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Guanghua Guan
Professor, State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan, PR China

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Research paper
Published: 11 January 2021 in Journal of Hydraulic Research
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For design and management of large scale tunnels, it is important to model the transitions between pressurized and free-surface flows inside them. The pressurized and free-surface flow regimes are separated by a discontinuity with different wave speeds on two sides, which makes efficient and accurate simulations still challenging. A robust and conservative space-time adaptive mesh refinement (AMR) strategy is proposed to simulate such transient mixed flow. In the present AMR, the mesh resolution is refined adaptively near the interface between two flow regimes, and the flow states at child meshes are determined by a conservative approach which can avoid numerical oscillations. The numerical results from the AMR strategy are validated with analytical and experimental results, which indicates its good ability to capture the interface between two flow regimes and prevent numerical oscillations. The numerical test in a field scale tunnel shows that AMR can speed up simulations of transient mixed flow by 60 times.

ACS Style

Zhonghua Yang; Zhonghao Mao; Guanghua Guan; Wei Gao. Space-time mesh refinement method for simulating transient mixed flows. Journal of Hydraulic Research 2021, 1 -12.

AMA Style

Zhonghua Yang, Zhonghao Mao, Guanghua Guan, Wei Gao. Space-time mesh refinement method for simulating transient mixed flows. Journal of Hydraulic Research. 2021; ():1-12.

Chicago/Turabian Style

Zhonghua Yang; Zhonghao Mao; Guanghua Guan; Wei Gao. 2021. "Space-time mesh refinement method for simulating transient mixed flows." Journal of Hydraulic Research , no. : 1-12.

Journal article
Published: 01 November 2020 in Journal of Water Resources Planning and Management
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Proportional-integral (PI) control, as one of the most popular classic control methods, has been applied widely to the real-world practice of canal automatic control. The performance of a PI controller largely depends on two key parameters, namely the proportional constant Kp and the integrational time constant Ti. Rather than tuning these parameters empirically or in terms of the canal morphology, this study proposes a linear quadratic regulator (LQR) to determine their optimal values. The proposed LQR utilizes an integrator delay model to represent the hydrodynamics of open canals in order to minimize changes in water levels and flow rates. In addition, the weights for the optimization objective in the LQR are determined by an optimized quadratic performance indicators estimate (OQPIE), using the precalculated nondimensional integrated square of error and nondimensional integrated absolute discharge change as well as inherent designed parameters, which potentially impact the stability of system states. In this way, the LQR can fit various canal automation applications, especially for low-gradient canals. The optimal PI controller was tested on two different-scaled canals. Results showed that the objective was met satisfactorily, and stability can be reached in hours.

ACS Style

Ke Zhong; Guanghua Guan; Xin Tian; José María Maestre; Zhonghao Mao. Evaluating Optimization Objectives in Linear Quadratic Control Applied to Open Canal Automation. Journal of Water Resources Planning and Management 2020, 146, 04020087 .

AMA Style

Ke Zhong, Guanghua Guan, Xin Tian, José María Maestre, Zhonghao Mao. Evaluating Optimization Objectives in Linear Quadratic Control Applied to Open Canal Automation. Journal of Water Resources Planning and Management. 2020; 146 (11):04020087.

Chicago/Turabian Style

Ke Zhong; Guanghua Guan; Xin Tian; José María Maestre; Zhonghao Mao. 2020. "Evaluating Optimization Objectives in Linear Quadratic Control Applied to Open Canal Automation." Journal of Water Resources Planning and Management 146, no. 11: 04020087.

Journal article
Published: 30 September 2020 in Water
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The emergency control of Menglou~Qifang inverted siphon, which is about 72 km long, is the key to the safety of the Northern Hubei Water Transfer Project. Given the complicated layout of this project, traditional emergency control method has been challenged with the fast hydraulic transient characteristics of pressurized flow. This paper describes the application of model predictive control (MPC), a popular automatic control algorithm advanced in explicitly accounting for various constraints and optimizing control operation, in emergency condition. For the fast prediction to the pipe-canal combination system, a linear model for large-scale inverted siphon proposed by the latest research and the integrator-delay (ID) model for open canals are used. Simulation results show that the proposed MPC algorithm has promising performance on guaranteeing the safety of the project when there are sudden flow obstruction incidents of varying degrees downstream. Compared with control groups, the peak pressure can be reduced by 17.2 m by MPC under the most critical scenario, albeit with more complicated gates operations and more water release (up to 9.75 × 104 m3). Based on the linear model for long inverted siphon, this work highlights the applicability of MPC in the emergency control of large-scale pipe-canal combination system.

