Automatic Downstream Water-Level Feedback Control of Branching Canal Networks: Theory

Most of the research on the design of feedback controllers for irrigation canals has been concentrated on single, in-line canals with no branches. Because the branches in a network are hydraulically coupled with each other, it may be difficult to automatically control a branching canal network by designing separate feedback controllers for each branch and then letting them run simultaneously. Thus feedback control of an entire branching canal system may be more efficient if the branching flow dynamics are explicitly taken into account during the feedback controller design process. This paper develops two different feedback controllers for branching canal networks. The first feedback controller was developed using linear quadratic regulator theory and the second using model predictive control. Both algorithms were able to effectively control a simple branching canal network example with relatively small flow changes.     

Performance of Historic Downstream Canal Control Algorithms on ASCE Test Canal 1

Researchers have developed several algorithms to automatically control water levels in irrigation canals. Proportional-integral (PI) control logic has been used for downstream water-level control, but its performance has not always been satisfactory. Heuristic downstream water-level controllers (e.g., canal automation for rapid demand deliveries, or CARDD) have also been proposed but not rigorously tested. The ASCE Task Committee on Canal Automation Algorithms developed a series of test cases to evaluate the performance of canal control algorithms. In this paper, simulation tests were performed on the ASCE Test Canal 1 using three downstream control algorithms: (1) The standard PI control logic; (2) The PI control logic with hydraulic decouplers; and (3) The heuristic CARDD control logic. These controllers were tuned manually using trial-and-error techniques. Performance of the PI control logic improved with the addition of hydraulic decouplers. CARDD did not perform as well as the PI controllers under the conditions imposed on ASCE Test Canal 1. Robustness of these controllers depends on the aggressiveness of the controller as well as the initial flow rate.     

Design of a Single-Pool Downstream Controller Using Quantitative Feedback Control Theory

A downstream controller is designed for an irrigation canal reach using a design technique called quantitative feedback control theory (QFT). The performance of this controller is compared to a proportional, integral, derivative (PID) controller and a linear quadratic regulator (LQR) controller. In this study, the QFT controller is designed for a single canal reach because it best demonstrates how a controller is designed. Previous research for this canal model provided data for comparison. For the operating conditions that are defined in this paper, the QFT controller is shown to have slightly better performance than the PID controller and better performance than the LQR controller. When the canal hydraulic roughness is increased, the QFT controller still performed better than the PID controller.     

Simple Optimal Downstream Feedback Canal Controllers: ASCE Test Case Results

In a companion paper, a class of downstream-water-level feedback canal controllers was described. Within this class, a particular controller is chosen by selecting which controller coefficients to optimize (tune), the remaining coefficients being set to zero. These controllers range from a series of simple proportional-integral (PI) controllers to a single centralized controller that considers lag times. In this paper, several controllers within this class were tuned with the same quadratic performance criteria (i.e., identical penalty functions for optimization). The resulting controllers were then tested through unsteady-flow simulation with the ASCE canal automation test cases for canal 1. Differences between canal and gate properties, as simulated and as assumed for tuning, reduced controller performance in terms of both water-level errors and gate movements. The test case restrictions placed on minimum gate movement caused water levels to oscillate around their set points. This resulted in steady-state errors and much more gate movement (hunting). More centralized controllers handle unscheduled flow changes better than a series of local PI controllers. Controllers that explicitly account for pool wave travel times did not improve control as much as expected. Sending control actions within a given pool to upstream pools improved performance, but caused oscillations in some cases, unless control signals were also sent downstream. A good compromise between controller performance and complexity is provided by controllers that pass feedback from a given water level to the check structure at the upstream end of its pool (i.e., that used for downstream control of an individual pool) and to all upstream and one downstream check structures.     

Performance of Model Predictive Control on ASCE Test Canal 1

Model predictive control (MPC) is a popular control algorithm in the process control industry that is particularly suited to the automatic control of irrigation water delivery systems because it explicitly accounts for the long delay times encountered in open-channel flow. In addition, a feedforward routine is easy to implement in MPC and many of the constraints that canal operators face can be directly incorporated into the MPC scheme. The ASCE Task Committee on Canal Automation Algorithms developed a series of test cases to evaluate the performance of canal control algorithms. In this paper, simulation tests were performed on ASCE test canal 1 using a remote downstream control configuration of MPC. The MPC algorithm effectively controls ASCE test canal 1, and its performance was similar to that of other proposed controllers. When there were no minimum gate movement constraints, MPC was fairly robust because the controller performance did not significantly degrade under untuned conditions. In the presence of minimum gate movement constraints, the water levels continually oscillate around the water level setpoint. Using the configuration presented in this paper, the feedforward portion of MPC does not perform as well as other proposed feedforward routines. This underperformance is related to the simplifications made by the underlying process model and not to MPC itself.     

