay Models for Control Objectives

Bolea

Puig

Grau

2014

Journal of Applied Mathematics

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A comparative study about two models, Muskingum and integrator-delay (ID) models, for canal control is presented. The former is a simplified hydrological model which is very simple and extensively used in hydraulic engineering for simulation and prediction. The latter is also a model with physical meaning and is widely used for irrigation canals control. Due to a lack of general awareness of Muskingum prediction model in regulation from the control community, authors present this comparative study with the ID control model. Both models have been studied and analyzed for control purposes. This study has been carried out and validated in a real irrigation canal, at Aghili irrigation district in Iran, using two traditional control approaches, PID with feedback and predictive control. The results demonstrate the advantages and drawbacks of both models, showing the benefits and limitations of using the widespread Muskingum model among the hydraulics scientific community for control design.

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Open channel transient flow control by discrete time LQR methods

Cited by 43 publications

References 7 publications

Fuzzy logic adaptive Kalman filtering in the control of irrigation canals

Fuzzy logic adaptive Kalman filtering in the control of irrigation canals

A modelling methodology for natural dam-river network systems

Discussion on Muskingum versus Integrator-Delay Models for Control Objectives

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