ACS Style

Zheli Zhu; Guanghua Guan; Zhonghao Mao; Kang Wang; Shixiang Gu; Gang Chen. Application of Model Predictive Control for Large-Scale Inverted Siphon in Water Distribution System in the Case of Emergency Operation. Water 2020, 12, 2733 .

AMA Style

Zheli Zhu, Guanghua Guan, Zhonghao Mao, Kang Wang, Shixiang Gu, Gang Chen. Application of Model Predictive Control for Large-Scale Inverted Siphon in Water Distribution System in the Case of Emergency Operation. Water. 2020; 12 (10):2733.

Chicago/Turabian Style

Zheli Zhu; Guanghua Guan; Zhonghao Mao; Kang Wang; Shixiang Gu; Gang Chen. 2020. "Application of Model Predictive Control for Large-Scale Inverted Siphon in Water Distribution System in the Case of Emergency Operation." Water 12, no. 10: 2733.

Journal article
Published: 07 August 2020 in Advances in Water Resources
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Urban pluvial flooding is a threatening natural hazard in urban areas all over the world, especially in recent years given its increasing frequency of occurrence. In order to prevent flood occurrence and mitigate the subsequent aftermath, urban water managers aim to predict precipitation characteristics, including peak intensity, arrival time and duration, so that they can further warn inhabitants in risky areas and take emergency actions when forecasting a pluvial flood. Previous studies that dealt with the prediction of urban pluvial flooding are mainly based on hydrological or hydraulic models, requiring a large volume of data for simulation accuracy. These methods are computationally expensive. Using a rainfall threshold to predict flooding based on a data-driven approach can decrease the computational complexity to a great extent. In order to prepare cities for frequent pluvial flood events – especially in the future climate – this paper uses a rainfall threshold for classifying flood vs. non-flood events, based on machine learning (ML) approaches, applied to a case study of Shenzhen city in China. In doing so, ML models can determine several rainfall threshold lines projected in a plane spanned by two principal components, which provides a binary result (flood or no flood). Compared to the conventional critical rainfall curve, the proposed models, especially the subspace discriminant analysis, can classify flooding and non-flooding by different combinations of multiple-resolution rainfall intensities, greatly raising the accuracy to 96.5% and lowering the false alert rate to 25%. Compared to the conventional model, the critical indices of accuracy and true positive rate (TPR) were 5%-15% higher in ML models. Such models are applicable to other urban catchments as well. The results are expected to be used to assist early warning systems and provide rational information for contingency and emergency planning.

ACS Style

Qian Ke; Xin Tian; Jeremy Bricker; Zhan Tian; Guanghua Guan; Huayang Cai; Xinxing Huang; Honglong Yang; Junguo Liu. Urban pluvial flooding prediction by machine learning approaches – a case study of Shenzhen city, China. Advances in Water Resources 2020, 145, 103719 .

AMA Style

Qian Ke, Xin Tian, Jeremy Bricker, Zhan Tian, Guanghua Guan, Huayang Cai, Xinxing Huang, Honglong Yang, Junguo Liu. Urban pluvial flooding prediction by machine learning approaches – a case study of Shenzhen city, China. Advances in Water Resources. 2020; 145 ():103719.

Chicago/Turabian Style

Qian Ke; Xin Tian; Jeremy Bricker; Zhan Tian; Guanghua Guan; Huayang Cai; Xinxing Huang; Honglong Yang; Junguo Liu. 2020. "Urban pluvial flooding prediction by machine learning approaches – a case study of Shenzhen city, China." Advances in Water Resources 145, no. : 103719.

Journal article
Published: 27 April 2020 in Water
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Transition between free-surface and pressurized flows is a crucial phenomenon in many hydraulic systems. During simulation of such phenomenon, severe numerical oscillations may appear behind filling-bores, causing unphysical pressure variations and computation failure. This paper reviews existing oscillation-suppressing methods, while only one of them can obtain a stable result under a realistic acoustic wave speed. We derive a new oscillation-suppressing method with first-order accuracy. This simple method contains two parameters, Pa and Pb, and their values can be determined easily. It can sufficiently suppress numerical oscillations under an acoustic wave speed of 1000 ms−1. Good agreement is found between simulation results and analytical results or experimental data. This paper can help readers to choose an appropriate oscillation-suppressing method for numerical simulations of flow regime transition under a realistic acoustic wave speed.