Simple Optimal Downstream Feedback Canal Controllers: Theory

A new class of downstream water-level feedback controllers is proposed that can vary from a series of individual proportional-integral (PI) controllers (each gate adjusted based on one water level) to fully centralized controllers (each gate adjusted based on all water levels) that include the effects of lag time. The controller design method uses discrete-time state-feedback control with a quadratic penalty function, physically based states, and no state estimation. A simple, linear model of canal pool response, the integrator-delay model, is used to define the state transitions. All controllers within this class are tuned for the entire canal using optimization techniques. This avoids the tedious task of manually tuning simple controllers. The relative performance of the various controllers within this class can be directly compared without simulation, since the same objective function is used to tune each controller. An example is provided which suggests that the fully centralized controller will perform better than a series of local controllers. However, reasonably good performance can be obtained for some intermediate PI controllers that pass information to one additional check structure upstream and downstream. This should limit some of the difficulties reported for full optimal controllers where all check structures respond to water-level errors in all pools (e.g., saturation of inputs). The results of simulation studies of these controllers are provided in a companion paper.     

Downstream-Water-Level Control Test Results on the WM Lateral Canal

On steep canals, distant downstream-water-level control can be challenging. The Software for Automated Canal Management was developed, in part, to test various distant downstream water-level controllers. It was implemented on the WM canal of the Maricopa Stanfield Irrigation and Drainage District, Stanfield, Ariz. to compare the performance of various controllers. In 2004, Clemmens and Schuurmans used optimization to determine the coefficients for a variety of controllers. These controllers vary in their complexity from a series of simple, single-input-single-output, proportional-integral controllers to a fully centralized, multiple-input-multiple-output, optimal controller. The controller design also varies regarding which pools are under downstream, or upstream, control and according to the conditions (e.g., flow rate) assumed for controller design. These controllers were tested under actual operating conditions and with unscheduled disturbances. The results of these tests are presented in this paper.     

Automatic Tuning of PI Controllers for an Irrigation Canal Pool

This paper presents a method to automatically tune decentralized proportional integral (PI) controllers for an irrigation canal pool. The auto tune variation (ATV) method is based on a relay experiment, which generates small amplitude oscillations of the canal pool. The ATV procedure can be used to get the integrator delay model parameters of a canal pool, which in turn can be used to tune a PI controller using classic rules, or other rules such as the ones proposed by Litrico and Fromion. This method does not require advanced automatic control knowledge and is implemented in the SIC software developed by Cemagref, which also incorporates a supervisory control and data acquisition module for real-time control. The ATV method is evaluated by simulations and experiments on a real irrigation canal located in the South of France, for local upstream, local downstream, and distant downstream controller tuning.     

Simulation of Automatic Canal Control Systems

Simulation models for unsteady open channel flows have been commercially available for more than 2 decades. Most of these models are now available for personal computers and can be used to study the control of irrigation canals. Studies on automatic control methods and algorithms have been performed on at least half a dozen of the available unsteady-flow simulation models. Although, many of these automation studies have been conducted by the institution that created the simulation model, these simulation models were not created with automatic gate control in mind, and thus one has to be intimately familiar with the source code in order to implement sophisticated control features. Three commercially available unsteady-flow simulation software packages that allow automatic control of gates based on algorithms written by users are: CanalCAD from the Univ. of Iowa, Hydraulics Lab; Mike 11 version 3.2 from the Danish Hydraulic Institute; and Sobek from Delft Hydraulics. In this paper, we describe the various features of these unsteady-flow simulation packages and how they interface to control engineering software/code. There are a number of tradeoffs between simplicity and functionality. All these models present difficulties and have limitations. The hope is to provide guidance on the next generation of unsteady-flow canal simulation models so that control functions can be routinely applied.     

Salt River Project Canal Automation Pilot Project: Simulation Tests

The feasibility of automatically controlling water levels and deliveries on the Salt River Project (SRP) canal system through computer-based algorithms is being investigated. The proposed control system automates and enhances functions already performed by SRP operators, namely feedforward routing of scheduled demand changes, feedback control of downstream water levels, and flow control at check structures. Performance of the control system was tested with unsteady flow simulation. Test scenarios were defined by the operators for a 30 km, four-pool canal reach. The tests considered the effect of imperfect knowledge of check gate head-discharge relationships. The combined feedback-feedforward controller easily kept water level deviations close to the target when dealing with routine, scheduled flow changes. Those same routine changes, when unscheduled, were handled effectively by the feedback controller alone. The combined system had greater difficulty in dealing with large demand changes, especially if unscheduled. Because feedback flow changes are computed independently of feedforward changes, the feedback controller tends to counteract feedforward control actions. The effect is unimportant when dealing with routine flow changes but is more significant when dealing with large changes, especially in cases where the demand change cannot be fully anticipated.     

