Stochastic Optimal and Suboptimal Control of Irrigation Canals

Reddy, J. Mohan; Jacquot, Raymond G.

doi:10.1061/(asce)0733-9496(1999)125:6(369)

Cited by 13 publications

(24 citation statements)

References 15 publications

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“…As the disturbance component, q i,N (k), becomes significant compared with the overall withdrawal rate, then a mechanism to incorporate the random nature of the disturbances into the operation of the irrigation canal is required [9]. In this study, the variance of the random disturbances is considered through the optimal estimator.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…where A is the nxn system feedback matrix, B the lxm control distribution matrix, C the pxl disturbance matrix, x(k) the lx1 state vector, u(k) the mx1 control vector, q(k) the px1 matrix representing the random disturbances (changes in water withdrawal rates) at the turnouts, m 2 /s, l the number of dependent (state) variables in the system, m the number of controls (gates) in the canal, p the number of outlets in the canal, and k the time increment, s. The elements of the matrices A, B, and C depend upon the initial condition [9]. The dimensions of the control distribution matrix, B, depend on the number of state variables and the number of gates in the canal.…”

Section: ö F Durdumentioning

confidence: 99%

“…The required change in the opening of the gates can be computed by applying a proportional control, in which the change in the gate opening is proportional to the changes in flow depths and flow rates in the system, of the following form [9]:…”

Section: Linear Quadratic Regulatormentioning

confidence: 99%

“…In a single input-single output system, the elements of matrix K can be obtained by a pole placement technique. But in the case of a multi inputmulti output system, since the poles are not uniquely determined, some systematic procedure for selection of the elements of the matrix K is required [9]. In optimal control theory, this is achieved by formulating the LQR control problem as an optimization problem in which the cost function, J , to be minimized is given as follows:…”

Section: Linear Quadratic Regulatormentioning

confidence: 99%

“…He indicated that the steady-state Kalman filters, with minimal computational complexity, performed well and were found to be appropriate for irrigation canals. Reddy 189 et al, [9] developed a proportional-plus-integral (PI) controller for an irrigation canal with five pools. As the order of the controller gain matrix was large, he designed a Kalman filter to estimate the values for the state variables that were not measured.…”

Section: Introductionmentioning

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: Mathematical Modelmentioning

confidence: 99%

Section: ö F Durdumentioning

confidence: 99%

Section: Linear Quadratic Regulatormentioning

confidence: 99%

Section: Linear Quadratic Regulatormentioning

confidence: 99%

Section: Introductionmentioning

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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Control of transient flow in irrigation canals using Lyapunov fuzzy filter-based Gaussian regulator

Durdu

2005

Int. J. Numer. Meth. Fluids

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An optimal fuzzy ÿlter was applied to solve the state estimation problem of the controlled irrigation canals. Using linearized ÿnite-di erence model of the open-channel ow, a canal operation problem was formulated as an optimal control problem and an algorithm for gate openings in the presence of unknown external disturbances was derived. A fuzzy ÿlter was designed to estimate the state variables at the intermediate nodes based upon measured values of depth at the points in the canal. A Lyapunov function was utilized as a performance index to formulate the fuzzy interference rules of the optimal fuzzy ÿlter. A linear quadratic Gaussian (LQG) optimal controller for a multi-pool irrigation canal was considered as an example. The state estimation problem in the controller was simulated using two techniques: Kalman estimator and the proposed fuzzy ÿlter. The performance of the fuzzy state estimator designed using the Lyapunov fuzzy technique was compared with the results obtained using the Kalman estimator technique. The obvious advantages of the fuzzy ÿlter were the lower computational costs and ease of implementation. The results of this study demonstrated that proposed Lyapunov-type fuzzy ÿlter provides both good stability and simplicity in the control of irrigation canals more than a Kalman ÿlter. 493 in which Q is the ow rate (m 3 =s), A the wetted area (m 2 ), q l the lateral ow (m 2 =s), y the water depth (m), t the time (s), x the longitudinal direction of channel (m), g the gravitational acceleration (m 2 =s), S 0 the canal bottom slope (m=m), n the roughness coe cient (s=m 1=3 ), and S f the friction slope (m=m) and is deÿned asin which K is the hydraulic conveyance of canal = AR 2=3 =n, R the hydraulic radius (m). In Equations (1) and (2), the spatial derivatives were replaced by ÿnite-di erence approximations, by dividing the pool into few segments (N = number of nodes). A central-di erence scheme was used for the interior nodes (1¡j¡N ), and a forward di erence and a backward di erence were applied to the ÿrst and the last nodes, respectively [5]. Both forward and backward ÿnite-di erence approximations (the neglected terms are of the ÿrst order of x) are referred to as ÿrst-order accurate. Central ÿnite-di erence approximation (the neglected terms is of the order of ( x) 2 ) is referred to as second-order accurate [16]. The central ÿnite-di erence approximation is more accurate than the forward or backward ÿnite-di erence approximations. The water levels or the volumes of water stored in the canal pools are regulated using a series of spatially distributed gates (control elements). Hence, open irrigation canals are modelled as distributed control systems. To solve Equations (1) and (2), the boundary conditions were expressed in terms of the continuity equation:

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Research progress on operation control and optimal scheduling of irrigation canal systems

Zhou,

Fan,

Gao

et al. 2024

Irrigation and Drainage

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Open canals are a common water transfer method used in water transfer projects and agricultural irrigation and drainage projects. With the emergence of drawbacks in traditional canal control models and the increasingly severe shortage of water resources, accurate transport and distribution of water in the canal system of the irrigation district, rational allocation of water resources, reduction in water loss, improvement in the efficiency and benefit of water resource utilization, and satisfaction of the water demand of different water users are needed. Many scholars have conducted extensive research on canal operation control and optimal scheduling. This paper systematically reviews and summarizes the relevant research progress, including the theory of unsteady flow in open canals, the operation mode of the canal system, the operation control model and algorithm of canal systems, and the optimization of water distribution in canal systems. By summarizing the research progress already achieved, the existing problems and future development directions are identified according to actual needs, providing a reference for the ongoing modernization of irrigation districts and the research and application of digital twin irrigation district technology.

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Stochastic Optimal and Suboptimal Control of Irrigation Canals

Cited by 13 publications

References 15 publications

Fuzzy logic adaptive Kalman filtering in the control of irrigation canals

Fuzzy logic adaptive Kalman filtering in the control of irrigation canals

Control of transient flow in irrigation canals using Lyapunov fuzzy filter-based Gaussian regulator

Research progress on operation control and optimal scheduling of irrigation canal systems

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