ACS Style

Zhonghao Mao; Guanghua Guan; Zhonghua Yang. Suppress Numerical Oscillations in Transient Mixed Flow Simulations with a Modified HLL Solver. Water 2020, 12, 1245 .

AMA Style

Zhonghao Mao, Guanghua Guan, Zhonghua Yang. Suppress Numerical Oscillations in Transient Mixed Flow Simulations with a Modified HLL Solver. Water. 2020; 12 (5):1245.

Chicago/Turabian Style

Zhonghao Mao; Guanghua Guan; Zhonghua Yang. 2020. "Suppress Numerical Oscillations in Transient Mixed Flow Simulations with a Modified HLL Solver." Water 12, no. 5: 1245.

Preprint content
Published: 23 March 2020
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Canal automatic control is an important tool to improve the management level of water distribution systems, while an important method to evaluate the effect is controller is using numerical simulations. The free-surface flow in such system can be modelled using the Saint-Venant equations, while the regulating gates are usually treated as inner boundaries where gate discharge formula is adopted. In the previous research, the Saint-Venant equations are normally discretized using the implicit finite difference methods because of their accuracy and simplicity. However, it is difficult to incorporate the inner boundary conditions in the computation of implicit method. To circumvent this problem, this paper presents a hybrid discretization method, which adopts the state-of-art finite volume methods at regulating gates and finite difference methods elsewhere. This new discretization method can preserve the computational speed advantage of finite difference method and capture the wave propagation near the regulating gates. Which can provide reliable evidence for the design of controllers.

ACS Style

Zhonghao Mao; Guanghua Guan; Zheli Zhu. Modelling free-surface flow in water distribution systems with regulating gates. 2020, 1 .

AMA Style

Zhonghao Mao, Guanghua Guan, Zheli Zhu. Modelling free-surface flow in water distribution systems with regulating gates. . 2020; ():1.

Chicago/Turabian Style

Zhonghao Mao; Guanghua Guan; Zheli Zhu. 2020. "Modelling free-surface flow in water distribution systems with regulating gates." , no. : 1.

Journal article
Published: 18 March 2020 in Water
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A new Proportional-Integral (PI) tuning method based on Linear Matrix Inequalities (LMIs) is presented. In particular, an LMI-based optimal control problem is solved to obtain a sparse feedback that provides the PI tuning. The ASCE Test Canal 1 is used as a case study. Using a linearised model of the canal, different tunings for the design of the PI controller are developed and tested using the software Sobek. Furthermore, the proposed method is also compared with other tunings proposed for the same canal available in the literature. Our results show that the proposed method reduces by half the maximum errors with respect to other assessed alternatives and minimizes undesired mutual interactions between canal pools. Also, our method improves the optimality degree of the PI tuning by 30%. Therefore, it is concluded that the LMI based PI controllers lead to satisfactory performance in regulating water levels and canal flows/structure outflows, outperforming other tested alternatives, thus becoming a useful tool for irrigation canal control.

ACS Style

Teresa Arauz; José M. Maestre; Xin Tian; Guanghua Guan. Design of PI Controllers for Irrigation Canals Based on Linear Matrix Inequalities. Water 2020, 12, 855 .

AMA Style

Teresa Arauz, José M. Maestre, Xin Tian, Guanghua Guan. Design of PI Controllers for Irrigation Canals Based on Linear Matrix Inequalities. Water. 2020; 12 (3):855.

Chicago/Turabian Style

Teresa Arauz; José M. Maestre; Xin Tian; Guanghua Guan. 2020. "Design of PI Controllers for Irrigation Canals Based on Linear Matrix Inequalities." Water 12, no. 3: 855.

Preprint
Published: 24 February 2020
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Transition between free-surface and pressurized flows is an crucial phenomenon in many hydraulic systems, including water distribution systems, urban drainage systems, etc. During the transition, the force exerted on the structures changes drastically, thus it is meaningful to simulate this process. However, severe numerical oscillations are widely observed behind filling-bores, causing unphysical pressure variations and even computation failure. In this paper, some oscillation-suppressing approaches are reviewed and evaluated on a benchmark model. Then a new oscillation-suppressing approach is proposed to admit numerical viscosity when the water surface is at proximity of conduct roof which has first order accuracy. This approach adds numerical viscosity when water surface is at the proximity of conduct roof. It can sufficiently suppress numerical oscillations under an acoustic wave speed of 1000m/s and is simple to apply. In comparison with two experiments, the simulation results of this method show good agreement and little numerical oscillations. The results in this paper can help readers to choose an appropriate oscillation-suppressing method to improve the robustness and accuracy of flow regime transition simulations.