Canal Structure Automation Rules Using an Accuracy-Based Learning Classifier System, a Genetic Algorithm, and a Hydraulic Simulation Model. II: Results

An accuracy-based learning classifier system (XCS), as described in a companion paper (Part I: Design), was developed and evaluated to produce operational rules for canal gate structures. The XCS was applied together with a genetic algorithm and an unsteady hydraulic simulation model, which was used to predict responses to gate operation rules. In the tested cases, from 100 to 2,000 XCS simulations, each involving thousands of hydraulic simulations, were required to produce satisfactory rules. However, the overall fitness of the set of rules increased monotonically as XCS simulations progressed. Initial fitness started at an arbitrary value, and rules increased in strength by better achieving operational objectives during the training process. Fewer XCS iterations were required to increase the fitness as the rule population evolved. Calculated water depths approached the respective target depths for variable water delivery demand through turnout structures in the simulated canal systems. The water depth achieved stabilization inside a dead band of? ±?8% of the target depth after applying different turnout demand hydrographs to each reach. The calculated depth was inside the dead band 92% of the time in Reach 1, and 73% of the time in Reach 2 for the constant supply experiment. The water depth was inside the dead band 100% of the time in Reach 1, and 76% of the time in Reach 2 for the variable-supply experiment.     

Application of Software for Automatic Canal Management (SacMan) to the WM Lateral Canal

Simulation studies have demonstrated that automatic control of canals is more effective when feedforward scheduling, or routing of know demand changes, is combined with centralized, automatic, distant, downstream water level control. In practice, few canals use this approach. To help further develop and test this strategy, the writers developed SacMan, or Software for Automatic Canal Management. The software was tested on the WM lateral of the Maricopa Stanfield Irrigation and Drainage District, Stanfield, Arizona. Initial testing was done during 2002 and 2003. In 2004, SacMan was used to operate the canal nearly continuously for a period of 30 days. Tests were conducted during normal operations, during which more than 50 delivery changes to users were scheduled and implemented with SacMan. In addition, SacMan responded to unscheduled changes such as emergency shut off and power outages that reduced well flow that had been pumping into the canal. Additional “manufactured” tests were conducted to compare different control methods. This paper describes the overall SacMan control scheme and presents a summary of the tests conducted and typical results. Companion papers examine the results of these tests in more detail.     

Tuning of Robust Distant Downstream PI Controllers for an Irrigation Canal Pool. I: Theory

The paper proposes a new method to tune robust distant downstream proportional integral (PI) controllers for an irrigation canal pool. The method emphasizes the role of gain and phase margins in the controller design, by linking the selection of these robustness indicators to the time domain specifications. This leads to link the frequency domain approach used by automatic control engineers to the time domain approach used by hydraulic engineers. The maximum error corresponding to an unpredicted perturbation is shown to be directly linked to the gain margin and the settling time to the phase margin of the controlled system. The tuning method gives analytical expressions for the controller parameters as function of physical parameters of the canal pool in order to satisfy desired performance requirements. The model is first expressed in terms of dimensionless variables, in order to get generic tuning formulas. The dimensionless PI coefficients are then expressed as functions of time-domain performance requirements. The PI tuning method is evaluated by simulation on a full nonlinear model for a canal pool taken from the ASCE test cases.     

Hydraulic Modeling of an Automatic Upstream Water-Level Control Gate

This paper proposes an efficient mathematical model of an automatic upstream water-level control gate, called a Begemann or flap gate. This automatic gate controls the upstream level close to a reference level for free gate flow, using a counterweight to compensate for the hydraulic pressure on the gate. The proposed gate model is designed to be included in a hydraulic simulation model. A discharge law for the gate is first derived using simple physical assumptions. Then a method to compute the static equilibrium is obtained by modeling the opening force exerted by the water on the gate. This mathematical model is validated on experimental data from a small-scale gate and on other data from the literature in order to show the ability of the model to simulate various gates.     

Influence of Regulators in Controlling Upstream Water Depth

Control of irrigation canals usually consists of control of water levels upstream from regulators or check structures. Regulators provide the necessary head to offtakes. Generally, influence factor is used to express the extension of the backwater curve effect within the controlled reach. This factor shows how a change in water depth exercised by a regulator can influence the water surface profile along an irrigation canal. No direct equation is available in the technical literature up until now for calculating this factor on the basis of the steady gradually varied flow theorem. In current research, using the steady gradually varied flow equation for a prismatic canal, an elegant algebraic equation for this factor is derived. Control of water levels upstream from regulators is an important application of this equation in irrigation networks.     

