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.

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.

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.

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.