ACS Style

Zhonghao Mao; Guanghua Guan; Zhonghua Yang. Suppress Numerical Oscillations in Transient Mixed Flow Simulations with a Modified HLL Solver. 2020, 1 .

AMA Style

Zhonghao Mao, Guanghua Guan, Zhonghua Yang. Suppress Numerical Oscillations in Transient Mixed Flow Simulations with a Modified HLL Solver. . 2020; ():1.

Chicago/Turabian Style

Zhonghao Mao; Guanghua Guan; Zhonghua Yang. 2020. "Suppress Numerical Oscillations in Transient Mixed Flow Simulations with a Modified HLL Solver." , no. : 1.

Journal article
Published: 23 May 2019 in Water
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In the open channel control algorithm, good feed-forward controllers will reduce the transition time of the canal and improve performance. Feedforward control algorithms based on active storage compensation are greatly affected by delay time. However, there is no literature comparing the three most commonly used algorithms, namely volume step compensation, dynamic wave principle and water balance models, under the operation mode of constant water level downstream. In order to compare the existing three algorithms, and to avoid storage calculation by calculating the constant non-uniform water surface line or identification of relevant parameters, combined with the open channel constant gradient flow theory with the storage compensation algorithm, a delay time explicit algorithm is proposed in this study. Tested on the first canal pool of the American Society of Civil Engineers (ASCE) Test Canal 2, the performance of the delay time explicit algorithm is assessed and compared to that of the three conventional algorithms. In the current water intake plan, i.e. in the second hour, the intake begins to take 1.2 m3/s, and the upstream flow of the canal pool changes from 6 m3/s to 7.2 m3/s, among the three existing algorithms, the volume step compensation algorithm has better performance in terms of time to achieve stability, i.e., 1.25 h. The actual adjusted storage accounts for 99.6% of the target adjusted storage, which can basically meet the requirement of compensated storage of the canal pool. The delay time explicit algorithm only needs 1.47 h to stabilize the regulation system. The fluctuation of water level and discharge in the regulation process is small. The actual adjusted storage accounts for 99.6% of the target adjusted storage, which can basically meet the requirement of compensated storage for the canal pool. The delay time calculated by explicit algorithm can provide references for the determination of delay time in feedforward control.

ACS Style

Wenjun Liao; Guanghua Guan; Xin Tian; Liao; Guan; Tian. Exploring Explicit Delay Time for Volume Compensation in Feedforward Control of Canal Systems. Water 2019, 11, 1080 .

AMA Style

Wenjun Liao, Guanghua Guan, Xin Tian, Liao, Guan, Tian. Exploring Explicit Delay Time for Volume Compensation in Feedforward Control of Canal Systems. Water. 2019; 11 (5):1080.

Chicago/Turabian Style

Wenjun Liao; Guanghua Guan; Xin Tian; Liao; Guan; Tian. 2019. "Exploring Explicit Delay Time for Volume Compensation in Feedforward Control of Canal Systems." Water 11, no. 5: 1080.

Conference paper
Published: 07 December 2018 in MATEC Web of Conferences
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The key point of PI feedback control is how to design appropriate controller parameters. This paper combined the linear quadratic optimizing control theory to design an online controller for constant downstream water-level operation which could respond to different working condition properly and rapidly avoiding complex controller parameters adjusting. Based on the Integrator-Delay (ID) model simplified from Saint-Venant Equations, we established the discretized linear time invariant system of canals. Then transferred it into the state-space equations and obtained the state-feedback equation. Water level deviations and flow rate increments were chosen to form the objective function and this paper recommended values of Q and R weight matrices among it should be set according to the optimum quadratic form indicators correspondingly. This controller was applied to two practical canal systems which had diverse scales. Results showed the system under control quickly regained stability; optimizing the objective function with recommended weight matrices could well balance demands on water level deviations and flow rate changes; dynamic performances of water movements and gate movements were acceptable. Through simulations, we preliminarily proved the practicability of this online PI controller implementing LQR. This work proposed an available solutions for the design and operation of water conveyance systems around the world.