Tuning of Robust Distant Downstream PI Controllers for an Irrigation Canal Pool. II: Implementation Issues

Based on the companion paper results, this paper presents a robust tuning method to tune a proportional integral (PI) controller that fulfills the design requirements for a single pool with different hydraulic conditions. The robust PI controller parameters are obtained analytically as a function of the physical parameters of the canal pool. Important implementation issues are also considered. Rules are provided for the sampling time selection in order to recover the continuous-time performance. When the sampling time is imposed, it has to be included in the controller design, by modifying the delay of the system. A simple way is proposed to take account of the gate opening as control action variable, instead of the upstream discharge. This robust PI tuning method is evaluated by simulation on a full nonlinear model of two different canal pools for different flow conditions and different implementations: continuous-time control, discrete-time control, using the discharge or the gate opening as control action variable. Simulation results show that the method leads to efficient realistic PI controllers for a canal pool.     

Adaptive Output Feedback Control of Spacecraft Formation Flying Using Chebyshev Neural Networks

This paper proposes two adaptive neural controllers, termed adaptive NN controller-I and adaptive NN controller-II, for the output feedback control of spacecraft formation flying in the presence of structured and unstructured uncertainties. The proposed control scheme employs the linear reduced-order observer to generate pseudo–velocity related signals and Chebyshev neural networks to approximate unknown nonlinearities in the system dynamics. The adaptive NN controller-II, which employs a switching function to generate a switch between the robust control, using the smooth hyperbolic tangent function, and the adaptive NN control, can efficiently avoid the overestimation problem (i.e., the bound of the Chebyshev neural network’s output is larger than the corresponding bond of the approximated unknown function) existing in the adaptive NN controller-I. Hence, it requires small control input. The uniform ultimate boundedness of all signals in the closed-loop system is guaranteed by the Lyapunov direct approach. Simulation studies are presented to show the advantages of the proposed approach over the standard adaptive output feedback approach.     

Algorithm for Automatic Detection of Topological Changes in Water Distribution Networks

Topological and pressure-driven analyses are an integral part of reliability/risk considerations for a water distribution system. For example, it is often necessary to identify which parts of the distribution network are isolated from water sources after the valves have been closed in response to a mechanical pipe failure. Pressure-driven analysis is then necessary to ascertain the consequences of pipe failures in terms of the performance of the functioning subsystem while pipe breaks are being fixed in the isolated area. Therefore, it is extremely useful to have an algorithm for the automatic identification of nodes/pipes disconnected from the water source(s). However, this is a complex problem because valves sometimes significantly modify the network topology. Furthermore, the use of isolation valves can cause a demand shortage to some customers (due to pressure reduction) during the abnormal operating conditions in the system. Thus, pressure-driven simulation of the network behavior is required. For these reasons, a novel algorithm capable of automatic detection of topological network changes is coupled with a robust pressure-driven simulation model. This algorithm is tested on two case studies involving a small artificial water distribution system and a larger, real-life network. The results obtained clearly demonstrate the robustness of the algorithm developed.     

Volume Compensation Method for Routing Irrigation Canal Demand Changes

This paper examines the problem of routing known water demands through gate-controlled, open-channel irrigation delivery systems. Volume-compensation principles were used to route multiple demands in multiple-pool canal systems. The volume-compensation method schedules each demand change individually under the assumption of a series of steady states and superimposes the individual results. Volume-compensation routing schedules were computed for two of the test cases proposed by the ASCE Task Committee on Canal Automation. Alternative routing schedules were computed with the gate-stroking method, which is an inverse solution of the unsteady-flow equations. Both solutions were tested through unsteady-flow simulation. While not as effective as gate-stroking solutions, volume-compensation solutions performed satisfactorily under ideal flow control conditions. When subjected to realistic operational constraints, specifically constraints on the flow regulation interval, and also to incorrect canal hydraulic roughness information, both methods performed similarly.     

Improved Control of Pressure Reducing Valves in Water Distribution Networks

The behavior of transients in water pipe networks is well understood but the influence of modulating control valves on this behavior is less well known. Experimental work on networks supplied through pressure reducing valves (PRVs) has demonstrated that, in certain conditions, undesirable phenomena such as sustained or slowly decaying oscillation and large pressure overshoot can occur. This paper presents results from modeling studies to investigate interaction between PRVs and water network transients. Transient pipe network models incorporating random demand are combined with a behavioral PRV model to demonstrate how the response of the system to changes in demand can produce large or persistent pressure variations, similar to those seen in practical experiments. A proportional-integral-derivative (PID) control mechanism, to replace the existing PRV hydraulic controller, is proposed and this alternative controller is shown to significantly improve the network response. PID controllers are commonly used in industrial settings and the methods described are easy to implement in practice.