ACS Style

Ke Zhong; Guanghua Guan; Zhonghao Mao; Wenjun Liao; Changcheng Xiao; Haiwang Su. Linear Quadratic Optimal Controller Design for Constant Downstream Water-Level PI Feedback Control of Open-Canal Systems. MATEC Web of Conferences 2018, 246, 01056 .

AMA Style

Ke Zhong, Guanghua Guan, Zhonghao Mao, Wenjun Liao, Changcheng Xiao, Haiwang Su. Linear Quadratic Optimal Controller Design for Constant Downstream Water-Level PI Feedback Control of Open-Canal Systems. MATEC Web of Conferences. 2018; 246 ():01056.

Chicago/Turabian Style

Ke Zhong; Guanghua Guan; Zhonghao Mao; Wenjun Liao; Changcheng Xiao; Haiwang Su. 2018. "Linear Quadratic Optimal Controller Design for Constant Downstream Water-Level PI Feedback Control of Open-Canal Systems." MATEC Web of Conferences 246, no. : 01056.

Conference paper
Published: 07 December 2018 in MATEC Web of Conferences
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In the control of open-channel, it is difficult to estimate wave propergation time because of the complexity of reflection, superposition and energy attenuation of shallow water waves. Although Saint-Venant equation have reasonable accuracy in describing the motion law of unsteady flow, mathematically it is the first order quasilinear hyperbolic partial differential equations which makes it difficult to be used as control model in the design optimized controller. The Channel Integrator Delay Zero (IDZ) model linearizes the Saint-Venant equation and ensures the accuracy of the response of water level and discharge in high frequency band. However, there is still a considerable difference between the theoretical value and the actual response. In order to avoid this difference caused by theoretical derivation, this paper uses the single channel model of Zhanghe Irrigation District to play online identification of the relevant parameters by using the existing periodic response process of the canal system. The reliability of model identification under step water intake is verified, and the effect of this method on periodic water intakes in long channel is verified. The results show that the identified model can catch most dynamic action of the canal system with water intakes, which ensures its validity to be used for controller design. Meanwhile, it is simple in application.

ACS Style

Wenjun Liao; Guanghua Guan; Le Zhong; Changcheng Xiao; Ke Zhong; Huiyong Huang. Online Model Identification Of Open-Channel System With High Order IDZ Model. MATEC Web of Conferences 2018, 246, 01036 .

AMA Style

Wenjun Liao, Guanghua Guan, Le Zhong, Changcheng Xiao, Ke Zhong, Huiyong Huang. Online Model Identification Of Open-Channel System With High Order IDZ Model. MATEC Web of Conferences. 2018; 246 ():01036.

Chicago/Turabian Style

Wenjun Liao; Guanghua Guan; Le Zhong; Changcheng Xiao; Ke Zhong; Huiyong Huang. 2018. "Online Model Identification Of Open-Channel System With High Order IDZ Model." MATEC Web of Conferences 246, no. : 01036.

Conference paper
Published: 07 December 2018 in MATEC Web of Conferences
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In order to design controllers for canals with inverted siphon especially for very long siphon, it is necessary to learn its response property. Compared to open canals, the water movement in inverted siphon is very different due to the fast travelling speed of wave and high water pressure. It is impossible to use openchannel model describe invert siphon section, and the delay caused by the siphon haven’t been discussed in existing literature. This paper proposes a response model of inverted siphon which contains a delay and an integrator in low frequencies, a constant gain in high frequencies. By comparing the response model to the results of simulation, this paper shows the response model is a good approximation. This paper studies a water distribution project consists of two canals and one inverted siphon. The result shows that the water level change at downstream end is significantly smaller than water change at upstream end. By applying response model of inverted siphon, this paper shows it is due to the delay of flow rate change from upstream end to downstream end.

ACS Style

Zhonghao Mao; Guanghua Guan; Zhonghua Yang; Ke Zhong. The Response Property of Inverted Siphon in Long Distance Water Distribution System. MATEC Web of Conferences 2018, 246, 01041 .

AMA Style

Zhonghao Mao, Guanghua Guan, Zhonghua Yang, Ke Zhong. The Response Property of Inverted Siphon in Long Distance Water Distribution System. MATEC Web of Conferences. 2018; 246 ():01041.

Chicago/Turabian Style

Zhonghao Mao; Guanghua Guan; Zhonghua Yang; Ke Zhong. 2018. "The Response Property of Inverted Siphon in Long Distance Water Distribution System." MATEC Web of Conferences 246, no. : 01041.

Journal article
Published: 01 March 2015 in Journal of Cold Regions Engineering
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ACS Style

Mengkai Liu; Xiaobo Feng; Changde Wang; Guanghua Guan. Regulating a Long-Distance Canal System with Floating Ice Cover in the Winter. Journal of Cold Regions Engineering 2015, 29, 04014009 .

AMA Style

Mengkai Liu, Xiaobo Feng, Changde Wang, Guanghua Guan. Regulating a Long-Distance Canal System with Floating Ice Cover in the Winter. Journal of Cold Regions Engineering. 2015; 29 (1):04014009.

Chicago/Turabian Style

Mengkai Liu; Xiaobo Feng; Changde Wang; Guanghua Guan. 2015. "Regulating a Long-Distance Canal System with Floating Ice Cover in the Winter." Journal of Cold Regions Engineering 29, no. 1: 04014009.

Journal article
Published: 09 October 2012 in Journal of Hydroinformatics
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In order to automatically and safely control long distance water delivery projects in winter, there is a need for a reasonable and feasible transition mode to avoid the emergence of ice jam. Based on open canal hydraulics, a mathematical model of canal system operated by constant downstream depth method is developed. The principle of combining feed-forward control of discharges with feedback control of water level is adopted for operation of check gates and a simulation model of multiple serial canal sections is established. Also, reasonable parameters of proportional-integral (PI) controller and logical dead band are obtained by trial and optimizing. The model is applied to simulate the operation process of the canal sections part of the main canal of the middle route of the South-to-North Water Transfer Project in China. Flow velocities are reduced to less than 0.4 m/s by decreasing discharges of canal pools and turnouts in terms of 3 days' cold current forecast in advance. As a result, discharge in canal was reduced from 70% designed capacity to less than 30%, which is a big challenge for the controller. This paper tests the suggested transition mode from open-channel water transfer state to a low flow ice-forming state at the MATLAB platform, and the results show that this model can achieve the expected goals.

ACS Style

Guoqiang Liu; Guanghua Guan; Changde Wang. Transition mode of long distance water delivery project before freezing in winter. Journal of Hydroinformatics 2012, 15, 306 -320.

AMA Style

Guoqiang Liu, Guanghua Guan, Changde Wang. Transition mode of long distance water delivery project before freezing in winter. Journal of Hydroinformatics. 2012; 15 (2):306-320.

Chicago/Turabian Style

Guoqiang Liu; Guanghua Guan; Changde Wang. 2012. "Transition mode of long distance water delivery project before freezing in winter." Journal of Hydroinformatics 15, no. 2: 306-320.

Journal article
Published: 01 December 2011 in Journal of Irrigation and Drainage Engineering
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The Central Arizona Project (CAP) has been supplying Colorado River water to Central Arizona for roughly 25 years. The CAP canal is operated remotely with a supervisory control and data acquisition (SCADA) system. Gate-position changes are made either manually or through the use of automatic controls with a controlled-volume approach. In this paper, the writers examine the potential application to the CAP canal of water-level difference control, a new feedback canal-control method. The main objective of this method is to keep the downstream water-level errors in equal pools. The control model is a multiple input and multiple output (MIMO) system, and the controller is solved as a linear quadratic regulator (LQR). A feed-forward routine called volume compensation was also used to route the flow changes. Simulation results show that this method is stable and can deal with different kinds of changes relatively quickly. For small changes, the water-level difference controller can operate well even without routing flow changes. For large flow changes, the water-level difference control alone can take up to 12 h to stabilize all water levels. Performance is greatly improved with the inclusion of the feed-forward routine. This new method provides better water-level control than the current method, and it is much less sensitive to errors in gate calibration. The writers suggest that this water-level difference-control method is quite promising, especially for large canals.

ACS Style

G. Guan; A. J. Clemmens; T. F. Kacerek; B. T. Wahlin. Applying Water-Level Difference Control to Central Arizona Project. Journal of Irrigation and Drainage Engineering 2011, 137, 747 -753.

AMA Style

G. Guan, A. J. Clemmens, T. F. Kacerek, B. T. Wahlin. Applying Water-Level Difference Control to Central Arizona Project. Journal of Irrigation and Drainage Engineering. 2011; 137 (12):747-753.

Chicago/Turabian Style

G. Guan; A. J. Clemmens; T. F. Kacerek; B. T. Wahlin. 2011. "Applying Water-Level Difference Control to Central Arizona Project." Journal of Irrigation and Drainage Engineering 137, no. 12: 747-753.